2sin (example 3.3)

Time bar (total: 11.4s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze71.0ms (0.6%)

Memory
-17.4MiB live, 56.1MiB 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)

sample6.2s (54.6%)

Memory
-185.0MiB live, 6 436.9MiB allocated
Samples
3.3s26 180×0invalid
806.0ms5 436×0valid
588.0ms2 820×1valid
Precisions
Click to see histograms. Total time spent on operations: 3.3s
const: 968.0ms (28.9% of total)
ival-sin: 591.0ms (17.7% of total)
ival-fabs: 320.0ms (9.6% of total)
ival-mult: 282.0ms (8.4% of total)
ival-sub: 244.0ms (7.3% of total)
ival-<=: 240.0ms (7.2% of total)
ival-add: 237.0ms (7.1% of total)
ival-<: 193.0ms (5.8% of total)
adjust: 108.0ms (3.2% of total)
ival-and: 105.0ms (3.1% of total)
exact: 44.0ms (1.3% of total)
ival-assert: 12.0ms (0.4% of total)
Bogosity

explain90.0ms (0.8%)

Memory
-21.0MiB live, 141.9MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2182(5.3089441455613766e-253 3.4100069241956767e-255)5(6.120695573457875e-129 6.395734314235492e-131)(-.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))cancellation21511
sin.f64(sin.f64 (+.f64 x eps))sensitivity20
Confusion
Predicted +Predicted -
+2145
-235
Precision
0.9907407407407407
Recall
0.9771689497716894
Confusion?
Predicted +Predicted MaybePredicted -
+21450
-2629
Precision?
0.9647577092511013
Recall?
1.0
Freqs
test
numberfreq
040
1215
21
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
21.0ms368×0valid
18.0ms144×1valid
Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 21.0ms
ival-sin: 9.0ms (43.8% of total)
adjust: 6.0ms (29.2% of total)
ival-sub: 3.0ms (14.6% of total)
ival-add: 3.0ms (14.6% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess22.0ms (0.2%)

Memory
19.9MiB live, 19.9MiB allocated
Algorithm
egg-herbie
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))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
64.7%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0.1%)

Memory
4.6MiB live, 4.6MiB 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))
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))
(-.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)

localize61.0ms (0.5%)

Memory
-1.1MiB live, 36.2MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(+.f64 x eps)
accuracy0
(sin.f64 x)
accuracy0.09032750399669962
(sin.f64 (+.f64 x eps))
accuracy22.519507728125337
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Samples
45.0ms72×1valid
10.0ms184×0valid
Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 48.0ms
ival-add: 41.0ms (85% of total)
ival-sin: 4.0ms (8.3% of total)
adjust: 1.0ms (2.1% of total)
ival-sub: 1.0ms (2.1% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series4.0ms (0%)

Memory
6.4MiB live, 6.4MiB allocated
Counts
4 → 31
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
(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 (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
eps
(+ eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(* x (+ 1 (/ eps x)))
(sin x)
(- (sin (- eps (* -1 x))) (sin x))
(sin (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(+ (sin x) (* 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))))))))
(* eps (+ 1 (/ x eps)))
(- (sin (- x (* -1 eps))) (sin x))
(sin (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
Calls

6 calls:

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

simplify158.0ms (1.4%)

Memory
-17.9MiB live, 133.2MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107291
1314291
2779284
32842284
46177284
08125253
Stop Event
iter limit
node limit
Counts
31 → 29
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 (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
eps
(+ eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(* x (+ 1 (/ eps x)))
(sin x)
(- (sin (- eps (* -1 x))) (sin x))
(sin (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(+ (sin x) (* 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))))))))
(* eps (+ 1 (/ x eps)))
(- (sin (- x (* -1 eps))) (sin x))
(sin (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
Outputs
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (cos eps)))
(fma.f64 (cos.f64 eps) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (cos.f64 eps)) x (sin.f64 eps))
eps
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) x)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(sin x)
(sin.f64 x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)) eps (cos.f64 x)) eps)
(+ (sin x) (* eps (cos x)))
(fma.f64 (cos.f64 x) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps (sin.f64 x))
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)

rewrite183.0ms (1.6%)

Memory
14.4MiB live, 140.4MiB allocated
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
(*.f64 (pow.f64 (/.f64 (fma.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 9 binary64)) (pow.f64 (sin.f64 x) #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) #s(literal -1 binary64)) (pow.f64 (/.f64 (*.f64 (cos.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x))))
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)))) (fma.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) (-.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #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 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
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(fma.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x))) #s(literal 1/2 binary64) (*.f64 (sin.f64 eps) (cos.f64 x)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (sin.f64 eps) (cos.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x)))
(sin.f64 (+.f64 eps x))
(-.f64 (*.f64 (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (*.f64 x x) (-.f64 eps x)))) (*.f64 (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 eps x)))))
(-.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x eps))) (/.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x eps))))
(-.f64 (*.f64 (sin.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) (*.f64 (cos.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))))
(+.f64 (*.f64 (sin.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (*.f64 (cos.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))))
(+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x)))
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))
(exp.f64 (*.f64 (log.f64 (sin.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 eps eps (*.f64 x x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (*.f64 x x)))
(*.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 x x) (*.f64 (-.f64 eps x) eps)))
(*.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (*.f64 (-.f64 eps x) eps) (-.f64 (*.f64 (-.f64 eps x) eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x))
(*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (pow.f64 (pow.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (*.f64 (-.f64 x eps) (+.f64 eps x)))
(*.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 #s(literal 1 binary64) (+.f64 eps x))
(*.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (pow.f64 (neg.f64 (-.f64 x eps)) #s(literal -1 binary64)))
(*.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))) #s(literal -1 binary64)))
(*.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))
(*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (/.f64 (+.f64 eps x) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (*.f64 (+.f64 eps x) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))))
(*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)))
(*.f64 (+.f64 eps x) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(*.f64 (+.f64 eps x) (*.f64 (-.f64 x eps) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 eps eps (*.f64 x x)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))))
(/.f64 (-.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (pow.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (-.f64 x eps)) (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(/.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal -3 binary64))) (*.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal -3 binary64)))) (+.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64)) (*.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 eps eps (*.f64 x x)) (-.f64 x eps)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 x eps)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x eps)) (*.f64 (-.f64 x eps) (*.f64 eps eps))) (pow.f64 (-.f64 x eps) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (-.f64 x eps) (fma.f64 eps eps (*.f64 x x))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (-.f64 x eps) (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 eps x) #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps)))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(neg.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (*.f64 x x)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x)))
(-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))
(+.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(+.f64 eps x)
(+.f64 x eps)
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(pow.f64 (sin.f64 x) #s(literal 1 binary64))
(sin.f64 x)
(exp.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 1 binary64)))

eval51.0ms (0.4%)

Memory
10.5MiB live, 47.3MiB allocated
Compiler

Compiled 6 283 to 852 computations (86.4% saved)

prune25.0ms (0.2%)

Memory
-20.3MiB live, 24.0MiB allocated
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2305235
Fresh000
Picked011
Done000
Total2306236
Accuracy
100.0%
Counts
236 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
64.8%
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
64.7%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.9%
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
99.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
97.5%
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
Compiler

Compiled 145 to 112 computations (22.8% saved)

simplify263.0ms (2.3%)

Memory
13.8MiB live, 86.3MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
cost-diff0
(cos.f64 eps)
cost-diff0
(sin.f64 x)
cost-diff6400
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
cost-diff0
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
cost-diff0
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
cost-diff0
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
cost-diff0
(cos.f64 x)
cost-diff0
(*.f64 (cos.f64 x) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
cost-diff0
(sin.f64 eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff0
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff128
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
cost-diff192
(+.f64 #s(literal 0 binary64) eps)
cost-diff576
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033175
056165
191165
2170165
3295165
4415165
5597165
6800165
7993165
81484165
91746165
102257165
112315165
122422165
132558162
142744162
152882162
163196162
173993162
185028162
195192162
205240162
215264162
225278162
235290162
246038162
256430162
266558162
276782162
286878162
296878162
306878162
316878162
08018159
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
#s(literal 1/2 binary64)
(+.f64 #s(literal 0 binary64) eps)
#s(literal 0 binary64)
eps
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
x
#s(literal -2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
x
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(sin.f64 x)
x
#s(literal -1/2 binary64)
eps
(cos.f64 x)
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
(sin.f64 x)
x
(cos.f64 eps)
eps
(fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(sin.f64 eps)
(cos.f64 x)
(neg.f64 (sin.f64 x))
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
(*.f64 eps #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(+.f64 #s(literal 0 binary64) eps)
eps
#s(literal 0 binary64)
eps
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(neg.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal -2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
x
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(sin.f64 x)
x
#s(literal -1/2 binary64)
eps
(cos.f64 x)
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
(sin.f64 x)
x
(cos.f64 eps)
eps
(fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x)))
(sin.f64 eps)
(cos.f64 x)
(neg.f64 (sin.f64 x))

localize136.0ms (1.2%)

Memory
-25.2MiB live, 175.1MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy0
(cos.f64 x)
accuracy0
(cos.f64 eps)
accuracy0.033535009768442016
(fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
accuracy22.50025521964394
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
accuracy0
(sin.f64 x)
accuracy0
(cos.f64 x)
accuracy0.0078125
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
accuracy0.3528853443781967
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
accuracy0
(cos.f64 x)
accuracy0.01171875
(*.f64 (cos.f64 x) eps)
accuracy0.5427885752721306
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
accuracy0
(sin.f64 eps)
accuracy1.589419116948026
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy0
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
accuracy0
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy0.00390625
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy0.08511931943147477
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
Samples
50.0ms177×0valid
48.0ms77×1valid
2.0ms3valid
1.0ms2valid
Compiler

Compiled 342 to 68 computations (80.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 67.0ms
ival-mult: 31.0ms (46.4% of total)
ival-add: 10.0ms (15% of total)
ival-sin: 9.0ms (13.5% of total)
ival-cos: 6.0ms (9% of total)
adjust: 5.0ms (7.5% of total)
ival-div: 2.0ms (3% of total)
ival-neg: 1.0ms (1.5% of total)
ival-sub: 1.0ms (1.5% of total)
exact: 1.0ms (1.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series29.0ms (0.3%)

Memory
0.5MiB live, 48.9MiB allocated
Counts
19 → 92
Calls
Call 1
Inputs
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(+.f64 #s(literal 0 binary64) eps)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
(sin.f64 x)
(cos.f64 eps)
(fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
Outputs
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 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)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(+ (sin eps) (* -1 x))
(+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1)))
(+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1)))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(cos (* -1/2 (+ eps (* 2 x))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(sin x)
(- (* (cos x) (sin eps)) (sin x))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(cos (* -1/2 (- eps (* -2 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 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))))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* -1 (sin x))
(- (* eps (cos x)) (sin x))
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x))
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(cos eps)
(sin (* 1/2 eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
Calls

6 calls:

TimeVariablePointExpression
9.0ms
eps
@0
((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (sin x) (cos eps) (+ (* (sin eps) (cos x)) (neg (sin x))) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)))
5.0ms
x
@inf
((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (sin x) (cos eps) (+ (* (sin eps) (cos x)) (neg (sin x))) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)))
4.0ms
x
@-inf
((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (sin x) (cos eps) (+ (* (sin eps) (cos x)) (neg (sin x))) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)))
4.0ms
eps
@-inf
((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (sin x) (cos eps) (+ (* (sin eps) (cos x)) (neg (sin x))) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)))
4.0ms
eps
@inf
((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (sin x) (cos eps) (+ (* (sin eps) (cos x)) (neg (sin x))) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)))

simplify166.0ms (1.5%)

Memory
16.7MiB live, 206.4MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03521138
110441080
228011044
363041042
08496942
Stop Event
iter limit
node limit
Counts
92 → 90
Calls
Call 1
Inputs
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 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)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(+ (sin eps) (* -1 x))
(+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1)))
(+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1)))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(cos (* -1/2 (+ eps (* 2 x))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(sin x)
(- (* (cos x) (sin eps)) (sin x))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(cos (* -1/2 (- eps (* -2 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 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))))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* -1 (sin x))
(- (* eps (cos x)) (sin x))
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x))
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(cos eps)
(sin (* 1/2 eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
Outputs
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1 x) (* -1/2 eps))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(cos (* -1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (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)))))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(fma.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) x) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal 2 binary64) (*.f64 (neg.f64 x) x))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (*.f64 x x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (neg.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps x) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (*.f64 (*.f64 x x) eps) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps x) eps))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (*.f64 (*.f64 eps eps) x) (*.f64 (*.f64 eps (+.f64 eps x)) #s(literal -1/2 binary64))) x eps)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(*.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/2 binary64)) x)
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (*.f64 x x) #s(literal -1/240 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) x)
(+ (sin eps) (* -1 x))
(-.f64 (sin.f64 eps) x)
(+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1)))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sin.f64 eps) #s(literal -1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x #s(literal -1 binary64)) x (sin.f64 eps))
(* -1 x)
(neg.f64 x)
(* x (- (* -1/2 (/ eps x)) 1))
(neg.f64 (fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) eps) x))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 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 (neg.f64 x))))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos x)
(cos.f64 x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
(sin x)
(sin.f64 x)
(- (* (cos x) (sin eps)) (sin x))
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(neg.f64 (fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) eps) x))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 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 (neg.f64 x))))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) eps) (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal -1/8 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)) eps (cos.f64 x)) eps)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(- (* eps (cos x)) (sin x))
(fma.f64 (cos.f64 x) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x))
(fma.f64 (cos.f64 x) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps) (neg.f64 (sin.f64 x)))
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64))) (fma.f64 (cos.f64 x) eps (neg.f64 (sin.f64 x))))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (- (* -1 (/ x eps)) 1/2))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps)
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (*.f64 eps eps))
(* -1/2 (* eps (sin x)))
(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(cos eps)
(cos.f64 eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 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 (neg.f64 x))))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)

rewrite215.0ms (1.9%)

Memory
-1.3MiB live, 198.3MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033138
056124
1198124
21609124
08421124
Stop Event
iter limit
node limit
iter limit
Counts
19 → 479
Calls
Call 1
Inputs
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(+.f64 #s(literal 0 binary64) eps)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
(sin.f64 x)
(cos.f64 eps)
(fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
Outputs
(*.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal -2 binary64)) (/.f64 (fma.f64 x #s(literal 2 binary64) eps) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(*.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(*.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (pow.f64 (pow.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(*.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) (/.f64 (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps))))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal -1/2 binary64))) (neg.f64 (fma.f64 x #s(literal 2 binary64) (neg.f64 eps))))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1/2 binary64))) (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64))
(/.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal -1/2 binary64)) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))
(/.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps))) #s(literal -2 binary64))
(/.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps))) (neg.f64 (*.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (*.f64 #s(literal -2 binary64) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))))
(/.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)) (*.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 #s(literal -2 binary64) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 2 binary64))
(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))
(neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))
(-.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))) (/.f64 (*.f64 eps eps) (*.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))))
(-.f64 (/.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps))) #s(literal -2 binary64)) (/.f64 (/.f64 (*.f64 eps eps) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps))) #s(literal -2 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (-.f64 eps #s(literal 0 binary64))))
(*.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps))
(*.f64 (/.f64 eps eps) (/.f64 (*.f64 eps eps) eps))
(*.f64 (/.f64 eps eps) eps)
(*.f64 (/.f64 (*.f64 eps eps) eps) (/.f64 eps (-.f64 eps #s(literal 0 binary64))))
(*.f64 (/.f64 (*.f64 eps eps) eps) (/.f64 eps eps))
(*.f64 (neg.f64 (*.f64 eps eps)) (pow.f64 (neg.f64 eps) #s(literal -1 binary64)))
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal -2 binary64)))
(pow.f64 (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))) #s(literal -1 binary64))
(pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 eps #s(literal 1 binary64))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (*.f64 eps eps)))) (neg.f64 (neg.f64 (neg.f64 eps))))
(/.f64 (neg.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (neg.f64 (neg.f64 (*.f64 eps eps))))
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (neg.f64 eps)) (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (*.f64 eps eps))
(/.f64 (neg.f64 (neg.f64 (*.f64 eps eps))) (neg.f64 (neg.f64 eps)))
(/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 (-.f64 eps #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 eps #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))))
(/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal -1 binary64)))
(/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (-.f64 eps #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) #s(literal 0 binary64))
(fma.f64 (/.f64 eps eps) (/.f64 (*.f64 eps eps) eps) #s(literal 0 binary64))
(fma.f64 (/.f64 eps eps) eps #s(literal 0 binary64))
(fma.f64 (/.f64 (*.f64 eps eps) eps) (/.f64 eps (-.f64 eps #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (*.f64 eps eps) eps) (/.f64 eps eps) #s(literal 0 binary64))
(fma.f64 (neg.f64 (*.f64 eps eps)) (pow.f64 (neg.f64 eps) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal -2 binary64)) #s(literal 0 binary64))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps)) (/.f64 (*.f64 eps eps) (neg.f64 eps)))
(-.f64 eps (/.f64 #s(literal 0 binary64) (-.f64 eps #s(literal 0 binary64))))
(+.f64 #s(literal 0 binary64) eps)
(+.f64 eps #s(literal 0 binary64))
eps
(cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))
(cos.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)))
(*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (*.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 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 0 binary64) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 1 binary64) (sin.f64 eps)) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 0 binary64) (cos.f64 eps)) (*.f64 #s(literal 0 binary64) (cos.f64 eps)) (-.f64 (*.f64 (*.f64 #s(literal 1 binary64) (sin.f64 eps)) (*.f64 #s(literal 1 binary64) (sin.f64 eps))) (*.f64 (*.f64 #s(literal 0 binary64) (cos.f64 eps)) (*.f64 #s(literal 1 binary64) (sin.f64 eps))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) #s(literal 0 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (-.f64 (*.f64 (*.f64 (cos.f64 eps) #s(literal 0 binary64)) (*.f64 (cos.f64 eps) #s(literal 0 binary64))) (*.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 eps) #s(literal 0 binary64))))))
(fma.f64 (sin.f64 eps) #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (cos.f64 eps) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
(sin.f64 eps)
(-.f64 (*.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps))) (cos.f64 (/.f64 (*.f64 eps eps) (neg.f64 eps)))) (*.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps))) (sin.f64 (/.f64 (*.f64 eps eps) (neg.f64 eps)))))
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 eps)) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
(+.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 eps) #s(literal 0 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (/.f64 (cos.f64 x) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps #s(literal 0 binary64))))
(*.f64 (/.f64 (cos.f64 x) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps))
(*.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 (cos.f64 x) (-.f64 eps #s(literal 0 binary64))))
(*.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(*.f64 eps (cos.f64 x))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 0 binary64) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 0 binary64) (cos.f64 x)) (*.f64 #s(literal 0 binary64) (cos.f64 x)) (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) (*.f64 (cos.f64 x) eps)) (*.f64 (*.f64 #s(literal 0 binary64) (cos.f64 x)) (*.f64 (cos.f64 x) eps)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 0 binary64)) (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) (*.f64 (cos.f64 x) eps)) (*.f64 (*.f64 (cos.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) eps)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 x) eps) (*.f64 (cos.f64 x) eps) (-.f64 (*.f64 (*.f64 #s(literal 0 binary64) (cos.f64 x)) (*.f64 #s(literal 0 binary64) (cos.f64 x))) (*.f64 (*.f64 (cos.f64 x) eps) (*.f64 #s(literal 0 binary64) (cos.f64 x))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) #s(literal 0 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 x) eps) (*.f64 (cos.f64 x) eps) (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 0 binary64))) (*.f64 (*.f64 (cos.f64 x) eps) (*.f64 (cos.f64 x) #s(literal 0 binary64))))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (cos.f64 x))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (*.f64 (cos.f64 x) (neg.f64 (*.f64 eps eps)))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (*.f64 (cos.f64 x) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (*.f64 eps eps)))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (cos.f64 x)) (*.f64 eps eps))
(/.f64 (*.f64 (cos.f64 x) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (*.f64 (cos.f64 x) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(fma.f64 (/.f64 (cos.f64 x) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps #s(literal 0 binary64))) (*.f64 #s(literal 0 binary64) (cos.f64 x)))
(fma.f64 (/.f64 (cos.f64 x) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps #s(literal 0 binary64))) (*.f64 (cos.f64 x) #s(literal 0 binary64)))
(fma.f64 (/.f64 (cos.f64 x) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (*.f64 #s(literal 0 binary64) (cos.f64 x)))
(fma.f64 (/.f64 (cos.f64 x) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (*.f64 (cos.f64 x) #s(literal 0 binary64)))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 (cos.f64 x) (-.f64 eps #s(literal 0 binary64))) (*.f64 #s(literal 0 binary64) (cos.f64 x)))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 (cos.f64 x) (-.f64 eps #s(literal 0 binary64))) (*.f64 (cos.f64 x) #s(literal 0 binary64)))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 (cos.f64 x) eps) (*.f64 #s(literal 0 binary64) (cos.f64 x)))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 (cos.f64 x) eps) (*.f64 (cos.f64 x) #s(literal 0 binary64)))
(fma.f64 (cos.f64 x) #s(literal 0 binary64) (*.f64 (cos.f64 x) eps))
(fma.f64 (cos.f64 x) eps (*.f64 #s(literal 0 binary64) (cos.f64 x)))
(fma.f64 (cos.f64 x) eps (*.f64 (cos.f64 x) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (cos.f64 x) (*.f64 (cos.f64 x) eps))
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(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps)))
(/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)))) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps)))))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 #s(literal 1/2 binary64) (-.f64 eps #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 #s(literal 1/2 binary64) eps) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64))
(fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps))

eval152.0ms (1.3%)

Memory
-52.6MiB live, 105.8MiB allocated
Compiler

Compiled 19 390 to 2 245 computations (88.4% saved)

prune35.0ms (0.3%)

Memory
-0.1MiB live, 39.3MiB allocated
Pruning

15 alts after pruning (12 fresh and 3 done)

PrunedKeptTotal
New57912591
Fresh000
Picked325
Done011
Total58215597
Accuracy
100.0%
Counts
597 → 15
Alt Table
Click to see full alt table
StatusAccuracyProgram
38.2%
(-.f64 (/.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))) #s(literal 2 binary64)) (-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))) (*.f64 (cos.f64 eps) (sin.f64 x)))) (/.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))) (*.f64 (cos.f64 eps) (sin.f64 x)))))
64.7%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.5%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.4%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
56.5%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
99.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
99.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
98.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
98.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
97.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
97.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
99.7%
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
99.9%
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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 (neg.f64 x)))))
Compiler

Compiled 649 to 438 computations (32.5% saved)

simplify123.0ms (1.1%)

Memory
36.2MiB live, 74.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
(neg.f64 (*.f64 eps eps))
cost-diff0
(*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x))
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
cost-diff1280
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))
cost-diff0
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
cost-diff0
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
cost-diff0
(*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
cost-diff0
(fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
cost-diff0
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
cost-diff0
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
cost-diff0
#s(approx (cos x) #s(literal 1 binary64))
cost-diff0
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
cost-diff0
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
cost-diff0
(*.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 (neg.f64 x))))
cost-diff0
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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 (neg.f64 x)))))
cost-diff128
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058346
087344
1153344
2330340
3854332
42065332
53174332
63946332
75099332
86046332
97471332
08118325
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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 (neg.f64 x)))))
(*.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 (neg.f64 x))))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(literal 2 binary64)
(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 (neg.f64 x)))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
#s(literal -1/2 binary64)
(neg.f64 x)
x
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
#s(approx (cos x) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(*.f64 (+.f64 eps x) #s(literal -1/2 binary64))
(+.f64 eps x)
eps
x
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
(*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))
(*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x))
(neg.f64 (*.f64 eps eps))
(*.f64 eps eps)
eps
(cos.f64 x)
x
(neg.f64 eps)
Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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 (neg.f64 x)))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64))))
(*.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 (neg.f64 x))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64)))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64))
#s(literal 2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
eps
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
#s(literal -1/2 binary64)
(neg.f64 x)
x
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
#s(approx (cos x) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(*.f64 (+.f64 eps x) #s(literal -1/2 binary64))
(*.f64 (+.f64 x eps) #s(literal -1/2 binary64))
(+.f64 eps x)
(+.f64 x eps)
eps
x
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
(*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
(*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))
(*.f64 (cos.f64 x) eps)
(*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x))
(*.f64 (*.f64 (cos.f64 x) eps) (neg.f64 eps))
(neg.f64 (*.f64 eps eps))
(*.f64 (neg.f64 eps) eps)
(*.f64 eps eps)
eps
(cos.f64 x)
x
(neg.f64 eps)

localize187.0ms (1.6%)

Memory
-15.0MiB live, 105.7MiB allocated
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0
(cos.f64 x)
accuracy0.01171875
(*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x))
accuracy0.5427885752721306
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
accuracy27.27942686511972
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))
accuracy0.01171875
(*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
accuracy0.041347509768442016
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy0.5427885752721306
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
accuracy1.0253405771124984
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy0
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
accuracy0.00390625
(fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
accuracy0.3528853443781967
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
accuracy1.1990759344798205
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
accuracy0.01171875
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
accuracy0.5427885752721306
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
accuracy1.5639367308243681
#s(approx (cos x) #s(literal 1 binary64))
accuracy0
(neg.f64 x)
accuracy0
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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 (neg.f64 x)))))
accuracy0.00390625
(*.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 (neg.f64 x))))
accuracy0.08511931943147477
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
Samples
102.0ms184×0valid
42.0ms72×1valid
Compiler

Compiled 573 to 116 computations (79.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 119.0ms
ival-mult: 46.0ms (38.6% of total)
const: 24.0ms (20.1% of total)
ival-add: 20.0ms (16.8% of total)
ival-sin: 7.0ms (5.9% of total)
adjust: 6.0ms (5% of total)
ival-cos: 6.0ms (5% of total)
ival-div: 4.0ms (3.4% of total)
ival-neg: 3.0ms (2.5% of total)
ival-sub: 1.0ms (0.8% of total)
exact: 1.0ms (0.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series34.0ms (0.3%)

Memory
-9.5MiB live, 27.1MiB allocated
Counts
22 → 87
Calls
Call 1
Inputs
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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 (neg.f64 x)))))
(*.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 (neg.f64 x))))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
(*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
(*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x))
(neg.f64 (*.f64 eps eps))
(neg.f64 x)
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(cos.f64 x)
Outputs
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 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)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* -1 (pow eps 2))
(+ (* -1 (pow eps 2)) (* 1/2 (* (pow eps 2) (pow x 2))))
(+ (* -1 (pow eps 2)) (* (pow x 2) (+ (* -1/24 (* (pow eps 2) (pow x 2))) (* 1/2 (pow eps 2)))))
(+ (* -1 (pow eps 2)) (* (pow x 2) (+ (* 1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/24 (pow eps 2)) (* 1/720 (* (pow eps 2) (pow x 2))))))))
(* -1 x)
1/24
(+ 1/24 (* -1/720 (pow x 2)))
(cos (- (* -1/2 eps) x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1 (* (pow eps 2) (cos x)))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(cos (+ (* -1 x) (* -1/2 eps)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(cos (neg x))
(+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))
(+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x))))))
(+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg x))))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (cos (neg x)))
(* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))))
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 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)))))))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(cos (neg (+ x (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* 2 (sin (* 1/2 eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
Calls

6 calls:

TimeVariablePointExpression
16.0ms
eps
@inf
((cos (+ (* -1/2 eps) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* 2 (sin (* 1/2 eps))) (cos (+ (* -1/2 eps) (neg x)))) (* 2 (sin (* 1/2 eps))) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (* (+ eps x) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (cos x)) (neg (* eps eps)) (neg x) (+ (* -1/720 (* x x)) 1/24) (cos x))
4.0ms
x
@inf
((cos (+ (* -1/2 eps) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* 2 (sin (* 1/2 eps))) (cos (+ (* -1/2 eps) (neg x)))) (* 2 (sin (* 1/2 eps))) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (* (+ eps x) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (cos x)) (neg (* eps eps)) (neg x) (+ (* -1/720 (* x x)) 1/24) (cos x))
4.0ms
x
@-inf
((cos (+ (* -1/2 eps) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* 2 (sin (* 1/2 eps))) (cos (+ (* -1/2 eps) (neg x)))) (* 2 (sin (* 1/2 eps))) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (* (+ eps x) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (cos x)) (neg (* eps eps)) (neg x) (+ (* -1/720 (* x x)) 1/24) (cos x))
3.0ms
eps
@-inf
((cos (+ (* -1/2 eps) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* 2 (sin (* 1/2 eps))) (cos (+ (* -1/2 eps) (neg x)))) (* 2 (sin (* 1/2 eps))) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (* (+ eps x) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (cos x)) (neg (* eps eps)) (neg x) (+ (* -1/720 (* x x)) 1/24) (cos x))
3.0ms
eps
@0
((cos (+ (* -1/2 eps) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* 2 (sin (* 1/2 eps))) (cos (+ (* -1/2 eps) (neg x)))) (* 2 (sin (* 1/2 eps))) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (* (+ eps x) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (cos x)) (neg (* eps eps)) (neg x) (+ (* -1/720 (* x x)) 1/24) (cos x))

simplify211.0ms (1.9%)

Memory
-3.5MiB live, 114.3MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03491153
110931101
226681055
360781045
08314953
Stop Event
iter limit
node limit
Counts
87 → 86
Calls
Call 1
Inputs
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 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)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* -1 (pow eps 2))
(+ (* -1 (pow eps 2)) (* 1/2 (* (pow eps 2) (pow x 2))))
(+ (* -1 (pow eps 2)) (* (pow x 2) (+ (* -1/24 (* (pow eps 2) (pow x 2))) (* 1/2 (pow eps 2)))))
(+ (* -1 (pow eps 2)) (* (pow x 2) (+ (* 1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/24 (pow eps 2)) (* 1/720 (* (pow eps 2) (pow x 2))))))))
(* -1 x)
1/24
(+ 1/24 (* -1/720 (pow x 2)))
(cos (- (* -1/2 eps) x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1 (* (pow eps 2) (cos x)))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(cos (+ (* -1 x) (* -1/2 eps)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(cos (neg x))
(+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))
(+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x))))))
(+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg x))))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (cos (neg x)))
(* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))))
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 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)))))))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(cos (neg (+ x (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* 2 (sin (* 1/2 eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
Outputs
(cos (* -1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (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)))))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (fma.f64 x (*.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) x) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal 2 binary64) (*.f64 (neg.f64 x) x))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64) (*.f64 (*.f64 x x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (neg.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (*.f64 (*.f64 x x) eps) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) eps) (pow.f64 x #s(literal 4 binary64)) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))) x) x eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (*.f64 (*.f64 eps eps) x) (*.f64 (*.f64 eps (+.f64 x eps)) #s(literal -1/2 binary64))) x eps)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x eps) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(* -1 (pow eps 2))
(*.f64 (neg.f64 eps) eps)
(+ (* -1 (pow eps 2)) (* 1/2 (* (pow eps 2) (pow x 2))))
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal -1 binary64)))
(+ (* -1 (pow eps 2)) (* (pow x 2) (+ (* -1/24 (* (pow eps 2) (pow x 2))) (* 1/2 (pow eps 2)))))
(fma.f64 (*.f64 (*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))) x) x (*.f64 (neg.f64 eps) eps))
(+ (* -1 (pow eps 2)) (* (pow x 2) (+ (* 1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/24 (pow eps 2)) (* 1/720 (* (pow eps 2) (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) (*.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal -1 binary64))))
(* -1 x)
(neg.f64 x)
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* -1/720 (pow x 2)))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(cos (- (* -1/2 eps) x))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.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)))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(*.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)))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos x)
(cos.f64 x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(* -1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(*.f64 (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) x) x)
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) x) x))
(* -1/720 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/720 binary64))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(*.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64))))
(* -1 (* (pow eps 2) (cos x)))
(*.f64 (neg.f64 eps) (*.f64 (cos.f64 x) eps))
(* -1/720 (pow x 2))
(*.f64 #s(literal -1/720 binary64) (*.f64 x x))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) x) x)
(cos (+ (* -1 x) (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.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)))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(*.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)))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) x) x))
(cos (neg x))
(cos.f64 x)
(+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x))))))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/8 binary64))) eps (cos.f64 x))
(+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg x))))))
(fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 eps (*.f64 #s(literal -1/48 binary64) eps) #s(literal 1/2 binary64)) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/8 binary64))) eps (cos.f64 x))
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) #s(literal -1/24 binary64)) (sin.f64 x) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (cos (neg x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) #s(literal -1/24 binary64)) (sin.f64 x) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ 1 (* -1/24 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/1920 binary64) (*.f64 eps eps) #s(literal -1/24 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps)
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))
(cos (neg (+ x (* 1/2 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(*.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)))
(* 2 (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (*.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal -1/2 binary64))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(* -1/2 (* eps (sin x)))
(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(* -1/2 (* eps x))
(*.f64 (*.f64 x eps) #s(literal -1/2 binary64))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 x eps) x x)) eps #s(literal 1 binary64))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(*.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)))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) eps (fma.f64 (neg.f64 x) (*.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64))))

rewrite228.0ms (2%)

Memory
33.8MiB live, 225.1MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058288
087286
1314274
22290274
09222270
Stop Event
iter limit
node limit
iter limit
Counts
22 → 453
Calls
Call 1
Inputs
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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 (neg.f64 x)))))
(*.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 (neg.f64 x))))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
(*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
(*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x))
(neg.f64 (*.f64 eps eps))
(neg.f64 x)
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(cos.f64 x)
Outputs
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))) #s(literal 2 binary64)))) (neg.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))))))))
(/.f64 (-.f64 (*.f64 (+.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))) #s(literal 4 binary64))
(/.f64 (-.f64 (+.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x)))) (-.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64))))))))
(fma.f64 (cos.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x)))) (cos.f64 (/.f64 (*.f64 x x) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x)))) (*.f64 (sin.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (/.f64 (*.f64 x x) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x))))))
(fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 x))))
(fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (neg.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64))))))
(fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))
(fma.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 #s(literal 0 binary64) (sin.f64 (-.f64 x (*.f64 eps #s(literal -1/2 binary64))))))
(fma.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (*.f64 (neg.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 x))))
(fma.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (neg.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64))))))
(fma.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))
(-.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x)))) (/.f64 (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))) #s(literal 2 binary64)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x)))))
(-.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))))))) (/.f64 (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))) #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))))))))
(-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x)))) (cos.f64 (/.f64 (*.f64 x x) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x))))) (*.f64 (sin.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (/.f64 (*.f64 x x) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x))))))
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (*.f64 #s(literal 0 binary64) (sin.f64 (-.f64 x (*.f64 eps #s(literal -1/2 binary64))))))
(+.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 x))))
(+.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) (neg.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64))))))
(+.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
(*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.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)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
(*.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 eps))
(*.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps #s(literal 0 binary64))))
(*.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps))
(*.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (-.f64 eps #s(literal 0 binary64))))
(*.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
(*.f64 (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
(*.f64 (neg.f64 eps) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
(*.f64 eps #s(approx (cos x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (cos x) #s(literal 1 binary64)))) (*.f64 (neg.f64 eps) eps))
(/.f64 (neg.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (cos x) #s(literal 1 binary64)))) eps)
(/.f64 (neg.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (neg.f64 eps) eps))
(/.f64 (neg.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) (*.f64 (neg.f64 eps) eps))) eps)
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 eps eps))
(/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (cos x) #s(literal 1 binary64))) (neg.f64 eps))
(/.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(/.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps))
(fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 eps) (*.f64 #s(literal 0 binary64) #s(approx (cos x) #s(literal 1 binary64))))
(fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 eps) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps #s(literal 0 binary64))) (*.f64 #s(literal 0 binary64) #s(approx (cos x) #s(literal 1 binary64))))
(fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps #s(literal 0 binary64))) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (*.f64 #s(literal 0 binary64) #s(approx (cos x) #s(literal 1 binary64))))
(fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)) (*.f64 #s(literal 0 binary64) #s(approx (cos x) #s(literal 1 binary64))))
(fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 0 binary64)))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (-.f64 eps #s(literal 0 binary64))) (*.f64 #s(literal 0 binary64) #s(approx (cos x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (-.f64 eps #s(literal 0 binary64))) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 0 binary64)))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) (*.f64 #s(literal 0 binary64) #s(approx (cos x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 0 binary64)))
(fma.f64 (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) (*.f64 #s(literal 0 binary64) #s(approx (cos x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 0 binary64)))
(fma.f64 (neg.f64 eps) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 #s(literal 0 binary64) #s(approx (cos x) #s(literal 1 binary64))))
(fma.f64 (neg.f64 eps) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 0 binary64) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
(fma.f64 #s(approx (cos x) #s(literal 1 binary64)) eps (*.f64 #s(literal 0 binary64) #s(approx (cos x) #s(literal 1 binary64))))
(fma.f64 #s(approx (cos x) #s(literal 1 binary64)) eps (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) #s(approx (cos x) #s(literal 1 binary64)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
(fma.f64 eps #s(approx (cos x) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) #s(approx (cos x) #s(literal 1 binary64))))
(fma.f64 eps #s(approx (cos x) #s(literal 1 binary64)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 0 binary64)))
(+.f64 (*.f64 #s(literal 0 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
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(fma.f64 (/.f64 eps #s(literal 1 binary64)) (neg.f64 eps) (*.f64 (neg.f64 eps) #s(literal 0 binary64)))
(fma.f64 (/.f64 (neg.f64 eps) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps #s(literal 0 binary64))) (*.f64 #s(literal 0 binary64) (neg.f64 eps)))
(fma.f64 (/.f64 (neg.f64 eps) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps #s(literal 0 binary64))) (*.f64 (neg.f64 eps) #s(literal 0 binary64)))
(fma.f64 (/.f64 (neg.f64 eps) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (*.f64 #s(literal 0 binary64) (neg.f64 eps)))
(fma.f64 (/.f64 (neg.f64 eps) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (*.f64 (neg.f64 eps) #s(literal 0 binary64)))
(fma.f64 (/.f64 (neg.f64 eps) eps) (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)) (*.f64 #s(literal 0 binary64) (neg.f64 eps)))
(fma.f64 (/.f64 (neg.f64 eps) eps) (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)) (*.f64 (neg.f64 eps) #s(literal 0 binary64)))
(fma.f64 #s(literal -1 binary64) (*.f64 eps eps) (*.f64 #s(literal 0 binary64) (neg.f64 eps)))
(fma.f64 #s(literal -1 binary64) (*.f64 eps eps) (*.f64 (neg.f64 eps) #s(literal 0 binary64)))
(fma.f64 (neg.f64 eps) (/.f64 eps #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (neg.f64 eps)))
(fma.f64 (neg.f64 eps) (/.f64 eps #s(literal 1 binary64)) (*.f64 (neg.f64 eps) #s(literal 0 binary64)))
(fma.f64 (neg.f64 eps) #s(literal 0 binary64) (*.f64 (neg.f64 eps) eps))
(fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 0 binary64) (neg.f64 eps)))
(fma.f64 (neg.f64 eps) eps (*.f64 (neg.f64 eps) #s(literal 0 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal -1 binary64) (*.f64 #s(literal 0 binary64) (neg.f64 eps)))
(fma.f64 (*.f64 eps eps) #s(literal -1 binary64) (*.f64 (neg.f64 eps) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (neg.f64 eps) (*.f64 (neg.f64 eps) eps))
(fma.f64 eps (neg.f64 eps) (*.f64 #s(literal 0 binary64) (neg.f64 eps)))
(fma.f64 eps (neg.f64 eps) (*.f64 (neg.f64 eps) #s(literal 0 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 eps eps))))) (/.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 eps eps))))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps)) (*.f64 eps eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps eps))
(+.f64 (*.f64 #s(literal 0 binary64) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps))
(+.f64 (*.f64 (neg.f64 eps) #s(literal 0 binary64)) (*.f64 (neg.f64 eps) eps))
(+.f64 (*.f64 (neg.f64 eps) eps) (*.f64 #s(literal 0 binary64) (neg.f64 eps)))
(+.f64 (*.f64 (neg.f64 eps) eps) (*.f64 (neg.f64 eps) #s(literal 0 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 (neg.f64 eps) eps))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))) (neg.f64 (+.f64 #s(literal 0 binary64) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (+.f64 #s(literal 0 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x))))
(neg.f64 x)
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) x)) (/.f64 (*.f64 x x) (+.f64 #s(literal 0 binary64) x)))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))))
(-.f64 #s(literal 0 binary64) x)
(+.f64 #s(literal 0 binary64) (neg.f64 x))
(*.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)) (pow.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) #s(literal -1 binary64)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/373248000 binary64) #s(literal 1/13824 binary64)) (pow.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (*.f64 (*.f64 x x) #s(literal -1/17280 binary64)))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (*.f64 (*.f64 x x) #s(literal -1/17280 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/373248000 binary64) #s(literal 1/13824 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1/576 binary64) (*.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (-.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)))) (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/373248000 binary64) #s(literal 1/13824 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (*.f64 (*.f64 x x) #s(literal -1/17280 binary64)))))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/576 binary64))) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(/.f64 (-.f64 #s(literal 1/576 binary64) (*.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/373248000 binary64) #s(literal 1/13824 binary64))) (neg.f64 (+.f64 #s(literal 1/576 binary64) (-.f64 (*.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 x x) #s(literal -1/17280 binary64))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/373248000 binary64) #s(literal 1/13824 binary64))) (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (*.f64 (*.f64 x x) #s(literal -1/17280 binary64))))))
(/.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (*.f64 (*.f64 x x) #s(literal -1/17280 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/373248000 binary64) #s(literal 1/13824 binary64)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/373248000 binary64) #s(literal 1/13824 binary64)) (+.f64 #s(literal 1/576 binary64) (-.f64 (*.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 x x) #s(literal -1/17280 binary64)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/373248000 binary64) #s(literal 1/13824 binary64)) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (*.f64 (*.f64 x x) #s(literal -1/17280 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (*.f64 (*.f64 x x) #s(literal -1/17280 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/373248000 binary64) #s(literal 1/13824 binary64))))
(fma.f64 (*.f64 #s(literal -1/720 binary64) x) x #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 x (*.f64 #s(literal -1/720 binary64) x) #s(literal 1/24 binary64))
(-.f64 (/.f64 #s(literal 1/576 binary64) (-.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64)))) (/.f64 (*.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64)))))
(-.f64 (/.f64 (*.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(+.f64 (*.f64 (*.f64 x x) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))
(+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64)))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(-.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x)))

eval112.0ms (1%)

Memory
-15.9MiB live, 76.7MiB allocated
Compiler

Compiled 17 484 to 2 108 computations (87.9% saved)

prune29.0ms (0.3%)

Memory
8.1MiB live, 45.4MiB allocated
Pruning

19 alts after pruning (13 fresh and 6 done)

PrunedKeptTotal
New5188526
Fresh257
Picked235
Done033
Total52219541
Accuracy
100.0%
Counts
541 → 19
Alt Table
Click to see full alt table
StatusAccuracyProgram
38.2%
(-.f64 (/.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))) #s(literal 2 binary64)) (-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))) (*.f64 (cos.f64 eps) (sin.f64 x)))) (/.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))) (*.f64 (cos.f64 eps) (sin.f64 x)))))
64.7%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.5%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.4%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
55.4%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps)))
56.5%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps))
55.0%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
99.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
55.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)) (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)))
56.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (cos.f64 x) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
99.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
98.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
98.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
97.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
97.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
99.7%
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
99.5%
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 #s(approx (* 2 (sin (* 1/2 eps))) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
Compiler

Compiled 824 to 550 computations (33.3% saved)

simplify164.0ms (1.4%)

Memory
-31.9MiB live, 51.8MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
cost-diff0
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
cost-diff0
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
cost-diff0
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff0
(*.f64 eps eps)
cost-diff0
(*.f64 (*.f64 eps eps) (cos.f64 x))
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps))
cost-diff1024
(/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps)
cost-diff0
(*.f64 (neg.f64 eps) eps)
cost-diff0
(*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps)))
cost-diff1280
(/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps))
cost-diff0
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
cost-diff0
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
cost-diff0
(*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
cost-diff0
(sin.f64 eps)
cost-diff0
(cos.f64 x)
cost-diff0
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
cost-diff0
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
061375
095368
1163366
2354362
3812346
41760346
52765346
64106346
75658346
86592346
97295346
107958346
08195342
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
(cos.f64 x)
x
(sin.f64 eps)
eps
(*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(sin.f64 x)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
(*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal -1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps)))
(/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps))
(*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(*.f64 (neg.f64 eps) eps)
(neg.f64 eps)
eps
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(*.f64 (+.f64 x eps) #s(literal -1/2 binary64))
(+.f64 x eps)
x
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps))
(/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps)
(*.f64 (*.f64 eps eps) (cos.f64 x))
(*.f64 eps eps)
eps
(cos.f64 x)
x
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
#s(literal -1/48 binary64)
(*.f64 eps eps)
eps
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
x
#s(literal -2 binary64)
Outputs
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x) (*.f64 (sin.f64 eps) (cos.f64 x))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x) (*.f64 (sin.f64 eps) (cos.f64 x)))
(cos.f64 x)
x
(sin.f64 eps)
eps
(*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x))
(sin.f64 x)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) eps))
(*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
(*.f64 #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal -1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
(*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(*.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (neg.f64 eps)) eps)
(*.f64 (neg.f64 eps) eps)
(neg.f64 eps)
eps
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(*.f64 (+.f64 x eps) #s(literal -1/2 binary64))
(*.f64 (+.f64 eps x) #s(literal -1/2 binary64))
(+.f64 x eps)
(+.f64 eps x)
x
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps)
(*.f64 (cos.f64 x) eps)
(*.f64 (*.f64 eps eps) (cos.f64 x))
(*.f64 (*.f64 (cos.f64 x) eps) eps)
(*.f64 eps eps)
eps
(cos.f64 x)
x
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
#s(literal -1/48 binary64)
(*.f64 eps eps)
eps
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
x
#s(literal -2 binary64)

localize318.0ms (2.8%)

Memory
29.8MiB live, 262.1MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy0.01171875
(*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
accuracy0.08511931943147477
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
accuracy0.24612965000286047
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
accuracy0
(cos.f64 x)
accuracy0.01171875
(*.f64 (*.f64 eps eps) (cos.f64 x))
accuracy0.5427885752721306
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps))
accuracy27.27942686511972
(/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps)
accuracy0.0234375
(*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
accuracy0.3528853443781967
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps)))
accuracy1.1990759344798205
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
accuracy27.27552061511972
(/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps))
accuracy0
(*.f64 x x)
accuracy0.01171875
(*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
accuracy0.5427885752721306
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
accuracy1.1961429291973134
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy0
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
accuracy0.01171875
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
accuracy0.08984375
(*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy31.777135702379912
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
Samples
176.0ms175×2valid
61.0ms79×1valid
1.0ms0valid
Compiler

Compiled 632 to 119 computations (81.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 192.0ms
ival-mult: 74.0ms (38.6% of total)
adjust: 39.0ms (20.3% of total)
ival-cos: 29.0ms (15.1% of total)
ival-add: 18.0ms (9.4% of total)
ival-sin: 12.0ms (6.3% of total)
ival-div: 8.0ms (4.2% of total)
ival-sub: 5.0ms (2.6% of total)
const: 4.0ms (2.1% of total)
ival-neg: 3.0ms (1.6% of total)
exact: 1.0ms (0.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series30.0ms (0.3%)

Memory
18.6MiB live, 54.7MiB allocated
Counts
25 → 103
Calls
Call 1
Inputs
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
(cos.f64 x)
(sin.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
(*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps)))
(*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(*.f64 (neg.f64 eps) eps)
(/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps))
(*.f64 (*.f64 eps eps) (cos.f64 x))
(*.f64 eps eps)
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(*.f64 x x)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
Outputs
(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 (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (- (cos eps) 1)))))) 1)))
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)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* -1 (pow eps 2))
(+ (* -1 (pow eps 2)) (* 1/2 (* (pow eps 3) x)))
(+ (* -1 (pow eps 2)) (* x (+ (* 1/2 (* (pow eps 2) x)) (* 1/2 (pow eps 3)))))
(+ (* -1 (pow eps 2)) (* x (+ (* 1/2 (pow eps 3)) (* x (+ (* -1/12 (* (pow eps 3) x)) (* 1/2 (pow eps 2)))))))
(pow eps 2)
(+ (* -1/2 (* (pow eps 2) (pow x 2))) (pow eps 2))
(+ (* (pow x 2) (+ (* -1/2 (pow eps 2)) (* 1/24 (* (pow eps 2) (pow x 2))))) (pow eps 2))
(+ (* (pow x 2) (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/720 (* (pow eps 2) (pow x 2))) (* 1/24 (pow eps 2)))))) (pow eps 2))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(* x (- (cos eps) 1))
(* x (- (+ (cos eps) (* -1/6 (* (pow x 2) (- (cos eps) 1)))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ (* -1/6 (- (cos eps) 1)) (* 1/120 (* (pow x 2) (- (cos eps) 1)))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ (* -1/6 (- (cos eps) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (cos eps) 1))) (* 1/120 (- (cos eps) 1))))))) 1))
(pow x 2)
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(cos x)
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(* (pow eps 2) (cos x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* (sin x) (- (cos eps) 1))
(+ (cos x) (* -1/2 (* eps (sin x))))
(cos (* -1/2 (+ eps (* 2 x))))
(- (sin (- eps (* -1 x))) (sin x))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(cos (* -1/2 (- eps (* -2 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 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))))
(* -1 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (cos x)) (* 1/2 (* eps (sin x)))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* 1/2 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(- (cos eps) 1)
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* (pow eps 3) (+ (* -1/2 (sin x)) (/ (cos x) eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
Calls

6 calls:

TimeVariablePointExpression
8.0ms
x
@inf
((+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) (cos x) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (/ (* (* (neg eps) eps) (+ (* (* (sin x) -1/2) eps) (cos x))) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (* (neg eps) eps) (+ (* (* (sin x) -1/2) eps) (cos x))) (* (neg eps) eps) (/ (* (* eps eps) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (* eps eps) (cos x)) (* eps eps) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (- (cos eps) 1) (* (sin x) (- (cos eps) 1)) (* x x) (+ (* (* (sin x) -1/2) eps) (cos x)) (cos (/ (+ (* 2 x) eps) -2)))
6.0ms
x
@0
((+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) (cos x) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (/ (* (* (neg eps) eps) (+ (* (* (sin x) -1/2) eps) (cos x))) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (* (neg eps) eps) (+ (* (* (sin x) -1/2) eps) (cos x))) (* (neg eps) eps) (/ (* (* eps eps) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (* eps eps) (cos x)) (* eps eps) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (- (cos eps) 1) (* (sin x) (- (cos eps) 1)) (* x x) (+ (* (* (sin x) -1/2) eps) (cos x)) (cos (/ (+ (* 2 x) eps) -2)))
4.0ms
x
@-inf
((+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) (cos x) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (/ (* (* (neg eps) eps) (+ (* (* (sin x) -1/2) eps) (cos x))) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (* (neg eps) eps) (+ (* (* (sin x) -1/2) eps) (cos x))) (* (neg eps) eps) (/ (* (* eps eps) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (* eps eps) (cos x)) (* eps eps) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (- (cos eps) 1) (* (sin x) (- (cos eps) 1)) (* x x) (+ (* (* (sin x) -1/2) eps) (cos x)) (cos (/ (+ (* 2 x) eps) -2)))
4.0ms
eps
@-inf
((+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) (cos x) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (/ (* (* (neg eps) eps) (+ (* (* (sin x) -1/2) eps) (cos x))) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (* (neg eps) eps) (+ (* (* (sin x) -1/2) eps) (cos x))) (* (neg eps) eps) (/ (* (* eps eps) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (* eps eps) (cos x)) (* eps eps) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (- (cos eps) 1) (* (sin x) (- (cos eps) 1)) (* x x) (+ (* (* (sin x) -1/2) eps) (cos x)) (cos (/ (+ (* 2 x) eps) -2)))
4.0ms
eps
@inf
((+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) (cos x) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (/ (* (* (neg eps) eps) (+ (* (* (sin x) -1/2) eps) (cos x))) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (* (neg eps) eps) (+ (* (* (sin x) -1/2) eps) (cos x))) (* (neg eps) eps) (/ (* (* eps eps) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (* eps eps) (cos x)) (* eps eps) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (- (cos eps) 1) (* (sin x) (- (cos eps) 1)) (* x x) (+ (* (* (sin x) -1/2) eps) (cos x)) (cos (/ (+ (* 2 x) eps) -2)))

simplify196.0ms (1.7%)

Memory
-26.3MiB live, 217.7MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04061430
112551351
237051302
080581195
Stop Event
iter limit
node limit
Counts
103 → 102
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 (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (- (cos eps) 1)))))) 1)))
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)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* -1 (pow eps 2))
(+ (* -1 (pow eps 2)) (* 1/2 (* (pow eps 3) x)))
(+ (* -1 (pow eps 2)) (* x (+ (* 1/2 (* (pow eps 2) x)) (* 1/2 (pow eps 3)))))
(+ (* -1 (pow eps 2)) (* x (+ (* 1/2 (pow eps 3)) (* x (+ (* -1/12 (* (pow eps 3) x)) (* 1/2 (pow eps 2)))))))
(pow eps 2)
(+ (* -1/2 (* (pow eps 2) (pow x 2))) (pow eps 2))
(+ (* (pow x 2) (+ (* -1/2 (pow eps 2)) (* 1/24 (* (pow eps 2) (pow x 2))))) (pow eps 2))
(+ (* (pow x 2) (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/720 (* (pow eps 2) (pow x 2))) (* 1/24 (pow eps 2)))))) (pow eps 2))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(* x (- (cos eps) 1))
(* x (- (+ (cos eps) (* -1/6 (* (pow x 2) (- (cos eps) 1)))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ (* -1/6 (- (cos eps) 1)) (* 1/120 (* (pow x 2) (- (cos eps) 1)))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ (* -1/6 (- (cos eps) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (cos eps) 1))) (* 1/120 (- (cos eps) 1))))))) 1))
(pow x 2)
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(cos x)
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(* (pow eps 2) (cos x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* (sin x) (- (cos eps) 1))
(+ (cos x) (* -1/2 (* eps (sin x))))
(cos (* -1/2 (+ eps (* 2 x))))
(- (sin (- eps (* -1 x))) (sin x))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(cos (* -1/2 (- eps (* -2 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 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))))
(* -1 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (cos x)) (* 1/2 (* eps (sin x)))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* 1/2 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(- (cos eps) 1)
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* (pow eps 3) (+ (* -1/2 (sin x)) (/ (cos x) eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
Outputs
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (- (cos eps) 1)))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps x) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps x) eps))
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (*.f64 (*.f64 eps eps) x) (*.f64 (*.f64 eps (+.f64 eps x)) #s(literal -1/2 binary64))) x eps)
(* -1 (pow eps 2))
(*.f64 (neg.f64 eps) eps)
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(* eps (+ 1 (* -1/6 (pow eps 2))))
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(* -1 (* (pow eps 2) (cos x)))
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(* (pow eps 2) (+ (* -1 (cos x)) (* 1/2 (* eps (sin x)))))
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(* eps (cos (* -1 x)))
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(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
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(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
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(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ 1 (* -1/24 (pow eps 2))))
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(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
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(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps)
(* 1/2 eps)
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(* eps (+ 1/2 (* -1/48 (pow eps 2))))
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(* -1/2 (* (pow eps 2) (sin x)))
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(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(*.f64 (*.f64 (*.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) eps)
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(*.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))
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(cos (* -1 x))
(cos.f64 x)
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(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
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(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))) eps (cos.f64 x))
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(cos (* -1/2 (- (* 2 x) (* -1 eps))))
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rewrite159.0ms (1.4%)

Memory
29.5MiB live, 260.7MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
061313
095299
1345269
22694269
08196265
Stop Event
iter limit
node limit
iter limit
Counts
25 → 451
Calls
Call 1
Inputs
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
(cos.f64 x)
(sin.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
(*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps)))
(*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(*.f64 (neg.f64 eps) eps)
(/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps))
(*.f64 (*.f64 eps eps) (cos.f64 x))
(*.f64 eps eps)
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(*.f64 x x)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))))
(*.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 2 binary64))) (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (sin.f64 x))) #s(literal -1 binary64)))
(*.f64 (*.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 x))) (pow.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 x)) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (pow.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (fma.f64 (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) (-.f64 (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))) (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (+.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (fma.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (-.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (*.f64 (cos.f64 eps) (sin.f64 x))) (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (*.f64 (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(pow.f64 (/.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (sin.f64 x))) (-.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) (-.f64 (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))) (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 x)) (*.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (-.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (*.f64 (cos.f64 eps) (sin.f64 x))) (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64))) (+.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (-.f64 (*.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (sin.f64 x)))) (*.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (sin.f64 x))) (pow.f64 (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 2 binary64)))) (*.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (sin.f64 x))) (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (sin.f64 x)))))
(/.f64 (-.f64 (*.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) (*.f64 (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (*.f64 (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))))
(/.f64 (-.f64 (*.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 x))) (*.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 x)) (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #s(literal 2 binary64)))) (*.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 x)) (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 x))))
(/.f64 (-.f64 (*.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (*.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (*.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 (sin.f64 (-.f64 x eps)) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (*.f64 (sin.f64 (-.f64 x eps)) (+.f64 #s(literal 0 binary64) (sin.f64 x))))
(/.f64 (fma.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))) (*.f64 (sin.f64 (-.f64 x eps)) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) (*.f64 (sin.f64 (-.f64 x eps)) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x))))))
(/.f64 (fma.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))))) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (*.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))))) (+.f64 #s(literal 0 binary64) (sin.f64 x))))
(/.f64 (fma.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))) (*.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))))) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) (*.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))))) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x))))))
(/.f64 (fma.f64 (fma.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))) (+.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 #s(literal 4 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal 4 binary64) (+.f64 #s(literal 0 binary64) (sin.f64 x))))
(/.f64 (fma.f64 (fma.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))) (*.f64 #s(literal 4 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) (*.f64 #s(literal 4 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x))))))
(/.f64 (fma.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (sin.f64 x)) #s(literal -2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (neg.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x)))))) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal -2 binary64)))
(/.f64 (fma.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (sin.f64 x)) #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x)))) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))))
(/.f64 (fma.f64 (*.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (sin.f64 x)) #s(literal -2 binary64) (*.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (neg.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x)))))) (*.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal -2 binary64)))
(/.f64 (fma.f64 (*.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 2 binary64) (*.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))) (*.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal 2 binary64)))
(/.f64 (fma.f64 (*.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x)))) (*.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal 1 binary64))) (*.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))))
(/.f64 (fma.f64 (*.f64 (sin.f64 x) (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) #s(literal -2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (neg.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x)))))) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal -2 binary64)))
(/.f64 (fma.f64 (*.f64 (sin.f64 x) (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (*.f64 (sin.f64 x) (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x)))) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))))
(/.f64 (fma.f64 (*.f64 (sin.f64 x) (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal -2 binary64) (*.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (neg.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x)))))) (*.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal -2 binary64)))
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(*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
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(*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
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(/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64))) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
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(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64))) (*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/110592 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64))) (*.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/96 binary64))))))
(fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) eps (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) #s(literal 0 binary64) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps (*.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) eps))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(fma.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 eps (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))))
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(fma.f64 eps #s(literal 1/2 binary64) (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) eps))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(+.f64 (*.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(+.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) eps) (*.f64 #s(literal 1/2 binary64) eps))
(+.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) #s(literal 0 binary64)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(+.f64 (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (*.f64 #s(literal 1/2 binary64) eps))
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) eps))
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(+.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) (*.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))))
(+.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) #s(literal 0 binary64)))
(*.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (pow.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps)))) (*.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal 1 binary64))) (*.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps)))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps)))))
(/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (-.f64 (cos.f64 eps) #s(literal -1 binary64)))
(/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (cos.f64 eps)))
(/.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal -1 binary64)))))
(/.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64))))
(fma.f64 #s(literal 1 binary64) (cos.f64 eps) #s(literal -1 binary64))
(fma.f64 (cos.f64 eps) #s(literal 1 binary64) #s(literal -1 binary64))
(-.f64 (/.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (pow.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps)))) (pow.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal -1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x))
(*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(/.f64 (fma.f64 (neg.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x)))) (+.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 0 binary64) (sin.f64 x))))
(/.f64 (fma.f64 (neg.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x)))) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))) (*.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x))))))
(/.f64 (fma.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x))) (+.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal 2 binary64) (+.f64 #s(literal 0 binary64) (sin.f64 x))))
(/.f64 (fma.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x))) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) (*.f64 #s(literal 2 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x))))))
(/.f64 (fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x)))) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (*.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x)))) (+.f64 #s(literal 0 binary64) (sin.f64 x))))
(/.f64 (fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))) (*.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x)))) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) (*.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x)))) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x))))))
(/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 eps)))
(/.f64 (*.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))))
(/.f64 (*.f64 (sin.f64 x) (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (cos.f64 eps)))
(/.f64 (*.f64 (sin.f64 x) (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))))
(fma.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x))) #s(literal 1/2 binary64) (neg.f64 (sin.f64 x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (neg.f64 (sin.f64 x)))
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (sin.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))
(cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -1/2 binary64)))

eval80.0ms (0.7%)

Memory
-17.6MiB live, 185.6MiB allocated
Compiler

Compiled 22 952 to 2 525 computations (89% saved)

prune23.0ms (0.2%)

Memory
12.5MiB live, 90.8MiB allocated
Pruning

19 alts after pruning (10 fresh and 9 done)

PrunedKeptTotal
New5727579
Fresh538
Picked235
Done066
Total57919598
Accuracy
100.0%
Counts
598 → 19
Alt Table
Click to see full alt table
StatusAccuracyProgram
64.7%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.5%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) eps (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.5%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
99.4%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
56.5%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps))
55.0%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (* eps eps) (cos x)) (*.f64 eps eps)) eps))
99.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
56.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (cos.f64 x) eps) (*.f64 eps eps)))
55.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
97.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (neg.f64 eps) (*.f64 eps (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (neg.f64 eps)))))
99.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
98.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
98.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
97.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
97.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
99.7%
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
57.2%
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (/.f64 (-.f64 (pow.f64 (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (-.f64 (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))))
Compiler

Compiled 1 264 to 523 computations (58.6% saved)

regimes60.0ms (0.5%)

Memory
-24.9MiB live, 102.8MiB allocated
Counts
33 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (* eps eps) (cos x)) (*.f64 eps eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (neg.f64 eps) (*.f64 eps (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (neg.f64 eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)) (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (cos.f64 x) eps) (*.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (cos.f64 x) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) eps (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 #s(approx (* 2 (sin (* 1/2 eps))) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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 (neg.f64 x)))))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (/.f64 (-.f64 (pow.f64 (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (-.f64 (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))))
(-.f64 (/.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))) #s(literal 2 binary64)) (-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))) (*.f64 (cos.f64 eps) (sin.f64 x)))) (/.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))) (*.f64 (cos.f64 eps) (sin.f64 x)))))
Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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 (neg.f64 x)))))
Calls

3 calls:

41.0ms
x
10.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms
eps
Results
AccuracySegmentsBranch
99.9%1x
99.9%1eps
99.9%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes23.0ms (0.2%)

Memory
13.2MiB live, 52.3MiB allocated
Counts
27 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (* eps eps) (cos x)) (*.f64 eps eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (neg.f64 eps) (*.f64 eps (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (neg.f64 eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)) (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (cos.f64 x) eps) (*.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (cos.f64 x) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) eps (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 #s(approx (* 2 (sin (* 1/2 eps))) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
Outputs
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) eps (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
Calls

3 calls:

8.0ms
eps
7.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms
x
Results
AccuracySegmentsBranch
99.5%1x
99.5%1eps
99.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.2%)

Memory
0.2MiB live, 39.5MiB allocated
Counts
23 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (* eps eps) (cos x)) (*.f64 eps eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (neg.f64 eps) (*.f64 eps (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (neg.f64 eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)) (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (cos.f64 x) eps) (*.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (cos.f64 x) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
Outputs
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
Calls

3 calls:

7.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
eps
6.0ms
x
Results
AccuracySegmentsBranch
99.5%1x
99.5%1eps
99.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes19.0ms (0.2%)

Memory
2.2MiB live, 44.6MiB allocated
Counts
21 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (* eps eps) (cos x)) (*.f64 eps eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (neg.f64 eps) (*.f64 eps (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (neg.f64 eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)) (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (cos.f64 x) eps) (*.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (cos.f64 x) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
Outputs
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
Calls

3 calls:

7.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
x
6.0ms
eps
Results
AccuracySegmentsBranch
99.4%1x
99.4%1eps
99.4%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes33.0ms (0.3%)

Memory
-31.0MiB live, 48.1MiB allocated
Counts
20 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (* eps eps) (cos x)) (*.f64 eps eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (neg.f64 eps) (*.f64 eps (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (neg.f64 eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)) (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (cos.f64 x) eps) (*.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (cos.f64 x) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
Calls

3 calls:

7.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
eps
5.0ms
x
Results
AccuracySegmentsBranch
99.2%1x
99.2%1eps
99.2%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory
24.8MiB live, 24.9MiB allocated
Counts
14 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (* eps eps) (cos x)) (*.f64 eps eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (neg.f64 eps) (*.f64 eps (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (neg.f64 eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)) (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
Calls

3 calls:

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

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.1%)

Memory
12.3MiB live, 12.3MiB allocated
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (* eps eps) (cos x)) (*.f64 eps eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
Calls

3 calls:

2.0ms
x
2.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms
eps
Results
AccuracySegmentsBranch
98.0%1x
98.0%1eps
98.0%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes27.0ms (0.2%)

Memory
-25.7MiB live, 13.7MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (* eps eps) (cos x)) (*.f64 eps eps)) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
Calls

3 calls:

23.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
97.9%1x
97.9%1eps
97.9%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory
9.9MiB live, 9.9MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

3 calls:

1.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms
eps
1.0ms
x
Results
AccuracySegmentsBranch
97.6%1x
97.6%1eps
97.6%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify53.0ms (0.5%)

Memory
9.5MiB live, 50.9MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
076208
1100208
2102208
3103208
Stop Event
saturated
Calls
Call 1
Inputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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 (neg.f64 x)))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) eps (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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 (neg.f64 x)))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) eps (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) eps (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(*.f64 #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))

soundness1.3s (11.4%)

Memory
-11.3MiB live, 497.3MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03521138
110441080
228011044
363041042
08496942
0616
01016
15316
238016
3476616
0821016
061313
095299
1345269
22694269
08196265
04061430
112551351
237051302
080581195
0107291
1314291
2779284
32842284
46177284
08125253
Stop Event
fuel
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
iter limit
node limit
Compiler

Compiled 384 to 234 computations (39.1% saved)

preprocess60.0ms (0.5%)

Memory
7.5MiB live, 124.0MiB allocated
Compiler

Compiled 460 to 198 computations (57% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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