2sin (example 3.3)

Time bar (total: 14.1s)

analyze38.0ms (0.3%)

Memory
38.8MiB live, 38.8MiB 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 (42.6%)

Memory
-200.9MiB live, 6 915.5MiB allocated
Samples
3.1s25 541×0invalid
734.0ms5 406×0valid
474.0ms2 850×1valid
Precisions
Click to see histograms. Total time spent on operations: 3.2s
const: 638.0ms (19.9% of total)
ival-sin: 579.0ms (18% of total)
ival-sub: 480.0ms (14.9% of total)
ival-<=: 386.0ms (12% of total)
ival-add: 262.0ms (8.2% of total)
ival-mult: 248.0ms (7.7% of total)
ival-fabs: 232.0ms (7.2% of total)
ival-<: 169.0ms (5.3% of total)
ival-and: 96.0ms (3% of total)
adjust: 70.0ms (2.2% of total)
exact: 43.0ms (1.3% of total)
ival-assert: 11.0ms (0.3% of total)
Bogosity

preprocess29.0ms (0.2%)

Memory
3.1MiB live, 38.3MiB 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))

explain84.0ms (0.6%)

Memory
7.9MiB live, 174.8MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2211(-5.670654569479482e-178 5.008009389092732e-181)2(3.225780371294668e-135 3.531463027326352e-137)(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
20-0-(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))cancellation2207
sin.f64(sin.f64 (+.f64 x eps))sensitivity20
Confusion
Predicted +Predicted -
+2212
-132
Precision
0.9954954954954955
Recall
0.9910313901345291
Confusion?
Predicted +Predicted MaybePredicted -
+22120
-1527
Precision?
0.9737991266375546
Recall?
1.0
Freqs
test
numberfreq
034
1222
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
19.0ms354×0valid
15.0ms154×1valid
1.0ms3valid
0.0ms2valid
Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 19.0ms
ival-sin: 9.0ms (48.3% of total)
adjust: 3.0ms (16.1% of total)
ival-add: 3.0ms (16.1% of total)
ival-sub: 3.0ms (16.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.3MiB live, 1.3MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.5%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify13.0ms (0.1%)

Memory
-25.5MiB live, 13.6MiB 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)

localize23.0ms (0.2%)

Memory
-0.1MiB live, 39.4MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 x eps)
accuracy100.0%
(sin.f64 x)
accuracy99.8%
(sin.f64 (+.f64 x eps))
accuracy63.7%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Samples
8.0ms177×0valid
7.0ms77×1valid
0.0ms3valid
0.0ms2valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-sin: 4.0ms (45.8% of total)
adjust: 1.0ms (11.5% of total)
ival-add: 1.0ms (11.5% of total)
ival-sub: 1.0ms (11.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series4.0ms (0%)

Memory
7.9MiB live, 7.9MiB 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 (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 x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps 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 (* 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 (+ 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 (* -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) (* 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 (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 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 (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps 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 x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x 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 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 x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
Calls

21 calls:

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

rewrite335.0ms (2.4%)

Memory
17.2MiB live, 372.1MiB allocated
Algorithm
batch-egg-rewrite
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))))))))
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(/.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 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (/.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 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))) #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))

simplify350.0ms (2.5%)

Memory
-27.2MiB live, 549.3MiB 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
32836489
46173489
08126458
Stop Event
iter limit
node limit
Counts
84 → 77
Calls
Call 1
Inputs
(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 x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps 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 (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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (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 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))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 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))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x 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 x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
Outputs
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 eps))
(+ (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 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps) (*.f64 #s(literal 1/6 binary64) (*.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 (* -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))
(* 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 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(- (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 (- 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 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)))
(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))
(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))
(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))))
(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))
(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
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.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)
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)
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.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)
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)
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 x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)

eval35.0ms (0.2%)

Memory
1.2MiB live, 78.0MiB allocated
Compiler

Compiled 7 746 to 844 computations (89.1% saved)

prune38.0ms (0.3%)

Memory
10.8MiB live, 94.7MiB 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
99.6%
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
7.8%
(/.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)))
63.5%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
63.7%
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
61.9%
(-.f64 (sin.f64 (+.f64 x eps)) (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))
63.5%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 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))
98.7%
(*.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))))
98.7%
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
98.2%
(*.f64 eps (cos.f64 x))
96.8%
(sin.f64 eps)
Compiler

Compiled 319 to 208 computations (34.8% saved)

simplify395.0ms (2.8%)

Memory
-10.3MiB live, 340.1MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.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)))
cost-diff128
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))
cost-diff192
(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)))))
cost-diff256
(-.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))))))
cost-diff0
(sin.f64 (+.f64 x eps))
cost-diff0
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
cost-diff0
(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
cost-diff1408
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
cost-diff0
(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-diff128
(-.f64 (sin.f64 (+.f64 x eps)) (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
(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
15 492×lower-fma.f32
15 482×lower-fma.f64
3 322×lower-*.f32
3 304×lower-*.f64
2 536×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042307
079287
1138287
2302281
3749273
42327272
55626272
08336266
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)
(sin.f64 eps)
eps
(-.f64 (sin.f64 (+.f64 x eps)) (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
(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))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.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 #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 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)))))
(cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))
(*.f64 (+.f64 x eps) #s(literal 2 binary64))
(+.f64 x eps)
x
eps
#s(literal 2 binary64)
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))
#s(literal -1/2 binary64)
(cos.f64 (+.f64 x x))
(+.f64 x x)
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(sin.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)
(+.f64 eps (+.f64 x x))
x
#s(literal 2 binary64)
(sin.f64 eps)
eps
(-.f64 (sin.f64 (+.f64 x eps)) (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 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
(sin.f64 (+.f64 x eps))
(sin.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
(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 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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 x (*.f64 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)))
(*.f64 x (fma.f64 x (*.f64 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))
(fma.f64 x (*.f64 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))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(sin.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
(sin.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 (/.f64 #s(literal 1/2 binary64) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) (-.f64 (cos.f64 (+.f64 x x)) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))))
(-.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 #s(literal 1/2 binary64) (-.f64 (cos.f64 (+.f64 x x)) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))))
#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)))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64))
(cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(*.f64 (+.f64 x eps) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
#s(literal 2 binary64)
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))
#s(literal -1/2 binary64)
(cos.f64 (+.f64 x x))
(+.f64 x x)
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(sin.f64 (+.f64 eps x))
(sin.f64 x)

localize517.0ms (3.7%)

Memory
-7.2MiB live, 275.5MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy99.6%
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
accuracy55.7%
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))
accuracy55.1%
(-.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))))))
accuracy53.9%
(/.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)))
accuracy100.0%
(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
accuracy99.8%
(sin.f64 (+.f64 x eps))
accuracy99.7%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
accuracy63.7%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
accuracy99.9%
(*.f64 x (*.f64 x x))
accuracy99.8%
(sin.f64 (+.f64 x eps))
accuracy99.8%
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
accuracy63.8%
(-.f64 (sin.f64 (+.f64 x eps)) (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))
accuracy100.0%
(sin.f64 eps)
accuracy100.0%
(*.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))
accuracy100.0%
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
accuracy100.0%
(*.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))))
accuracy99.9%
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
Samples
184.0ms141×2valid
158.0ms37×3valid
45.0ms71×1valid
3.0ms0valid
Compiler

Compiled 327 to 49 computations (85% saved)

Precisions
Click to see histograms. Total time spent on operations: 313.0ms
ival-cos: 177.0ms (56.6% of total)
adjust: 45.0ms (14.4% of total)
ival-mult: 29.0ms (9.3% of total)
ival-add: 18.0ms (5.8% of total)
const: 15.0ms (4.8% of total)
ival-sin: 11.0ms (3.5% of total)
ival-div: 10.0ms (3.2% of total)
ival-sub: 7.0ms (2.2% of total)
exact: 1.0ms (0.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series113.0ms (0.8%)

Memory
30.5MiB live, 67.2MiB allocated
Counts
21 → 420
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 (sin.f64 eps)>
#<alt (-.f64 (sin.f64 (+.f64 x eps)) (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 (sin.f64 (+.f64 x eps))>
#<alt (+.f64 x eps)>
#<alt (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 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))>
#<alt (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))>
#<alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))>
#<alt (-.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))))))>
#<alt (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)))))>
#<alt (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))>
#<alt (/.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)))>
#<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 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))>
#<alt (*.f64 x (*.f64 x x))>
#<alt (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))>
Outputs
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 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 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 x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x 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 eps>
#<alt eps>
#<alt eps>
#<alt 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 (* 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 (* 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 (* 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 (* 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 (* 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 (* 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 (* (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 (- (* 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 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 (* 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)))) (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 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 (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin 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 (* 1/5040 (pow x 7))>
#<alt (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))>
#<alt (* 1/5040 (pow x 7))>
#<alt (* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))>
#<alt (* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))>
#<alt (* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))>
#<alt (- (sin x) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (+ (sin x) (* eps (cos x))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<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 (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 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 (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps 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 x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x 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 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 (* -1/5040 (pow x 7))>
#<alt (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* -1/5040 (pow x 7))>
#<alt (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 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 (- (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 (* -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 (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 (+ 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 (* -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 (sin eps))>
#<alt (+ (* x (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))>
#<alt (+ (* x (- (+ (* x (- (* 1/2 (/ 1 (sin eps))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (/ 1 (pow (sin eps) 2))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))>
#<alt (+ (* x (- (+ (* x (- (+ (* -1 (* x (+ (* -1/2 (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/6 (/ 1 (pow (sin eps) 2))) (/ (* (- (cos eps) 1) (- (* 1/2 (/ 1 (sin eps))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (sin eps))))))) (* 1/2 (/ 1 (sin eps)))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (/ 1 (pow (sin eps) 2))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))>
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))>
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))>
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))>
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))>
#<alt (/ 1 (- (sin (- eps (* -1 x))) (sin x)))>
#<alt (/ 1 (- (sin (- eps (* -1 x))) (sin x)))>
#<alt (/ 1 (- (sin (- eps (* -1 x))) (sin x)))>
#<alt (/ 1 (- (sin (- eps (* -1 x))) (sin x)))>
#<alt (/ 1 (* eps (cos x)))>
#<alt (/ (+ (* 1/2 (/ (* eps (sin x)) (pow (cos x) 2))) (/ 1 (cos x))) eps)>
#<alt (/ (+ (* eps (- (* eps (- (* 1/6 (/ 1 (cos x))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/2 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) eps)>
#<alt (/ (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- (* 1/6 (/ 1 (cos x))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/12 (/ (sin x) (pow (cos x) 2))) (* 1/24 (/ (sin x) (pow (cos x) 2))))))) (* 1/6 (/ 1 (cos x)))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/2 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) eps)>
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))>
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))>
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))>
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))>
#<alt (/ 1 (- (sin (- x (* -1 eps))) (sin x)))>
#<alt (/ 1 (- (sin (- x (* -1 eps))) (sin x)))>
#<alt (/ 1 (- (sin (- x (* -1 eps))) (sin x)))>
#<alt (/ 1 (- (sin (- x (* -1 eps))) (sin 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 (- (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 (* -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 (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 (+ 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 (* -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 (- 1/2 (* 1/2 (cos (* 2 eps))))>
#<alt (- (+ 1/2 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps))))>
#<alt (- (+ 1/2 (* x (- (* -1 (* x (+ 1 (* -1 (cos (* 2 eps)))))) (* -1 (sin (* 2 eps)))))) (* 1/2 (cos (* 2 eps))))>
#<alt (- (+ 1/2 (* x (- (* x (- (* -2/3 (* x (sin (* 2 eps)))) (+ 1 (* -1 (cos (* 2 eps)))))) (* -1 (sin (* 2 eps)))))) (* 1/2 (cos (* 2 eps))))>
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
#<alt (* -1 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))>
#<alt (* -1 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))>
#<alt (* -1 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))>
#<alt (* -1 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))>
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))>
#<alt (- (* eps (sin (* 2 x))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))>
#<alt (- (* eps (- (* eps (cos (* 2 x))) (* -1 (sin (* 2 x))))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))>
#<alt (- (* eps (- (* eps (- (* -2/3 (* eps (sin (* 2 x)))) (* -1 (cos (* 2 x))))) (* -1 (sin (* 2 x))))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))>
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))>
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))>
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))>
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))>
#<alt (* 1/2 (cos (* 2 eps)))>
#<alt (+ (* -1 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps))))>
#<alt (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (* -1 (cos (* 2 eps))))))))>
#<alt (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (+ (* -1 (cos (* 2 eps))) (* 2/3 (* x (sin (* 2 eps))))))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))>
#<alt (+ 1/2 (+ (* -1 (* eps (sin (* 2 x)))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* -1 (* eps (cos (* 2 x)))))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x)))))))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))>
#<alt (+ 1/2 (* -1/2 (cos (* 2 x))))>
#<alt (+ 1/2 (* -1/2 (cos (* 2 x))))>
#<alt (+ 1/2 (* -1/2 (cos (* 2 x))))>
#<alt (+ 1/2 (* -1/2 (cos (* 2 x))))>
#<alt (+ 1/2 (* -1/2 (cos (neg (* -2 x)))))>
#<alt (+ 1/2 (* -1/2 (cos (neg (* -2 x)))))>
#<alt (+ 1/2 (* -1/2 (cos (neg (* -2 x)))))>
#<alt (+ 1/2 (* -1/2 (cos (neg (* -2 x)))))>
#<alt (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps)))>
#<alt (+ (* -1 (* x (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2))))) (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))))>
#<alt (+ (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (* x (+ (* -1 (* x (- (+ (* -1 (/ (cos (* 2 eps)) (sin eps))) (/ 1 (sin eps))) (+ (* -1/2 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (sin eps)))))) (* -1 (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))))))>
#<alt (+ (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (* x (+ (* -1 (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (* x (+ (* -1 (* x (- (* 2/3 (/ (sin (* 2 eps)) (sin eps))) (+ (* -1/2 (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (+ (/ (* (+ 1 (cos eps)) (- (+ (* -1 (/ (cos (* 2 eps)) (sin eps))) (/ 1 (sin eps))) (+ (* -1/2 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (sin eps))))) (sin eps)) (/ (* (- (* -1/6 (cos eps)) 1/6) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2))))))) (* -1 (- (+ (* -1 (/ (cos (* 2 eps)) (sin eps))) (/ 1 (sin eps))) (+ (* -1/2 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (sin eps))))))))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))>
#<alt (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x)))>
#<alt (+ (* -1 (* eps (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2)))))) (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))))>
#<alt (+ (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* eps (+ (* -1 (* eps (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x))))))) (* -1 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))))))>
#<alt (+ (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* eps (+ (* -1 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (* eps (+ (* -1 (* eps (- (* 1/3 (/ (sin (* 2 x)) (sin x))) (+ (* -1/4 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (+ (* -1/24 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x)))))) (sin x)))))))) (* -1 (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x)))))))))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 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 (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 (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 (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 (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 (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 (* 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 (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 (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<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 (* -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 (* -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))))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (+ 1 (cos eps))))>
#<alt (+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps)))))))>
#<alt (+ (sin eps) (* x (+ 1 (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (- (* -1/6 (cos eps)) 1/6))))))))>
#<alt (+ (sin x) (sin (+ eps x)))>
#<alt (+ (sin x) (sin (+ eps x)))>
#<alt (+ (sin x) (sin (+ eps x)))>
#<alt (+ (sin x) (sin (+ eps x)))>
#<alt (+ (sin x) (sin (- eps (* -1 x))))>
#<alt (+ (sin x) (sin (- eps (* -1 x))))>
#<alt (+ (sin x) (sin (- eps (* -1 x))))>
#<alt (+ (sin x) (sin (- eps (* -1 x))))>
#<alt (* 2 (sin x))>
#<alt (+ (* 2 (sin x)) (* eps (cos x)))>
#<alt (+ (* 2 (sin x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (* 2 (sin x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (+ (sin x) (sin (+ eps x)))>
#<alt (+ (sin x) (sin (+ eps x)))>
#<alt (+ (sin x) (sin (+ eps x)))>
#<alt (+ (sin x) (sin (+ eps x)))>
#<alt (+ (sin x) (sin (- x (* -1 eps))))>
#<alt (+ (sin x) (sin (- x (* -1 eps))))>
#<alt (+ (sin x) (sin (- x (* -1 eps))))>
#<alt (+ (sin x) (sin (- x (* -1 eps))))>
Calls

105 calls:

TimeVariablePointExpression
60.0ms
x
@0
(+ 1/2 (* -1/2 (cos (+ x x))))
3.0ms
x
@0
(- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x))))))
2.0ms
x
@0
(/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x)))
2.0ms
eps
@-inf
(/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x)))
2.0ms
eps
@inf
(/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x)))

rewrite197.0ms (1.4%)

Memory
-0.5MiB live, 235.3MiB allocated
Algorithm
batch-egg-rewrite
Rules
1 270×lower-*.f32
1 254×lower-*.f64
1 244×lower-fma.f32
1 236×lower-fma.f64
994×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042217
079220
1321169
02837164
Stop Event
iter limit
iter limit
node limit
iter limit
Counts
21 → 575
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))))
(sin.f64 eps)
(-.f64 (sin.f64 (+.f64 x eps)) (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)
(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 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(-.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))))))
(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 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x 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)))
(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 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
(*.f64 x (*.f64 x x))
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Outputs
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 0 binary64))
(-.f64 (/.f64 (+.f64 x eps) #s(literal 2 binary64)) (/.f64 x #s(literal 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 eps #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) eps))
(/.f64 (neg.f64 eps) #s(literal -2 binary64))
(/.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 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 eps eps))) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps))
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) eps))
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
eps
(+.f64 x (+.f64 x eps))
(+.f64 x (-.f64 eps x))
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(+.f64 (+.f64 x eps) x)
(+.f64 (+.f64 x eps) (neg.f64 x))
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(-.f64 (+.f64 x eps) x)
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (/.f64 (*.f64 eps eps) (-.f64 #s(literal 0 binary64) eps)))
(fma.f64 x #s(literal 2 binary64) eps)
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
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(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.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 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))) (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))))))
(/.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(/.f64 (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal -1 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 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))))
(/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))) (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (*.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))) (fma.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 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (*.f64 #s(literal 1 binary64) (fma.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 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))))))
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) (+.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 (fma.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))))))
(/.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))))) (neg.f64 (+.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 (fma.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 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))))))
(/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x))) (*.f64 (sin.f64 (+.f64 x eps)) (neg.f64 (sin.f64 x))))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))))
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x)))) (-.f64 (sin.f64 (+.f64 x eps)) (neg.f64 (sin.f64 x))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.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 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps eps))))) #s(literal 2 binary64))
(/.f64 (*.f64 (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps eps)))) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) #s(literal 1 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal -1 binary64))
(pow.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(*.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1 binary64))
(*.f64 (cos.f64 (*.f64 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 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (+.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 #s(literal 1 binary64) (fma.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))))))
(*.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.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 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))))))
(*.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.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 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))))
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))))

simplify319.0ms (2.3%)

Memory
12.5MiB live, 599.6MiB allocated
Algorithm
egg-herbie
Rules
8 230×lower-fma.f64
8 230×lower-fma.f32
5 272×lower-*.f64
5 272×lower-*.f32
3 282×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06265677
119245339
256695205
081034828
Stop Event
iter limit
node limit
Counts
420 → 397
Calls
Call 1
Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x 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
eps
eps
eps
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))))))))))
(* 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))))
(* 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))))
(* 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))))))))
(* 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))))
(* 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))))
(* 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))))))))))
(* (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 (- (* 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 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 (* 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)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
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))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin 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)))
(* 1/5040 (pow x 7))
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(* 1/5040 (pow x 7))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))
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x
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x
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(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))
(* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))
(* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))
(* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))
(* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))
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(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))
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(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))
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(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))
(cos (* 1/2 eps))
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(cos (* 1/2 (+ 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))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 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)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 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))))
(* 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))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 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))))
(* -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))
(* -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))))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(sin eps)
(+ (sin eps) (* x (+ 1 (cos eps))))
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps)))))))
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (- (* -1/6 (cos eps)) 1/6))))))))
(+ (sin x) (sin (+ eps x)))
(+ (sin x) (sin (+ eps x)))
(+ (sin x) (sin (+ eps x)))
(+ (sin x) (sin (+ eps 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))))
(* 2 (sin x))
(+ (* 2 (sin x)) (* eps (cos x)))
(+ (* 2 (sin x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (* 2 (sin x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos 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 (* -1 eps))))
(+ (sin x) (sin (- x (* -1 eps))))
(+ (sin x) (sin (- x (* -1 eps))))
(+ (sin x) (sin (- x (* -1 eps))))
Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ 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)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) 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)
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)
(* 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)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (neg.f64 eps))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (neg.f64 eps))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (neg.f64 eps))
eps
eps
eps
eps
eps
eps
eps
eps
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 (fma.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.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)))
(* 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))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (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 (- (* 2 x) (* -1 eps)))) (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 (- (* 2 x) (* -1 eps)))) (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 (- (* 2 x) (* -1 eps)))) (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)) (sin (* 1/2 eps))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(fma.f64 x (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) 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))))))))
(fma.f64 x (-.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) 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))))))))
(fma.f64 x (fma.f64 x (-.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x #s(literal 1/3 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* 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))))
(* 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))))
(* 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 (*.f64 eps (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 #s(literal 1/2 binary64) (cos.f64 x) (*.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))))))
(* (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 (- (* 2 x) (* -1 eps)))) (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 (- (* 2 x) (* -1 eps)))) (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 (- (* 2 x) (* -1 eps)))) (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 (- (* 2 x) (* -1 eps)))) (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)) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(+ (* 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))))
(fma.f64 x (-.f64 (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) 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))))
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) (neg.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* (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)))) (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)))
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)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 x (+.f64 (cos.f64 eps) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) #s(literal -1 binary64))) (sin.f64 eps))
(* 1/5040 (pow x 7))
(*.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64)))
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(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(cos (* 1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 x (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (-.f64 (*.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x #s(literal 1/6 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) 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))
(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))
(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 eps (*.f64 (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 (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/48 binary64)) (*.f64 (cos.f64 x) #s(literal -1/8 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.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))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps 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 eps (*.f64 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 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* 1/120 x)
(*.f64 x #s(literal 1/120 binary64))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(*.f64 x (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(*.f64 x (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(*.f64 x (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)))
(* -1/5040 (pow x 3))
(*.f64 #s(literal -1/5040 binary64) (*.f64 x (*.f64 x x)))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (*.f64 x (*.f64 x x)))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (*.f64 x (*.f64 x x)))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (*.f64 x (*.f64 x x)))
(* -1/5040 (pow x 3))
(*.f64 #s(literal -1/5040 binary64) (*.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(*.f64 (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x))) (neg.f64 (*.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(*.f64 (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x))) (neg.f64 (*.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(*.f64 (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x))) (neg.f64 (*.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))
(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))
(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))
(pow x 3)
(*.f64 x (*.f64 x x))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (+ 1 (cos eps))))
(+.f64 x (fma.f64 x (cos.f64 eps) (sin.f64 eps)))
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps)))))))
(+.f64 x (fma.f64 x (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (cos.f64 eps)) (sin.f64 eps)))
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (- (* -1/6 (cos eps)) 1/6))))))))
(fma.f64 x (+.f64 (cos.f64 eps) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal -1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) #s(literal 1 binary64))) (sin.f64 eps))
(+ (sin x) (sin (+ eps x)))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(+ (sin x) (sin (+ eps x)))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(+ (sin x) (sin (+ eps x)))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(+ (sin x) (sin (+ eps x)))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(+ (sin x) (sin (- eps (* -1 x))))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(+ (sin x) (sin (- eps (* -1 x))))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(+ (sin x) (sin (- eps (* -1 x))))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(+ (sin x) (sin (- eps (* -1 x))))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(* 2 (sin x))
(*.f64 (sin.f64 x) #s(literal 2 binary64))
(+ (* 2 (sin x)) (* eps (cos x)))
(fma.f64 eps (cos.f64 x) (*.f64 (sin.f64 x) #s(literal 2 binary64)))
(+ (* 2 (sin x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 2 binary64)))
(+ (* 2 (sin x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 2 binary64)))
(+ (sin x) (sin (+ eps x)))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(+ (sin x) (sin (+ eps x)))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(+ (sin x) (sin (+ eps x)))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(+ (sin x) (sin (+ eps x)))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(+ (sin x) (sin (- x (* -1 eps))))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(+ (sin x) (sin (- x (* -1 eps))))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(+ (sin x) (sin (- x (* -1 eps))))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(+ (sin x) (sin (- x (* -1 eps))))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))

eval154.0ms (1.1%)

Memory
-18.6MiB live, 301.0MiB allocated
Compiler

Compiled 30 648 to 2 421 computations (92.1% saved)

prune131.0ms (0.9%)

Memory
10.8MiB live, 251.9MiB allocated
Pruning

18 alts after pruning (16 fresh and 2 done)

PrunedKeptTotal
New1 154131 167
Fresh235
Picked415
Done011
Total1 160181 178
Accuracy
100.0%
Counts
1 178 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
96.8%
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
7.8%
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
98.4%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))))
63.5%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.1%
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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))
98.9%
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.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))
98.9%
(*.f64 (*.f64 (*.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))
98.6%
(*.f64 (*.f64 (*.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))
25.4%
(*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 0 binary64)) eps (*.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 eps eps))) (*.f64 (fma.f64 x x #s(literal 0 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))
21.1%
(*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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))
63.6%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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))
53.0%
(*.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))
99.9%
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
98.7%
(*.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))))
98.2%
(*.f64 eps (cos.f64 x))
96.8%
(sin.f64 eps)
5.5%
#s(literal 0 binary64)
Compiler

Compiled 649 to 407 computations (37.3% saved)

simplify378.0ms (2.7%)

Memory
-2.1MiB live, 445.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff192
(fma.f64 x x (*.f64 (+.f64 x eps) x))
cost-diff256
(fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))
cost-diff320
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff5440
(pow.f64 (+.f64 x eps) #s(literal 3 binary64))
cost-diff0
(*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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 x (-.f64 eps x)) #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-diff384
(+.f64 x (-.f64 eps x))
cost-diff0
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
cost-diff0
(*.f64 (*.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))))
cost-diff320
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff320
(*.f64 (*.f64 (*.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))
cost-diff0
(*.f64 #s(literal 1/2 binary64) eps)
cost-diff0
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
cost-diff0
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
cost-diff0
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
Rules
19 884×lower-fma.f32
19 874×lower-fma.f64
4 868×lower-*.f32
4 838×lower-*.f64
3 210×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040435
076378
1140378
2299365
3706356
41983348
56507348
08369341
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
#s(literal 2 binary64)
#s(literal 0 binary64)
(*.f64 (*.f64 (*.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 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))))
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
eps
(fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(*.f64 eps #s(literal -1/48 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)
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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 x (-.f64 eps x)) #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 x (-.f64 eps x)) #s(literal 1/2 binary64)))
(*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))
(+.f64 x (-.f64 eps x))
x
(-.f64 eps x)
eps
#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)
#s(literal 2 binary64)
(*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #s(literal 1/2 binary64))
(/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x))))
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x)))
(pow.f64 (+.f64 x eps) #s(literal 3 binary64))
(+.f64 x eps)
x
eps
#s(literal 3 binary64)
(*.f64 x (*.f64 x x))
(*.f64 x x)
(fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))
(fma.f64 x x (*.f64 (+.f64 x eps) x))
(*.f64 (+.f64 x eps) x)
#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)
#s(literal 2 binary64)
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.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))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
#s(literal 2 binary64)
#s(literal 0 binary64)
(*.f64 (*.f64 (*.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 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/24 binary64)) eps))
(*.f64 (*.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))))
(*.f64 (*.f64 eps (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(*.f64 eps (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))
eps
(fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
(*.f64 eps #s(literal -1/48 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 #s(literal 1/2 binary64) eps x))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 x #s(literal 2 binary64) eps)
(+.f64 eps (+.f64 x x))
x
#s(literal 2 binary64)
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
(+.f64 x (-.f64 eps x))
eps
x
(-.f64 eps x)
eps
#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 #s(literal 1/2 binary64) eps x))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 x #s(literal 2 binary64) eps)
(+.f64 eps (+.f64 x x))
#s(literal 2 binary64)
(*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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 #s(literal 1/2 binary64) (fma.f64 eps (*.f64 (+.f64 eps x) (+.f64 eps (+.f64 x x))) (*.f64 eps (*.f64 x x)))) (fma.f64 eps eps (*.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)))))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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 #s(literal 1/2 binary64) eps x)) (sin.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 eps (*.f64 (+.f64 eps x) (+.f64 eps (+.f64 x x))) (*.f64 eps (*.f64 x x)))) (fma.f64 eps eps (*.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)))))))
(sin.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #s(literal 1/2 binary64)))
(sin.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 eps (*.f64 (+.f64 eps x) (+.f64 eps (+.f64 x x))) (*.f64 eps (*.f64 x x)))) (fma.f64 eps eps (*.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x))))))
(*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #s(literal 1/2 binary64))
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 eps (*.f64 (+.f64 eps x) (+.f64 eps (+.f64 x x))) (*.f64 eps (*.f64 x x)))) (fma.f64 eps eps (*.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)))))
(/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x))))
(/.f64 (fma.f64 eps (*.f64 (+.f64 eps x) (+.f64 eps (+.f64 x x))) (*.f64 eps (*.f64 x x))) (fma.f64 eps eps (*.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)))))
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x)))
(fma.f64 eps (*.f64 (+.f64 eps x) (+.f64 eps (+.f64 x x))) (*.f64 eps (*.f64 x x)))
(pow.f64 (+.f64 x eps) #s(literal 3 binary64))
(*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))
(+.f64 x eps)
(+.f64 eps x)
x
eps
#s(literal 3 binary64)
(*.f64 x (*.f64 x x))
(*.f64 x x)
(fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))
(fma.f64 eps eps (*.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x))))
(fma.f64 x x (*.f64 (+.f64 x eps) x))
(*.f64 x (+.f64 eps (+.f64 x x)))
(*.f64 (+.f64 x eps) x)
(*.f64 x (+.f64 eps x))
#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 #s(literal 1/2 binary64) eps x))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 x #s(literal 2 binary64) eps)
(+.f64 eps (+.f64 x x))
#s(literal 2 binary64)

localize132.0ms (0.9%)

Memory
-12.3MiB live, 142.1MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy99.8%
(fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))
accuracy99.6%
(pow.f64 (+.f64 x eps) #s(literal 3 binary64))
accuracy89.1%
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x)))
accuracy33.7%
(/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x))))
accuracy100.0%
(sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64)))
accuracy100.0%
(*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy99.9%
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy63.7%
(+.f64 x (-.f64 eps x))
accuracy100.0%
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
accuracy100.0%
(*.f64 (*.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))))
accuracy99.9%
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy99.4%
(*.f64 eps #s(literal -1/48 binary64))
accuracy100.0%
(*.f64 #s(literal 1/2 binary64) eps)
accuracy100.0%
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
accuracy100.0%
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
accuracy99.9%
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
Samples
78.0ms256×0valid
Compiler

Compiled 473 to 45 computations (90.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 56.0ms
ival-mult: 29.0ms (51.5% of total)
ival-add: 7.0ms (12.4% of total)
ival-sin: 5.0ms (8.9% of total)
ival-pow: 4.0ms (7.1% of total)
ival-cos: 3.0ms (5.3% of total)
const: 3.0ms (5.3% of total)
ival-div: 2.0ms (3.6% of total)
ival-sub: 2.0ms (3.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series53.0ms (0.4%)

Memory
16.5MiB live, 57.4MiB allocated
Counts
20 → 432
Calls
Call 1
Inputs
#<alt (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))>
#<alt (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))>
#<alt (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))>
#<alt (*.f64 #s(literal 1/2 binary64) eps)>
#<alt (*.f64 (*.f64 (*.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))>
#<alt (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))>
#<alt (*.f64 (*.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))))>
#<alt (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))>
#<alt (+.f64 x (-.f64 eps x))>
#<alt (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))>
#<alt (pow.f64 (+.f64 x eps) #s(literal 3 binary64))>
#<alt (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))>
#<alt (fma.f64 x x (*.f64 (+.f64 x eps) x))>
#<alt (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))>
#<alt (*.f64 eps #s(literal -1/48 binary64))>
#<alt (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))>
#<alt (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64)))>
#<alt (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x))))>
#<alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x)))>
Outputs
#<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 (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -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 (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
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#<alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))>
#<alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 x)) eps))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps))))>
#<alt (* eps x)>
#<alt (* x (+ eps (* 2 x)))>
#<alt (* x (+ eps (* 2 x)))>
#<alt (* x (+ eps (* 2 x)))>
#<alt (* 2 (pow x 2))>
#<alt (* (pow x 2) (+ 2 (/ eps x)))>
#<alt (* (pow x 2) (+ 2 (/ eps x)))>
#<alt (* (pow x 2) (+ 2 (/ eps x)))>
#<alt (* 2 (pow x 2))>
#<alt (* (pow x 2) (+ 2 (/ eps x)))>
#<alt (* (pow x 2) (+ 2 (/ eps x)))>
#<alt (* (pow x 2) (+ 2 (/ eps x)))>
#<alt (* 2 (pow x 2))>
#<alt (+ (* 2 (pow x 2)) (* eps x))>
#<alt (+ (* 2 (pow x 2)) (* eps x))>
#<alt (+ (* 2 (pow x 2)) (* eps x))>
#<alt (* eps x)>
#<alt (* eps (+ x (* 2 (/ (pow x 2) eps))))>
#<alt (* eps (+ x (* 2 (/ (pow x 2) eps))))>
#<alt (* eps (+ x (* 2 (/ (pow x 2) eps))))>
#<alt (* eps x)>
#<alt (* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 x))))>
#<alt (* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 x))))>
#<alt (* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 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 (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -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 (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 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 (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 (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 (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 (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 (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 (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 (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<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 (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 (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* 1/3 (+ eps (* 2 eps)))>
#<alt (- (+ (* 1/3 (+ eps (* 2 eps))) (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x))) (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)))>
#<alt (- (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2))))) (+ (* 1/9 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))) (pow x 2))))))>
#<alt (- (+ (* -1 (/ (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))))) (pow x 3))) (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2)))))) (+ (* 1/9 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))) (pow x 2))))))>
#<alt (* 1/3 (+ eps (* 2 eps)))>
#<alt (+ (* -1 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))>
#<alt (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))>
#<alt (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* 1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps)))))))))) x)) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps)))))) x)) (* 1/3 (pow eps 3)))) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (pow x 2)) (+ (/ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) eps) (/ (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))) eps)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))>
#<alt (pow eps 3)>
#<alt (+ (* x (+ (* 2 (pow eps 2)) (pow eps 2))) (pow eps 3))>
#<alt (+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3))>
#<alt (+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3))>
#<alt (* (pow x 2) (+ eps (* 2 eps)))>
#<alt (* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (/ (pow eps 2) x)))))>
#<alt (* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (+ (/ (pow eps 2) x) (/ (pow eps 3) (pow x 2)))))))>
#<alt (* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (+ (/ (pow eps 2) x) (/ (pow eps 3) (pow x 2)))))))>
#<alt (* (pow x 2) (+ eps (* 2 eps)))>
#<alt (* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))) x)) (* 2 eps))))>
#<alt (* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))))>
#<alt (* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))))>
#<alt (* eps (+ (* 2 (pow x 2)) (pow x 2)))>
#<alt (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2))))>
#<alt (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2))))>
#<alt (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2))))>
#<alt (pow eps 3)>
#<alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))>
#<alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))>
#<alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))>
#<alt (pow eps 3)>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (* 2 x)) eps)) 1)))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))>
Calls

108 calls:

TimeVariablePointExpression
6.0ms
x
@0
(* (* (* eps (+ (* eps (* eps -1/48)) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)
3.0ms
x
@0
(sin (* (+ x (- eps x)) 1/2))
2.0ms
eps
@0
(/ (- (pow (+ x eps) 3) (* x (* x x))) (+ (* (+ x eps) (+ x eps)) (+ (* x x) (* (+ x eps) x))))
2.0ms
eps
@inf
(/ (- (pow (+ x eps) 3) (* x (* x x))) (+ (* (+ x eps) (+ x eps)) (+ (* x x) (* (+ x eps) x))))
1.0ms
x
@inf
(* (* (* eps (+ (* eps (* eps -1/48)) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)

rewrite338.0ms (2.4%)

Memory
10.2MiB live, 365.0MiB allocated
Algorithm
batch-egg-rewrite
Rules
5 254×lower-*.f32
5 226×lower-*.f64
3 716×lower-/.f32
3 714×lower-/.f64
3 626×lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
035205
067178
1257178
21964178
08141177
Stop Event
iter limit
node limit
iter limit
Counts
20 → 584
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 (*.f64 (*.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 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 (*.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))))
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(+.f64 x (-.f64 eps x))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(pow.f64 (+.f64 x eps) #s(literal 3 binary64))
(fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))
(fma.f64 x x (*.f64 (+.f64 x eps) x))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(*.f64 eps #s(literal -1/48 binary64))
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x))))
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x)))
Outputs
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 2 binary64))
(/.f64 (*.f64 (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(*.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)))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(/.f64 (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))))
(/.f64 (neg.f64 (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal -1 binary64))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 1/2 binary64))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 eps (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))))
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simplify374.0ms (2.6%)

Memory
13.1MiB live, 480.1MiB allocated
Algorithm
egg-herbie
Rules
11 836×lower-fma.f64
11 836×lower-fma.f32
5 620×lower-*.f64
5 620×lower-*.f32
3 700×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05765604
119595182
272434885
084074503
Stop Event
iter limit
node limit
Counts
432 → 392
Calls
Call 1
Inputs
(* 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))))))))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 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))))))))
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(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
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(* 1/2 (* eps (cos x)))
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(* 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))))))))))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
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(+ (* 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
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(* 1/2 eps)
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(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 1/2 eps)
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x
(* x (+ 1 (* 1/2 (/ eps x))))
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(* eps (+ 1/2 (/ x eps)))
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(* 1/2 (* eps (cos x)))
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(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
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(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
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(* 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 (- (* 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 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 (* 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)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* 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))))))))))
(* (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 (- (* 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)))
(pow eps 3)
(+ (* x (+ (* 2 (pow eps 2)) (pow eps 2))) (pow eps 3))
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3))
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (+ x (* 2 eps)))) (pow eps 2)))) (pow eps 3))
(pow x 3)
(* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (/ eps x))))
(* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (+ (* 2 (/ (pow eps 2) (pow x 2))) (+ (/ eps x) (/ (pow eps 2) (pow x 2)))))))
(* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (+ (* 2 (/ (pow eps 2) (pow x 2))) (+ (/ eps x) (+ (/ (pow eps 2) (pow x 2)) (/ (pow eps 3) (pow x 3))))))))
(pow x 3)
(* -1 (* (pow x 3) (- (* -1 (/ (+ eps (* 2 eps)) x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))) x)) (* 2 eps))) x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))) x)) 1)))
(pow x 3)
(+ (* eps (+ (* 2 (pow x 2)) (pow x 2))) (pow x 3))
(+ (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2)))) (pow x 3))
(+ (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))) (pow x 3))
(pow eps 3)
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (+ (/ (pow x 2) (pow eps 2)) (/ (pow x 3) (pow eps 3))))))))
(pow eps 3)
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (* 2 x)) eps)) 1)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (+ (* -1 (/ (pow x 3) eps)) (* -1 (pow x 2)))) eps)) (* 2 x))) eps)) 1)))
(pow eps 2)
(+ (* x (+ eps (* 2 eps))) (pow eps 2))
(+ (* x (+ eps (+ (* 2 eps) (* 3 x)))) (pow eps 2))
(+ (* x (+ eps (+ (* 2 eps) (* 3 x)))) (pow eps 2))
(* 3 (pow x 2))
(* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (/ eps x))))
(* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))))
(* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))))
(* 3 (pow x 2))
(* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (* -1 eps)) x))))
(* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))) x))))
(* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))) x))))
(+ (* 2 (pow x 2)) (pow x 2))
(+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2)))
(+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))
(+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))
(pow eps 2)
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 x)) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps))))
(* eps x)
(* x (+ eps (* 2 x)))
(* x (+ eps (* 2 x)))
(* x (+ eps (* 2 x)))
(* 2 (pow x 2))
(* (pow x 2) (+ 2 (/ eps x)))
(* (pow x 2) (+ 2 (/ eps x)))
(* (pow x 2) (+ 2 (/ eps x)))
(* 2 (pow x 2))
(* (pow x 2) (+ 2 (/ eps x)))
(* (pow x 2) (+ 2 (/ eps x)))
(* (pow x 2) (+ 2 (/ eps x)))
(* 2 (pow x 2))
(+ (* 2 (pow x 2)) (* eps x))
(+ (* 2 (pow x 2)) (* eps x))
(+ (* 2 (pow x 2)) (* eps x))
(* eps x)
(* eps (+ x (* 2 (/ (pow x 2) eps))))
(* eps (+ x (* 2 (/ (pow x 2) eps))))
(* eps (+ x (* 2 (/ (pow x 2) eps))))
(* eps x)
(* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 x))))
(* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 x))))
(* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 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)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -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)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 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)))))
(cos (* 1/2 (+ 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))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 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)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 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))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 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))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
eps
eps
eps
eps
(* 1/3 (+ eps (* 2 eps)))
(- (+ (* 1/3 (+ eps (* 2 eps))) (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x))) (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)))
(- (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2))))) (+ (* 1/9 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))) (pow x 2))))))
(- (+ (* -1 (/ (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))))) (pow x 3))) (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2)))))) (+ (* 1/9 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))) (pow x 2))))))
(* 1/3 (+ eps (* 2 eps)))
(+ (* -1 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))
(+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))
(+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* 1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps)))))))))) x)) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps)))))) x)) (* 1/3 (pow eps 3)))) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (- (* -1 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (pow x 2)) (+ (/ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) eps) (/ (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))) eps)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))
(pow eps 3)
(+ (* x (+ (* 2 (pow eps 2)) (pow eps 2))) (pow eps 3))
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3))
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3))
(* (pow x 2) (+ eps (* 2 eps)))
(* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (/ (pow eps 2) x)))))
(* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (+ (/ (pow eps 2) x) (/ (pow eps 3) (pow x 2)))))))
(* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (+ (/ (pow eps 2) x) (/ (pow eps 3) (pow x 2)))))))
(* (pow x 2) (+ eps (* 2 eps)))
(* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))) x)) (* 2 eps))))
(* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))))
(* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))))
(* eps (+ (* 2 (pow x 2)) (pow x 2)))
(* eps (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2))))
(* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2))))
(* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2))))
(pow eps 3)
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(pow eps 3)
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (* 2 x)) eps)) 1)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))
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)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.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)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(*.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))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(*.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))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(*.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))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(*.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))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(*.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))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(*.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))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(*.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))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(*.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))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
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(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 x (/.f64 x (*.f64 eps eps)) (/.f64 x eps)) (fma.f64 x (/.f64 x (*.f64 eps eps)) (/.f64 x eps)))))
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 x (/.f64 x (*.f64 eps eps)) (/.f64 x eps)) (fma.f64 x (/.f64 x (*.f64 eps eps)) (/.f64 x eps)))))
(pow eps 3)
(*.f64 eps (*.f64 eps eps))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (* 2 x)) eps)) 1)))
(*.f64 (fma.f64 x (/.f64 #s(literal -3 binary64) eps) #s(literal -1 binary64)) (*.f64 (*.f64 eps (neg.f64 eps)) eps))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))
(*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (fma.f64 x #s(literal -3 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -3 binary64)) eps)) eps)) (*.f64 (*.f64 eps (neg.f64 eps)) eps))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))
(*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (fma.f64 x #s(literal -3 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -3 binary64)) eps)) eps)) (*.f64 (*.f64 eps (neg.f64 eps)) eps))

eval180.0ms (1.3%)

Memory
-9.9MiB live, 270.5MiB allocated
Compiler

Compiled 57 226 to 4 436 computations (92.2% saved)

prune124.0ms (0.9%)

Memory
-2.4MiB live, 230.8MiB allocated
Pruning

25 alts after pruning (21 fresh and 4 done)

PrunedKeptTotal
New1 093151 108
Fresh5611
Picked325
Done022
Total1 101251 126
Accuracy
100.0%
Counts
1 126 → 25
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
96.8%
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
98.4%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))))
63.5%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.9%
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))))
98.9%
(*.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64)))
99.1%
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
98.9%
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
98.6%
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
11.0%
(*.f64 (*.f64 (sin.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 x (+.f64 x (+.f64 eps x))))))) (fma.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (-.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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))
21.8%
(*.f64 (*.f64 (sin.f64 (*.f64 (fma.f64 (+.f64 eps x) (/.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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))
21.0%
(*.f64 (*.f64 (sin.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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))
21.3%
(*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (fma.f64 (*.f64 (neg.f64 x) x) x (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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))
35.5%
(*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x)) (+.f64 x (+.f64 eps x))) #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))
21.1%
(*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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))
35.5%
(*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 x x) (+.f64 (-.f64 x eps) x)) (/.f64 (*.f64 (-.f64 eps x) (-.f64 eps x)) (+.f64 (-.f64 x eps) x))) #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))
63.6%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64))
53.0%
(*.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))
100.0%
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64))
99.9%
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
30.7%
(*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 eps eps))))
98.7%
(*.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))))
98.2%
(*.f64 eps (cos.f64 x))
96.8%
(sin.f64 eps)
5.5%
#s(literal 0 binary64)
Compiler

Compiled 1 420 to 650 computations (54.2% saved)

simplify418.0ms (3%)

Memory
-3.7MiB live, 559.7MiB allocated
Algorithm
egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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-diff256
(fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))
cost-diff320
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff1920
(*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64))
cost-diff0
(*.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))))
cost-diff0
(*.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))
cost-diff320
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff1344
(*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
cost-diff0
(fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
cost-diff0
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
cost-diff0
(*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
cost-diff128
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
cost-diff0
(*.f64 eps eps)
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
(*.f64 #s(literal 1/2 binary64) eps)
cost-diff0
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
cost-diff0
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))))
cost-diff0
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64))
Rules
15 314×lower-fma.f32
15 300×lower-fma.f64
5 238×lower-*.f32
5 194×lower-*.f64
2 718×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
052669
0102586
1200574
2494547
31247539
43313482
55954478
08434468
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(cos.f64 x)
x
(*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))
(neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(sin.f64 x)
#s(literal 2 binary64)
(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)
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.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 (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(*.f64 eps eps)
(fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 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 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
#s(literal 2 binary64)
(*.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 (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))))
(sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64)))
(*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))
(*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
(*.f64 eps eps)
eps
(/.f64 #s(literal 1 binary64) eps)
#s(literal 1 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)
(*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64)))
(*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64))
(-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))
(/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))
(*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))
(+.f64 eps x)
eps
x
(*.f64 (+.f64 eps x) (+.f64 eps x))
(fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))
(+.f64 x (+.f64 eps x))
(/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))
(*.f64 x (*.f64 x x))
(*.f64 x x)
#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)
#s(literal 2 binary64)
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64))
(*.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (cos.f64 x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))
(-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(cos.f64 x)
x
(*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))
(neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(sin.f64 x)
#s(literal 2 binary64)
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(fma.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) 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)
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (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)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (+.f64 eps eps)))
(*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(*.f64 (*.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))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.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 (*.f64 eps 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 (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(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))
(*.f64 eps eps)
(fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 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 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
#s(literal 2 binary64)
(*.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 (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))))
(*.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))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
eps
(*.f64 eps eps)
eps
(/.f64 #s(literal 1 binary64) eps)
#s(literal 1 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 #s(literal 1/2 binary64) eps x))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 x #s(literal 2 binary64) eps)
(+.f64 x (+.f64 eps x))
x
#s(literal 2 binary64)
(*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps))) (-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x)))))))
(*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps))) (-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x))))))
(sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64)))
(sin.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps))) (-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x)))))
(*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps))) (-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x))))
(-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))
(-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (/.f64 (+.f64 eps x) (fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps))))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps))))
(/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))
(*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (/.f64 (+.f64 eps x) (fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps)))))
(*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))
(+.f64 eps x)
eps
x
(*.f64 (+.f64 eps x) (+.f64 eps x))
(fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))
(fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps))
(+.f64 x (+.f64 eps x))
(/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))
(/.f64 (*.f64 x (*.f64 x x)) (fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps)))
(*.f64 x (*.f64 x x))
(*.f64 x x)
#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 #s(literal 1/2 binary64) eps x))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 x #s(literal 2 binary64) eps)
(+.f64 x (+.f64 eps x))
#s(literal 2 binary64)

localize194.0ms (1.4%)

Memory
7.4MiB live, 342.8MiB allocated
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy99.6%
(*.f64 (+.f64 eps x) (+.f64 eps x))
accuracy65.4%
(-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))
accuracy34.1%
(/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))
accuracy34.1%
(/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))
accuracy100.0%
(sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64)))
accuracy100.0%
(*.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))))
accuracy99.9%
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy53.1%
(*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
accuracy100.0%
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
accuracy100.0%
(*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
accuracy99.9%
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
accuracy99.8%
(*.f64 eps #s(literal 1/3840 binary64))
accuracy100.0%
(*.f64 eps eps)
accuracy100.0%
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
accuracy99.7%
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))
accuracy100.0%
(cos.f64 x)
accuracy100.0%
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))
accuracy100.0%
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))))
accuracy100.0%
(*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))
Samples
108.0ms256×0valid
Compiler

Compiled 711 to 60 computations (91.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 83.0ms
ival-mult: 39.0ms (47.2% of total)
ival-sin: 12.0ms (14.5% of total)
ival-add: 9.0ms (10.9% of total)
const: 9.0ms (10.9% of total)
ival-cos: 6.0ms (7.3% of total)
ival-div: 5.0ms (6.1% of total)
ival-sub: 1.0ms (1.2% of total)
ival-neg: 1.0ms (1.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series165.0ms (1.2%)

Memory
9.2MiB live, 164.7MiB allocated
Counts
29 → 564
Calls
Call 1
Inputs
#<alt (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64))>
#<alt (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))))>
#<alt (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))>
#<alt (*.f64 #s(literal 1/2 binary64) 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 (*.f64 eps eps)>
#<alt (*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))>
#<alt (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))>
#<alt (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))>
#<alt (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))>
#<alt (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))>
#<alt (*.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))>
#<alt (*.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))))>
#<alt (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64))>
#<alt (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))>
#<alt (*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))>
#<alt (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))>
#<alt (cos.f64 x)>
#<alt (*.f64 eps #s(literal 1/3840 binary64))>
#<alt (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))>
#<alt (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))>
#<alt (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64)))>
#<alt (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))>
#<alt (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))>
#<alt (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))>
#<alt (*.f64 (+.f64 eps x) (+.f64 eps x))>
Outputs
#<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 (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 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 (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))>
#<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 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))>
#<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 (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))>
#<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 (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 (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<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 (* (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 (* (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 (* -1/6 (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 (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<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 (* 1/1920 (* (pow eps 5) (cos (+ x (* 1/2 eps)))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/1920 (cos (+ x (* 1/2 eps))))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))>
#<alt (* 1/1920 (* (pow eps 5) (cos (- x (* -1/2 eps)))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))>
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<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 (* 1/3840 (* (pow eps 5) (cos (+ x (* 1/2 eps)))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/3840 (cos (+ x (* 1/2 eps))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))))))>
#<alt (* 1/3840 (* (pow eps 5) (cos (- x (* -1/2 eps)))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))>
#<alt (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))>
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<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) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* 1/3840 (pow eps 5))>
#<alt (* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* 1/3840 (pow eps 5))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/48 (pow eps 2)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))>
#<alt (* 1/3840 (pow eps 4))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* 1/3840 (pow eps 4))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 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 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 x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x 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 (cos x))>
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#<alt (pow eps 2)>
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#<alt (pow eps 2)>
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#<alt (pow eps 2)>
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#<alt (* eps (cos x))>
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#<alt eps>
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#<alt eps>
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#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (/ (- (pow x 3) (+ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* -1 (pow x 2)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))>
#<alt eps>
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#<alt (* x (- (+ 1/3 (+ (* 1/3 (/ (+ eps (* 2 eps)) x)) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (pow x 2))) (* 1/3 (/ (pow eps 3) (pow x 3)))))) (+ (* 1/9 (/ (+ eps (* 2 eps)) x)) (+ (* 1/9 (/ (pow eps 2) (pow x 2))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 2))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 3))) (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 3)))))))))>
#<alt (* 1/3 x)>
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#<alt (* (pow x 3) (+ (* -3 (/ x (pow eps 3))) (/ 1 (pow eps 2))))>
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#<alt (* 1/3 x)>
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#<alt (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))>
#<alt (+ (* -1 (/ (* eps (* (pow x 3) (+ x (* 2 x)))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))>
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#<alt (+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))))) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))>
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#<alt (/ (pow x 3) (pow eps 2))>
#<alt (/ (+ (/ (* (pow x 3) (+ (* -2 x) (* -1 x))) eps) (pow x 3)) (pow eps 2))>
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#<alt (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (+ (* -2 x) (* -1 x)) (+ (* -1 (* (pow x 3) (pow (+ (* -2 x) (* -1 x)) 2))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) eps)) (* -1 (/ (* (pow x 3) (* (+ (* -2 x) (* -1 x)) (+ (* 2 (pow x 2)) (pow x 2)))) eps))) (+ (* -1 (* (pow x 3) (pow (+ (* -2 x) (* -1 x)) 2))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) eps)) (* (pow x 3) (+ (* -2 x) (* -1 x)))) eps)) (pow x 3)) (pow eps 2))>
#<alt eps>
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#<alt (* eps (+ 1 (* eps (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* eps (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))))>
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#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
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#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (pow x 2)) (+ (/ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) eps) (/ (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))) eps)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
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#<alt (- (+ (* -1/3 (/ (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2)))) (pow x 2))) (+ (* -1/27 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* -1/27 (/ (pow (+ eps (* 2 eps)) 2) x)) (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2)))))))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) x)) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 2))) (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 2))))))>
#<alt (- (+ (* -1/3 (/ (* (+ eps (* 2 eps)) (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ eps (* 2 eps)))))) (pow x 3))) (+ (* -1/3 (/ (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2)))) (pow x 2))) (+ (* -1/3 (/ (* (pow eps 2) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2)))) (pow x 3))) (+ (* -1/27 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* -1/27 (/ (pow (+ eps (* 2 eps)) 2) x)) (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2)))))))))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) x)) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 2))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 3))) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 2))) (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 3))))))))>
#<alt (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps)))))>
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#<alt (- (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))))) x)) (+ (* -1/3 (/ (* (pow eps 2) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2)))) x)) (+ (* 1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))) x)) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (pow eps 3)))))) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ eps (* 2 eps)))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps)))))>
#<alt (pow x 2)>
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#<alt (pow eps 2)>
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#<alt (pow eps 2)>
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#<alt (pow x 2)>
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#<alt (pow x 2)>
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#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))>
Calls

141 calls:

TimeVariablePointExpression
25.0ms
x
@inf
(* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (+ (* 1/2 eps) x)))
23.0ms
x
@0
(* (- (/ (* (+ eps x) (* (+ eps x) (+ eps x))) (+ (* x (+ x (+ eps x))) (* (+ eps x) (+ eps x)))) (/ (* x (* x x)) (+ (* x (+ x (+ eps x))) (* (+ eps x) (+ eps x))))) 1/2)
9.0ms
eps
@inf
(* (- (/ (* (+ eps x) (* (+ eps x) (+ eps x))) (+ (* x (+ x (+ eps x))) (* (+ eps x) (+ eps x)))) (/ (* x (* x x)) (+ (* x (+ x (+ eps x))) (* (+ eps x) (+ eps x))))) 1/2)
6.0ms
x
@inf
(* (* (sin (* 1/2 eps)) (+ (* (cos (* 1/2 eps)) (cos x)) (* (neg (sin (* 1/2 eps))) (sin x)))) 2)
5.0ms
eps
@0
(- (/ (* (+ eps x) (* (+ eps x) (+ eps x))) (+ (* x (+ x (+ eps x))) (* (+ eps x) (+ eps x)))) (/ (* x (* x x)) (+ (* x (+ x (+ eps x))) (* (+ eps x) (+ eps x)))))

rewrite418.0ms (3%)

Memory
8.0MiB live, 522.8MiB allocated
Algorithm
batch-egg-rewrite
Rules
7 394×lower-fma.f32
7 380×lower-fma.f64
5 278×lower-*.f32
5 234×lower-*.f64
4 654×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
052453
0102360
1356307
22834307
010220306
Stop Event
iter limit
node limit
iter limit
Counts
29 → 737
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))
(*.f64 eps eps)
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.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 (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))))
(*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64))
(fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))
(*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))
(cos.f64 x)
(*.f64 eps #s(literal 1/3840 binary64))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))
(/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))
(-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))
(*.f64 (+.f64 eps x) (+.f64 eps x))
Outputs
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))))
(+.f64 (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 2 binary64)))
(fma.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))))
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 2 binary64)))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 2 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 2 binary64))))))
(*.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))))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.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)))
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))))
(-.f64 (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64)) (-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 2 binary64)) (-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))
(fma.f64 (cos.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))
(fma.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))))
(fma.f64 (sin.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))))
(fma.f64 (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))))
(fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))))
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))))
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))))))
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 2 binary64))) (-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))))
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(/.f64 (neg.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (*.f64 (+.f64 eps x) (-.f64 eps x)))) (neg.f64 (*.f64 (-.f64 eps x) (-.f64 eps x))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x))))) (neg.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) (*.f64 eps (+.f64 eps x)) (-.f64 (*.f64 (*.f64 x x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 eps (+.f64 eps x)) (*.f64 x (+.f64 eps x)))))))
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(pow.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 eps x))) #s(literal 2 binary64))
(*.f64 (+.f64 eps x) (+.f64 eps x))
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(*.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (*.f64 (+.f64 eps x) (-.f64 eps x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps x)) #s(literal 2 binary64)))
(*.f64 (exp.f64 (log.f64 (+.f64 eps x))) (exp.f64 (log.f64 (+.f64 eps x))))

simplify543.0ms (3.8%)

Memory
-15.0MiB live, 690.8MiB allocated
Algorithm
egg-herbie
Rules
10 464×lower-fma.f64
10 464×lower-fma.f32
6 204×lower-+.f64
6 204×lower-+.f32
5 248×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0124015067
1420614389
0832513528
Stop Event
iter limit
node limit
Counts
564 → 534
Calls
Call 1
Inputs
(* 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))))))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 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))))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(* 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))))))))))
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))
(* (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 (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))
(* 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))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
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))
(* (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 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))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* 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))))))))))
(* 1/1920 (* (pow eps 5) (cos (+ x (* 1/2 eps)))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/1920 (cos (+ x (* 1/2 eps))))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))
(* 1/1920 (* (pow eps 5) (cos (- x (* -1/2 eps)))))
(* -1 (* (pow eps 5) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 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))))))))))
(* 1/3840 (* (pow eps 5) (cos (+ x (* 1/2 eps)))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/3840 (cos (+ x (* 1/2 eps))))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))))))
(* 1/3840 (* (pow eps 5) (cos (- x (* -1/2 eps)))))
(* -1 (* (pow eps 5) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))
(* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* 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) (- (* 1/3840 (pow eps 2)) 1/48))))
(* 1/3840 (pow eps 5))
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(* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 5))
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))
1/2
(+ 1/2 (* -1/48 (pow eps 2)))
(+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))
(+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))
(* 1/3840 (pow eps 4))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 4))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x 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 (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))))))))))
(* 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))))
(* 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))))
(* 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))))))))
(* 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))))
(* 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))))
(* 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))))))))))
(* (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 (- (* 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 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 (* 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)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* 1/2 eps)
(* eps (+ 1/2 (* 1/2 (* eps (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))))))))
(* eps (+ 1/2 (* eps (+ (* 1/2 (* eps (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))))) (* 1/2 (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))))))
(* eps (+ 1/2 (* eps (+ (* 1/2 (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (+ (* 1/2 (* eps (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))))) (+ (* 2 (/ x (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (+ (/ x (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (/ (* (+ x (* 2 x)) (- (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* 2 (pow x 2)) (pow x 2)))))))) (* 1/2 (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))))))))))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1 (* eps (- (* -1/2 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ (+ (* -1/2 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 1/2 (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))) eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) (* 1/2 (/ (+ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))) eps))) eps)) (* 1/2 (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))) eps)) 1/2)))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/6 (+ eps (* 2 eps)))
(+ (* 1/6 (+ eps (* 2 eps))) (* 1/2 (/ (- (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))) x)))
(+ (* 1/6 (+ eps (* 2 eps))) (+ (* 1/2 (/ (- (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (pow eps 3)))) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))) (pow x 2))) (* 1/2 (/ (- (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))) x))))
(+ (* 1/6 (+ eps (* 2 eps))) (+ (* 1/2 (/ (- (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ eps (* 2 eps))))))) (* -1/3 (* (pow eps 2) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2)))))) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))))) (pow x 3))) (+ (* 1/2 (/ (- (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (pow eps 3)))) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))) (pow x 2))) (* 1/2 (/ (- (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))) x)))))
(* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))))
(+ (* -1/2 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps)))))))
(+ (* -1 (/ (+ (* -1/2 (/ (- (* 1/3 (pow eps 3)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/2 (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))))) x)) (* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps)))))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (- (* 1/3 (pow eps 3)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))))) (* 1/2 (/ (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps))))))) (+ (* -1/3 (* (pow eps 2) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))))))) x))) x)) (* 1/2 (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))))) x)) (* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps)))))))
(pow eps 2)
(+ (* x (+ eps (* 2 eps))) (pow eps 2))
(+ (* x (+ eps (+ (* 2 eps) (* 3 x)))) (pow eps 2))
(+ (* x (+ eps (+ (* 2 eps) (* 3 x)))) (pow eps 2))
(* 3 (pow x 2))
(* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (/ eps x))))
(* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))))
(* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))))
(* 3 (pow x 2))
(* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (* -1 eps)) x))))
(* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))) x))))
(* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))) x))))
(+ (* 2 (pow x 2)) (pow x 2))
(+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2)))
(+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))
(+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))
(pow eps 2)
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 x)) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps))))
(* eps (cos x))
(* eps (+ (cos x) (* 2 (* eps (+ (* -1/4 (sin x)) (* 1/2 (* (cos x) (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))))))))
(* eps (+ (cos x) (* eps (+ (* 2 (* eps (+ (* -1/4 (* (sin x) (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))) (+ (* -1/16 (cos x)) (* (cos x) (- (* 1/2 (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) 1/48)))))) (* 2 (+ (* -1/4 (sin x)) (* 1/2 (* (cos x) (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))))))))))))
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(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (* 1/48 (* (pow eps 2) (sin x)))))
(* eps (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/3840 (* (pow eps 2) (sin x))) (* 1/48 (sin x))))))
(* eps (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/48 (sin x)) (* (pow eps 2) (+ (* -1/3840 (sin x)) (* 1/645120 (* (pow eps 2) (sin x)))))))))
(* -1 (* (sin x) (sin (* 1/2 eps))))
(* -1 (* (sin x) (sin (* 1/2 eps))))
(* -1 (* (sin x) (sin (* 1/2 eps))))
(* -1 (* (sin x) (sin (* 1/2 eps))))
(* -1 (* (sin x) (sin (* 1/2 eps))))
(* -1 (* (sin x) (sin (* 1/2 eps))))
(* -1 (* (sin x) (sin (* 1/2 eps))))
(* -1 (* (sin x) (sin (* 1/2 eps))))
(* -1 (* x (sin (* 1/2 eps))))
(* x (+ (* -1 (sin (* 1/2 eps))) (* 1/6 (* (pow x 2) (sin (* 1/2 eps))))))
(* x (+ (* -1 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/120 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/6 (sin (* 1/2 eps)))))))
(* x (+ (* -1 (sin (* 1/2 eps))) (* (pow x 2) (+ (* 1/6 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/120 (sin (* 1/2 eps))) (* 1/5040 (* (pow x 2) (sin (* 1/2 eps))))))))))
(* -1 (* (sin x) (sin (* 1/2 eps))))
(* -1 (* (sin x) (sin (* 1/2 eps))))
(* -1 (* (sin x) (sin (* 1/2 eps))))
(* -1 (* (sin x) (sin (* 1/2 eps))))
(* -1 (* (sin x) (sin (* 1/2 eps))))
(* -1 (* (sin x) (sin (* 1/2 eps))))
(* -1 (* (sin x) (sin (* 1/2 eps))))
(* -1 (* (sin x) (sin (* 1/2 eps))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))))))
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(cos (* 1/2 eps))
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(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))
(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))
(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(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)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
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(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
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(cos (* 1/2 (+ eps (* 2 x))))
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(cos x)
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(cos (* 1/2 (+ eps (* 2 x))))
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(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(* 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))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))
(+ (* eps (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))
(+ (* eps (- (+ 1 (* eps (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))
(+ (* eps (- (+ 1 (* eps (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* eps (- (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))
eps
(* eps (+ 1 (/ (pow x 3) (pow eps 3))))
(* eps (+ 1 (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow eps 4))) (/ (pow x 3) (pow eps 3)))))
(* eps (- (+ 1 (+ (* -1 (/ (+ (* -1 (* (pow x 3) (pow (+ x (* 2 x)) 2))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))) (pow eps 5))) (/ (pow x 3) (pow eps 3)))) (/ (* (pow x 3) (+ x (* 2 x))) (pow eps 4))))
eps
(* -1 (* eps (- (* -1 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (/ (- (pow x 3) (+ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* -1 (pow x 2)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))
eps
eps
(+ eps (/ (pow x 3) (pow eps 2)))
(+ eps (* (pow x 3) (+ (* -3 (/ x (pow eps 3))) (/ 1 (pow eps 2)))))
(* 1/3 x)
(* x (- (+ 1/3 (* 1/3 (/ (+ eps (* 2 eps)) x))) (* 1/9 (/ (+ eps (* 2 eps)) x))))
(* x (- (+ 1/3 (+ (* 1/3 (/ (+ eps (* 2 eps)) x)) (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (pow x 2))))) (+ (* 1/9 (/ (+ eps (* 2 eps)) x)) (+ (* 1/9 (/ (pow eps 2) (pow x 2))) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 2)))))))
(* x (- (+ 1/3 (+ (* 1/3 (/ (+ eps (* 2 eps)) x)) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (pow x 2))) (* 1/3 (/ (pow eps 3) (pow x 3)))))) (+ (* 1/9 (/ (+ eps (* 2 eps)) x)) (+ (* 1/9 (/ (pow eps 2) (pow x 2))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 2))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 3))) (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 3)))))))))
(* 1/3 x)
(* -1 (* x (- (* -1 (/ (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))) x)) 1/3)))
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))) x)) (* 1/3 (+ eps (* 2 eps)))) (* -1/9 (+ (* -2 eps) (* -1 eps)))) x)) 1/3)))
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))) x)) (* 1/3 (+ eps (* 2 eps)))) (* -1/9 (+ (* -2 eps) (* -1 eps)))) x)) 1/3)))
(/ (pow x 3) (pow eps 2))
(* (pow x 3) (+ (* -3 (/ x (pow eps 3))) (/ 1 (pow eps 2))))
(* (pow x 3) (+ (* x (- (* -1 (* x (+ (* -3 (/ (+ eps (* 2 eps)) (pow eps 5))) (* 3 (/ 1 (pow eps 4)))))) (* 3 (/ 1 (pow eps 3))))) (/ 1 (pow eps 2))))
(* (pow x 3) (+ (* x (- (* x (- (* x (- (* 9 (/ 1 (pow eps 5))) (* -1 (/ (* (+ eps (* 2 eps)) (+ (* -3 (/ (+ eps (* 2 eps)) (pow eps 5))) (* 3 (/ 1 (pow eps 4))))) (pow eps 2))))) (+ (* -3 (/ (+ eps (* 2 eps)) (pow eps 5))) (* 3 (/ 1 (pow eps 4)))))) (* 3 (/ 1 (pow eps 3))))) (/ 1 (pow eps 2))))
(* 1/3 x)
(* x (+ 1/3 (* -1/9 (/ (+ eps (* 2 eps)) x))))
(* x (- (+ 1/3 (* -1 (/ (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))) (pow x 2)))) (* 1/9 (/ (+ eps (* 2 eps)) x))))
(* x (- (+ 1/3 (* -1 (/ (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ eps (* 2 eps))))) (pow x 3)))) (+ (* -1/27 (/ (pow (+ eps (* 2 eps)) 2) (pow x 2))) (+ (* 1/9 (/ (+ eps (* 2 eps)) x)) (* 1/9 (/ (pow eps 2) (pow x 2)))))))
(* 1/3 x)
(* -1 (* x (- (* -1/9 (/ (+ (* -2 eps) (* -1 eps)) x)) 1/3)))
(* -1 (* x (- (* -1 (/ (- (+ (* -1/9 (/ (pow eps 2) x)) (* 1/27 (/ (pow (+ (* -2 eps) (* -1 eps)) 2) x))) (* -1/9 (+ (* -2 eps) (* -1 eps)))) x)) 1/3)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/9 (pow eps 2)) (* 1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)))) x)) (* 1/27 (/ (* (pow eps 2) (+ (* -2 eps) (* -1 eps))) x))) (+ (* -1/9 (pow eps 2)) (* 1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)))) x)) (* -1/9 (+ (* -2 eps) (* -1 eps)))) x)) 1/3)))
(/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))
(+ (* -1 (/ (* eps (* (pow x 3) (+ x (* 2 x)))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))))) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))
(/ (pow x 3) (pow eps 2))
(/ (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) eps)) (pow x 3)) (pow eps 2))
(/ (- (+ (* -1 (/ (+ (* -1 (* (pow x 3) (pow (+ x (* 2 x)) 2))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))) (pow eps 2))) (pow x 3)) (/ (* (pow x 3) (+ x (* 2 x))) eps)) (pow eps 2))
(/ (- (+ (* -1 (/ (+ (* -1 (* (+ x (* 2 x)) (+ (* -1 (* (pow x 3) (pow (+ x (* 2 x)) 2))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))))) (* -1 (* (pow x 3) (* (+ x (* 2 x)) (+ (* 2 (pow x 2)) (pow x 2)))))) (pow eps 3))) (pow x 3)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow eps 2))) (+ (/ (* (pow x 3) (+ x (* 2 x))) eps) (/ (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))) (pow eps 2))))) (pow eps 2))
(/ (pow x 3) (pow eps 2))
(/ (+ (/ (* (pow x 3) (+ (* -2 x) (* -1 x))) eps) (pow x 3)) (pow eps 2))
(/ (+ (* -1 (/ (- (+ (* -1 (/ (* (pow x 3) (pow (+ (* -2 x) (* -1 x)) 2)) eps)) (/ (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))) eps)) (* (pow x 3) (+ (* -2 x) (* -1 x)))) eps)) (pow x 3)) (pow eps 2))
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (+ (* -2 x) (* -1 x)) (+ (* -1 (* (pow x 3) (pow (+ (* -2 x) (* -1 x)) 2))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) eps)) (* -1 (/ (* (pow x 3) (* (+ (* -2 x) (* -1 x)) (+ (* 2 (pow x 2)) (pow x 2)))) eps))) (+ (* -1 (* (pow x 3) (pow (+ (* -2 x) (* -1 x)) 2))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) eps)) (* (pow x 3) (+ (* -2 x) (* -1 x)))) eps)) (pow x 3)) (pow eps 2))
eps
(* eps (+ 1 (* eps (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))))
(* eps (+ 1 (* eps (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* eps (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))))
(* eps (+ 1 (* eps (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* eps (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* eps (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))))) (+ (* 2 (/ x (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (+ (/ x (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (/ (* (+ x (* 2 x)) (- (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* 2 (pow x 2)) (pow x 2))))))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))))
eps
eps
eps
eps
eps
(* -1 (* eps (- (* -1 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (pow x 2)) (+ (/ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) eps) (/ (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))) eps)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))
eps
eps
eps
eps
(* 1/3 (+ eps (* 2 eps)))
(- (+ (* -1/27 (/ (pow (+ eps (* 2 eps)) 2) x)) (+ (* 1/3 (+ eps (* 2 eps))) (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)))) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) x)))
(- (+ (* -1/3 (/ (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2)))) (pow x 2))) (+ (* -1/27 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* -1/27 (/ (pow (+ eps (* 2 eps)) 2) x)) (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2)))))))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) x)) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 2))) (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 2))))))
(- (+ (* -1/3 (/ (* (+ eps (* 2 eps)) (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ eps (* 2 eps)))))) (pow x 3))) (+ (* -1/3 (/ (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2)))) (pow x 2))) (+ (* -1/3 (/ (* (pow eps 2) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2)))) (pow x 3))) (+ (* -1/27 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* -1/27 (/ (pow (+ eps (* 2 eps)) 2) x)) (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2)))))))))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) x)) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 2))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 3))) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 2))) (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 3))))))))
(- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps)))))
(- (+ (* -1 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ eps (* 2 eps)))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps)))))
(- (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/3 (pow eps 3)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ eps (* 2 eps)))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps)))))
(- (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))))) x)) (+ (* -1/3 (/ (* (pow eps 2) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2)))) x)) (+ (* 1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))) x)) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (pow eps 3)))))) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ eps (* 2 eps)))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps)))))
(pow x 2)
(+ (* 2 (* eps x)) (pow x 2))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
Outputs
(* 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 eps (fma.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.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 (*.f64 eps (sin.f64 x)) #s(literal 1/24 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 x) #s(literal -1/12 binary64)))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))
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eps
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eps
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eps
eps
(+ eps (/ (pow x 3) (pow eps 2)))
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(* 1/3 x)
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(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
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eps
(* eps (+ 1 (* eps (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))))
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(pow x 2)
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(*.f64 x (fma.f64 eps #s(literal 2 binary64) x))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
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(fma.f64 eps (fma.f64 x #s(literal 2 binary64) eps) (*.f64 x x))
(pow eps 2)
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(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
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(+ (* x (+ x (* 2 eps))) (pow eps 2))
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(*.f64 (*.f64 x x) (fma.f64 #s(literal 2 binary64) (/.f64 eps x) #s(literal 1 binary64)))
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eval293.0ms (2.1%)

Memory
26.2MiB live, 404.3MiB allocated
Compiler

Compiled 89 816 to 6 599 computations (92.7% saved)

prune204.0ms (1.4%)

Memory
9.1MiB live, 448.9MiB allocated
Pruning

29 alts after pruning (23 fresh and 6 done)

PrunedKeptTotal
New1 658121 670
Fresh51116
Picked325
Done044
Total1 666291 695
Accuracy
100.0%
Counts
1 695 → 29
Alt Table
Click to see full alt table
StatusAccuracyProgram
28.6%
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
50.0%
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
99.6%
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
96.8%
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
63.5%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.9%
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))))
52.0%
(*.f64 (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (*.f64 eps eps) (*.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (*.f64 eps (*.f64 eps eps)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
98.9%
(*.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64)))
99.1%
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
98.9%
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
98.6%
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
21.8%
(*.f64 (*.f64 (sin.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (+.f64 eps x) (/.f64 (neg.f64 (*.f64 x (*.f64 x x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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))
21.0%
(*.f64 (*.f64 (sin.f64 (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (/.f64 (neg.f64 (*.f64 x (*.f64 x x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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))
21.6%
(*.f64 (*.f64 (sin.f64 (*.f64 (fma.f64 (neg.f64 x) (/.f64 (*.f64 x x) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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))
21.3%
(*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (fma.f64 (*.f64 (neg.f64 x) x) x (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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))
35.5%
(*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x)) (+.f64 x (+.f64 eps x))) #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))
21.1%
(*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64))
20.9%
(*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x x) (+.f64 (fma.f64 #s(literal 3 binary64) (/.f64 eps x) #s(literal 3 binary64)) (/.f64 (*.f64 eps eps) (*.f64 x x))))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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))
35.5%
(*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 x x) (+.f64 (-.f64 x eps) x)) (/.f64 (*.f64 (-.f64 eps x) (-.f64 eps x)) (+.f64 (-.f64 x eps) x))) #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))
63.6%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64))
99.2%
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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)))) (sin.f64 x)))) #s(literal 2 binary64))
99.9%
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
99.4%
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 #s(literal 3 binary64) eps))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
28.7%
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64)))
98.7%
(*.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))))
98.2%
(*.f64 eps (cos.f64 x))
5.4%
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)))
96.8%
(sin.f64 eps)
5.5%
#s(literal 0 binary64)
Compiler

Compiled 2 189 to 680 computations (68.9% saved)

regimes49.0ms (0.3%)

Memory
32.8MiB live, 104.3MiB allocated
Counts
51 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.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 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.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 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))))
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (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 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.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 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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 (fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (*.f64 eps eps) (*.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (*.f64 eps (*.f64 eps eps)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.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))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 #s(literal 3 binary64) eps))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.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 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))))
(*.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 eps (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 eps eps))))
(*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x)) (+.f64 x (+.f64 eps x))) #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 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 x x) (+.f64 (-.f64 x eps) x)) (/.f64 (*.f64 (-.f64 eps x) (-.f64 eps x)) (+.f64 (-.f64 x eps) x))) #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 (sin.f64 (*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 0 binary64)) eps (*.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 eps eps))) (*.f64 (fma.f64 x x #s(literal 0 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 (sin.f64 (*.f64 (/.f64 (fma.f64 (*.f64 (neg.f64 x) x) x (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (sin.f64 (*.f64 (fma.f64 (neg.f64 x) (/.f64 (*.f64 x x) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (sin.f64 (*.f64 (fma.f64 (+.f64 eps x) (/.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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 (sin.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (+.f64 eps x) (/.f64 (neg.f64 (*.f64 x (*.f64 x x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (sin.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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 (sin.f64 (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (/.f64 (neg.f64 (*.f64 x (*.f64 x x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x x) (+.f64 (fma.f64 #s(literal 3 binary64) (/.f64 eps x) #s(literal 3 binary64)) (/.f64 (*.f64 eps eps) (*.f64 x x))))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (sin.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.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 (*.f64 (sin.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 x (+.f64 x (+.f64 eps x))))))) (fma.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (-.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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)))) (sin.f64 x)))) #s(literal 2 binary64))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.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))))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64))
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64))
Calls

3 calls:

16.0ms
eps
16.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
14.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
100.0%1eps
100.0%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes52.0ms (0.4%)

Memory
-6.6MiB live, 111.0MiB allocated
Counts
50 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.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 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.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 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))))
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (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 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.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 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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 (fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (*.f64 eps eps) (*.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (*.f64 eps (*.f64 eps eps)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.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))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 #s(literal 3 binary64) eps))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.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 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))))
(*.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 eps (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 eps eps))))
(*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x)) (+.f64 x (+.f64 eps x))) #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 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 x x) (+.f64 (-.f64 x eps) x)) (/.f64 (*.f64 (-.f64 eps x) (-.f64 eps x)) (+.f64 (-.f64 x eps) x))) #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 (sin.f64 (*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 0 binary64)) eps (*.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 eps eps))) (*.f64 (fma.f64 x x #s(literal 0 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 (sin.f64 (*.f64 (/.f64 (fma.f64 (*.f64 (neg.f64 x) x) x (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (sin.f64 (*.f64 (fma.f64 (neg.f64 x) (/.f64 (*.f64 x x) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (sin.f64 (*.f64 (fma.f64 (+.f64 eps x) (/.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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 (sin.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (+.f64 eps x) (/.f64 (neg.f64 (*.f64 x (*.f64 x x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (sin.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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 (sin.f64 (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (/.f64 (neg.f64 (*.f64 x (*.f64 x x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x x) (+.f64 (fma.f64 #s(literal 3 binary64) (/.f64 eps x) #s(literal 3 binary64)) (/.f64 (*.f64 eps eps) (*.f64 x x))))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (sin.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.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 (*.f64 (sin.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 x (+.f64 x (+.f64 eps x))))))) (fma.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (-.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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)))) (sin.f64 x)))) #s(literal 2 binary64))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.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))))
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
Calls

3 calls:

19.0ms
eps
15.0ms
x
14.0ms
(-.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)

regimes24.0ms (0.2%)

Memory
-23.7MiB live, 50.8MiB allocated
Counts
21 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.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 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.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 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))))
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (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 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.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 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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 (fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (*.f64 eps eps) (*.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (*.f64 eps (*.f64 eps eps)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
Outputs
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
Calls

3 calls:

10.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
x
6.0ms
eps
Results
AccuracySegmentsBranch
99.1%1x
99.1%1eps
99.1%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes32.0ms (0.2%)

Memory
-37.5MiB live, 42.8MiB allocated
Counts
16 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.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 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.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 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))))
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (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 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.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 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
Calls

3 calls:

21.0ms
x
5.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms
eps
Results
AccuracySegmentsBranch
98.9%1x
98.9%1eps
98.9%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes14.0ms (0.1%)

Memory
-0.9MiB live, 38.7MiB allocated
Counts
13 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.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 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.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 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))))
Outputs
(*.f64 (*.f64 (*.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:

5.0ms
x
4.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
eps
Results
AccuracySegmentsBranch
98.9%1x
98.9%1eps
98.9%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory
31.3MiB live, 31.3MiB allocated
Counts
11 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.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 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64)))
Outputs
(*.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64)))
Calls

3 calls:

4.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
x
4.0ms
eps
Results
AccuracySegmentsBranch
98.9%1x
98.9%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.9%1eps
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory
-7.0MiB live, 32.3MiB allocated
Counts
10 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.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))
Outputs
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
Calls

3 calls:

4.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
x
4.0ms
eps
Results
AccuracySegmentsBranch
98.6%1x
98.6%1eps
98.6%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes11.0ms (0.1%)

Memory
-19.7MiB live, 19.3MiB allocated
Counts
8 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
Outputs
(*.f64 eps (cos.f64 x))
Calls

3 calls:

4.0ms
x
3.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms
eps
Results
AccuracySegmentsBranch
98.2%1x
98.2%1eps
98.2%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0.1%)

Memory
23.6MiB live, 23.6MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(sin.f64 eps)
Outputs
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
Calls

3 calls:

3.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms
x
3.0ms
eps
Results
AccuracySegmentsBranch
96.8%1x
96.8%1eps
96.8%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0%)

Memory
11.6MiB live, 11.6MiB allocated
Accuracy

Total -0.2b remaining (-0.3%)

Threshold costs -0.2b (-0.3%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)))
Outputs
#s(literal 0 binary64)
Calls

3 calls:

2.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms
eps
1.0ms
x
Results
AccuracySegmentsBranch
5.5%1x
5.5%1eps
5.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify10.0ms (0.1%)

Memory
-18.7MiB live, 22.0MiB allocated
Algorithm
egg-herbie
Rules
58×*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056139
187139
295139
3102139
4105139
5106139
Stop Event
saturated
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.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 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 eps (cos.f64 x))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
#s(literal 0 binary64)
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x))))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
(*.f64 (*.f64 (*.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 (*.f64 eps (fma.f64 eps (*.f64 eps #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 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 eps (cos.f64 x))
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)
(fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
#s(literal 0 binary64)

soundness1.0s (7.3%)

Memory
15.3MiB live, 612.6MiB allocated
Rules
16 678×lower-fma.f64
16 678×lower-fma.f32
11 836×lower-fma.f64
11 836×lower-fma.f32
8 230×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
035205
067178
1257178
21964178
08141177
05765604
119595182
272434885
084074503
06265677
119245339
256695205
081034828
0107496
1314496
2775489
32836489
46173489
08126458
0616
01016
15316
238016
3476616
0821016
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
Compiler

Compiled 380 to 219 computations (42.4% saved)

preprocess254.0ms (1.8%)

Memory
-21.1MiB live, 175.4MiB allocated
Compiler

Compiled 394 to 188 computations (52.3% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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