2sin (example 3.3)

Time bar (total: 11.9s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze59.0ms (0.5%)

Memory
-0.9MiB live, 48.0MiB allocated; 24ms collecting garbage
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)

sample6.9s (58%)

Memory
-124.2MiB live, 7 378.5MiB allocated; 2.6s collecting garbage
Samples
3.4s25 643×0invalid
1.4s5 126×1valid
297.0ms3 130×0valid
Precisions
Click to see histograms. Total time spent on operations: 3.3s
ival-sin: 723.0ms (22.1% of total)
const: 598.0ms (18.3% of total)
ival-add: 291.0ms (8.9% of total)
ival-sub: 259.0ms (7.9% of total)
ival-<: 259.0ms (7.9% of total)
ival-fabs: 256.0ms (7.8% of total)
ival-<=: 248.0ms (7.6% of total)
ival-mult: 245.0ms (7.5% of total)
adjust: 220.0ms (6.7% of total)
ival-and: 109.0ms (3.3% of total)
exact: 45.0ms (1.4% of total)
ival-assert: 12.0ms (0.4% of total)
Bogosity

explain106.0ms (0.9%)

Memory
32.9MiB live, 134.1MiB allocated; 19ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2271(6.684622507753595e-264 6.067263533790162e-266)2(-3.454990883413934e-238 3.9539246232771345e-240)(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
40-0-(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))cancellation2264
sin.f64(sin.f64 (+.f64 x eps))sensitivity40
Confusion
Predicted +Predicted -
+2272
-126
Precision
0.9956140350877193
Recall
0.9912663755458515
Confusion?
Predicted +Predicted MaybePredicted -
+22720
-1224
Precision?
0.9870689655172413
Recall?
1.0
Freqs
test
numberfreq
028
1226
22
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
49.0ms336×1valid
9.0ms176×0valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 35.0ms
ival-sin: 12.0ms (33.9% of total)
adjust: 10.0ms (28.2% of total)
ival-add: 9.0ms (25.4% of total)
ival-sub: 4.0ms (11.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess48.0ms (0.4%)

Memory
-3.5MiB live, 41.5MiB allocated; 9ms collecting garbage
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01843
12243
22943
33743
44943
57143
69343
714743
823143
938543
10101043
11437143
067
0107
1117
0117
Stop Event
iter limit
saturated
iter limit
node limit
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
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.6%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Memory
4.0MiB live, 4.0MiB allocated; 0ms collecting garbage
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
11118
01118
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)

localize40.0ms (0.3%)

Memory
-3.7MiB live, 40.9MiB allocated; 10ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(+.f64 x eps)
accuracy0.0
(sin.f64 x)
accuracy0.1746749880282053
(sin.f64 (+.f64 x eps))
accuracy24.38699009277732
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Samples
29.0ms168×1valid
5.0ms88×0valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 22.0ms
ival-sin: 12.0ms (55.6% of total)
adjust: 5.0ms (23.2% of total)
ival-add: 2.0ms (9.3% of total)
ival-sub: 2.0ms (9.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series4.0ms (0%)

Memory
7.1MiB live, 7.1MiB allocated; 0ms collecting garbage
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))

simplify193.0ms (1.6%)

Memory
-23.9MiB live, 209.2MiB allocated; 26ms collecting garbage
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107303
1366303
21224296
34149296
47986296
08046267
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)) (-.f64 (*.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 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/5040 binary64) (-.f64 (*.f64 #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 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (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) eps) #s(literal -1/6 binary64))) 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) eps) #s(literal -1/2 binary64) (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 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)))

rewrite212.0ms (1.8%)

Memory
33.7MiB live, 228.2MiB allocated; 25ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
01016
15116
236516
3445216
0817716
Stop Event
iter limit
node limit
iter limit
Counts
4 → 154
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 (/.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 x) #s(literal 3 binary64)) (pow.f64 (sin.f64 (+.f64 eps 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 (-.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 #s(literal 2 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))
(*.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (*.f64 (cos.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (/.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(*.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 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (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 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #s(literal 2 binary64)))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) (+.f64 (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 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))))
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(/.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 (neg.f64 (+.f64 eps x)) (-.f64 x eps)) (-.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 (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 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 (/.f64 (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 (pow.f64 eps #s(literal 3 binary64)) (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)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(fma.f64 (/.f64 (pow.f64 eps #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 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 (/.f64 (pow.f64 eps #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 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 (pow.f64 eps #s(literal 3/2 binary64)) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 (fabs.f64 x) (/.f64 (fabs.f64 x) (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(fma.f64 (neg.f64 x) (/.f64 (neg.f64 x) (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(fma.f64 (*.f64 eps eps) (/.f64 eps (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 eps (/.f64 (*.f64 eps eps) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) 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 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(+.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(+.f64 eps x)
(+.f64 x eps)
(sin.f64 x)

eval47.0ms (0.4%)

Memory
-19.8MiB live, 76.9MiB allocated; 21ms collecting garbage
Compiler

Compiled 5 510 to 734 computations (86.7% saved)

prune12.0ms (0.1%)

Memory
-21.7MiB live, 23.6MiB allocated; 6ms collecting garbage
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1689177
Fresh000
Picked011
Done000
Total16810178
Accuracy
100.0%
Counts
178 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.9%
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
37.1%
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
36.5%
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))) (*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))))))
61.9%
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
61.6%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.7%
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.0%
#s(approx (- (sin (+ x eps)) (sin 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))
98.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
97.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
95.4%
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
Compiler

Compiled 501 to 220 computations (56.1% saved)

simplify132.0ms (1.1%)

Memory
36.5MiB live, 226.0MiB allocated; 27ms collecting garbage
Algorithm
egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sin.f64 (+.f64 eps x))
cost-diff0
(pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))
cost-diff0
(-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
cost-diff12
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
cost-diff0
(cos.f64 eps)
cost-diff0
(sin.f64 x)
cost-diff0
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x)))
cost-diff1
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
cost-diff0
(*.f64 (sin.f64 x) eps)
cost-diff0
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
cost-diff0
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
cost-diff0
(sin.f64 eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff0
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
cost-diff0
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff1
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
cost-diff2
(+.f64 #s(literal 0 binary64) eps)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037217
065207
1118207
2262207
3737204
41839194
53895192
08134191
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
(/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 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 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
eps
#s(literal -1/2 binary64)
(cos.f64 x)
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x)))
(sin.f64 x)
x
(cos.f64 eps)
eps
(*.f64 (sin.f64 eps) (cos.f64 x))
(sin.f64 eps)
(cos.f64 x)
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))
(sin.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
#s(literal 2 binary64)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin.f64 x)
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
Outputs
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (cos.f64 (+.f64 x (/.f64 eps #s(literal 2 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) #s(literal -2 binary64)))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
(*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) #s(literal -2 binary64))
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
(sin.f64 (/.f64 eps #s(literal 2 binary64)))
(/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))
(/.f64 eps #s(literal 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 (+.f64 x (/.f64 eps #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(-.f64 (/.f64 eps #s(literal -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 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
eps
#s(literal -1/2 binary64)
(cos.f64 x)
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
(sin.f64 x)
x
(cos.f64 eps)
eps
(*.f64 (sin.f64 eps) (cos.f64 x))
(*.f64 (cos.f64 x) (sin.f64 eps))
(sin.f64 eps)
(cos.f64 x)
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(-.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 x eps)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))
(pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64))
(sin.f64 (+.f64 eps x))
(sin.f64 (+.f64 x eps))
(+.f64 eps x)
(+.f64 x eps)
eps
x
#s(literal 2 binary64)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin.f64 x)
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

localize313.0ms (2.6%)

Memory
-33.6MiB live, 305.7MiB allocated; 52ms collecting garbage
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy0.213222509768442
(pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))
accuracy0.24609375
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
accuracy12.540347119725714
(-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
accuracy27.261825083011527
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
accuracy0.0
(cos.f64 eps)
accuracy0.0078125
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x)))
accuracy0.01953125
(*.f64 (sin.f64 eps) (cos.f64 x))
accuracy24.38699009277732
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
accuracy0.0078125
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
accuracy0.015625
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
accuracy0.0234375
(*.f64 (sin.f64 x) eps)
accuracy0.7864239630799743
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
accuracy0.0
(sin.f64 eps)
accuracy2.958749351561334
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy0.0
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
accuracy0.0
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
accuracy0.0234375
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy0.15970553043532218
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
Samples
209.0ms173×1valid
28.0ms81×0valid
5.0ms3valid
Compiler

Compiled 213 to 39 computations (81.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 186.0ms
adjust: 63.0ms (33.9% of total)
ival-mult: 37.0ms (19.9% of total)
ival-add: 32.0ms (17.2% of total)
ival-sin: 19.0ms (10.2% of total)
ival-cos: 10.0ms (5.4% of total)
ival-pow2: 9.0ms (4.8% of total)
ival-div: 7.0ms (3.8% of total)
ival-sub: 7.0ms (3.8% of total)
exact: 1.0ms (0.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series58.0ms (0.5%)

Memory
3.8MiB live, 47.9MiB allocated; 11ms collecting garbage
Counts
22 → 138
Calls
Call 1
Inputs
(+.f64 #s(literal 0 binary64) eps)
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #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 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x)))
(sin.f64 x)
(cos.f64 eps)
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))
(sin.f64 (+.f64 eps x))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
(*.f64 (sin.f64 eps) (cos.f64 x))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
Outputs
(* -1/2 eps)
(+ (* -1 x) (* -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 (* (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 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
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 (- (* 2 (cos eps)) (+ 1 (cos eps)))))
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))))) (+ 1 (cos eps)))))
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (+ (* x (- (+ 1/6 (+ (* -1 (cos eps)) (* -1/3 (cos eps)))) (+ (* -1/2 (- (* 2 (cos eps)) (+ 1 (cos eps)))) (+ (* -1/6 (cos eps)) (/ (* (+ 1 (cos eps)) (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (sin eps)))))) (/ (pow (cos eps) 2) (sin eps)))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))))) (+ 1 (cos eps)))))
(pow (sin eps) 2)
(+ (* 2 (* x (* (cos eps) (sin eps)))) (pow (sin eps) 2))
(+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (- (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2)) 1)))) (pow (sin eps) 2))
(+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (- (+ (* -1 (pow (sin eps) 2)) (+ (* x (+ (* -1 (* (cos eps) (sin eps))) (* -1/3 (* (cos eps) (sin eps))))) (pow (cos eps) 2))) 1)))) (pow (sin eps) 2))
(+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))))) (pow (sin eps) 2))
(+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (+ (* -1 (pow (sin eps) 2)) (+ (* x (+ (* -1 (* (cos eps) (sin eps))) (* -1/3 (* (cos eps) (sin eps))))) (pow (cos eps) 2)))))) (pow (sin eps) 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))))))
(+ (sin eps) (* -1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps))))))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps)))))))
(+ (sin eps) (* x (+ 1 (cos eps))))
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps)))))))
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (- (* -1/6 (cos eps)) 1/6))))))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(+ (* (cos eps) (sin x)) (* (cos x) (sin eps)))
(sin x)
(/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x))))
(- (pow (sin (+ eps x)) 2) (pow (sin x) 2))
(pow (sin (+ eps x)) 2)
(sin (+ eps x))
(cos (* -1/2 (+ eps (* 2 x))))
(* (cos x) (sin eps))
(+ (sin x) (sin (+ eps x)))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(/ (- (pow (sin (- eps (* -1 x))) 2) (pow (sin x) 2)) (+ (sin x) (sin (- eps (* -1 x)))))
(- (pow (sin (- eps (* -1 x))) 2) (pow (sin x) 2))
(pow (sin (- eps (* -1 x))) 2)
(sin (- eps (* -1 x)))
(cos (* -1/2 (- eps (* -2 x))))
(+ (sin x) (sin (- eps (* -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 (+ 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 (+ (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))))
(cos 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))))))))
(+ 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)))
(* eps (+ (cos x) (* eps (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x)))))))
(* eps (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x))))))) (* 1/2 (/ (pow (cos x) 2) (sin x)))))))
(* eps (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (+ (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))) (sin x))) (+ (* -1/4 (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (+ (* -1/12 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x)))))) (sin x)))))))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x))))))) (* 1/2 (/ (pow (cos x) 2) (sin x)))))))
(* 2 (* eps (* (cos x) (sin x))))
(* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))
(* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))) (pow (cos x) 2))))))
(* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (+ (* -1/3 (* (cos x) (sin x))) (* eps (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))))))) (pow (cos x) 2))))))
(pow (sin x) 2)
(+ (* 2 (* eps (* (cos x) (sin x)))) (pow (sin x) 2))
(+ (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))
(+ (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))) (pow (cos x) 2)))))) (pow (sin x) 2))
(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))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x)))))))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x))))))))
(* 2 (sin x))
(+ (* 2 (sin x)) (* eps (cos x)))
(+ (* 2 (sin x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (* 2 (sin x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 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)))
(cos eps)
(sin (* 1/2 eps))
(* -1 (* eps (+ 1/2 (/ x 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)))))
(/ (- (pow (sin (- x (* -1 eps))) 2) (pow (sin x) 2)) (+ (sin x) (sin (- x (* -1 eps)))))
(- (pow (sin (- x (* -1 eps))) 2) (pow (sin x) 2))
(pow (sin (- x (* -1 eps))) 2)
(sin (- x (* -1 eps)))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(+ (sin x) (sin (- x (* -1 eps))))
Calls

6 calls:

TimeVariablePointExpression
27.0ms
eps
@-inf
((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (+ (* (sin x) (cos eps)) (* (sin eps) (cos x))) (sin x)) (+ (* (sin x) (cos eps)) (* (sin eps) (cos x))) (sin x) (cos eps) (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (pow (sin (+ eps x)) 2) (sin (+ eps x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (sin eps) (cos x)) (+ (sin x) (sin (+ eps x))))
8.0ms
eps
@0
((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (+ (* (sin x) (cos eps)) (* (sin eps) (cos x))) (sin x)) (+ (* (sin x) (cos eps)) (* (sin eps) (cos x))) (sin x) (cos eps) (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (pow (sin (+ eps x)) 2) (sin (+ eps x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (sin eps) (cos x)) (+ (sin x) (sin (+ eps x))))
6.0ms
x
@inf
((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (+ (* (sin x) (cos eps)) (* (sin eps) (cos x))) (sin x)) (+ (* (sin x) (cos eps)) (* (sin eps) (cos x))) (sin x) (cos eps) (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (pow (sin (+ eps x)) 2) (sin (+ eps x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (sin eps) (cos x)) (+ (sin x) (sin (+ eps x))))
5.0ms
eps
@inf
((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (+ (* (sin x) (cos eps)) (* (sin eps) (cos x))) (sin x)) (+ (* (sin x) (cos eps)) (* (sin eps) (cos x))) (sin x) (cos eps) (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (pow (sin (+ eps x)) 2) (sin (+ eps x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (sin eps) (cos x)) (+ (sin x) (sin (+ eps x))))
5.0ms
x
@0
((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (+ (* (sin x) (cos eps)) (* (sin eps) (cos x))) (sin x)) (+ (* (sin x) (cos eps)) (* (sin eps) (cos x))) (sin x) (cos eps) (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (pow (sin (+ eps x)) 2) (sin (+ eps x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (sin eps) (cos x)) (+ (sin x) (sin (+ eps x))))

simplify192.0ms (1.6%)

Memory
24.7MiB live, 360.5MiB allocated; 40ms collecting garbage
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05452332
120192265
277272238
081082062
Stop Event
iter limit
node limit
Counts
138 → 136
Calls
Call 1
Inputs
(* -1/2 eps)
(+ (* -1 x) (* -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 (* (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 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
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 (- (* 2 (cos eps)) (+ 1 (cos eps)))))
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))))) (+ 1 (cos eps)))))
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (+ (* x (- (+ 1/6 (+ (* -1 (cos eps)) (* -1/3 (cos eps)))) (+ (* -1/2 (- (* 2 (cos eps)) (+ 1 (cos eps)))) (+ (* -1/6 (cos eps)) (/ (* (+ 1 (cos eps)) (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (sin eps)))))) (/ (pow (cos eps) 2) (sin eps)))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))))) (+ 1 (cos eps)))))
(pow (sin eps) 2)
(+ (* 2 (* x (* (cos eps) (sin eps)))) (pow (sin eps) 2))
(+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (- (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2)) 1)))) (pow (sin eps) 2))
(+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (- (+ (* -1 (pow (sin eps) 2)) (+ (* x (+ (* -1 (* (cos eps) (sin eps))) (* -1/3 (* (cos eps) (sin eps))))) (pow (cos eps) 2))) 1)))) (pow (sin eps) 2))
(+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))))) (pow (sin eps) 2))
(+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (+ (* -1 (pow (sin eps) 2)) (+ (* x (+ (* -1 (* (cos eps) (sin eps))) (* -1/3 (* (cos eps) (sin eps))))) (pow (cos eps) 2)))))) (pow (sin eps) 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))))))
(+ (sin eps) (* -1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps))))))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps)))))))
(+ (sin eps) (* x (+ 1 (cos eps))))
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps)))))))
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (- (* -1/6 (cos eps)) 1/6))))))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(+ (* (cos eps) (sin x)) (* (cos x) (sin eps)))
(sin x)
(/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x))))
(- (pow (sin (+ eps x)) 2) (pow (sin x) 2))
(pow (sin (+ eps x)) 2)
(sin (+ eps x))
(cos (* -1/2 (+ eps (* 2 x))))
(* (cos x) (sin eps))
(+ (sin x) (sin (+ eps x)))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(/ (- (pow (sin (- eps (* -1 x))) 2) (pow (sin x) 2)) (+ (sin x) (sin (- eps (* -1 x)))))
(- (pow (sin (- eps (* -1 x))) 2) (pow (sin x) 2))
(pow (sin (- eps (* -1 x))) 2)
(sin (- eps (* -1 x)))
(cos (* -1/2 (- eps (* -2 x))))
(+ (sin x) (sin (- eps (* -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 (+ 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 (+ (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))))
(cos 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))))))))
(+ 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)))
(* eps (+ (cos x) (* eps (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x)))))))
(* eps (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x))))))) (* 1/2 (/ (pow (cos x) 2) (sin x)))))))
(* eps (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (+ (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))) (sin x))) (+ (* -1/4 (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (+ (* -1/12 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x)))))) (sin x)))))))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x))))))) (* 1/2 (/ (pow (cos x) 2) (sin x)))))))
(* 2 (* eps (* (cos x) (sin x))))
(* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))
(* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))) (pow (cos x) 2))))))
(* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (+ (* -1/3 (* (cos x) (sin x))) (* eps (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))))))) (pow (cos x) 2))))))
(pow (sin x) 2)
(+ (* 2 (* eps (* (cos x) (sin x)))) (pow (sin x) 2))
(+ (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))
(+ (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))) (pow (cos x) 2)))))) (pow (sin x) 2))
(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))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x)))))))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x))))))))
(* 2 (sin x))
(+ (* 2 (sin x)) (* eps (cos x)))
(+ (* 2 (sin x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (* 2 (sin x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 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)))
(cos eps)
(sin (* 1/2 eps))
(* -1 (* eps (+ 1/2 (/ x 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)))))
(/ (- (pow (sin (- x (* -1 eps))) 2) (pow (sin x) 2)) (+ (sin x) (sin (- x (* -1 eps)))))
(- (pow (sin (- x (* -1 eps))) 2) (pow (sin x) 2))
(pow (sin (- x (* -1 eps))) 2)
(sin (- x (* -1 eps)))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(+ (sin x) (sin (- x (* -1 eps))))
Outputs
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1 x) (* -1/2 eps))
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)
(* 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 (neg.f64 x) x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) 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 (+ (* 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) (fma.f64 (*.f64 (*.f64 #s(literal -1/3 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (PI.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 #s(literal -1/6 binary64) (cos.f64 eps) #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 (* (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 eps (+.f64 x eps)) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) x)) x)) x eps)
1
#s(literal 1 binary64)
(+ 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 (+.f64 x eps) #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 (-.f64 (*.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))
(* eps x)
(*.f64 x eps)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x)
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x)
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/120 binary64) eps)) x) x (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x 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 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) x (sin.f64 eps))
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)) (-.f64 (*.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)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)
(+ (sin eps) (* x (- (* 2 (cos eps)) (+ 1 (cos eps)))))
(fma.f64 (-.f64 (-.f64 (*.f64 (cos.f64 eps) #s(literal 2 binary64)) #s(literal 1 binary64)) (cos.f64 eps)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))))) (+ 1 (cos eps)))))
(fma.f64 (fma.f64 (-.f64 (fma.f64 (sin.f64 eps) #s(literal -1 binary64) (/.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (sin.f64 eps))) (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (fma.f64 (-.f64 (-.f64 (*.f64 (cos.f64 eps) #s(literal 2 binary64)) #s(literal 1 binary64)) (cos.f64 eps)) (+.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (sin.f64 eps)))) x (-.f64 (-.f64 (*.f64 (cos.f64 eps) #s(literal 2 binary64)) #s(literal 1 binary64)) (cos.f64 eps))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (+ (* x (- (+ 1/6 (+ (* -1 (cos eps)) (* -1/3 (cos eps)))) (+ (* -1/2 (- (* 2 (cos eps)) (+ 1 (cos eps)))) (+ (* -1/6 (cos eps)) (/ (* (+ 1 (cos eps)) (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (sin eps)))))) (/ (pow (cos eps) 2) (sin eps)))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))))) (+ 1 (cos eps)))))
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(* eps (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (+ (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))) (sin x))) (+ (* -1/4 (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (+ (* -1/12 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x)))))) (sin x)))))))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x))))))) (* 1/2 (/ (pow (cos x) 2) (sin x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (sin.f64 x)) #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (sin.f64 x)))) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) (-.f64 (fma.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 x)) (/.f64 #s(literal -4/3 binary64) (sin.f64 x))) #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (cos.f64 x))) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) (/.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 x)))) (*.f64 #s(literal -1/12 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (sin.f64 x))) eps (-.f64 (fma.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 x)) (/.f64 #s(literal -4/3 binary64) (sin.f64 x))) #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (cos.f64 x))) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) (/.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 x))))) eps (/.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (sin.f64 x))) eps (cos.f64 x)) eps)
(* 2 (* eps (* (cos x) (sin x))))
(*.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x))
(* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))
(*.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x) (*.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) eps)
(* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))) (pow (cos x) 2))))))
(*.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x) (*.f64 (fma.f64 (*.f64 (*.f64 (cos.f64 x) eps) (sin.f64 x)) #s(literal -4/3 binary64) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) eps)
(* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (+ (* -1/3 (* (cos x) (sin x))) (* eps (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))))))) (pow (cos x) 2))))))
(*.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x) (*.f64 (fma.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 (cos.f64 x) (sin.f64 x)) (*.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) eps)) eps (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) eps)
(pow (sin x) 2)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(+ (* 2 (* eps (* (cos x) (sin x)))) (pow (sin x) 2))
(fma.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))
(fma.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x) (*.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) eps (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))) (pow (cos x) 2)))))) (pow (sin x) 2))
(fma.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x) (*.f64 (fma.f64 (*.f64 (*.f64 (cos.f64 x) eps) (sin.f64 x)) #s(literal -4/3 binary64) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) eps (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (neg.f64 (sin.f64 x)) (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (cos.f64 x) eps) (*.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 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) (neg.f64 (sin.f64 x)) (*.f64 #s(literal -1/8 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.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 (-.f64 (*.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))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) eps) eps) #s(literal 1/48 binary64)) (*.f64 #s(literal 1/2 binary64) eps))
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(*.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) (cos.f64 x)) eps)
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x)))))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 #s(literal 1/120 binary64) eps) eps #s(literal -1/6 binary64))) (*.f64 (cos.f64 x) eps))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x))))))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 (cos.f64 x) (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64))) (*.f64 eps eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 (cos.f64 x) eps))
(* 2 (sin x))
(*.f64 #s(literal 2 binary64) (sin.f64 x))
(+ (* 2 (sin x)) (* eps (cos x)))
(fma.f64 (cos.f64 x) eps (*.f64 #s(literal 2 binary64) (sin.f64 x)))
(+ (* 2 (sin x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 #s(literal 2 binary64) (sin.f64 x)))
(+ (* 2 (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) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps (*.f64 #s(literal 2 binary64) (sin.f64 x)))
(* eps (- (* -1 (/ x eps)) 1/2))
(*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #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 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps)
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) 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))))
(*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 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)))))
(*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps))))
(/ (- (pow (sin (- x (* -1 eps))) 2) (pow (sin x) 2)) (+ (sin x) (sin (- x (* -1 eps)))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(- (pow (sin (- x (* -1 eps))) 2) (pow (sin x) 2))
(-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(pow (sin (- x (* -1 eps))) 2)
(pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 x eps))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(+ (sin x) (sin (- x (* -1 eps))))
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

rewrite236.0ms (2%)

Memory
26.0MiB live, 300.4MiB allocated; 28ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037177
065145
1288145
22159145
09044145
Stop Event
iter limit
node limit
iter limit
Counts
22 → 606
Calls
Call 1
Inputs
(+.f64 #s(literal 0 binary64) eps)
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #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 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x)))
(sin.f64 x)
(cos.f64 eps)
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))
(sin.f64 (+.f64 eps x))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
(*.f64 (sin.f64 eps) (cos.f64 x))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
Outputs
(pow.f64 eps #s(literal 1 binary64))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 (neg.f64 eps)) (*.f64 (*.f64 eps eps) (neg.f64 (neg.f64 (*.f64 eps eps))))) (*.f64 (*.f64 eps eps) (neg.f64 (neg.f64 eps))))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 (*.f64 eps eps)) (*.f64 (*.f64 eps eps) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))) (*.f64 (*.f64 eps eps) (neg.f64 (*.f64 eps eps))))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 eps) (*.f64 (*.f64 eps eps) (neg.f64 (*.f64 eps eps)))) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))
(/.f64 (fma.f64 #s(literal 0 binary64) (-.f64 eps #s(literal 0 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64))))
(/.f64 (fma.f64 #s(literal 0 binary64) (*.f64 eps eps) (*.f64 (*.f64 eps eps) (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 eps #s(literal 4 binary64)))
(/.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 eps))
(/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps)) (neg.f64 eps))
(+.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps)) eps)
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
eps
(/.f64 (fma.f64 (neg.f64 eps) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 (*.f64 x #s(literal 2 binary64))))) #s(literal 4 binary64))
(/.f64 (fma.f64 (neg.f64 eps) #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 2 binary64)))) #s(literal -4 binary64))
(/.f64 (fma.f64 (neg.f64 (*.f64 eps eps)) #s(literal 2 binary64) (*.f64 (*.f64 (neg.f64 eps) #s(literal -2 binary64)) (neg.f64 (*.f64 x #s(literal 2 binary64))))) (*.f64 (*.f64 (neg.f64 eps) #s(literal -2 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (neg.f64 (*.f64 eps eps)) #s(literal -2 binary64) (*.f64 (*.f64 (neg.f64 eps) #s(literal -2 binary64)) (*.f64 x #s(literal 2 binary64)))) (*.f64 (*.f64 (neg.f64 eps) #s(literal -2 binary64)) #s(literal -2 binary64)))
(/.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -2 binary64)) (neg.f64 (*.f64 x #s(literal 2 binary64))))) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -2 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -2 binary64) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -2 binary64)) (*.f64 x #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -2 binary64)) #s(literal -2 binary64)))
(/.f64 (fma.f64 eps #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) (neg.f64 (*.f64 x #s(literal 2 binary64))))) #s(literal -4 binary64))
(/.f64 (fma.f64 eps #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) (*.f64 x #s(literal 2 binary64)))) #s(literal 4 binary64))
(/.f64 (fma.f64 (neg.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 eps))) #s(literal 4 binary64))
(/.f64 (fma.f64 (neg.f64 (*.f64 x #s(literal 2 binary64))) (*.f64 (neg.f64 eps) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (neg.f64 (*.f64 eps eps)))) (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 eps) #s(literal -2 binary64))))
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(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (sin.f64 (+.f64 x eps)) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 (fma.f64 (sin.f64 (+.f64 x eps)) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)))) (*.f64 (fma.f64 (sin.f64 (+.f64 x eps)) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 (+.f64 x eps)) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (+.f64 (sin.f64 (/.f64 (-.f64 (fma.f64 x #s(literal 2 binary64) eps) (-.f64 x (+.f64 x eps))) #s(literal 2 binary64))) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 (fma.f64 x #s(literal 2 binary64) eps) (-.f64 x (+.f64 x eps))) #s(literal 2 binary64))) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))))))) #s(literal 4 binary64))
(/.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sin.f64 (+.f64 x eps)) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64))) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))))
(/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (sin.f64 (+.f64 x eps)) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(fma.f64 (neg.f64 (sqrt.f64 (sin.f64 x))) (neg.f64 (sqrt.f64 (sin.f64 x))) (sin.f64 (+.f64 x eps)))
(fma.f64 (neg.f64 (sqrt.f64 (sin.f64 (+.f64 x eps)))) (neg.f64 (sqrt.f64 (sin.f64 (+.f64 x eps)))) (sin.f64 x))
(fma.f64 (fabs.f64 (sqrt.f64 (sin.f64 x))) (fabs.f64 (sqrt.f64 (sin.f64 x))) (sin.f64 (+.f64 x eps)))
(fma.f64 (fabs.f64 (sqrt.f64 (sin.f64 (+.f64 x eps)))) (fabs.f64 (sqrt.f64 (sin.f64 (+.f64 x eps)))) (sin.f64 x))
(fma.f64 (pow.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) #s(literal 1 binary64)) (sin.f64 x))
(fma.f64 (pow.f64 (sqrt.f64 (sin.f64 x)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (sin.f64 x)) #s(literal 1 binary64)) (sin.f64 (+.f64 x eps)))
(fma.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) (sqrt.f64 (sin.f64 (+.f64 x eps))) (sin.f64 x))
(fma.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (sin.f64 x)) (sin.f64 (+.f64 x eps)))
(fma.f64 (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))))
(fma.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 eps) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 x)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 x)))
(-.f64 (+.f64 (sin.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x))) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)))
(-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps)))) (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps)))))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (-.f64 (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (sin.f64 x)))
(+.f64 (+.f64 (sin.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x))) (*.f64 (cos.f64 x) (sin.f64 eps)))
(+.f64 (+.f64 (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (cos.f64 eps) (sin.f64 x)))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (sin.f64 (+.f64 x eps)) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (sin.f64 (+.f64 x eps)) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))
(+.f64 (*.f64 (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))))
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 x)))
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 x)))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 x eps)))

eval149.0ms (1.3%)

Memory
-37.1MiB live, 190.2MiB allocated; 49ms collecting garbage
Compiler

Compiled 18 546 to 2 584 computations (86.1% saved)

prune23.0ms (0.2%)

Memory
-20.4MiB live, 37.0MiB allocated; 5ms collecting garbage
Pruning

19 alts after pruning (16 fresh and 3 done)

PrunedKeptTotal
New64114655
Fresh224
Picked325
Done011
Total64619665
Accuracy
100.0%
Counts
665 → 19
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.9%
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
61.9%
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
61.6%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
28.0%
(*.f64 (*.f64 (sin.f64 (/.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (-.f64 eps #s(literal 0 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
100.0%
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64))))))
99.3%
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #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))))
99.0%
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.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))))
98.7%
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.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))))
98.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
97.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
97.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
96.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps))
96.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
5.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
95.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
96.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps)))
95.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
95.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)))
99.7%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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))))
Compiler

Compiled 828 to 588 computations (29% saved)

simplify107.0ms (0.9%)

Memory
-21.0MiB live, 71.5MiB allocated; 5ms collecting garbage
Algorithm
egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
cost-diff0
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
cost-diff0
(*.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)))
cost-diff0
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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))))
cost-diff0
#s(approx (* (sin x) eps) (*.f64 x eps))
cost-diff0
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
cost-diff0
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
cost-diff0
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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)))
cost-diff0
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps))
cost-diff1
(-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64))
cost-diff0
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
cost-diff0
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
cost-diff1
(*.f64 x #s(literal -1 binary64))
cost-diff1
(cos.f64 (*.f64 x #s(literal -1 binary64)))
cost-diff1
(-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64)))))
cost-diff2
(+.f64 #s(literal 0 binary64) eps)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
065433
099423
1175407
2422404
31208403
44016403
08354389
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64))))))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
(/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))
(+.f64 #s(literal 0 binary64) eps)
#s(literal 0 binary64)
eps
#s(literal 2 binary64)
(-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64)))))
(*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64))))
(cos.f64 (/.f64 eps #s(literal -2 binary64)))
(/.f64 eps #s(literal -2 binary64))
#s(literal -2 binary64)
(cos.f64 (*.f64 x #s(literal -1 binary64)))
(*.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64))))
(sin.f64 (/.f64 eps #s(literal -2 binary64)))
(sin.f64 (*.f64 x #s(literal -1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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)))
(fma.f64 (fma.f64 (-.f64 (*.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))
(fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/12 binary64) (*.f64 x eps))
#s(literal 1/12 binary64)
(*.f64 x eps)
x
eps
#s(literal 1/2 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
#s(approx (* (sin x) eps) (*.f64 x eps))
(*.f64 x eps)
x
eps
#s(literal -1/2 binary64)
(cos.f64 x)
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
#s(literal 1/2 binary64)
eps
x
#s(literal 2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
Outputs
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64))))))
(*.f64 (fma.f64 (sin.f64 x) (sin.f64 (/.f64 eps #s(literal -2 binary64))) (*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64))))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) #s(literal -2 binary64)))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
(*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) #s(literal -2 binary64))
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
(sin.f64 (/.f64 eps #s(literal 2 binary64)))
(/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))
(/.f64 eps #s(literal 2 binary64))
(+.f64 #s(literal 0 binary64) eps)
eps
#s(literal 0 binary64)
eps
#s(literal 2 binary64)
(-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64)))))
(fma.f64 (sin.f64 x) (sin.f64 (/.f64 eps #s(literal -2 binary64))) (*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))))
(*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64))))
(*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64))))
(cos.f64 (/.f64 eps #s(literal -2 binary64)))
(cos.f64 (/.f64 eps #s(literal 2 binary64)))
(/.f64 eps #s(literal -2 binary64))
#s(literal -2 binary64)
(cos.f64 (*.f64 x #s(literal -1 binary64)))
(cos.f64 x)
(*.f64 x #s(literal -1 binary64))
(neg.f64 x)
x
#s(literal -1 binary64)
(*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64))))
(*.f64 (sin.f64 x) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(sin.f64 (/.f64 eps #s(literal -2 binary64)))
(sin.f64 (*.f64 x #s(literal -1 binary64)))
(neg.f64 (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps)
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (-.f64 (*.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))
(fma.f64 (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))
(*.f64 #s(literal 1/12 binary64) (*.f64 x eps))
(*.f64 (*.f64 x eps) #s(literal 1/12 binary64))
#s(literal 1/12 binary64)
(*.f64 x eps)
x
eps
#s(literal 1/2 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
#s(approx (* (sin x) eps) (*.f64 x eps))
(*.f64 x eps)
x
eps
#s(literal -1/2 binary64)
(cos.f64 x)
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))))
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
#s(literal 1/2 binary64)
eps
x
#s(literal 2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)

localize234.0ms (2%)

Memory
23.6MiB live, 166.2MiB allocated; 13ms collecting garbage
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
accuracy0.0
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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))))
accuracy0.0234375
(*.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)))
accuracy0.15970553043532218
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
accuracy0.0078125
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
accuracy0.015625
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
accuracy0.7864239630799743
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
accuracy2.9041579007667697
#s(approx (* (sin x) eps) (*.f64 x eps))
accuracy0.015625
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps)
accuracy0.15625
(*.f64 #s(literal 1/12 binary64) (*.f64 x eps))
accuracy0.7864239630799743
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps))
accuracy2.3681380844757673
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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)))
accuracy0.015625
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
accuracy0.7864239630799743
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
accuracy2.9804340930301367
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
accuracy0.0078125
(*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64))))
accuracy0.01171875
(-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64)))))
accuracy0.01953125
(*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64))))
accuracy0.0234375
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64))))))
Samples
107.0ms168×1valid
47.0ms87×0valid
1.0ms3valid
Compiler

Compiled 326 to 54 computations (83.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 108.0ms
ival-mult: 34.0ms (31.6% of total)
adjust: 24.0ms (22.3% of total)
ival-cos: 12.0ms (11.1% of total)
ival-add: 11.0ms (10.2% of total)
ival-sin: 11.0ms (10.2% of total)
ival-sub: 6.0ms (5.6% of total)
ival-div: 5.0ms (4.6% of total)
const: 4.0ms (3.7% of total)
exact: 1.0ms (0.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series38.0ms (0.3%)

Memory
0.0MiB live, 42.6MiB allocated; 8ms collecting garbage
Counts
24 → 113
Calls
Call 1
Inputs
(+.f64 #s(literal 0 binary64) eps)
(-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64)))))
(cos.f64 (*.f64 x #s(literal -1 binary64)))
(*.f64 x #s(literal -1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
#s(approx (* (sin x) eps) (*.f64 x eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64))))))
(*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64))))
(*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64))))
(*.f64 #s(literal 1/12 binary64) (*.f64 x eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
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))))))
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)))
(* -1 x)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ 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
(- (* 1/12 (* eps x)) 1/2)
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 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))))))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (cos (* 1/2 eps)))
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps)))))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps)))))))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(* -1 (* x (sin (* -1/2 eps))))
(* x (+ (* -1 (sin (* -1/2 eps))) (* 1/6 (* (pow x 2) (sin (* -1/2 eps))))))
(* x (+ (* -1 (sin (* -1/2 eps))) (* (pow x 2) (+ (* -1/120 (* (pow x 2) (sin (* -1/2 eps)))) (* 1/6 (sin (* -1/2 eps)))))))
(* x (+ (* -1 (sin (* -1/2 eps))) (* (pow x 2) (+ (* 1/6 (sin (* -1/2 eps))) (* (pow x 2) (+ (* -1/120 (sin (* -1/2 eps))) (* 1/5040 (* (pow x 2) (sin (* -1/2 eps))))))))))
(+ (cos (* -1/2 eps)) (* -1/2 (* (pow x 2) (cos (* -1/2 eps)))))
(+ (cos (* -1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* -1/2 eps))) (* 1/24 (* (pow x 2) (cos (* -1/2 eps)))))))
(+ (cos (* -1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* -1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* -1/2 eps)))) (* 1/24 (cos (* -1/2 eps))))))))
(* 1/12 (* eps x))
(- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))
(cos (* -1 x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* x (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* eps (sin x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (cos (+ x (* 1/2 eps))))
(cos (+ x (* 1/2 eps)))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))))
(* (sin (* -1 x)) (sin (* -1/2 eps)))
(* (cos (* -1 x)) (cos (* -1/2 eps)))
(- (sin (- eps (* -1 x))) (sin x))
(* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (cos (- (* 1/2 eps) (* -1 x))))
(cos (- (* 1/2 eps) (* -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 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)))))))))
(cos 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)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (cos x))
(+ (* -1 (* eps (sin x))) (* 2 (cos x)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(* -1/2 (* eps (sin (* -1 x))))
(* eps (+ (* -1/2 (sin (* -1 x))) (* 1/48 (* (pow eps 2) (sin (* -1 x))))))
(* eps (+ (* -1/2 (sin (* -1 x))) (* (pow eps 2) (+ (* -1/3840 (* (pow eps 2) (sin (* -1 x)))) (* 1/48 (sin (* -1 x)))))))
(* eps (+ (* -1/2 (sin (* -1 x))) (* (pow eps 2) (+ (* 1/48 (sin (* -1 x))) (* (pow eps 2) (+ (* -1/3840 (sin (* -1 x))) (* 1/645120 (* (pow eps 2) (sin (* -1 x))))))))))
(+ (cos (* -1 x)) (* -1/8 (* (pow eps 2) (cos (* -1 x)))))
(+ (cos (* -1 x)) (* (pow eps 2) (+ (* -1/8 (cos (* -1 x))) (* 1/384 (* (pow eps 2) (cos (* -1 x)))))))
(+ (cos (* -1 x)) (* (pow eps 2) (+ (* -1/8 (cos (* -1 x))) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos (* -1 x)))) (* 1/384 (cos (* -1 x))))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* -1/2 (* (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)))
(* eps (- (* 1/12 x) (* 1/2 (/ 1 eps))))
(sin (* 1/2 eps))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (cos (- x (* -1/2 eps))))
(cos (- x (* -1/2 eps)))
Calls

6 calls:

TimeVariablePointExpression
10.0ms
x
@inf
((+ 0 eps) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1)))) (cos (* x -1)) (* x -1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (* 1/12 (* x eps)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (sin (/ eps -2)) (sin (* x -1))) (* (cos (/ eps -2)) (cos (* x -1))) (* 1/12 (* x eps)) (sin (* 1/2 eps)))
9.0ms
x
@-inf
((+ 0 eps) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1)))) (cos (* x -1)) (* x -1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (* 1/12 (* x eps)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (sin (/ eps -2)) (sin (* x -1))) (* (cos (/ eps -2)) (cos (* x -1))) (* 1/12 (* x eps)) (sin (* 1/2 eps)))
5.0ms
eps
@-inf
((+ 0 eps) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1)))) (cos (* x -1)) (* x -1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (* 1/12 (* x eps)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (sin (/ eps -2)) (sin (* x -1))) (* (cos (/ eps -2)) (cos (* x -1))) (* 1/12 (* x eps)) (sin (* 1/2 eps)))
5.0ms
eps
@inf
((+ 0 eps) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1)))) (cos (* x -1)) (* x -1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (* 1/12 (* x eps)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (sin (/ eps -2)) (sin (* x -1))) (* (cos (/ eps -2)) (cos (* x -1))) (* 1/12 (* x eps)) (sin (* 1/2 eps)))
4.0ms
eps
@0
((+ 0 eps) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1)))) (cos (* x -1)) (* x -1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (* 1/12 (* x eps)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (sin (/ eps -2)) (sin (* x -1))) (* (cos (/ eps -2)) (cos (* x -1))) (* 1/12 (* x eps)) (sin (* 1/2 eps)))

simplify126.0ms (1.1%)

Memory
5.8MiB live, 148.3MiB allocated; 14ms collecting garbage
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04571689
117851578
266181556
084491422
Stop Event
iter limit
node limit
Counts
113 → 112
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))))))
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)))
(* -1 x)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ 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
(- (* 1/12 (* eps x)) 1/2)
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 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))))))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (cos (* 1/2 eps)))
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps)))))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps)))))))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(* -1 (* x (sin (* -1/2 eps))))
(* x (+ (* -1 (sin (* -1/2 eps))) (* 1/6 (* (pow x 2) (sin (* -1/2 eps))))))
(* x (+ (* -1 (sin (* -1/2 eps))) (* (pow x 2) (+ (* -1/120 (* (pow x 2) (sin (* -1/2 eps)))) (* 1/6 (sin (* -1/2 eps)))))))
(* x (+ (* -1 (sin (* -1/2 eps))) (* (pow x 2) (+ (* 1/6 (sin (* -1/2 eps))) (* (pow x 2) (+ (* -1/120 (sin (* -1/2 eps))) (* 1/5040 (* (pow x 2) (sin (* -1/2 eps))))))))))
(+ (cos (* -1/2 eps)) (* -1/2 (* (pow x 2) (cos (* -1/2 eps)))))
(+ (cos (* -1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* -1/2 eps))) (* 1/24 (* (pow x 2) (cos (* -1/2 eps)))))))
(+ (cos (* -1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* -1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* -1/2 eps)))) (* 1/24 (cos (* -1/2 eps))))))))
(* 1/12 (* eps x))
(- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))
(cos (* -1 x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* x (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* eps (sin x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (cos (+ x (* 1/2 eps))))
(cos (+ x (* 1/2 eps)))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))))
(* (sin (* -1 x)) (sin (* -1/2 eps)))
(* (cos (* -1 x)) (cos (* -1/2 eps)))
(- (sin (- eps (* -1 x))) (sin x))
(* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (cos (- (* 1/2 eps) (* -1 x))))
(cos (- (* 1/2 eps) (* -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 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)))))))))
(cos 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)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (cos x))
(+ (* -1 (* eps (sin x))) (* 2 (cos x)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(* -1/2 (* eps (sin (* -1 x))))
(* eps (+ (* -1/2 (sin (* -1 x))) (* 1/48 (* (pow eps 2) (sin (* -1 x))))))
(* eps (+ (* -1/2 (sin (* -1 x))) (* (pow eps 2) (+ (* -1/3840 (* (pow eps 2) (sin (* -1 x)))) (* 1/48 (sin (* -1 x)))))))
(* eps (+ (* -1/2 (sin (* -1 x))) (* (pow eps 2) (+ (* 1/48 (sin (* -1 x))) (* (pow eps 2) (+ (* -1/3840 (sin (* -1 x))) (* 1/645120 (* (pow eps 2) (sin (* -1 x))))))))))
(+ (cos (* -1 x)) (* -1/8 (* (pow eps 2) (cos (* -1 x)))))
(+ (cos (* -1 x)) (* (pow eps 2) (+ (* -1/8 (cos (* -1 x))) (* 1/384 (* (pow eps 2) (cos (* -1 x)))))))
(+ (cos (* -1 x)) (* (pow eps 2) (+ (* -1/8 (cos (* -1 x))) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos (* -1 x)))) (* 1/384 (cos (* -1 x))))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* -1/2 (* (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)))
(* eps (- (* 1/12 x) (* 1/2 (/ 1 eps))))
(sin (* 1/2 eps))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (cos (- x (* -1/2 eps))))
(cos (- x (* -1/2 eps)))
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 (*.f64 #s(literal -1/6 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) 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 (-.f64 (*.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)))
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(* -1 x)
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(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
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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)))))
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(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
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-1/2
#s(literal -1/2 binary64)
(- (* 1/12 (* eps x)) 1/2)
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(cos (* 1/2 eps))
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(* x (+ (* -1 (sin (* -1/2 eps))) (* (pow x 2) (+ (* 1/6 (sin (* -1/2 eps))) (* (pow x 2) (+ (* -1/120 (sin (* -1/2 eps))) (* 1/5040 (* (pow x 2) (sin (* -1/2 eps))))))))))
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(cos (* -1 x))
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(* eps (sin x))
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(fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 x) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (neg.f64 (sin.f64 x))) eps (*.f64 #s(literal 2 binary64) (cos.f64 x)))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (*.f64 (fma.f64 #s(literal 1/48 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/8 binary64) (cos.f64 x))) eps)) eps (cos.f64 x))
(* -1/2 (* eps (sin (* -1 x))))
(*.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* -1/2 (sin (* -1 x))) (* 1/48 (* (pow eps 2) (sin (* -1 x))))))
(*.f64 (*.f64 (neg.f64 (sin.f64 x)) (fma.f64 (*.f64 #s(literal 1/48 binary64) eps) eps #s(literal -1/2 binary64))) eps)
(* eps (+ (* -1/2 (sin (* -1 x))) (* (pow eps 2) (+ (* -1/3840 (* (pow eps 2) (sin (* -1 x)))) (* 1/48 (sin (* -1 x)))))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 (neg.f64 (sin.f64 x)) (fma.f64 #s(literal -1/3840 binary64) (*.f64 eps eps) #s(literal 1/48 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 x)) eps))
(* eps (+ (* -1/2 (sin (* -1 x))) (* (pow eps 2) (+ (* 1/48 (sin (* -1 x))) (* (pow eps 2) (+ (* -1/3840 (sin (* -1 x))) (* 1/645120 (* (pow eps 2) (sin (* -1 x))))))))))
(*.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (*.f64 #s(literal 1/48 binary64) eps) eps #s(literal -1/2 binary64)) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 (neg.f64 (sin.f64 x)) (fma.f64 #s(literal 1/645120 binary64) (*.f64 eps eps) #s(literal -1/3840 binary64))))) eps)
(+ (cos (* -1 x)) (* -1/8 (* (pow eps 2) (cos (* -1 x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) eps) eps #s(literal 1 binary64)) (cos.f64 x))
(+ (cos (* -1 x)) (* (pow eps 2) (+ (* -1/8 (cos (* -1 x))) (* 1/384 (* (pow eps 2) (cos (* -1 x)))))))
(fma.f64 (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/384 binary64) (*.f64 eps eps) #s(literal -1/8 binary64))) (*.f64 eps eps) (cos.f64 x))
(+ (cos (* -1 x)) (* (pow eps 2) (+ (* -1/8 (cos (* -1 x))) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos (* -1 x)))) (* 1/384 (cos (* -1 x))))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) eps) eps #s(literal 1 binary64)) (cos.f64 x) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 (cos.f64 x) (fma.f64 #s(literal -1/46080 binary64) (*.f64 eps eps) #s(literal 1/384 binary64)))))
(* 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 (-.f64 (*.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))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) eps) eps) #s(literal 1/48 binary64)) (*.f64 #s(literal 1/2 binary64) eps))
(* -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 (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) 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)
(* eps (- (* 1/12 x) (* 1/2 (/ 1 eps))))
(*.f64 (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) eps)
(sin (* 1/2 eps))
(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)))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))
(*.f64 (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) eps)
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 2 (cos (- x (* -1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos (- x (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite254.0ms (2.1%)

Memory
-14.0MiB live, 181.2MiB allocated; 27ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
065333
099305
1339296
22737296
010925290
Stop Event
iter limit
node limit
iter limit
Counts
24 → 341
Calls
Call 1
Inputs
(+.f64 #s(literal 0 binary64) eps)
(-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64)))))
(cos.f64 (*.f64 x #s(literal -1 binary64)))
(*.f64 x #s(literal -1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
#s(approx (* (sin x) eps) (*.f64 x eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64))))))
(*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64))))
(*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64))))
(*.f64 #s(literal 1/12 binary64) (*.f64 x eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
Outputs
(pow.f64 eps #s(literal 1 binary64))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 (neg.f64 eps)) (*.f64 (*.f64 eps eps) (neg.f64 (neg.f64 (*.f64 eps eps))))) (*.f64 (*.f64 eps eps) (neg.f64 (neg.f64 eps))))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 (*.f64 eps eps)) (*.f64 (*.f64 eps eps) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))) (*.f64 (*.f64 eps eps) (neg.f64 (*.f64 eps eps))))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 eps) (*.f64 (*.f64 eps eps) (neg.f64 (*.f64 eps eps)))) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))
(/.f64 (fma.f64 #s(literal 0 binary64) (-.f64 eps #s(literal 0 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64))))
(/.f64 (fma.f64 #s(literal 0 binary64) (*.f64 eps eps) (*.f64 (*.f64 eps eps) (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 eps #s(literal 4 binary64)))
(/.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 eps))
(/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps)) (neg.f64 eps))
(+.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps)) eps)
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
eps
(/.f64 (-.f64 (neg.f64 (+.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x (/.f64 eps #s(literal -2 binary64)))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))) (neg.f64 (-.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x (/.f64 eps #s(literal -2 binary64)))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))) #s(literal -2 binary64))
(/.f64 (-.f64 (+.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) x))) (cos.f64 (-.f64 (/.f64 eps #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) x)))) (-.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x (/.f64 eps #s(literal -2 binary64)))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 (-.f64 (-.f64 (cos.f64 (-.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)))) (cos.f64 (+.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64))))) (-.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x (/.f64 eps #s(literal -2 binary64)))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 (-.f64 (-.f64 (cos.f64 (-.f64 (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))) (-.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x (/.f64 eps #s(literal -2 binary64)))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 (-.f64 (+.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (cos.f64 (-.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 eps #s(literal 2 binary64))))) (-.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x (/.f64 eps #s(literal -2 binary64)))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (neg.f64 (sin.f64 x))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (neg.f64 (sin.f64 x))) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (neg.f64 (sin.f64 x)))))))
(/.f64 (neg.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x (/.f64 eps #s(literal -2 binary64)))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))) (neg.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x (/.f64 eps #s(literal -2 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (/.f64 eps #s(literal -2 binary64)))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (/.f64 eps #s(literal -2 binary64)))) (cos.f64 (fma.f64 #s(literal 1 binary64) x (/.f64 eps #s(literal -2 binary64)))) (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(/.f64 (-.f64 (*.f64 (+.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x (/.f64 eps #s(literal -2 binary64)))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x (/.f64 eps #s(literal -2 binary64)))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))) #s(literal 4 binary64))
(/.f64 (-.f64 (+.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x (/.f64 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 #s(literal 1 binary64) x (/.f64 eps #s(literal -2 binary64)))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x (/.f64 eps #s(literal -2 binary64)))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) (cos.f64 (fma.f64 #s(literal 1 binary64) x (/.f64 eps #s(literal -2 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (/.f64 eps #s(literal -2 binary64)))) #s(literal 3 binary64))) (fma.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (/.f64 eps #s(literal -2 binary64)))) (cos.f64 (fma.f64 #s(literal 1 binary64) x (/.f64 eps #s(literal -2 binary64)))) (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 2 binary64))))
(fma.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 1 binary64)))
(fma.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 1 binary64)))
(fma.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))))
(fma.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x))))
(fma.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1 binary64) x)) (sin.f64 (/.f64 eps #s(literal -2 binary64)))))
(fma.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (neg.f64 (sin.f64 x))))
(fma.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (*.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))))
(fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))))
(fma.f64 (cos.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x))))
(fma.f64 (cos.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal 1 binary64) x)) (sin.f64 (/.f64 eps #s(literal -2 binary64)))))
(fma.f64 (cos.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (neg.f64 (sin.f64 x))))
(sin.f64 (+.f64 (-.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 eps #s(literal -2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (-.f64 (neg.f64 x) (/.f64 eps #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (-.f64 (/.f64 eps #s(literal 2 binary64)) (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
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(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 0 binary64)))
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))

eval87.0ms (0.7%)

Memory
34.4MiB live, 79.6MiB allocated; 2ms collecting garbage
Compiler

Compiled 17 539 to 2 203 computations (87.4% saved)

prune21.0ms (0.2%)

Memory
-3.6MiB live, 39.5MiB allocated; 5ms collecting garbage
Pruning

20 alts after pruning (13 fresh and 7 done)

PrunedKeptTotal
New4426448
Fresh4711
Picked145
Done033
Total44720467
Accuracy
100.0%
Counts
467 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.9%
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
61.6%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
28.0%
(*.f64 (*.f64 (sin.f64 (/.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (-.f64 eps #s(literal 0 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
52.8%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps)))
98.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
97.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
97.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
96.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps))
96.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
5.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
95.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
96.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps)))
95.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
95.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)))
100.0%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
99.7%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
99.7%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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))))
99.3%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
99.0%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
98.7%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
Compiler

Compiled 972 to 686 computations (29.4% saved)

simplify121.0ms (1%)

Memory
-31.7MiB live, 113.3MiB allocated; 16ms collecting garbage
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
cost-diff0
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
cost-diff0
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
cost-diff1
(-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64))
cost-diff0
(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
cost-diff0
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))
cost-diff0
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
cost-diff0
(*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))))
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps)))
cost-diff1
(-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
cost-diff4
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps))
cost-diff0
(*.f64 #s(literal -1/2 binary64) x)
cost-diff0
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)
cost-diff0
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
cost-diff0
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
cost-diff0
(*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))))
cost-diff0
(*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
cost-diff0
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
085618
0125614
1248610
2765604
32958600
47240600
08564577
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))))
#s(literal 2 binary64)
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(sin.f64 (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
eps
(sin.f64 x)
x
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
(cos.f64 x)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(*.f64 eps eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps)))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps))
(*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))))
(neg.f64 (*.f64 eps eps))
(*.f64 eps eps)
eps
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
(*.f64 (*.f64 x eps) #s(literal 1/12 binary64))
(*.f64 x eps)
x
#s(literal 1/12 binary64)
#s(literal 1/2 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(neg.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))
(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
#s(literal -1/2 binary64)
(sin.f64 x)
x
eps
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
#s(literal 1/2 binary64)
eps
x
#s(literal 2 binary64)
#s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
(-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64))
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
#s(literal 1/48 binary64)
Outputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (fma.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (fma.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))))
(*.f64 (fma.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(fma.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(sin.f64 (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
eps
(sin.f64 x)
x
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))
(*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
(cos.f64 x)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64)) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64)) eps))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64)) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(*.f64 eps eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (*.f64 #s(literal 1 binary64) eps) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (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)))))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps))
(*.f64 (*.f64 #s(literal 1 binary64) eps) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (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))))
(*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (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))) (*.f64 (neg.f64 eps) eps))
(neg.f64 (*.f64 eps eps))
(*.f64 (neg.f64 eps) eps)
(*.f64 eps eps)
eps
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (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)))
(fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(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))
(fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(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))
(-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/12 binary64) (*.f64 x eps) #s(literal -1/2 binary64))
(*.f64 (*.f64 x eps) #s(literal 1/12 binary64))
(*.f64 #s(literal 1/12 binary64) (*.f64 x eps))
(*.f64 x eps)
x
#s(literal 1/12 binary64)
#s(literal 1/2 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(neg.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps)
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(sin.f64 x)
x
eps
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.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)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))))
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(*.f64 #s(approx (sin (* 1/2 eps)) (*.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)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
#s(literal 1/2 binary64)
eps
x
#s(literal 2 binary64)
#s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (* 1/2 eps)) (*.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))
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(*.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)
(fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
(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))
(-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
#s(literal 1/48 binary64)

localize322.0ms (2.7%)

Memory
37.5MiB live, 327.4MiB allocated; 28ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.0234375
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
accuracy0.1328125
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))
accuracy0.15970553043532218
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
accuracy0.33445727992714375
#s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
accuracy0.015625
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps)
accuracy0.0234375
(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
accuracy0.7864239630799743
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
accuracy61.568371537310476
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))
accuracy0.15625
(*.f64 (*.f64 x eps) #s(literal 1/12 binary64))
accuracy0.7864239630799743
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps)))
accuracy2.3681380844757673
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
accuracy27.885842090058215
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps))
accuracy0.0
(*.f64 eps eps)
accuracy0.0
(*.f64 #s(literal -1/2 binary64) x)
accuracy0.7864239630799743
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
accuracy2.9310766400240205
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))
accuracy0.0
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
accuracy0.0078125
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))
accuracy0.01171875
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
accuracy0.0234375
(*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
Samples
201.0ms168×1valid
71.0ms87×0valid
1.0ms3valid
Compiler

Compiled 408 to 78 computations (80.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 204.0ms
ival-mult: 90.0ms (44.2% of total)
adjust: 41.0ms (20.1% of total)
ival-cos: 15.0ms (7.4% of total)
ival-add: 15.0ms (7.4% of total)
ival-sin: 13.0ms (6.4% of total)
const: 11.0ms (5.4% of total)
ival-div: 8.0ms (3.9% of total)
ival-sub: 7.0ms (3.4% of total)
ival-neg: 2.0ms (1% of total)
exact: 1.0ms (0.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series48.0ms (0.4%)

Memory
-17.1MiB live, 28.4MiB allocated; 6ms collecting garbage
Counts
27 → 125
Calls
Call 1
Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))))
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)
(*.f64 #s(literal -1/2 binary64) x)
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps))
(-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps)))
(*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))
(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))
(*.f64 eps eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
(*.f64 (*.f64 x eps) #s(literal 1/12 binary64))
#s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))
Outputs
(* 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))))))))))
(* 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))))))))))
(* 2 (cos (* 1/2 eps)))
(+ (* 2 (cos (* 1/2 eps))) (* 2 (* x (sin (* -1/2 eps)))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -1 (* x (cos (* 1/2 eps)))) (* 2 (sin (* -1/2 eps))))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* 2 (sin (* -1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* -1/3 (* x (sin (* -1/2 eps)))))))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* 1/2 eps)) (* x (+ (sin (* -1/2 eps)) (* -1/2 (* x (cos (* 1/2 eps)))))))
(+ (cos (* 1/2 eps)) (* x (+ (sin (* -1/2 eps)) (* x (+ (* -1/2 (cos (* 1/2 eps))) (* -1/6 (* x (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 (* (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)))))))
(* -1/2 x)
-1/2
(- (* 1/12 (* eps x)) 1/2)
(* -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)))))))
1
(+ 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 (* eps x))
(* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps)))))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps)))))))))
(+ (cos (* 1/2 eps)) (* -1/2 (* (pow x 2) (cos (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* 1/24 (* (pow x 2) (cos (* 1/2 eps)))))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/24 (cos (* 1/2 eps))))))))
(* 1/12 (* eps x))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* -1/2 eps))))))
(* 2 (+ (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* -1/2 eps)))))
(+ (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* -1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) x))
(* x (+ (* -1/2 (pow eps 2)) (/ eps x)))
(* x (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (* eps (sin x)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (cos (+ x (* 1/2 eps))))
(* (cos x) (cos (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(- (sin (- eps (* -1 x))) (sin x))
(* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))
(* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (cos (- (* 1/2 eps) (* -1 x))))
(cos (- (* 1/2 eps) (* -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 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (cos x))
(+ (* -1 (* eps (sin x))) (* 2 (cos x)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))
(cos x)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))))))
(* 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 (* -1/2 (* eps x))))
(* -1 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (cos x)) (* 1/2 (* eps (sin x)))))
-1/48
(- (* 1/3840 (pow eps 2)) 1/48)
(+ (cos x) (* -1/8 (* (pow eps 2) (cos x))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* 1/384 (* (pow eps 2) (cos x))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos x))) (* 1/384 (cos x)))))))
(pow eps 2)
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(* 1/3840 (pow eps 2))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* eps (- (* 1/12 x) (* 1/2 (/ 1 eps))))
(* 1/2 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(sin (* 1/2 eps))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))
(* -1 (* (pow eps 3) (+ (* -1/2 (sin x)) (/ (cos x) eps))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (cos (- x (* -1/2 eps))))
(cos (- x (* -1/2 eps)))
Calls

6 calls:

TimeVariablePointExpression
17.0ms
x
@0
((* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos (* 1/2 eps)) (cos x)))) (sin (* 1/2 eps))) (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos (* 1/2 eps)) (cos x)))) (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos (* 1/2 eps)) (cos x))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps eps)) eps) (* -1/2 x) (/ (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (neg eps)) (- (* (* x eps) 1/12) 1/2) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (* -1/2 (sin x)) eps) (- (* 1/3840 (* eps eps)) 1/48) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (* (cos (* 1/2 eps)) (cos x)) (* eps eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (* x eps) 1/12) (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x)) (* 1/3840 (* eps eps)))
7.0ms
x
@inf
((* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos (* 1/2 eps)) (cos x)))) (sin (* 1/2 eps))) (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos (* 1/2 eps)) (cos x)))) (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos (* 1/2 eps)) (cos x))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps eps)) eps) (* -1/2 x) (/ (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (neg eps)) (- (* (* x eps) 1/12) 1/2) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (* -1/2 (sin x)) eps) (- (* 1/3840 (* eps eps)) 1/48) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (* (cos (* 1/2 eps)) (cos x)) (* eps eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (* x eps) 1/12) (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x)) (* 1/3840 (* eps eps)))
6.0ms
eps
@inf
((* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos (* 1/2 eps)) (cos x)))) (sin (* 1/2 eps))) (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos (* 1/2 eps)) (cos x)))) (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos (* 1/2 eps)) (cos x))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps eps)) eps) (* -1/2 x) (/ (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (neg eps)) (- (* (* x eps) 1/12) 1/2) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (* -1/2 (sin x)) eps) (- (* 1/3840 (* eps eps)) 1/48) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (* (cos (* 1/2 eps)) (cos x)) (* eps eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (* x eps) 1/12) (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x)) (* 1/3840 (* eps eps)))
6.0ms
x
@-inf
((* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos (* 1/2 eps)) (cos x)))) (sin (* 1/2 eps))) (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos (* 1/2 eps)) (cos x)))) (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos (* 1/2 eps)) (cos x))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps eps)) eps) (* -1/2 x) (/ (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (neg eps)) (- (* (* x eps) 1/12) 1/2) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (* -1/2 (sin x)) eps) (- (* 1/3840 (* eps eps)) 1/48) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (* (cos (* 1/2 eps)) (cos x)) (* eps eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (* x eps) 1/12) (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x)) (* 1/3840 (* eps eps)))
6.0ms
eps
@-inf
((* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos (* 1/2 eps)) (cos x)))) (sin (* 1/2 eps))) (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos (* 1/2 eps)) (cos x)))) (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos (* 1/2 eps)) (cos x))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps eps)) eps) (* -1/2 x) (/ (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (neg eps)) (- (* (* x eps) 1/12) 1/2) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (* -1/2 (sin x)) eps) (- (* 1/3840 (* eps eps)) 1/48) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (* (cos (* 1/2 eps)) (cos x)) (* eps eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (* x eps) 1/12) (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x)) (* 1/3840 (* eps eps)))

simplify163.0ms (1.4%)

Memory
7.0MiB live, 154.4MiB allocated; 22ms collecting garbage
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04631888
118321779
269911755
083921618
Stop Event
iter limit
node limit
Counts
125 → 124
Calls
Call 1
Inputs
(* 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))))))))))
(* 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))))))))))
(* 2 (cos (* 1/2 eps)))
(+ (* 2 (cos (* 1/2 eps))) (* 2 (* x (sin (* -1/2 eps)))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -1 (* x (cos (* 1/2 eps)))) (* 2 (sin (* -1/2 eps))))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* 2 (sin (* -1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* -1/3 (* x (sin (* -1/2 eps)))))))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* 1/2 eps)) (* x (+ (sin (* -1/2 eps)) (* -1/2 (* x (cos (* 1/2 eps)))))))
(+ (cos (* 1/2 eps)) (* x (+ (sin (* -1/2 eps)) (* x (+ (* -1/2 (cos (* 1/2 eps))) (* -1/6 (* x (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 (* (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)))))))
(* -1/2 x)
-1/2
(- (* 1/12 (* eps x)) 1/2)
(* -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)))))))
1
(+ 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 (* eps x))
(* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps)))))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps)))))))))
(+ (cos (* 1/2 eps)) (* -1/2 (* (pow x 2) (cos (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* 1/24 (* (pow x 2) (cos (* 1/2 eps)))))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/24 (cos (* 1/2 eps))))))))
(* 1/12 (* eps x))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* -1/2 eps))))))
(* 2 (+ (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* -1/2 eps)))))
(+ (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* -1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) x))
(* x (+ (* -1/2 (pow eps 2)) (/ eps x)))
(* x (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (* eps (sin x)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (cos (+ x (* 1/2 eps))))
(* (cos x) (cos (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(- (sin (- eps (* -1 x))) (sin x))
(* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))
(* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (cos (- (* 1/2 eps) (* -1 x))))
(cos (- (* 1/2 eps) (* -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 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (cos x))
(+ (* -1 (* eps (sin x))) (* 2 (cos x)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))
(cos x)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))))))
(* 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 (* -1/2 (* eps x))))
(* -1 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (cos x)) (* 1/2 (* eps (sin x)))))
-1/48
(- (* 1/3840 (pow eps 2)) 1/48)
(+ (cos x) (* -1/8 (* (pow eps 2) (cos x))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* 1/384 (* (pow eps 2) (cos x))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos x))) (* 1/384 (cos x)))))))
(pow eps 2)
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(* 1/3840 (pow eps 2))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* eps (- (* 1/12 x) (* 1/2 (/ 1 eps))))
(* 1/2 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(sin (* 1/2 eps))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))
(* -1 (* (pow eps 3) (+ (* -1/2 (sin x)) (/ (cos x) eps))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (cos (- x (* -1/2 eps))))
(cos (- x (* -1/2 eps)))
Outputs
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64)) (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)) (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 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (*.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 (+ (* 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) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal -1/2 binary64) 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)) (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)) (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 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (*.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 (+ (* 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) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))))))
(* 2 (cos (* 1/2 eps)))
(*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64))
(+ (* 2 (cos (* 1/2 eps))) (* 2 (* x (sin (* -1/2 eps)))))
(*.f64 (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))) (* x (+ (* -1 (* x (cos (* 1/2 eps)))) (* 2 (sin (* -1/2 eps))))))
(fma.f64 (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 (neg.f64 x) x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* 2 (sin (* -1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* -1/3 (* x (sin (* -1/2 eps)))))))))
(fma.f64 (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 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (PI.f64)))) (*.f64 x 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 (+ (sin (* -1/2 eps)) (* -1/2 (* x (cos (* 1/2 eps)))))))
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(+ (cos (* 1/2 eps)) (* x (+ (sin (* -1/2 eps)) (* x (+ (* -1/2 (cos (* 1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -1/2 binary64))) x (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (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 (* (pow eps 2) x)))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64)) 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 eps (+.f64 x eps)) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) x)) x)) x eps)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
-1/2
#s(literal -1/2 binary64)
(- (* 1/12 (* eps x)) 1/2)
(-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64))
(* -1 (pow eps 2))
(*.f64 (neg.f64 eps) eps)
(+ (* -1 (pow eps 2)) (* 1/2 (* (pow eps 3) x)))
(fma.f64 (neg.f64 eps) eps (*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64)) x))
(+ (* -1 (pow eps 2)) (* x (+ (* 1/2 (* (pow eps 2) x)) (* 1/2 (pow eps 3)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 eps eps) (+.f64 x eps)) (*.f64 (neg.f64 eps) eps))
(+ (* -1 (pow eps 2)) (* x (+ (* 1/2 (pow eps 3)) (* x (+ (* -1/12 (* (pow eps 3) x)) (* 1/2 (pow eps 2)))))))
(fma.f64 (fma.f64 (*.f64 x (*.f64 (pow.f64 eps #s(literal 3 binary64)) x)) #s(literal -1/12 binary64) (*.f64 (*.f64 (*.f64 eps eps) (+.f64 x eps)) #s(literal 1/2 binary64))) x (*.f64 (neg.f64 eps) eps))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 (+.f64 x eps) #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 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(* -1/2 (* eps x))
(*.f64 (*.f64 x eps) #s(literal -1/2 binary64))
(* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64) (*.f64 #s(literal -1/2 binary64) eps)) x)
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal -1/240 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/12 binary64) eps)) (*.f64 (*.f64 x eps) #s(literal -1/2 binary64)))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/10080 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/240 binary64) eps)) x) x (*.f64 #s(literal 1/12 binary64) eps)) (*.f64 (*.f64 x eps) #s(literal -1/2 binary64)))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(*.f64 #s(literal -2 binary64) (-.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) x) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(fma.f64 (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (*.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 (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(fma.f64 (*.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) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))))))
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))
(*.f64 (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))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps)))))))
(fma.f64 (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 (neg.f64 x) x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps)))))))))
(fma.f64 (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 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (PI.f64)))) (*.f64 x x)))
(+ (cos (* 1/2 eps)) (* -1/2 (* (pow x 2) (cos (* 1/2 eps)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* 1/24 (* (pow x 2) (cos (* 1/2 eps)))))))
(fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/24 (cos (* 1/2 eps))))))))
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rewrite179.0ms (1.5%)

Memory
-7.7MiB live, 182.5MiB allocated; 13ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
085492
0125495
1456433
24056427
08107418
Stop Event
iter limit
node limit
iter limit
Counts
27 → 510
Calls
Call 1
Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
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(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))
(*.f64 eps eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
(*.f64 (*.f64 x eps) #s(literal 1/12 binary64))
#s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))
Outputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(fma.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (neg.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (neg.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (neg.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 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.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 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) (neg.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) (neg.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.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 2 binary64))) (cos.f64 (/.f64 (-.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 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (neg.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (neg.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))) #s(literal 2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (PI.f64))) (cos.f64 x))))
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64))) #s(literal 2 binary64)) (fma.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 2 binary64) (-.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)))) (fma.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (PI.f64))) (cos.f64 x))))
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64)))) (fma.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (-.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))
(/.f64 (-.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) (-.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(/.f64 (+.f64 (pow.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 3 binary64))) (fma.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (-.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))))
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(fma.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (neg.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (PI.f64)))) (cos.f64 x)))
(fma.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (neg.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (PI.f64)))) (cos.f64 x)))
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(sin.f64 (+.f64 (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (*.f64 #s(literal -1/2 binary64) eps)))
(sin.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) eps (/.f64 (PI.f64) #s(literal 2 binary64))) x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
(-.f64 (*.f64 (cos.f64 (/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 x (-.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 x (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))) (*.f64 (sin.f64 (/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 x (-.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 x (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))))
(-.f64 (/.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (PI.f64))) (cos.f64 x)))) (/.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (PI.f64))) (cos.f64 x)))))
(-.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(-.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (PI.f64))) (cos.f64 x)))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (neg.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (neg.f64 x))))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 x)))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(cos.f64 (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)))
(cos.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))) (cos.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))) (*.f64 (sin.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))))
(+.f64 (*.f64 (sin.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (*.f64 (sin.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (*.f64 (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (*.f64 (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x))) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (/.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64)) (fma.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (fma.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)))))
(+.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (neg.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (PI.f64)))) (cos.f64 x)))
(+.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(*.f64 (*.f64 #s(literal 1/3840 binary64) (fabs.f64 eps)) (fabs.f64 eps))
(*.f64 (*.f64 #s(literal 1/3840 binary64) (neg.f64 eps)) (neg.f64 eps))
(*.f64 (*.f64 #s(literal 1/3840 binary64) eps) eps)
(*.f64 (fabs.f64 eps) (*.f64 (fabs.f64 eps) #s(literal 1/3840 binary64)))
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))
(*.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) #s(literal 1/3840 binary64)))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(*.f64 eps (*.f64 #s(literal 1/3840 binary64) eps))
(/.f64 (*.f64 (*.f64 #s(literal 1/3840 binary64) eps) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps))
(/.f64 (*.f64 (*.f64 #s(literal 1/3840 binary64) eps) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(fma.f64 (*.f64 #s(literal 1/3840 binary64) (fabs.f64 eps)) (fabs.f64 eps) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/3840 binary64) eps)))
(fma.f64 (*.f64 #s(literal 1/3840 binary64) (fabs.f64 eps)) (fabs.f64 eps) (*.f64 (*.f64 #s(literal 1/3840 binary64) eps) #s(literal 0 binary64)))
(fma.f64 (*.f64 #s(literal 1/3840 binary64) (neg.f64 eps)) (neg.f64 eps) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/3840 binary64) eps)))
(fma.f64 (*.f64 #s(literal 1/3840 binary64) (neg.f64 eps)) (neg.f64 eps) (*.f64 (*.f64 #s(literal 1/3840 binary64) eps) #s(literal 0 binary64)))
(fma.f64 (*.f64 #s(literal 1/3840 binary64) eps) eps (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/3840 binary64) eps)))
(fma.f64 (*.f64 #s(literal 1/3840 binary64) eps) eps (*.f64 (*.f64 #s(literal 1/3840 binary64) eps) #s(literal 0 binary64)))
(fma.f64 (*.f64 #s(literal 1/3840 binary64) eps) #s(literal 0 binary64) (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))
(fma.f64 (fabs.f64 eps) (*.f64 (fabs.f64 eps) #s(literal 1/3840 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/3840 binary64) eps)))
(fma.f64 (fabs.f64 eps) (*.f64 (fabs.f64 eps) #s(literal 1/3840 binary64)) (*.f64 (*.f64 #s(literal 1/3840 binary64) eps) #s(literal 0 binary64)))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/3840 binary64) eps)))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 1/3840 binary64) eps) #s(literal 0 binary64)))
(fma.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) #s(literal 1/3840 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/3840 binary64) eps)))
(fma.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) #s(literal 1/3840 binary64)) (*.f64 (*.f64 #s(literal 1/3840 binary64) eps) #s(literal 0 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/3840 binary64) eps)))
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) (*.f64 (*.f64 #s(literal 1/3840 binary64) eps) #s(literal 0 binary64)))
(fma.f64 eps (*.f64 #s(literal 1/3840 binary64) eps) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/3840 binary64) eps)))
(fma.f64 eps (*.f64 #s(literal 1/3840 binary64) eps) (*.f64 (*.f64 #s(literal 1/3840 binary64) eps) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/3840 binary64) eps) (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))
(+.f64 (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/3840 binary64) eps)) (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))
(+.f64 (*.f64 (*.f64 #s(literal 1/3840 binary64) eps) #s(literal 0 binary64)) (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))
(+.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/3840 binary64) eps)))
(+.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) (*.f64 (*.f64 #s(literal 1/3840 binary64) eps) #s(literal 0 binary64)))

eval117.0ms (1%)

Memory
9.0MiB live, 99.4MiB allocated; 9ms collecting garbage
Compiler

Compiled 30 567 to 3 386 computations (88.9% saved)

prune51.0ms (0.4%)

Memory
-0.1MiB live, 46.6MiB allocated; 2ms collecting garbage
Pruning

26 alts after pruning (15 fresh and 11 done)

PrunedKeptTotal
New5979606
Fresh268
Picked145
Done077
Total60026626
Accuracy
100.0%
Counts
626 → 26
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.9%
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
61.6%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
28.0%
(*.f64 (*.f64 (sin.f64 (/.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (-.f64 eps #s(literal 0 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
52.8%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* (* x eps) 1/12) 1/2) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps)))
52.8%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) (*.f64 eps eps)) eps))
52.8%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 eps eps) (+.f64 x eps)) (*.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
98.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
97.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
97.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
96.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps))
96.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
5.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
5.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (* (* -1/2 (sin x)) eps) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64) (*.f64 #s(literal -1/2 binary64) eps)) x))) eps))
95.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
96.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps)))
95.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
95.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x) eps)))
95.2%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
5.7%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
95.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)))
100.0%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
99.7%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
99.7%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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))))
99.3%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
99.0%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
98.7%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
Compiler

Compiled 2 032 to 828 computations (59.3% saved)

regimes62.0ms (0.5%)

Memory
-35.2MiB live, 19.0MiB allocated; 5ms collecting garbage
Counts
39 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (* (* -1/2 (sin x)) eps) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64) (*.f64 #s(literal -1/2 binary64) eps)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* (* x eps) 1/12) 1/2) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 eps eps) (+.f64 x eps)) (*.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) (*.f64 eps eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 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)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.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 (/ (+ 0 eps) 2)) (*.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))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #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 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 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 (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))
(*.f64 (*.f64 (sin.f64 (/.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (-.f64 eps #s(literal 0 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64))))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))) (*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))))))
Outputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
Calls

3 calls:

9.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms
x
9.0ms
eps
Results
AccuracySegmentsBranch
100.0%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
100.0%1x
100.0%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes27.0ms (0.2%)

Memory
32.6MiB live, 32.6MiB allocated; 0ms collecting garbage
Counts
35 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (* (* -1/2 (sin x)) eps) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64) (*.f64 #s(literal -1/2 binary64) eps)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* (* x eps) 1/12) 1/2) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 eps eps) (+.f64 x eps)) (*.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) (*.f64 eps eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 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)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.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 (/ (+ 0 eps) 2)) (*.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))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #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 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 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 (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))
(*.f64 (*.f64 (sin.f64 (/.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (-.f64 eps #s(literal 0 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
Outputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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))))
Calls

3 calls:

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

Compiled 9 to 10 computations (-11.1% saved)

regimes32.0ms (0.3%)

Memory
-21.9MiB live, 24.1MiB allocated; 2ms collecting garbage
Counts
27 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (* (* -1/2 (sin x)) eps) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64) (*.f64 #s(literal -1/2 binary64) eps)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* (* x eps) 1/12) 1/2) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 eps eps) (+.f64 x eps)) (*.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) (*.f64 eps eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 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)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.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 (/ (+ 0 eps) 2)) (*.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))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #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 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
Outputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
Calls

3 calls:

17.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms
eps
7.0ms
x
Results
AccuracySegmentsBranch
99.3%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.3%1x
99.3%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes19.0ms (0.2%)

Memory
24.2MiB live, 24.2MiB allocated; 0ms collecting garbage
Counts
23 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (* (* -1/2 (sin x)) eps) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64) (*.f64 #s(literal -1/2 binary64) eps)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* (* x eps) 1/12) 1/2) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 eps eps) (+.f64 x eps)) (*.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) (*.f64 eps eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 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)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.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 (/ (+ 0 eps) 2)) (*.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
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
Calls

3 calls:

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

Compiled 9 to 10 computations (-11.1% saved)

regimes16.0ms (0.1%)

Memory
10.7MiB live, 10.7MiB allocated; 0ms collecting garbage
Counts
19 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (* (* -1/2 (sin x)) eps) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64) (*.f64 #s(literal -1/2 binary64) eps)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* (* x eps) 1/12) 1/2) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 eps eps) (+.f64 x eps)) (*.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) (*.f64 eps eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 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)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
Outputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
Calls

3 calls:

5.0ms
x
5.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms
eps
Results
AccuracySegmentsBranch
98.7%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.7%1x
98.7%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes37.0ms (0.3%)

Memory
-36.4MiB live, 10.6MiB allocated; 1ms collecting garbage
Counts
18 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (* (* -1/2 (sin x)) eps) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64) (*.f64 #s(literal -1/2 binary64) eps)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* (* x eps) 1/12) 1/2) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 eps eps) (+.f64 x eps)) (*.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) (*.f64 eps eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 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)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
Calls

3 calls:

27.0ms
x
5.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms
eps
Results
AccuracySegmentsBranch
97.9%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
97.9%1x
97.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.1%)

Memory
9.5MiB live, 9.5MiB allocated; 0ms collecting garbage
Counts
14 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (* (* -1/2 (sin x)) eps) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64) (*.f64 #s(literal -1/2 binary64) eps)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* (* x eps) 1/12) 1/2) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) eps) -1/2) (cos x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 eps eps) (+.f64 x eps)) (*.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.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))) (*.f64 eps eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps)))
Calls

3 calls:

4.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
eps
4.0ms
x
Results
AccuracySegmentsBranch
96.4%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
96.4%1x
96.4%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory
5.8MiB live, 5.8MiB allocated; 0ms collecting garbage
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x) eps)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
Calls

3 calls:

2.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
95.4%1x
95.4%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
95.4%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory
5.3MiB live, 5.3MiB allocated; 0ms collecting garbage
Accuracy

Total -57.4b remaining (-1939.9%)

Threshold costs -57.4b (-1939.9%)

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

3 calls:

1.0ms
x
1.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms
eps
Results
AccuracySegmentsBranch
95.4%1eps
95.4%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
95.4%1x
Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify58.0ms (0.5%)

Memory
-14.5MiB live, 30.6MiB allocated; 4ms collecting garbage
Algorithm
egg-herbie
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
089279
1142276
2303275
3894275
42582275
55286275
Stop Event
node limit
Calls
Call 1
Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
Outputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))

derivations946.0ms (8%)

Memory
39.9MiB live, 704.7MiB allocated; 44ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04571689
117851578
266181556
084491422
0107303
1366303
21224296
34149296
47986296
08046267
05452332
120192265
277272238
081082062
037177
065145
1288145
22159145
09044145
0616
01016
15116
236516
3445216
0817716
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 289 to 92 computations (68.2% saved)

preprocess70.0ms (0.6%)

Memory
9.2MiB live, 52.3MiB allocated; 12ms collecting garbage
Compiler

Compiled 622 to 222 computations (64.3% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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