2sin (example 3.3)

Time bar (total: 14.4s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze66.0ms (0.5%)

Memory
-31.5MiB live, 45.0MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50.6%49.4%0%0%0%0
0%0%50.6%49.4%0%0%0%1
0%0%50.6%49.4%0%0%0%2
0%0%25.3%49.4%0%25.3%0%3
0%0%25.3%49.4%0%25.3%0%4
0%0%19%49.4%0%31.6%0%5
0%0%15.8%49.4%0%34.8%0%6
0%0%11.1%49.4%0%39.5%0%7
0%0%8.7%49.4%0%41.9%0%8
0%0%5.9%49.4%0%44.6%0%9
0%0%4.5%49.4%0%46%0%10
0%0%3.1%49.4%0%47.5%0%11
0%0%2.7%49.4%0%47.9%0%12
Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.0s (41.7%)

Memory
137.2MiB live, 6 595.1MiB allocated
Samples
3.0s25 866×0invalid
940.0ms5 514×0valid
532.0ms2 742×1valid
Precisions
Click to see histograms. Total time spent on operations: 3.4s
ival-mult: 670.0ms (19.7% of total)
const: 594.0ms (17.5% of total)
ival-sin: 580.0ms (17.1% of total)
ival-add: 316.0ms (9.3% of total)
ival-fabs: 288.0ms (8.5% of total)
ival-<: 257.0ms (7.6% of total)
ival-<=: 227.0ms (6.7% of total)
ival-sub: 219.0ms (6.5% of total)
ival-and: 104.0ms (3.1% of total)
adjust: 81.0ms (2.4% of total)
exact: 46.0ms (1.4% of total)
ival-assert: 13.0ms (0.4% of total)
Bogosity

explain89.0ms (0.6%)

Memory
11.2MiB live, 129.2MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2214(-4.4038464755470124e-32 1.6329471573534814e-34)4(-2.367090113444104e-117 2.741910301514028e-119)(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
00-0-(sin.f64 (+.f64 x eps))
00-0-eps
00-0-(+.f64 x eps)
00-0-(sin.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))cancellation2219
Confusion
Predicted +Predicted -
+2174
-431
Precision
0.9819004524886877
Recall
0.9819004524886877
Confusion?
Predicted +Predicted MaybePredicted -
+21740
-4526
Precision?
0.9608695652173913
Recall?
1.0
Freqs
test
numberfreq
035
1221
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
22.0ms182×1valid
20.0ms326×0valid
2.0ms2valid
Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-sin: 11.0ms (44.2% of total)
adjust: 8.0ms (32.1% of total)
ival-add: 3.0ms (12.1% of total)
ival-sub: 3.0ms (12.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess29.0ms (0.2%)

Memory
-3.8MiB live, 34.1MiB allocated
Algorithm
egg-herbie
Rules
102×sub-neg
80×lower-fma.f64
80×lower-fma.f32
68×cancel-sign-sub-inv
64×associate--r+
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01839
13835
28635
316935
431035
536735
644535
748235
849135
067
0107
1137
2187
3247
4327
5477
6807
71077
81517
91667
101747
01747
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Outputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
62.1%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify7.0ms (0.1%)

Memory
9.4MiB live, 9.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sin.f64 x)
cost-diff0
(+.f64 x eps)
cost-diff0
(sin.f64 (+.f64 x eps))
cost-diff0
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Rules
80×lower-fma.f64
80×lower-fma.f32
48×lower-*.f64
48×lower-*.f32
36×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
01018
11318
21818
32418
43218
54718
68018
710718
815118
916618
1017418
017418
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 x)
Outputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 x)

localize35.0ms (0.2%)

Memory
-12.4MiB live, 35.3MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(+.f64 x eps)
accuracy0
(sin.f64 x)
accuracy0.028601281620653757
(sin.f64 (+.f64 x eps))
accuracy24.210456116733425
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Samples
20.0ms91×1valid
8.0ms163×0valid
1.0ms2valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 20.0ms
adjust: 11.0ms (56.2% of total)
ival-sin: 5.0ms (25.6% of total)
ival-add: 2.0ms (10.2% of total)
ival-sub: 1.0ms (5.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series4.0ms (0%)

Memory
6.3MiB live, 6.3MiB allocated
Counts
4 → 84
Calls
Call 1
Inputs
#<alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))>
#<alt (sin.f64 (+.f64 x eps))>
#<alt (+.f64 x eps)>
#<alt (sin.f64 x)>
Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
Calls

6 calls:

TimeVariablePointExpression
1.0ms
eps
@inf
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
1.0ms
x
@0
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
1.0ms
eps
@-inf
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
1.0ms
eps
@0
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
0.0ms
x
@-inf
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))

simplify230.0ms (1.6%)

Memory
7.8MiB live, 245.2MiB allocated
Algorithm
egg-herbie
Rules
16 678×lower-fma.f64
16 678×lower-fma.f32
4 132×lower-*.f64
4 132×lower-*.f32
2 614×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107496
1314496
2775489
32829489
46198489
08141458
Stop Event
iter limit
node limit
Counts
84 → 77
Calls
Call 1
Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
x
(+ eps x)
(+ eps x)
(+ eps x)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(sin x)
(sin x)
(sin x)
(sin x)
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(sin x)
(sin x)
(sin x)
(sin x)
Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps)))
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(fma.f64 eps (cos.f64 x) (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x) (*.f64 eps (cos.f64 x)))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x) (*.f64 (*.f64 eps (cos.f64 x)) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
eps
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(-.f64 (fma.f64 x (cos.f64 eps) (sin.f64 eps)) x)
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(-.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (*.f64 x (cos.f64 eps))) x)
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(-.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))))) x)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(fma.f64 x (cos.f64 eps) (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (*.f64 x (cos.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (*.f64 (cos.f64 eps) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))
eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
x
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)

rewrite289.0ms (2%)

Memory
-22.7MiB live, 286.8MiB allocated
Rules
4 986×lower-fma.f64
4 986×lower-fma.f32
4 676×lower-*.f64
4 676×lower-*.f32
2 176×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
01016
15316
238016
3476616
0821016
Stop Event
iter limit
node limit
iter limit
Counts
4 → 214
Calls
Call 1
Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
(sin.f64 x)
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) #s(literal -1 binary64)))
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (neg.f64 x)))
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(+.f64 (sin.f64 (neg.f64 x)) (sin.f64 (+.f64 x eps)))
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(+.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps)))
(+.f64 (+.f64 (sin.f64 (neg.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps)))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(-.f64 #s(literal 0 binary64) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))))
(-.f64 (+.f64 (sin.f64 (+.f64 x eps)) #s(literal 0 binary64)) (sin.f64 x))
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (sin.f64 (+.f64 x eps)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal -1 binary64) (sin.f64 (+.f64 x eps)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 eps) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(fma.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (/.f64 (sin.f64 (+.f64 x eps)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(fma.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 (-.f64 eps x))))) (sin.f64 (neg.f64 x)))
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (sin.f64 (+.f64 x eps)))
(fma.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))) (sin.f64 (neg.f64 x)))
(fma.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3/2 binary64)) (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3/2 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(fma.f64 (/.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (/.f64 (sin.f64 (+.f64 x eps)) (*.f64 (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(fma.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(fma.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 6 binary64)) (pow.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 3 binary64)))) (fma.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (-.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(fma.f64 (pow.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 (-.f64 eps x))))) #s(literal 1 binary64)) (sin.f64 (neg.f64 x)))
(fma.f64 (pow.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))) #s(literal 1 binary64)) (sin.f64 (neg.f64 x)))
(neg.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (neg.f64 (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(neg.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))
(neg.f64 (/.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))
(/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64) (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (neg.f64 x))))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))) (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
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(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps))) #s(literal -1 binary64)))
(+.f64 x eps)
(+.f64 eps x)
(+.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x)))
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) (fma.f64 x x (*.f64 eps (+.f64 x eps))) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(neg.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))))))
(neg.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(neg.f64 (/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (-.f64 x eps)))
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))
(/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (fma.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps))))
(/.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))))
(/.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) (*.f64 (-.f64 x eps) (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x)))))
(/.f64 (*.f64 (+.f64 x eps) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (*.f64 (-.f64 x eps) (fma.f64 x x (*.f64 eps eps))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x eps)) (*.f64 (-.f64 x eps) (*.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))
(/.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (fma.f64 x x (*.f64 eps (-.f64 eps x))))
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) #s(literal 1 binary64)) (*.f64 (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps)) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 x eps)))
(/.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal 1 binary64)) (*.f64 (fma.f64 x x (*.f64 eps eps)) (-.f64 x eps)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (-.f64 (*.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (/.f64 (*.f64 x x) (-.f64 x eps))) (*.f64 (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (fma.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps)) (fma.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)) (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (fma.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps)))
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))))
(/.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 x x (*.f64 eps eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))) #s(literal -1 binary64))
(*.f64 (+.f64 x eps) (*.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))))
(*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(*.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))))))
(*.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x eps))))
(*.f64 #s(literal 1 binary64) (+.f64 x eps))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)))
(*.f64 (*.f64 (+.f64 x eps) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(*.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps))
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 (-.f64 eps x) (-.f64 eps x)) (-.f64 eps x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (*.f64 eps (-.f64 eps x)) (-.f64 (*.f64 eps (-.f64 eps x)) (*.f64 x x)))))
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))
(*.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) (fma.f64 x x (*.f64 eps (+.f64 x eps))))
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x)))))
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps eps))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))))
(exp.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 1 binary64)))
(sin.f64 x)
(pow.f64 (sin.f64 x) #s(literal 1 binary64))

eval41.0ms (0.3%)

Memory
17.8MiB live, 54.7MiB allocated
Compiler

Compiled 7 823 to 844 computations (89.2% saved)

prune53.0ms (0.4%)

Memory
-12.3MiB live, 73.5MiB allocated
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New28110291
Fresh000
Picked011
Done000
Total28111292
Accuracy
100.0%
Counts
292 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.0%
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
62.1%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
61.4%
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
61.4%
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
60.8%
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))
99.9%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
99.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps))))
99.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
99.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
99.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
Compiler

Compiled 385 to 236 computations (38.7% saved)

simplify354.0ms (2.5%)

Memory
19.9MiB live, 256.5MiB allocated
Algorithm
egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
cost-diff0
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
cost-diff0
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
cost-diff0
#s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))
cost-diff0
(+.f64 x eps)
cost-diff0
(sin.f64 (+.f64 x eps))
cost-diff0
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
cost-diff0
#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))
cost-diff0
(+.f64 x eps)
cost-diff0
(sin.f64 (+.f64 x eps))
cost-diff0
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))
cost-diff0
(sin.f64 eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff0
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff0
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff192
(+.f64 eps #s(literal 0 binary64))
cost-diff320
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
Rules
10 866×lower-fma.f32
10 852×lower-fma.f64
4 398×lower-*.f32
4 376×lower-*.f64
1 816×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
046330
082304
1144304
2321304
3706300
41522300
53580300
64475300
74675300
84776300
94808300
104954300
115937300
126308300
136852300
147299300
157468300
167953300
08034293
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
eps
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))
(fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)
#s(literal -1/6 binary64)
(*.f64 x (*.f64 x x))
(*.f64 x x)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)
(fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))
(*.f64 x x)
#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
#s(literal -1/6 binary64)
(*.f64 x (*.f64 x x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
eps
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
#s(literal -1/2 binary64)
(sin.f64 x)
x
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))
(*.f64 eps #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(cos.f64 x)
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))
(*.f64 eps #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
eps
eps
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 eps #s(literal 1/2 binary64) x)
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))
(-.f64 (sin.f64 (+.f64 eps x)) #s(approx (sin x) (fma.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)))
(sin.f64 (+.f64 x eps))
(sin.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))
#s(approx (sin x) (fma.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)) x))
(fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)
(fma.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)
#s(literal -1/6 binary64)
(*.f64 x (*.f64 x x))
(*.f64 x x)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
(-.f64 (sin.f64 (+.f64 eps x)) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x)))
(sin.f64 (+.f64 x eps))
(sin.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
#s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))
#s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x))
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)
(fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x)
(fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))
(*.f64 x x)
#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
#s(literal -1/6 binary64)
(*.f64 x (*.f64 x x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(*.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
eps
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
(fma.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(sin.f64 x)
x
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))
(*.f64 eps #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(cos.f64 x)

localize204.0ms (1.4%)

Memory
-14.9MiB live, 301.3MiB allocated
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
accuracy0.01171875
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
accuracy0.19435856945876126
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
accuracy0.37890625
(*.f64 eps #s(literal -1/6 binary64))
accuracy0.09375
(*.f64 x (*.f64 x x))
accuracy0.1015625
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
accuracy0.5550165482334896
#s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))
accuracy24.210456116733425
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
accuracy0.028601281620653757
(sin.f64 (+.f64 x eps))
accuracy0.09375
(*.f64 x (*.f64 x x))
accuracy0.9491102518809771
#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))
accuracy24.210456116733425
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))
accuracy0
(sin.f64 eps)
accuracy1.6931742966796064
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy0
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
accuracy0
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
accuracy0.00390625
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy0.04096027073711682
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
Samples
61.0ms90×1valid
58.0ms164×0valid
2.0ms2valid
Compiler

Compiled 274 to 46 computations (83.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 93.0ms
ival-mult: 40.0ms (43% of total)
ival-add: 16.0ms (17.2% of total)
const: 14.0ms (15% of total)
adjust: 8.0ms (8.6% of total)
ival-sin: 8.0ms (8.6% of total)
ival-cos: 4.0ms (4.3% of total)
ival-sub: 2.0ms (2.1% of total)
exact: 1.0ms (1.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series29.0ms (0.2%)

Memory
5.9MiB live, 48.6MiB allocated
Counts
21 → 396
Calls
Call 1
Inputs
#<alt (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))>
#<alt (+.f64 eps #s(literal 0 binary64))>
#<alt (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))>
#<alt (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))>
#<alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))>
#<alt (sin.f64 eps)>
#<alt (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))>
#<alt (sin.f64 (+.f64 x eps))>
#<alt (+.f64 x eps)>
#<alt #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))>
#<alt (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))>
#<alt #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))>
#<alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))>
#<alt (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))>
#<alt (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))>
#<alt (*.f64 #s(literal -1/2 binary64) (sin.f64 x))>
#<alt (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))>
#<alt (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))>
#<alt (*.f64 x (*.f64 x x))>
#<alt (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))>
#<alt (*.f64 eps #s(literal -1/6 binary64))>
Outputs
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/12 (pow x 2)) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (* 1/120 x)>
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (* -1/5040 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (* -1/5040 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
Calls

6 calls:

TimeVariablePointExpression
9.0ms
x
@inf
((* (+ (* x 2) eps) 1/2) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin x) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (cos (* (+ (* x 2) eps) 1/2)) (sin (* (+ eps 0) 1/2)) (* x (* x x)) (* x (+ (* (* x x) -1/5040) 1/120)) (* eps -1/6))
4.0ms
x
@-inf
((* (+ (* x 2) eps) 1/2) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin x) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (cos (* (+ (* x 2) eps) 1/2)) (sin (* (+ eps 0) 1/2)) (* x (* x x)) (* x (+ (* (* x x) -1/5040) 1/120)) (* eps -1/6))
3.0ms
eps
@inf
((* (+ (* x 2) eps) 1/2) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin x) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (cos (* (+ (* x 2) eps) 1/2)) (sin (* (+ eps 0) 1/2)) (* x (* x x)) (* x (+ (* (* x x) -1/5040) 1/120)) (* eps -1/6))
3.0ms
eps
@0
((* (+ (* x 2) eps) 1/2) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin x) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (cos (* (+ (* x 2) eps) 1/2)) (sin (* (+ eps 0) 1/2)) (* x (* x x)) (* x (+ (* (* x x) -1/5040) 1/120)) (* eps -1/6))
3.0ms
x
@0
((* (+ (* x 2) eps) 1/2) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin x) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (cos (* (+ (* x 2) eps) 1/2)) (sin (* (+ eps 0) 1/2)) (* x (* x x)) (* x (+ (* (* x x) -1/5040) 1/120)) (* eps -1/6))

simplify338.0ms (2.3%)

Memory
-21.9MiB live, 361.9MiB allocated
Algorithm
egg-herbie
Rules
15 108×lower-fma.f64
15 108×lower-fma.f32
5 974×lower-*.f64
5 974×lower-*.f32
4 464×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03793701
111903521
233393483
082993200
Stop Event
iter limit
node limit
Counts
396 → 372
Calls
Call 1
Inputs
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
eps
eps
eps
eps
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
x
(+ eps x)
(+ eps x)
(+ eps x)
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
eps
eps
eps
eps
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 1/120 x)
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(sin x)
(sin x)
(sin x)
(sin x)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin x)
(sin x)
(sin x)
(sin x)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* -1/5040 (pow x 3))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(sin x)
(sin x)
(sin x)
(sin x)
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(sin x)
(sin x)
(sin x)
(sin x)
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* -1/5040 (pow x 3))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
Outputs
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
eps
eps
eps
eps
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(*.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (*.f64 eps #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)))
(* 1/2 (* eps (cos x)))
(*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/4 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/48 binary64) (*.f64 (cos.f64 x) #s(literal -1/12 binary64))) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (*.f64 eps #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (*.f64 eps #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)))
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(fma.f64 eps (cos.f64 x) (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 eps (cos.f64 x) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x)))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 eps (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x)))
x
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (*.f64 eps #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (*.f64 eps #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/8 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/48 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
eps
eps
eps
eps
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
eps
(* eps (+ 1 (/ x eps)))
(fma.f64 eps (/.f64 x eps) eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 eps (/.f64 x eps) eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 eps (/.f64 x eps) eps)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* -1/6 (* (pow eps 3) (cos x)))
(*.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (/.f64 (cos.f64 x) (*.f64 eps eps)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
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eps
eps
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eps
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(* -1 (* eps (- (* -1 (/ x eps)) 1)))
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(sin eps)
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(sin eps)
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eps
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x
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(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
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x
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(sin eps)
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(* eps (+ 1 (* -1/6 (pow eps 2))))
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(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(* -1/5040 (pow x 3))
(*.f64 (*.f64 x x) (*.f64 #s(literal -1/5040 binary64) x))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(*.f64 (*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) x) (*.f64 x x))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(*.f64 (*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) x) (*.f64 x x))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(*.f64 (*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) x) (*.f64 x x))

rewrite359.0ms (2.5%)

Memory
33.7MiB live, 413.7MiB allocated
Rules
7 050×lower-fma.f32
7 036×lower-fma.f64
5 248×lower-*.f32
5 226×lower-*.f64
4 432×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
046222
082204
1296204
22349204
09886204
Stop Event
iter limit
node limit
iter limit
Counts
21 → 549
Calls
Call 1
Inputs
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
#s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(*.f64 x (*.f64 x x))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
(*.f64 eps #s(literal -1/6 binary64))
Outputs
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/2 binary64) eps) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 (*.f64 eps eps) (*.f64 eps eps)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 (*.f64 eps eps) (*.f64 eps eps)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (*.f64 eps eps) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (*.f64 eps eps) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps)) (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps)) (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps)))) (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps))) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps))) #s(literal 1/2 binary64)) (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)))) (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps))) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64))) (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64)) (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))))))
(/.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64)) (-.f64 (*.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/8 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))) (-.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/8 binary64))) (fma.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64))))))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
eps
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(-.f64 eps (/.f64 #s(literal 0 binary64) (*.f64 eps eps)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (/.f64 (*.f64 eps eps) (-.f64 #s(literal 0 binary64) eps)))
(fma.f64 eps (/.f64 eps eps) #s(literal 0 binary64))
(fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(fma.f64 (/.f64 eps (*.f64 eps eps)) (/.f64 eps (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64))
(fma.f64 (/.f64 eps (*.f64 eps (*.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64))
(fma.f64 (/.f64 eps eps) eps #s(literal 0 binary64))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps eps))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(/.f64 (-.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) eps)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 eps (*.f64 eps eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) eps) (*.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) eps) eps))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) eps) (*.f64 (/.f64 eps (*.f64 eps eps)) #s(literal 0 binary64))) (*.f64 (/.f64 eps (*.f64 eps eps)) eps))
(/.f64 (-.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) eps) (*.f64 (*.f64 eps eps) #s(literal 0 binary64))) (*.f64 eps (*.f64 eps eps)))
(/.f64 (-.f64 (*.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) eps) (*.f64 (neg.f64 (*.f64 eps eps)) #s(literal 0 binary64))) (*.f64 (neg.f64 (*.f64 eps eps)) eps))
(/.f64 (-.f64 (*.f64 (-.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 0 binary64)) eps) (*.f64 (*.f64 eps eps) #s(literal 0 binary64))) (*.f64 eps (*.f64 eps eps)))
(/.f64 (-.f64 (*.f64 (neg.f64 (*.f64 eps eps)) eps) (*.f64 (neg.f64 eps) #s(literal 0 binary64))) (*.f64 (neg.f64 eps) eps))
(/.f64 (-.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) eps) (*.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal 0 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) eps) eps))
(/.f64 (neg.f64 (neg.f64 (*.f64 eps (*.f64 eps eps)))) (neg.f64 (neg.f64 (*.f64 eps eps))))
(/.f64 (neg.f64 (neg.f64 (*.f64 eps eps))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (-.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 0 binary64))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps))) (neg.f64 (-.f64 #s(literal 0 binary64) eps)))
(pow.f64 eps #s(literal 1 binary64))
(pow.f64 (/.f64 eps (*.f64 eps eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))
(*.f64 eps (/.f64 eps eps))
(*.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
(*.f64 (/.f64 eps (*.f64 eps eps)) (/.f64 eps (/.f64 #s(literal 1 binary64) eps)))
(*.f64 (/.f64 eps (*.f64 eps (*.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))
(*.f64 (/.f64 eps eps) eps)
(*.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps))
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))))) #s(literal 2 binary64))
(/.f64 (*.f64 (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (*.f64 (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))) #s(literal 2 binary64))) #s(literal -2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))))
(*.f64 (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))))))
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(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/128024064000 binary64)) #s(literal 1/1728000 binary64)) x)) (neg.f64 (-.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (*.f64 (*.f64 x x) #s(literal -1/604800 binary64)))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64)) x)) (neg.f64 (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal -1/120 binary64))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/1728000 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/128024064000 binary64))))) (fma.f64 (*.f64 x #s(literal 1/120 binary64)) (*.f64 x #s(literal 1/120 binary64)) (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64))) (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64)))) (*.f64 (*.f64 x #s(literal 1/120 binary64)) (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64)))))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))
(*.f64 (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) x)
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)))
(+.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64))
(fma.f64 eps #s(literal -1/6 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal -1/6 binary64) eps) #s(literal 0 binary64))
(fma.f64 (/.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64))
(fma.f64 (/.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64))
(fma.f64 (/.f64 eps (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64))
(fma.f64 (/.f64 eps (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 eps #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps eps)) (/.f64 eps (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps eps)) (/.f64 (*.f64 eps #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64))
(fma.f64 (/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64))
(fma.f64 (/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (*.f64 eps eps)) eps #s(literal 0 binary64))
(fma.f64 (/.f64 (*.f64 eps eps) (*.f64 eps eps)) (/.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1/6 binary64) eps) (*.f64 eps eps) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(/.f64 (neg.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps))
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)) (*.f64 eps eps))
(/.f64 (neg.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))) (neg.f64 (*.f64 eps eps)))
(/.f64 (+.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/216 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps #s(literal -1/6 binary64))) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64))))))
(/.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/216 binary64) #s(literal 0 binary64)) (fma.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps #s(literal -1/6 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64)))))
(*.f64 eps #s(literal -1/6 binary64))
(*.f64 #s(literal -1/6 binary64) eps)
(*.f64 (*.f64 eps eps) (/.f64 #s(literal -1/6 binary64) eps))
(*.f64 (/.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (/.f64 #s(literal 1 binary64) eps)))
(*.f64 (/.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) eps)))
(*.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))
(*.f64 (/.f64 eps (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))
(*.f64 (/.f64 eps (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))
(*.f64 (/.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))
(*.f64 (/.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)))
(*.f64 (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))
(*.f64 (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 eps #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))
(*.f64 (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps eps)) (/.f64 eps (/.f64 #s(literal 1 binary64) eps)))
(*.f64 (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps eps)) (/.f64 (*.f64 eps #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))
(*.f64 (/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))
(*.f64 (/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (*.f64 eps eps)) eps)
(*.f64 (/.f64 (*.f64 eps eps) (*.f64 eps eps)) (/.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) eps)))
(*.f64 (/.f64 #s(literal -1/6 binary64) eps) (*.f64 eps eps))

eval198.0ms (1.4%)

Memory
-20.5MiB live, 228.0MiB allocated
Compiler

Compiled 31 531 to 2 507 computations (92% saved)

prune120.0ms (0.8%)

Memory
-1.9MiB live, 228.8MiB allocated
Pruning

21 alts after pruning (18 fresh and 3 done)

PrunedKeptTotal
New1 038141 052
Fresh145
Picked325
Done011
Total1 042211 063
Accuracy
100.0%
Counts
1 063 → 21
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.0%
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
62.1%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
61.4%
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
61.4%
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
60.8%
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))
99.9%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
55.9%
(*.f64 (*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
99.8%
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
99.7%
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
99.7%
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
99.5%
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
99.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))))))
99.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
99.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
99.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64))))))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))))))))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
Compiler

Compiled 821 to 481 computations (41.4% saved)

simplify300.0ms (2.1%)

Memory
8.5MiB live, 330.9MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
cost-diff0
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff0
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff320
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff0
#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))
cost-diff0
(fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
cost-diff0
(*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
cost-diff0
(*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
cost-diff128
(+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps)))
cost-diff384
(fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64)))
cost-diff0
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))
cost-diff0
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
cost-diff0
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
cost-diff0
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
cost-diff0
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
cost-diff192
(+.f64 eps #s(literal 0 binary64))
cost-diff832
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
Rules
16 604×lower-fma.f32
16 586×lower-fma.f64
3 584×lower-*.f32
3 546×lower-*.f64
3 180×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
076678
0121661
1239661
2683658
31906626
43226626
53587626
65151626
76445626
87011626
08234591
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
eps
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
#s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.f64 x eps)
x
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
eps
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))
#s(literal -1/6 binary64)
(*.f64 eps eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
(*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
x
(fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64)))
(+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps)))
#s(literal -1/2 binary64)
(*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))
(*.f64 eps #s(literal 1/12 binary64))
#s(literal 1/12 binary64)
(+.f64 x eps)
(*.f64 eps #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))
(*.f64 eps #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
eps
(fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))
(*.f64 x #s(literal -1/2 binary64))
x
#s(literal -1/2 binary64)
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))
(*.f64 eps #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(cos.f64 x)
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
eps
(fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(*.f64 eps eps)
(fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))
(*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))
#s(literal -1/645120 binary64)
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal 2 binary64)
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(*.f64 (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))))
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))
(*.f64 eps #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
eps
eps
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
#s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.f64 x eps)
x
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)) eps)))
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)) eps))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)) eps)
eps
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))
(*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))
#s(literal -1/6 binary64)
(*.f64 eps eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64))))))
(*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64)))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64))))
(fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64)))
x
(fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 (+.f64 eps x) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps)))
(fma.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 eps x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))
(*.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)))
(*.f64 eps #s(literal 1/12 binary64))
#s(literal 1/12 binary64)
(+.f64 x eps)
(+.f64 eps x)
(*.f64 eps #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))
(*.f64 eps #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
eps
(fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))
(*.f64 x #s(literal -1/2 binary64))
x
#s(literal -1/2 binary64)
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))
(*.f64 eps #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(cos.f64 x)
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
eps
(fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(*.f64 eps eps)
(fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))
(*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))
#s(literal -1/645120 binary64)
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 eps #s(literal 1/2 binary64) x)
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal 2 binary64)

localize298.0ms (2.1%)

Memory
21.9MiB live, 458.1MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))
accuracy0.00390625
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy0.0347690109686748
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy0.1015625
(*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)))
accuracy0.00390625
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
accuracy0.01171875
(fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
accuracy0.36328125
(*.f64 eps #s(literal -1/6 binary64))
accuracy1.3530855079239983
#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))
accuracy0.15234375
(*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))
accuracy0.36328125
(*.f64 eps #s(literal 1/12 binary64))
accuracy0.36328125
(*.f64 eps #s(literal -1/6 binary64))
accuracy0.7815727822122579
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
accuracy0
(*.f64 eps eps)
accuracy0.00390625
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
accuracy0.15625
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))
accuracy1.4470883276804993
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))
accuracy0.00390625
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
accuracy0.015625
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
accuracy0.0347690109686748
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
accuracy0.265625
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
Samples
83.0ms90×1valid
80.0ms158×0valid
47.0ms5exit
1.0ms3valid
1.0ms2valid
Compiler

Compiled 466 to 60 computations (87.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 169.0ms
ival-mult: 103.0ms (61% of total)
const: 18.0ms (10.7% of total)
ival-add: 18.0ms (10.7% of total)
adjust: 13.0ms (7.7% of total)
ival-sin: 6.0ms (3.6% of total)
ival-cos: 5.0ms (3% of total)
ival-div: 3.0ms (1.8% of total)
ival-sub: 1.0ms (0.6% of total)
exact: 1.0ms (0.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series92.0ms (0.6%)

Memory
-28.9MiB live, 68.4MiB allocated
Counts
30 → 600
Calls
Call 1
Inputs
#<alt (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))>
#<alt (+.f64 eps #s(literal 0 binary64))>
#<alt (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))>
#<alt (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))>
#<alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))>
#<alt #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))>
#<alt (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)>
#<alt (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))>
#<alt (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64)))>
#<alt (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps)))>
#<alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))>
#<alt (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))>
#<alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))>
#<alt (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))>
#<alt (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))>
#<alt #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))>
#<alt (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))>
#<alt (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))>
#<alt (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))>
#<alt #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))>
#<alt (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))>
#<alt (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))>
#<alt (*.f64 eps eps)>
#<alt #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))>
#<alt (*.f64 eps #s(literal -1/6 binary64))>
#<alt (*.f64 eps #s(literal 1/12 binary64))>
#<alt (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))>
#<alt (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)))>
#<alt (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))>
#<alt (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))>
Outputs
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/2 x)>
#<alt (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))>
#<alt (+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2)))>
#<alt (+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2)))>
#<alt -1/2>
#<alt (- (* 1/12 (* eps x)) 1/2)>
#<alt (- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)>
#<alt (- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (/ x eps)>
#<alt (/ (+ x (* 1/2 eps)) eps)>
#<alt (/ (+ x (* 1/2 eps)) eps)>
#<alt (/ (+ x (* 1/2 eps)) eps)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 (* eps x))>
#<alt (* eps (+ (* 1/12 eps) (* 1/12 x)))>
#<alt (* eps (+ (* 1/12 eps) (* 1/12 x)))>
#<alt (* eps (+ (* 1/12 eps) (* 1/12 x)))>
#<alt (* 1/3840 eps)>
#<alt (* eps (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* eps (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* eps (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt -1/48>
#<alt (- (* 1/3840 (pow eps 2)) 1/48)>
#<alt (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)>
#<alt (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (- (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))>
#<alt (* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))>
#<alt (* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt 1/2>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))>
#<alt (* -1/645120 (pow eps 3))>
#<alt (* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (* -1/645120 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* -1/12 (pow x 2))) eps)) (* 1/12 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))) eps)) (* 1/12 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))) eps)) (* 1/12 x)))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))>
#<alt (* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt 1/2>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))>
#<alt (* -1/645120 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (* -1/645120 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)))>
#<alt (- (* 1/12 (pow eps 2)) 1/2)>
#<alt (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)>
#<alt (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)>
#<alt (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/12 (pow x 2)) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt 1/2>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))>
#<alt (* 1/12 (pow eps 2))>
#<alt (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2)))>
#<alt (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2)))>
#<alt (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2)))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* 1/12 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x))))>
#<alt (* 1/12 (* eps x))>
#<alt (* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (/ x eps)>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* 1/12 (* eps x))>
#<alt (* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))))>
#<alt (* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))))>
#<alt (* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* 1/12 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps)))>
#<alt (* 1/12 (* eps x))>
#<alt (* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))>
#<alt (* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))>
#<alt (* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (/ x eps)>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* 1/12 (* eps x))>
#<alt (* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x)))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
Calls

6 calls:

TimeVariablePointExpression
64.0ms
x
@-inf
((* eps (+ 1/2 (/ x eps))) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* -1/6 (* eps eps)) (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (+ -1/2 (* (* eps 1/12) (+ x eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* eps eps) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* eps -1/6) (* eps 1/12) (* (* eps 1/12) (+ x eps)) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (cos (* (+ (* x 2) eps) 1/2)) (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48))
6.0ms
eps
@0
((* eps (+ 1/2 (/ x eps))) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* -1/6 (* eps eps)) (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (+ -1/2 (* (* eps 1/12) (+ x eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* eps eps) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* eps -1/6) (* eps 1/12) (* (* eps 1/12) (+ x eps)) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (cos (* (+ (* x 2) eps) 1/2)) (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48))
4.0ms
eps
@-inf
((* eps (+ 1/2 (/ x eps))) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* -1/6 (* eps eps)) (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (+ -1/2 (* (* eps 1/12) (+ x eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* eps eps) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* eps -1/6) (* eps 1/12) (* (* eps 1/12) (+ x eps)) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (cos (* (+ (* x 2) eps) 1/2)) (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48))
4.0ms
eps
@inf
((* eps (+ 1/2 (/ x eps))) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* -1/6 (* eps eps)) (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (+ -1/2 (* (* eps 1/12) (+ x eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* eps eps) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* eps -1/6) (* eps 1/12) (* (* eps 1/12) (+ x eps)) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (cos (* (+ (* x 2) eps) 1/2)) (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48))
3.0ms
x
@inf
((* eps (+ 1/2 (/ x eps))) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* -1/6 (* eps eps)) (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (+ -1/2 (* (* eps 1/12) (+ x eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* eps eps) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* eps -1/6) (* eps 1/12) (* (* eps 1/12) (+ x eps)) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (cos (* (+ (* x 2) eps) 1/2)) (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48))

simplify296.0ms (2%)

Memory
12.3MiB live, 427.9MiB allocated
Algorithm
egg-herbie
Rules
14 778×lower-fma.f64
14 778×lower-fma.f32
7 318×lower-*.f64
7 318×lower-*.f32
3 516×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04326772
113436403
238556383
084565859
Stop Event
iter limit
node limit
Counts
600 → 581
Calls
Call 1
Inputs
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
eps
eps
eps
eps
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/2 x)
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2)))
(+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2)))
-1/2
(- (* 1/12 (* eps x)) 1/2)
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(/ x eps)
(/ (+ x (* 1/2 eps)) eps)
(/ (+ x (* 1/2 eps)) eps)
(/ (+ x (* 1/2 eps)) eps)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 (* eps x))
(* eps (+ (* 1/12 eps) (* 1/12 x)))
(* eps (+ (* 1/12 eps) (* 1/12 x)))
(* eps (+ (* 1/12 eps) (* 1/12 x)))
(* 1/3840 eps)
(* eps (+ 1/3840 (* -1/645120 (pow eps 2))))
(* eps (+ 1/3840 (* -1/645120 (pow eps 2))))
(* eps (+ 1/3840 (* -1/645120 (pow eps 2))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
-1/48
(- (* 1/3840 (pow eps 2)) 1/48)
(- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)
(- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
eps
eps
eps
eps
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (pow eps 3))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* 1/12 (* (pow eps 2) x))
(* (pow eps 2) (- (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* 1/12 (pow eps 2))
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))
(* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))
(* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 (pow eps 2))
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))
(* -1/645120 (pow eps 3))
(* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1/6 (pow eps 3))
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* 1/12 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* -1/12 (pow x 2))) eps)) (* 1/12 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))) eps)) (* 1/12 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))) eps)) (* 1/12 x)))
(* 1/12 (pow eps 2))
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))
(* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))
(* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 (pow eps 2))
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))
(* -1/645120 (pow eps 3))
(* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))
(+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)))
(+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)))
(- (* 1/12 (pow eps 2)) 1/2)
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))
(* 1/12 (pow eps 2))
(+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2)))
(+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2)))
(+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2)))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x))))
(* 1/12 (* eps x))
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(/ x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* 1/12 (* eps x))
(* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))))
(* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))))
(* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps)))
(* 1/12 (* eps x))
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(/ x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* 1/12 (* eps x))
(* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x)))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
Outputs
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
eps
eps
eps
eps
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* 1/2 (* eps (cos x)))
(*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/12 binary64) (*.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/48 binary64))) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(* -1/6 (pow eps 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))
(* -1/6 (pow eps 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))
(* -1/6 (pow eps 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))
(* -1/6 (pow eps 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(fma.f64 eps (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))
(+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2)))
(fma.f64 eps (fma.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))
(+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2)))
(fma.f64 eps (fma.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))
-1/2
#s(literal -1/2 binary64)
(- (* 1/12 (* eps x)) 1/2)
(fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)
(fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) #s(literal -1/2 binary64))
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)
(fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) #s(literal -1/2 binary64))
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(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(/ x eps)
(/.f64 x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))
(* 1/12 (* eps x))
(*.f64 x (*.f64 eps #s(literal 1/12 binary64)))
(* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x)))))
(*.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps))
(* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x)))))
(*.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps))
(* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x)))))
(*.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite392.0ms (2.7%)

Memory
19.7MiB live, 503.3MiB allocated
Rules
6 596×lower-*.f32
6 558×lower-*.f64
5 984×lower-fma.f32
5 966×lower-fma.f64
3 878×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
076521
0121509
1445506
24041506
010242489
Stop Event
iter limit
node limit
iter limit
Counts
30 → 843
Calls
Call 1
Inputs
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(+.f64 eps #s(literal 0 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))
(fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64)))
(+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
(*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(*.f64 eps eps)
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(*.f64 eps #s(literal -1/6 binary64))
(*.f64 eps #s(literal 1/12 binary64))
(*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))
(*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)))
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))
Outputs
(+.f64 (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64)))
(+.f64 (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))) (*.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x #s(literal 1 binary64)))
(+.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64)) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))))
(+.f64 (*.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64)))
(fma.f64 eps (/.f64 x eps) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64)))
(fma.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 x #s(literal 1 binary64)))
(fma.f64 x #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x eps) eps (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64)))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps (*.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))))
(fma.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))))
(fma.f64 (*.f64 eps x) (/.f64 #s(literal 1 binary64) eps) (*.f64 eps #s(literal 1/2 binary64)))
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (*.f64 (*.f64 eps eps) (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
(/.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (*.f64 eps (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(/.f64 (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
(/.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (*.f64 eps eps)))
(/.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 eps eps)) (*.f64 (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) eps))
(/.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps))) (*.f64 eps (*.f64 eps eps))) (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 eps eps)))
(/.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps))) (*.f64 eps eps)) (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps))
(/.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (fma.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64)) (-.f64 (*.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 x #s(literal 1 binary64))) (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x #s(literal 1 binary64))))))
(/.f64 (-.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 x #s(literal 1 binary64)))) (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x #s(literal 1 binary64))))
(/.f64 (*.f64 eps (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(/.f64 (*.f64 eps (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps)))) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps))
(/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 eps eps)) eps)
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 eps eps))
(/.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) eps)
(/.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) eps) (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps))) eps) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (/.f64 eps x) (*.f64 eps eps)) (*.f64 eps (/.f64 eps x)))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) eps (*.f64 eps (*.f64 eps x))) (*.f64 eps eps))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 x (*.f64 eps (*.f64 eps eps))))) (*.f64 eps (*.f64 eps (*.f64 eps eps))))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 (/.f64 eps x) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))))) (*.f64 eps (*.f64 (/.f64 eps x) (*.f64 eps eps))))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 (/.f64 eps x) eps) (*.f64 eps (*.f64 #s(literal 1 binary64) (*.f64 eps eps)))) (*.f64 eps (*.f64 (/.f64 eps x) eps)))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (neg.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 (neg.f64 x) (*.f64 eps (*.f64 eps eps))))) (*.f64 eps (neg.f64 (*.f64 eps (*.f64 eps eps)))))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 (neg.f64 eps) eps) (*.f64 eps (*.f64 (neg.f64 x) (*.f64 eps eps)))) (*.f64 eps (*.f64 (neg.f64 eps) eps)))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 (*.f64 eps (*.f64 eps eps)) x))) (*.f64 eps (*.f64 eps (*.f64 eps eps))))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 (*.f64 eps eps) (/.f64 eps x)) (*.f64 eps (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1 binary64)))) (*.f64 eps (*.f64 (*.f64 eps eps) (/.f64 eps x))))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (neg.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 (*.f64 eps (*.f64 eps eps)) (neg.f64 x)))) (*.f64 eps (neg.f64 (*.f64 eps (*.f64 eps eps)))))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 eps eps) (*.f64 eps (*.f64 (*.f64 eps eps) x))) (*.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 eps (neg.f64 eps)) (*.f64 eps (*.f64 (*.f64 eps eps) (neg.f64 x)))) (*.f64 eps (*.f64 eps (neg.f64 eps))))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (neg.f64 eps) (*.f64 eps (*.f64 (neg.f64 x) eps))) (*.f64 eps (neg.f64 eps)))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 eps (/.f64 eps x)) (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1 binary64)))) (*.f64 eps (*.f64 eps (/.f64 eps x))))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (/.f64 eps x) (*.f64 eps (*.f64 eps #s(literal 1 binary64)))) (*.f64 eps (/.f64 eps x)))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 eps eps) (*.f64 eps (*.f64 x (*.f64 eps eps)))) (*.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 eps eps) (*.f64 eps (*.f64 (/.f64 x eps) (*.f64 eps (*.f64 eps eps))))) (*.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) eps (*.f64 eps (*.f64 (/.f64 x eps) (*.f64 eps eps)))) (*.f64 eps eps))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (neg.f64 eps) (*.f64 eps (*.f64 eps (neg.f64 x)))) (*.f64 eps (neg.f64 eps)))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (/.f64 eps x) (*.f64 eps (*.f64 #s(literal 1 binary64) eps))) (*.f64 eps (/.f64 eps x)))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 eps eps) (*.f64 eps (*.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 x eps)))) (*.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) eps (*.f64 eps (*.f64 (*.f64 eps eps) (/.f64 x eps)))) (*.f64 eps eps))
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(/.f64 (neg.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal -1/2304 binary64))) (neg.f64 (fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal 1/48 binary64))))
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(pow.f64 (/.f64 (-.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal 1/2304 binary64)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) #s(literal -1/110592 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal 1/48 binary64)) (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal -1/2304 binary64))) #s(literal -1 binary64))
(*.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) #s(literal -1/110592 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal 1/2304 binary64)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))))))))
(*.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal -1/2304 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal 1/48 binary64))))

eval291.0ms (2%)

Memory
-15.8MiB live, 347.5MiB allocated
Compiler

Compiled 46 573 to 4 548 computations (90.2% saved)

prune221.0ms (1.5%)

Memory
1.6MiB live, 276.0MiB allocated
Pruning

25 alts after pruning (22 fresh and 3 done)

PrunedKeptTotal
New1 506141 520
Fresh5813
Picked415
Done123
Total1 516251 541
Accuracy
100.0%
Counts
1 541 → 25
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.0%
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
62.1%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
61.4%
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
61.4%
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
99.9%
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
99.8%
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
99.8%
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
99.7%
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
99.7%
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(approx (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
99.5%
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
55.3%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 eps eps)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps))
99.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))))))
99.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))))))
99.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
99.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
98.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
98.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
5.1%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
Compiler

Compiled 999 to 578 computations (42.1% saved)

simplify298.0ms (2.1%)

Memory
7.8MiB live, 238.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
cost-diff0
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff0
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff320
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff0
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
cost-diff0
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff0
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff320
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff0
(fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
cost-diff0
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
cost-diff0
(*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
cost-diff0
(*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))
cost-diff0
#s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
cost-diff0
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
cost-diff0
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
cost-diff0
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
cost-diff0
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
cost-diff832
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
Rules
6 930×lower-fma.f32
6 916×lower-fma.f64
4 320×lower-*.f32
4 282×lower-*.f64
2 626×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
082736
0120723
1230720
2585709
31306688
41776688
52374688
64451688
75536688
86199688
97451688
08259645
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
eps
#s(literal 1/2 binary64)
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
#s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.f64 x eps)
x
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))
#s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))
eps
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))
#s(literal -1/6 binary64)
(*.f64 eps eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
(*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
x
(fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64)))
#s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/12 binary64))
#s(literal 1/12 binary64)
#s(literal -1/2 binary64)
(*.f64 eps #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))
(*.f64 eps #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal 2 binary64)
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
eps
(fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(*.f64 eps eps)
(fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))
#s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64)))
(*.f64 eps #s(literal 1/3840 binary64))
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal 2 binary64)
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
eps
#s(literal 1/2 binary64)
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
#s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.f64 x eps)
x
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))))
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))))
#s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
#s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))
(*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))
eps
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))
(*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))
#s(literal -1/6 binary64)
(*.f64 eps eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
(*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
x
(fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64)))
#s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/12 binary64))
#s(literal 1/12 binary64)
#s(literal -1/2 binary64)
(*.f64 eps #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))
(*.f64 eps #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
eps
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 eps #s(literal 1/2 binary64) x)
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal 2 binary64)
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
eps
(fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))
(*.f64 eps eps)
(fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))
#s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64)))
(*.f64 eps #s(literal 1/3840 binary64))
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 eps #s(literal 1/2 binary64) x)
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal 2 binary64)

localize399.0ms (2.8%)

Memory
-5.4MiB live, 289.2MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy0.0347690109686748
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy0.09375
(*.f64 eps #s(literal 1/3840 binary64))
accuracy0.09405278396361128
#s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64)))
accuracy0
(*.f64 #s(literal 1/2 binary64) eps)
accuracy0.00390625
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy0.0347690109686748
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy0.13604784108788315
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
accuracy0.15592698211911837
#s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
accuracy0.33984375
(*.f64 x #s(literal 1/12 binary64))
accuracy0.36328125
(*.f64 eps #s(literal -1/6 binary64))
accuracy0.7815727822122579
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
accuracy0.0859375
(*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))
accuracy0.15625
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))
accuracy1.4470883276804993
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))
accuracy59.388952759127505
#s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
accuracy0.00390625
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
accuracy0.015625
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
accuracy0.0347690109686748
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
accuracy0.265625
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
Samples
83.0ms158×0valid
78.0ms90×1valid
38.0ms5exit
1.0ms3valid
1.0ms2valid
Compiler

Compiled 441 to 68 computations (84.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 166.0ms
ival-mult: 100.0ms (60.1% of total)
ival-add: 18.0ms (10.8% of total)
const: 17.0ms (10.2% of total)
adjust: 14.0ms (8.4% of total)
ival-sin: 8.0ms (4.8% of total)
ival-cos: 4.0ms (2.4% of total)
ival-div: 3.0ms (1.8% of total)
ival-sub: 2.0ms (1.2% of total)
exact: 1.0ms (0.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series48.0ms (0.3%)

Memory
-0.9MiB live, 36.6MiB allocated
Counts
29 → 564
Calls
Call 1
Inputs
#<alt (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))>
#<alt (*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))>
#<alt (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))>
#<alt (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))>
#<alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))>
#<alt #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))>
#<alt #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))>
#<alt (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))>
#<alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))>
#<alt (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))>
#<alt #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))>
#<alt (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))>
#<alt (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))>
#<alt (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))>
#<alt (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))>
#<alt #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))>
#<alt (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))>
#<alt (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))>
#<alt #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))>
#<alt (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))>
#<alt (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))>
#<alt (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))>
#<alt (*.f64 eps #s(literal -1/6 binary64))>
#<alt (*.f64 x #s(literal 1/12 binary64))>
#<alt #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))>
#<alt (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))>
#<alt (*.f64 #s(literal 1/2 binary64) eps)>
#<alt #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64)))>
#<alt (*.f64 eps #s(literal 1/3840 binary64))>
Outputs
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))>
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (* 1/12 (pow x 2)) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2))))))>
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (* 1/12 (pow x 2)) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2))))))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (/ x eps)>
#<alt (/ (+ x (* 1/2 eps)) eps)>
#<alt (/ (+ x (* 1/2 eps)) eps)>
#<alt (/ (+ x (* 1/2 eps)) eps)>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt -1/2>
#<alt (- (* 1/12 (* eps x)) 1/2)>
#<alt (- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)>
#<alt (- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/3840 eps)>
#<alt (* eps (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* eps (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* eps (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (+ (* 1/12 (pow x 2)) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) eps)) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (+ (/ 1 (pow eps 2)) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) eps)))) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (+ (/ 1 (pow eps 2)) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) eps)))) 1/6))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt 1/2>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* 1/12 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))>
#<alt (* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))>
#<alt (* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* -1/645120 (pow eps 3))>
#<alt (* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1/2 (* -1/12 (pow x 2)))) eps)) (* 1/12 (pow x 2))) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))) eps)) (* 1/12 (pow x 2))) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))) eps)) (* 1/12 (pow x 2))) 1/6))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt 1/2>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* 1/12 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))>
#<alt (* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* -1/645120 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
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#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt 1/2>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (- (* 1/12 (pow eps 2)) 1/2)>
#<alt (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)>
#<alt (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)>
#<alt (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* 1/12 (* eps (pow x 3)))>
#<alt (* (pow x 3) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/6 (/ (pow eps 2) (pow x 3))) (+ (* 1/12 eps) (+ (* 1/12 (/ (pow eps 2) x)) (/ 1 (pow x 3)))))) (* 1/2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (/ x eps)>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 (* eps x))>
#<alt (* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* 1/12 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (/ x eps)>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 (* eps x))>
#<alt (* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))>
#<alt (* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))>
#<alt (* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
Calls

6 calls:

TimeVariablePointExpression
26.0ms
eps
@-inf
((* eps (+ 1/2 (/ x eps))) (* (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* eps 1/2)) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* eps (* -1/6 (* eps eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* -1/6 (* eps eps)) (* eps -1/6) (* x 1/12) (+ -1/2 (* (* eps 1/12) (+ x eps))) (cos (* (+ (* x 2) eps) 1/2)) (* 1/2 eps) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (* eps 1/3840))
4.0ms
eps
@inf
((* eps (+ 1/2 (/ x eps))) (* (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* eps 1/2)) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* eps (* -1/6 (* eps eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* -1/6 (* eps eps)) (* eps -1/6) (* x 1/12) (+ -1/2 (* (* eps 1/12) (+ x eps))) (cos (* (+ (* x 2) eps) 1/2)) (* 1/2 eps) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (* eps 1/3840))
3.0ms
eps
@0
((* eps (+ 1/2 (/ x eps))) (* (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* eps 1/2)) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* eps (* -1/6 (* eps eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* -1/6 (* eps eps)) (* eps -1/6) (* x 1/12) (+ -1/2 (* (* eps 1/12) (+ x eps))) (cos (* (+ (* x 2) eps) 1/2)) (* 1/2 eps) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (* eps 1/3840))
3.0ms
x
@-inf
((* eps (+ 1/2 (/ x eps))) (* (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* eps 1/2)) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* eps (* -1/6 (* eps eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* -1/6 (* eps eps)) (* eps -1/6) (* x 1/12) (+ -1/2 (* (* eps 1/12) (+ x eps))) (cos (* (+ (* x 2) eps) 1/2)) (* 1/2 eps) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (* eps 1/3840))
3.0ms
x
@inf
((* eps (+ 1/2 (/ x eps))) (* (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* eps 1/2)) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* eps (* -1/6 (* eps eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* -1/6 (* eps eps)) (* eps -1/6) (* x 1/12) (+ -1/2 (* (* eps 1/12) (+ x eps))) (cos (* (+ (* x 2) eps) 1/2)) (* 1/2 eps) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (* eps 1/3840))

simplify292.0ms (2%)

Memory
23.5MiB live, 337.4MiB allocated
Algorithm
egg-herbie
Rules
12 802×lower-fma.f64
12 802×lower-fma.f32
7 180×lower-*.f64
7 180×lower-*.f32
2 982×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04446501
113966107
242266095
083795603
Stop Event
iter limit
node limit
Counts
564 → 557
Calls
Call 1
Inputs
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* -1/6 (pow eps 3))
(* -1/6 (pow eps 3))
(* -1/6 (pow eps 3))
(* -1/6 (pow eps 3))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (* 1/12 (pow x 2)) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2))))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (* 1/12 (pow x 2)) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2))))))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(/ x eps)
(/ (+ x (* 1/2 eps)) eps)
(/ (+ x (* 1/2 eps)) eps)
(/ (+ x (* 1/2 eps)) eps)
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
-1/2
(- (* 1/12 (* eps x)) 1/2)
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/3840 eps)
(* eps (+ 1/3840 (* -1/645120 (pow eps 2))))
(* eps (+ 1/3840 (* -1/645120 (pow eps 2))))
(* eps (+ 1/3840 (* -1/645120 (pow eps 2))))
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (pow eps 3))
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1/2
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1/2
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1/2
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x
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(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(/ x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 (* eps x))
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* 1/12 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(/ x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 (* eps x))
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
Outputs
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* 1/2 (* eps (cos x)))
(*.f64 eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/48 binary64)) (*.f64 (cos.f64 x) #s(literal -1/12 binary64))) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* -1/6 (pow eps 3))
(*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(* -1/6 (pow eps 3))
(*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(* -1/6 (pow eps 3))
(*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(* -1/6 (pow eps 3))
(*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))
(fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (* 1/12 (pow x 2)) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2))))))
(fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (*.f64 x (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (* 1/12 (pow x 2)) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2))))))
(fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (*.f64 x (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* 1/2 (* eps (cos x)))
(*.f64 eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/48 binary64)) (*.f64 (cos.f64 x) #s(literal -1/12 binary64))) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* 1/2 (* eps (cos x)))
(*.f64 eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
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(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(* 1/12 (* eps (pow x 3)))
(*.f64 eps (*.f64 #s(literal 1/12 binary64) (*.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 #s(literal 1/12 binary64) (fma.f64 eps (/.f64 eps x) eps)) #s(literal -1/2 binary64)))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps))))
(neg.f64 (*.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 eps #s(literal -1/12 binary64)) (/.f64 (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) x))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps))))
(neg.f64 (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 eps #s(literal -1/12 binary64) (/.f64 (-.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) x) (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(/ x eps)
(/.f64 x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 (* eps x))
(*.f64 x (*.f64 eps #s(literal 1/12 binary64)))
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(fma.f64 x (*.f64 #s(literal 1/12 binary64) (fma.f64 eps (/.f64 eps x) eps)) #s(literal -1/2 binary64))
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(fma.f64 x (*.f64 #s(literal 1/12 binary64) (fma.f64 eps (/.f64 eps x) eps)) #s(literal -1/2 binary64))
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(fma.f64 x (*.f64 #s(literal 1/12 binary64) (fma.f64 eps (/.f64 eps x) eps)) #s(literal -1/2 binary64))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite385.0ms (2.7%)

Memory
-5.1MiB live, 468.9MiB allocated
Rules
6 340×lower-*.f32
6 302×lower-*.f64
5 716×lower-fma.f32
5 702×lower-fma.f64
3 654×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
082571
0120559
1434545
23865545
09786524
Stop Event
iter limit
node limit
iter limit
Counts
29 → 549
Calls
Call 1
Inputs
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))
#s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
(*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))
(*.f64 eps #s(literal -1/6 binary64))
(*.f64 x #s(literal 1/12 binary64))
#s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
#s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64)))
(*.f64 eps #s(literal 1/3840 binary64))
Outputs
(+.f64 (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64)))
(+.f64 (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))) (*.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x #s(literal 1 binary64)))
(+.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64)) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))))
(+.f64 (*.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64)))
(fma.f64 eps (/.f64 x eps) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64)))
(fma.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 x #s(literal 1 binary64)))
(fma.f64 x #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x eps) eps (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64)))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps (*.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))))
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(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))))
(*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))))
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(+.f64 (/.f64 x eps) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (/.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
(fma.f64 x (/.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 x eps) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 eps)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) x #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (*.f64 eps eps)) eps #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (+.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) eps))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps))) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) #s(literal 1/4 binary64)) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)))
(pow.f64 (/.f64 (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps)))) #s(literal -1 binary64))
(*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64)))
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64))))
(+.f64 (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64)) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))
(+.f64 (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64))) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64)))
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64))))
(fma.f64 eps (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64)))
(fma.f64 eps (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64))))
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64))))
(fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1 binary64)) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64))))
(fma.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64))))
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64))))
(fma.f64 (*.f64 eps #s(literal -1/6 binary64)) eps (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64)))
(fma.f64 (*.f64 eps #s(literal -1/6 binary64)) eps (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64))))
(fma.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))
(fma.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps #s(literal 1 binary64)) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64)))
(fma.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64))))
(fma.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))
(fma.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64)))
(fma.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64))))
(/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) eps)
(/.f64 (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 eps eps))
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps #s(literal -1/6 binary64))) (*.f64 eps eps))
(*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))
(*.f64 eps (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))
(*.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))
(*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) eps)
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps #s(literal 1 binary64)))
(*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64))
(+.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)))
(fma.f64 eps #s(literal -1/6 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps))
(/.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)
(*.f64 eps #s(literal -1/6 binary64))
(*.f64 #s(literal -1/6 binary64) eps)
(*.f64 x #s(literal 1/12 binary64))
(*.f64 #s(literal 1/12 binary64) x)
#s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))))
(-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(-.f64 (*.f64 (cos.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64))
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps))
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps eps)) eps)
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps))
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
#s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/3840 binary64)))
(+.f64 (*.f64 eps #s(literal 1/3840 binary64)) #s(literal 0 binary64))
(fma.f64 eps #s(literal 1/3840 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1/3840 binary64) eps #s(literal 0 binary64))
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) eps)
(/.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps))
(/.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) eps)
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/3840 binary64)) (*.f64 eps eps))
(*.f64 eps #s(literal 1/3840 binary64))
(*.f64 #s(literal 1/3840 binary64) eps)

eval236.0ms (1.6%)

Memory
-13.8MiB live, 348.5MiB allocated
Compiler

Compiled 38 535 to 2 868 computations (92.6% saved)

prune131.0ms (0.9%)

Memory
34.5MiB live, 308.1MiB allocated
Pruning

25 alts after pruning (22 fresh and 3 done)

PrunedKeptTotal
New1 16481 172
Fresh31417
Picked325
Done213
Total1 172251 197
Accuracy
100.0%
Counts
1 197 → 25
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.0%
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
62.1%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
61.4%
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
99.9%
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
99.8%
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
99.8%
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
99.7%
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
99.7%
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(approx (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
99.5%
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
55.3%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 eps eps)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps))
99.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))))))
99.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))))))
99.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
99.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
98.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
98.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
98.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
98.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))
5.1%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
5.1%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps))))
5.1%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))))))
5.1%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
Compiler

Compiled 1 379 to 490 computations (64.5% saved)

regimes48.0ms (0.3%)

Memory
-26.0MiB live, 92.3MiB allocated
Counts
47 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(approx (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 eps eps)) eps))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))))))
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps))))
(*.f64 (*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
Calls

3 calls:

18.0ms
x
13.0ms
eps
12.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Results
AccuracySegmentsBranch
99.9%1x
99.9%1eps
99.9%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes36.0ms (0.2%)

Memory
5.4MiB live, 82.7MiB allocated
Counts
42 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(approx (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 eps eps)) eps))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))))))
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
Calls

3 calls:

12.0ms
x
11.0ms
eps
11.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Results
AccuracySegmentsBranch
99.9%1x
99.9%1eps
99.9%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes39.0ms (0.3%)

Memory
-23.1MiB live, 73.9MiB allocated
Counts
39 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(approx (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 eps eps)) eps))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
Outputs
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
Calls

3 calls:

16.0ms
x
12.0ms
eps
10.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
99.8%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes31.0ms (0.2%)

Memory
20.1MiB live, 59.0MiB allocated
Counts
36 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(approx (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 eps eps)) eps))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
Outputs
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
Calls

3 calls:

10.0ms
eps
10.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms
x
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
99.8%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes32.0ms (0.2%)

Memory
-5.6MiB live, 70.8MiB allocated
Counts
34 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(approx (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 eps eps)) eps))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
Outputs
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
Calls

3 calls:

11.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10.0ms
x
9.0ms
eps
Results
AccuracySegmentsBranch
99.7%1x
99.7%1eps
99.7%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes30.0ms (0.2%)

Memory
14.2MiB live, 54.8MiB allocated
Counts
29 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(approx (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
Outputs
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
Calls

3 calls:

13.0ms
eps
8.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms
x
Results
AccuracySegmentsBranch
99.7%1x
99.7%1eps
99.7%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes27.0ms (0.2%)

Memory
-21.6MiB live, 54.9MiB allocated
Counts
27 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))
Outputs
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
Calls

3 calls:

9.0ms
x
9.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms
eps
Results
AccuracySegmentsBranch
99.5%1x
99.5%1eps
99.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes21.0ms (0.1%)

Memory
15.8MiB live, 52.5MiB allocated
Counts
21 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
Calls

3 calls:

8.0ms
x
6.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
eps
Results
AccuracySegmentsBranch
99.0%1x
99.0%1eps
99.0%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes24.0ms (0.2%)

Memory
1.9MiB live, 41.0MiB allocated
Counts
20 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps))
Calls

3 calls:

12.0ms
eps
6.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
x
Results
AccuracySegmentsBranch
98.5%1x
98.5%1eps
98.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes15.0ms (0.1%)

Memory
-3.8MiB live, 35.6MiB allocated
Counts
15 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
Calls

3 calls:

5.0ms
eps
5.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms
x
Results
AccuracySegmentsBranch
98.5%1x
98.5%1eps
98.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory
-8.2MiB live, 31.3MiB allocated
Counts
12 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64))))))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64))))))
Calls

3 calls:

5.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
eps
4.0ms
x
Results
AccuracySegmentsBranch
98.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.5%1x
98.5%1eps
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory
31.1MiB live, 31.1MiB allocated
Counts
11 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
Calls

3 calls:

4.0ms
eps
4.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
x
Results
AccuracySegmentsBranch
98.5%1x
98.5%1eps
98.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes11.0ms (0.1%)

Memory
-12.4MiB live, 27.2MiB allocated
Counts
9 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
Calls

3 calls:

4.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms
eps
3.0ms
x
Results
AccuracySegmentsBranch
98.3%1x
98.3%1eps
98.3%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes11.0ms (0.1%)

Memory
-21.2MiB live, 20.9MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
Calls

3 calls:

6.0ms
x
2.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms
eps
Results
AccuracySegmentsBranch
97.4%1x
97.4%1eps
97.4%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0%)

Memory
17.7MiB live, 17.7MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
Calls

3 calls:

2.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
5.1%1x
5.1%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.1%1eps
Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify11.0ms (0.1%)

Memory
-17.0MiB live, 22.5MiB allocated
Algorithm
egg-herbie
Rules
74×*-commutative_binary64
+-commutative_binary64
+-rgt-identity_binary64
1-exp_binary64
1-exp_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0144577
1188577
Stop Event
saturated
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))))

soundness1.7s (12%)

Memory
39.6MiB live, 872.4MiB allocated
Rules
16 678×lower-fma.f64
16 678×lower-fma.f32
15 108×lower-fma.f64
15 108×lower-fma.f32
14 778×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107496
1314496
2775489
32829489
46198489
08141458
04326772
113436403
238556383
084565859
03793701
111903521
233393483
082993200
04446501
113966107
242266095
083795603
076521
0121509
1445506
24041506
010242489
0616
01016
15316
238016
3476616
0821016
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 828 to 436 computations (47.3% saved)

preprocess190.0ms (1.3%)

Memory
-3.7MiB live, 151.0MiB allocated
Compiler

Compiled 660 to 236 computations (64.2% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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