tanhf (example 3.4)

Time bar (total: 6.0s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze109.0ms (1.8%)

Memory
-4.0MiB live, 131.9MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
25%25%75%0%0%0%0%3
37.5%37.5%62.5%0%0%0%0%4
43.8%43.7%56.2%0%0%0%0%5
46.9%46.9%53.1%0%0%0%0%6
48.4%48.4%51.5%0%0%0%0%7
49.2%49.2%50.8%0%0%0%0%8
49.6%49.6%50.4%0%0%0%0%9
49.8%49.8%50.2%0%0%0%0%10
49.9%49.9%50.1%0%0%0%0%11
50%49.9%50%0%0%0%0%12
Compiler

Compiled 9 to 8 computations (11.1% saved)

sample2.1s (35.6%)

Memory
54.0MiB live, 1 639.7MiB allocated
Samples
725.0ms2 245×2valid
505.0ms567×3valid
500.0ms4 196×0valid
136.0ms1 245×1valid
3.0ms4valid
Precisions
Click to see histograms. Total time spent on operations: 1.6s
ival-cos: 1.1s (67.9% of total)
ival-sin: 167.0ms (10.1% of total)
adjust: 142.0ms (8.6% of total)
ival-div: 105.0ms (6.4% of total)
ival-sub: 101.0ms (6.1% of total)
ival-true: 6.0ms (0.4% of total)
exact: 5.0ms (0.3% of total)
ival-assert: 3.0ms (0.2% of total)
Bogosity

explain173.0ms (2.9%)

Memory
-21.1MiB live, 123.2MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
662(9.57973100975295e+33)0-(-.f64 #s(literal 1 binary64) (cos.f64 x))
650-3(-5.68879510000915e-158)(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
00-0-#s(literal 1 binary64)
00-0-(cos.f64 x)
00-0-(sin.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 #s(literal 1 binary64) (cos.f64 x))cancellation682
/.f64(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))u/n620
(-.f64 #s(literal 1 binary64) (cos.f64 x))underflow62
Confusion
Predicted +Predicted -
+1290
-1126
Precision
0.9923076923076923
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+12900
-12124
Precision?
0.9772727272727273
Recall?
1.0
Freqs
test
numberfreq
0126
1130
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
41.0ms144×2valid
28.0ms268×0valid
19.0ms44×3valid
6.0ms56×1valid
Compiler

Compiled 45 to 22 computations (51.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 76.0ms
ival-cos: 46.0ms (60.1% of total)
ival-sin: 11.0ms (14.4% of total)
adjust: 7.0ms (9.2% of total)
ival-div: 6.0ms (7.8% of total)
ival-sub: 5.0ms (6.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess212.0ms (3.5%)

Memory
-12.4MiB live, 190.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
1299
2688
31248
42688
56518
616578
735378
874978
067
0104
1244
2344
3434
4544
5804
61334
72764
86894
918164
1039214
1172004
083274
Stop Event
iter limit
node limit
iter limit
node limit
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Outputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
Symmetry

(negabs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
54.0%
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify131.0ms (2.2%)

Memory
34.8MiB live, 168.8MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sin.f64 x)
cost-diff0
(cos.f64 x)
cost-diff0
(-.f64 #s(literal 1 binary64) (cos.f64 x))
cost-diff3
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0617
01014
12414
23414
34314
45414
58014
613314
727614
868914
9181614
10392114
11720014
0832714
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)
Outputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)

localize98.0ms (1.6%)

Memory
3.5MiB live, 60.4MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(sin.f64 x)
accuracy0.0
(cos.f64 x)
accuracy14.241657995941432
(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy14.924156453521174
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Samples
36.0ms72×2valid
14.0ms134×0valid
7.0ms22×3valid
3.0ms28×1valid
Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 51.0ms
ival-cos: 21.0ms (41% of total)
adjust: 20.0ms (39% of total)
ival-sin: 5.0ms (9.8% of total)
ival-div: 3.0ms (5.9% of total)
ival-sub: 3.0ms (5.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series2.0ms (0%)

Memory
3.7MiB live, 3.7MiB allocated
Counts
4 → 20
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(sin.f64 x)
Outputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
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)))
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))))
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
(cos x)
(sin x)
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
((/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (cos x) (sin x))
1.0ms
x
@-inf
((/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (cos x) (sin x))
1.0ms
x
@inf
((/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (cos x) (sin x))

simplify185.0ms (3.1%)

Memory
13.4MiB live, 146.4MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079202
1266202
2777196
33247196
47420196
08622178
Stop Event
iter limit
node limit
Counts
20 → 19
Calls
Call 1
Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
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)))
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))))
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
(cos x)
(sin x)
Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/720 binary64) (*.f64 x x)) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(*.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/40320 binary64) (-.f64 (*.f64 #s(literal 1/720 binary64) (*.f64 x x)) #s(literal 1/24 binary64))) (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/720 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) (*.f64 x x) #s(literal 1 binary64))
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)
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)
(sin x)
(sin.f64 x)

rewrite199.0ms (3.3%)

Memory
-17.5MiB live, 171.2MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0615
01012
14112
227712
3270912
0829912
Stop Event
iter limit
node limit
iter limit
Counts
4 → 220
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(sin.f64 x)
Outputs
(*.f64 (/.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(*.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 (sin.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64))) (/.f64 (neg.f64 (sin.f64 x)) (sin.f64 x)))
(*.f64 (neg.f64 (sin.f64 x)) (/.f64 (neg.f64 (sin.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))))
(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) (sin.f64 x)))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))))
(/.f64 (+.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (sin.f64 (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (PI.f64)) (PI.f64))) (cos.f64 (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (PI.f64)) (PI.f64))))
(/.f64 (/.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x))) (neg.f64 (sin.f64 x))) (neg.f64 (sin.f64 x)))
(/.f64 (/.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x))) (sin.f64 x)) (sin.f64 x))
(/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (-.f64 (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) #s(literal 2 binary64)) (/.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (tan.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (tan.f64 (/.f64 x #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal -2 binary64)))))
(/.f64 (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x)))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (sin.f64 (/.f64 x #s(literal 2 binary64)))) (neg.f64 (cos.f64 (/.f64 x #s(literal -2 binary64)))))
(/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 x))) (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (sin.f64 x)) (*.f64 (sin.f64 x) (cos.f64 x))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 x))) (*.f64 (sin.f64 x) (neg.f64 (cos.f64 x)))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 x)) (*.f64 (sin.f64 x) (neg.f64 (cos.f64 x)))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 x))) (neg.f64 (sin.f64 x)))
(/.f64 (+.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 0 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 0 binary64))))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 (fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal -1 binary64)) (sin.f64 x)))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (neg.f64 (sin.f64 x))))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (*.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))))
(/.f64 (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 9 binary64))) (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))))
(/.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (tan.f64 (/.f64 x #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal -2 binary64))))
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(-.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (sin.f64 x))) (cos.f64 x))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (/.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))
(+.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))
(+.f64 #s(literal 1 binary64) (cos.f64 x))
(*.f64 (sqrt.f64 (neg.f64 (neg.f64 (cos.f64 x)))) (sqrt.f64 (neg.f64 (neg.f64 (cos.f64 x)))))
(*.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))))
(*.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)))
(*.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 x))
(pow.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (neg.f64 (cos.f64 x)))
(/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(literal 0 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) (cos.f64 x)))))
(/.f64 (-.f64 (cos.f64 x) (neg.f64 (cos.f64 x))) #s(literal 2 binary64))
(fma.f64 (sqrt.f64 (neg.f64 (neg.f64 (cos.f64 x)))) (sqrt.f64 (neg.f64 (neg.f64 (cos.f64 x)))) (*.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))
(fma.f64 (sqrt.f64 (neg.f64 (neg.f64 (cos.f64 x)))) (sqrt.f64 (neg.f64 (neg.f64 (cos.f64 x)))) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) (*.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))
(fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)) (*.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))
(fma.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (*.f64 x x)))) (cos.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (*.f64 x x)))) (*.f64 (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (*.f64 x x)))) (sin.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (*.f64 x x))))))
(fma.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal 1 binary64) (cos.f64 x))
(fma.f64 #s(literal 0 binary64) (sin.f64 x) (cos.f64 x))
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64) (cos.f64 x))
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (cos.f64 x))
(fma.f64 (cos.f64 x) #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))
(fma.f64 (cos.f64 x) #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (sin.f64 x)) (cos.f64 x))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(sin.f64 (+.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (acos.f64 (fabs.f64 (neg.f64 (sin.f64 x)))))
(sin.f64 (acos.f64 (fabs.f64 (sin.f64 x))))
(sin.f64 (acos.f64 (neg.f64 (sin.f64 x))))
(sin.f64 (acos.f64 (sin.f64 x)))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(sqrt.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(-.f64 (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))) (*.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))))
(-.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x)))
(fabs.f64 (neg.f64 (cos.f64 x)))
(fabs.f64 (cos.f64 x))
(cos.f64 (neg.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (asin.f64 (fabs.f64 (neg.f64 (sin.f64 x)))))
(cos.f64 (asin.f64 (fabs.f64 (sin.f64 x))))
(cos.f64 (asin.f64 (neg.f64 (sin.f64 x))))
(cos.f64 (asin.f64 (sin.f64 x)))
(cos.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (*.f64 (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (*.f64 x x)))) (cos.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (*.f64 x x))))) (*.f64 (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (*.f64 x x)))) (sin.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (*.f64 x x))))))
(+.f64 (cosh.f64 (log.f64 (cos.f64 x))) (sinh.f64 (log.f64 (cos.f64 x))))
(+.f64 (*.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal 1 binary64)) (cos.f64 x))
(+.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (sin.f64 x))) (cos.f64 x))
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (cos.f64 x))
(+.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) (cos.f64 x))
(+.f64 (cos.f64 x) (*.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))
(+.f64 (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(exp.f64 (/.f64 (log.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (cos.f64 x)))
(*.f64 (sin.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sin.f64 x))
(neg.f64 (neg.f64 (sin.f64 x)))
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64) (*.f64 (neg.f64 (cos.f64 x)) #s(literal 0 binary64)))
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64) (*.f64 (cos.f64 x) #s(literal 0 binary64)))
(sin.f64 (neg.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))) (PI.f64)))
(sin.f64 (+.f64 (+.f64 (+.f64 (PI.f64) x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (neg.f64 (+.f64 (PI.f64) x)))
(sin.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64)))
(sin.f64 (+.f64 (neg.f64 x) (PI.f64)))
(sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 x)
(-.f64 (*.f64 (neg.f64 (cos.f64 x)) #s(literal 0 binary64)) (*.f64 (neg.f64 (sin.f64 x)) #s(literal 1 binary64)))
(-.f64 (*.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64)) (*.f64 (cos.f64 x) #s(literal 0 binary64)))
(-.f64 (*.f64 #s(literal 0 binary64) (cos.f64 x)) (*.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 x))))
(-.f64 (*.f64 (cos.f64 x) #s(literal 0 binary64)) (*.f64 (neg.f64 (sin.f64 x)) #s(literal 1 binary64)))
(cos.f64 (neg.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64))))
(cos.f64 (neg.f64 (+.f64 (+.f64 (PI.f64) x) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (+.f64 (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (PI.f64)))
(cos.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64)))
(cos.f64 (+.f64 (+.f64 (PI.f64) x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64)) (*.f64 (neg.f64 (cos.f64 x)) #s(literal 0 binary64)))
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64)) (*.f64 (cos.f64 x) #s(literal 0 binary64)))

eval73.0ms (1.2%)

Memory
-26.8MiB live, 72.0MiB allocated
Compiler

Compiled 4 121 to 798 computations (80.6% saved)

prune6.0ms (0.1%)

Memory
13.7MiB live, 13.7MiB allocated
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2345239
Fresh000
Picked101
Done000
Total2355240
Accuracy
100.0%
Counts
240 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.3%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
50.2%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
50.2%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
50.3%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
100.0%
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
Compiler

Compiled 172 to 122 computations (29.1% saved)

simplify241.0ms (4%)

Memory
-8.7MiB live, 179.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64))
cost-diff0
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
cost-diff0
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
cost-diff0
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
cost-diff0
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
cost-diff0
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
cost-diff0
(*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
cost-diff0
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
cost-diff0
(*.f64 x x)
cost-diff0
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
cost-diff0
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
cost-diff0
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
cost-diff0
(*.f64 #s(literal 1/2 binary64) x)
cost-diff0
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
cost-diff0
(*.f64 #s(literal 1/2 binary64) x)
cost-diff0
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
cost-diff0
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027216
045201
192201
2270201
31093201
43980201
57396201
08255201
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
#s(literal 17/40320 binary64)
(*.f64 x x)
x
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
#s(literal 17/40320 binary64)
(*.f64 x x)
x
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)

localize184.0ms (3.1%)

Memory
35.7MiB live, 227.4MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy0.03125
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64))
accuracy0.03515625
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
accuracy0.11328125
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
accuracy31.783847653862576
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
accuracy0.03515625
(*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
accuracy0.05078125
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
accuracy0.0625
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy31.85055397633424
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
accuracy0.0
(*.f64 x x)
accuracy0.046875
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
accuracy0.0859375
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
accuracy31.88256610824091
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
accuracy0.0
(*.f64 #s(literal 1/2 binary64) x)
accuracy31.799938361587362
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
accuracy0.0
(*.f64 #s(literal 1/2 binary64) x)
accuracy0.0
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
accuracy0.0
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
Samples
55.0ms72×2valid
55.0ms22×3valid
43.0ms134×0valid
12.0ms28×1valid
Compiler

Compiled 183 to 30 computations (83.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 135.0ms
adjust: 51.0ms (37.8% of total)
ival-cos: 21.0ms (15.6% of total)
ival-mult: 20.0ms (14.8% of total)
const: 12.0ms (8.9% of total)
ival-tan: 9.0ms (6.7% of total)
ival-add: 9.0ms (6.7% of total)
ival-sin: 5.0ms (3.7% of total)
ival-div: 3.0ms (2.2% of total)
ival-sub: 3.0ms (2.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series13.0ms (0.2%)

Memory
-33.1MiB live, 12.4MiB allocated
Counts
17 → 44
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
Outputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(pow x 2)
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
1/240
(+ 1/240 (* 17/40320 (pow x 2)))
(/ (- 1 (cos x)) (sin x))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 4))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 17/40320 (pow x 7))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 6))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 4))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* 17/40320 (pow x 2))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
Calls

3 calls:

TimeVariablePointExpression
7.0ms
x
@-inf
((/ (- 1 (cos x)) (sin x)) (tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))
3.0ms
x
@inf
((/ (- 1 (cos x)) (sin x)) (tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))
2.0ms
x
@0
((/ (- 1 (cos x)) (sin x)) (tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))

simplify149.0ms (2.5%)

Memory
8.0MiB live, 109.2MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
097457
1359457
21105454
34199450
08296429
Stop Event
iter limit
node limit
Counts
44 → 44
Calls
Call 1
Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(pow x 2)
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
1/240
(+ 1/240 (* 17/40320 (pow x 2)))
(/ (- 1 (cos x)) (sin x))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 4))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 17/40320 (pow x 7))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 6))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 4))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* 17/40320 (pow x 2))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64))
1/240
#s(literal 1/240 binary64)
(+ 1/240 (* 17/40320 (pow x 2)))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) x)))
(* 1/24 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* 1/24 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(* 1/240 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/240 binary64))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(*.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/240 binary64)) (/.f64 #s(literal -1/24 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* 1/240 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/240 binary64))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal -1/240 binary64)))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/240 binary64)) (/.f64 #s(literal -1/24 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* 1/240 (pow x 2))
(*.f64 #s(literal 1/240 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(* 17/40320 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 17/40320 binary64))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(*.f64 (+.f64 (/.f64 #s(literal 1/240 binary64) (*.f64 x x)) #s(literal 17/40320 binary64)) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64)) (/.f64 #s(literal -1/240 binary64) (*.f64 x x))) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 17/40320 binary64)) (/.f64 (/.f64 (-.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))) x) x)) (pow.f64 x #s(literal 7 binary64)))
(* 17/40320 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 17/40320 binary64))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (/.f64 #s(literal 1/240 binary64) (*.f64 x x)) #s(literal -17/40320 binary64)))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64)) (/.f64 #s(literal -1/240 binary64) (*.f64 x x))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64)) (/.f64 #s(literal -1/240 binary64) (*.f64 x x))) #s(literal 1/2 binary64))
(* 17/40320 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 17/40320 binary64))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(*.f64 (+.f64 (/.f64 #s(literal 1/240 binary64) (*.f64 x x)) #s(literal 17/40320 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64)) (/.f64 #s(literal -1/240 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* 17/40320 (pow x 2))
(*.f64 #s(literal 17/40320 binary64) (*.f64 x x))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(*.f64 (neg.f64 (pow.f64 x #s(literal 5 binary64))) (+.f64 (/.f64 #s(literal -1/24 binary64) (*.f64 x x)) (-.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/240 binary64))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))
(*.f64 (neg.f64 (pow.f64 x #s(literal 7 binary64))) (+.f64 (/.f64 #s(literal -1/240 binary64) (*.f64 x x)) (-.f64 (/.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 7 binary64))) (-.f64 (/.f64 (-.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 1/240 binary64) (*.f64 x x)) #s(literal 17/40320 binary64))))

rewrite185.0ms (3.1%)

Memory
32.2MiB live, 221.3MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027191
045176
1185176
21341176
08252176
Stop Event
iter limit
node limit
iter limit
Counts
17 → 369
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (neg.f64 (+.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 0 binary64))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 0 binary64)))))
(/.f64 (neg.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)))) (neg.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)))))
(/.f64 (+.f64 #s(literal 0 binary64) (tan.f64 (*.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (sin.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)) (PI.f64))) (cos.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)) (PI.f64))))
(/.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64))))
(/.f64 (+.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 0 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 0 binary64))))
(/.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x)))
(tan.f64 (+.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)) (PI.f64)) (PI.f64)))
(tan.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)) (PI.f64)))
(tan.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (/.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 0 binary64)))) (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 0 binary64)))))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x)
(*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (-.f64 (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (-.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x))) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x)))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x) #s(literal 3 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) #s(literal 3 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x)) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 (*.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) #s(literal 1/4 binary64)) x)) (neg.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)) x)) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64))))))
(/.f64 (neg.f64 (*.f64 x (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (*.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64))))))
(/.f64 (*.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) #s(literal 1/4 binary64)) x) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)) x) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64)))))
(/.f64 (*.f64 x (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) #s(literal 1/4 binary64))) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
(/.f64 (*.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64)))))
(fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(fma.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(+.f64 (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))) (*.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))))) (+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/24 binary64) (*.f64 x x)) (*.f64 #s(literal -1/24 binary64) (*.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/24 binary64) (*.f64 x x))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (neg.f64 (*.f64 x x)) #s(literal 1/24 binary64)) (*.f64 (neg.f64 (*.f64 x x)) #s(literal 1/24 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (neg.f64 (*.f64 x x)) #s(literal 1/24 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (neg.f64 x) (*.f64 #s(literal 1/24 binary64) x)) (*.f64 (neg.f64 x) (*.f64 #s(literal 1/24 binary64) x)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (neg.f64 x) (*.f64 #s(literal 1/24 binary64) x))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64))))) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64)))))) (*.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64))))) (/.f64 #s(literal 1/8 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64))))))) (-.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64))))) (/.f64 #s(literal 1/8 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64)))))))
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(/.f64 (+.f64 (pow.f64 (/.f64 (*.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/13824000 binary64) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))) (/.f64 (*.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))) (-.f64 (*.f64 (/.f64 #s(literal 1/13824000 binary64) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))) (/.f64 #s(literal 1/13824000 binary64) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64)))))) (*.f64 (/.f64 (*.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))) (/.f64 #s(literal 1/13824000 binary64) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64)))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/57600 binary64) (*.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (-.f64 #s(literal 1/240 binary64) (*.f64 #s(literal 17/40320 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/57600 binary64)))) (neg.f64 (neg.f64 (-.f64 (*.f64 #s(literal 17/40320 binary64) (*.f64 x x)) #s(literal 1/240 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824000 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64)))))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 #s(literal 17/40320 binary64) (*.f64 x x)) #s(literal 1/240 binary64))) (*.f64 (-.f64 (*.f64 #s(literal 17/40320 binary64) (*.f64 x x)) #s(literal 1/240 binary64)) #s(literal 1/57600 binary64))) (*.f64 (-.f64 (*.f64 #s(literal 17/40320 binary64) (*.f64 x x)) #s(literal 1/240 binary64)) (-.f64 (*.f64 #s(literal 17/40320 binary64) (*.f64 x x)) #s(literal 1/240 binary64))))
(/.f64 (fma.f64 (*.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64)))) (*.f64 (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64)))) #s(literal 1/13824000 binary64))) (*.f64 (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64)))) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))))
(/.f64 (-.f64 #s(literal 1/57600 binary64) (*.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1/240 binary64) (*.f64 #s(literal 17/40320 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/57600 binary64))) (neg.f64 (-.f64 (*.f64 #s(literal 17/40320 binary64) (*.f64 x x)) #s(literal 1/240 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824000 binary64))) (neg.f64 (+.f64 #s(literal 1/57600 binary64) (-.f64 (*.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824000 binary64))) (neg.f64 (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))))
(/.f64 (-.f64 (*.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/57600 binary64)) (-.f64 (*.f64 #s(literal 17/40320 binary64) (*.f64 x x)) #s(literal 1/240 binary64)))
(/.f64 (fma.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824000 binary64)) (+.f64 #s(literal 1/57600 binary64) (-.f64 (*.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64)))))
(/.f64 (fma.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824000 binary64)) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64)))))
(fma.f64 (fabs.f64 (*.f64 #s(literal 17/40320 binary64) (neg.f64 x))) x #s(literal 1/240 binary64))
(fma.f64 (fabs.f64 (*.f64 #s(literal 17/40320 binary64) x)) x #s(literal 1/240 binary64))
(fma.f64 (*.f64 #s(literal 17/40320 binary64) (neg.f64 x)) (neg.f64 x) #s(literal 1/240 binary64))
(fma.f64 (*.f64 #s(literal 17/40320 binary64) x) x #s(literal 1/240 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
(fma.f64 x (fabs.f64 (*.f64 (neg.f64 x) #s(literal 17/40320 binary64))) #s(literal 1/240 binary64))
(fma.f64 x (fabs.f64 (*.f64 #s(literal 17/40320 binary64) x)) #s(literal 1/240 binary64))
(fma.f64 x (*.f64 #s(literal 17/40320 binary64) x) #s(literal 1/240 binary64))
(-.f64 (/.f64 #s(literal 1/57600 binary64) (-.f64 #s(literal 1/240 binary64) (*.f64 #s(literal 17/40320 binary64) (*.f64 x x)))) (/.f64 (*.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/240 binary64) (*.f64 #s(literal 17/40320 binary64) (*.f64 x x)))))
(-.f64 (/.f64 (*.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 #s(literal 17/40320 binary64) (*.f64 x x)) #s(literal 1/240 binary64))) (/.f64 #s(literal 1/57600 binary64) (-.f64 (*.f64 #s(literal 17/40320 binary64) (*.f64 x x)) #s(literal 1/240 binary64))))
(-.f64 #s(literal 1/240 binary64) (*.f64 (neg.f64 (*.f64 #s(literal 17/40320 binary64) x)) x))
(-.f64 #s(literal 1/240 binary64) (*.f64 #s(literal -17/40320 binary64) (*.f64 x x)))
(-.f64 #s(literal 1/240 binary64) (*.f64 (neg.f64 (*.f64 x x)) #s(literal 17/40320 binary64)))
(+.f64 (/.f64 #s(literal 1/13824000 binary64) (+.f64 #s(literal 1/57600 binary64) (-.f64 (*.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))) (/.f64 (*.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1/57600 binary64) (-.f64 (*.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))))
(+.f64 (/.f64 (*.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1/57600 binary64) (-.f64 (*.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))) (/.f64 #s(literal 1/13824000 binary64) (+.f64 #s(literal 1/57600 binary64) (-.f64 (*.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))))
(+.f64 (/.f64 #s(literal 1/13824000 binary64) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))) (/.f64 (*.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))))
(+.f64 (/.f64 (*.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))) (/.f64 #s(literal 1/13824000 binary64) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (*.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))))
(+.f64 (*.f64 #s(literal 17/40320 binary64) (*.f64 x x)) #s(literal 1/240 binary64))
(+.f64 #s(literal 1/240 binary64) (*.f64 #s(literal 17/40320 binary64) (*.f64 x x)))

eval88.0ms (1.5%)

Memory
-12.5MiB live, 123.2MiB allocated
Compiler

Compiled 22 012 to 2 482 computations (88.7% saved)

prune11.0ms (0.2%)

Memory
21.7MiB live, 21.7MiB allocated
Pruning

7 alts after pruning (2 fresh and 5 done)

PrunedKeptTotal
New5122514
Fresh000
Picked055
Done000
Total5127519
Accuracy
100.0%
Counts
519 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.2%
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
50.3%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
50.2%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
50.2%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
4.5%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x))
50.3%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
100.0%
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
Compiler

Compiled 127 to 91 computations (28.3% saved)

simplify227.0ms (3.8%)

Memory
-74.0MiB live, 101.3MiB allocated
Algorithm
egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
cost-diff0
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
cost-diff2
(fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
cost-diff0
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
cost-diff0
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64)))
cost-diff0
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x)
cost-diff0
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
020103
02795
16395
213495
329695
454895
565795
673695
790095
8131595
9244895
10454195
11782395
0800490
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x)
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
(fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
#s(literal 1/24 binary64)
(*.f64 x x)
x
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x)
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x))
(fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
(*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x)
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
(*.f64 x x)
x
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)

localize80.0ms (1.3%)

Memory
39.6MiB live, 83.8MiB allocated
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 #s(literal 1/2 binary64) x)
accuracy0.04296875
(fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
accuracy0.17578125
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
accuracy31.88256610824091
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
accuracy0.046875
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x)
accuracy0.17578125
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
accuracy30.85882979033244
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64)))
accuracy31.88256610824091
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x))
Samples
31.0ms72×2valid
23.0ms134×0valid
10.0ms22×3valid
6.0ms28×1valid
Compiler

Compiled 67 to 18 computations (73.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 57.0ms
ival-cos: 21.0ms (37.1% of total)
ival-mult: 8.0ms (14.1% of total)
ival-sin: 8.0ms (14.1% of total)
adjust: 7.0ms (12.4% of total)
const: 4.0ms (7.1% of total)
ival-div: 3.0ms (5.3% of total)
ival-sub: 3.0ms (5.3% of total)
ival-add: 2.0ms (3.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series28.0ms (0.5%)

Memory
-20.8MiB live, 31.3MiB allocated
Counts
9 → 12
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x)
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
(*.f64 x x)
(*.f64 #s(literal 1/2 binary64) x)
Outputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(* 1/24 (pow x 2))
(pow x 2)
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
Calls

3 calls:

TimeVariablePointExpression
26.0ms
x
@-inf
((/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* (* x x) 1/24) (+ (* (* 1/24 (* x x)) x) (* 1/2 x)) (/ (- 1 (cos x)) (sin x)) (* 1/24 (* x x)) (* x x) (* 1/2 x))
2.0ms
x
@inf
((/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* (* x x) 1/24) (+ (* (* 1/24 (* x x)) x) (* 1/2 x)) (/ (- 1 (cos x)) (sin x)) (* 1/24 (* x x)) (* x x) (* 1/2 x))
1.0ms
x
@0
((/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* (* x x) 1/24) (+ (* (* 1/24 (* x x)) x) (* 1/2 x)) (/ (- 1 (cos x)) (sin x)) (* 1/24 (* x x)) (* x x) (* 1/2 x))

simplify176.0ms (2.9%)

Memory
18.6MiB live, 199.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03689
113989
242389
3167489
4524689
0835180
Stop Event
iter limit
node limit
Counts
12 → 12
Calls
Call 1
Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(* 1/24 (pow x 2))
(pow x 2)
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(* 1/24 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
(pow x 2)
(*.f64 x x)
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 1/24 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))

rewrite185.0ms (3.1%)

Memory
17.1MiB live, 152.4MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02095
02787
110887
271287
3724487
0808882
Stop Event
iter limit
node limit
iter limit
Counts
9 → 186
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x)
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
(*.f64 x x)
(*.f64 #s(literal 1/2 binary64) x)
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x)
(*.f64 x #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))))
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(*.f64 (fabs.f64 (*.f64 #s(literal -1/24 binary64) x)) x)
(*.f64 (fabs.f64 (*.f64 #s(literal 1/24 binary64) x)) x)
(*.f64 (*.f64 #s(literal -1/24 binary64) x) (neg.f64 x))
(*.f64 (*.f64 #s(literal 1/24 binary64) x) x)
(*.f64 (neg.f64 x) (*.f64 #s(literal -1/24 binary64) x))
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
(*.f64 x (fabs.f64 (*.f64 #s(literal -1/24 binary64) x)))
(*.f64 x (fabs.f64 (*.f64 #s(literal 1/24 binary64) x)))
(*.f64 x (*.f64 #s(literal 1/24 binary64) x))
(neg.f64 (*.f64 #s(literal -1/24 binary64) (*.f64 x x)))
(sqrt.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)))
(fabs.f64 (*.f64 #s(literal -1/24 binary64) (*.f64 x x)))
(fabs.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) #s(literal 1/4 binary64)) x) (-.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) #s(literal 1/8 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (*.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) #s(literal 1/4 binary64)) x) (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) #s(literal 1/4 binary64))) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)))
(*.f64 (/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)) x) (-.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))) #s(literal 2 binary64)))) (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x)))))
(*.f64 (/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)) x) (fma.f64 (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) #s(literal 1/191102976 binary64) (pow.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))) #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))) (-.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64))) (pow.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 4 binary64))))
(*.f64 (/.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 #s(literal -1/4 binary64) (*.f64 x x))) (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (fma.f64 #s(literal 1/4 binary64) x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))))
(*.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64))) (-.f64 (pow.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64)) (pow.f64 (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(*.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64))) (fma.f64 #s(literal 1/191102976 binary64) (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))) #s(literal 3 binary64)))) (fma.f64 (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))) (-.f64 (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))) (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64))))
(*.f64 (/.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 #s(literal -1/4 binary64) (*.f64 x x))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(*.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (*.f64 #s(literal 1/2 binary64) x)) x) (/.f64 (*.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) x)
(*.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (*.f64 #s(literal 1/2 binary64) x)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (*.f64 #s(literal 1/2 binary64) x)) (/.f64 (*.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x)
(*.f64 x (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(*.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)))
(/.f64 (/.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64))) x) (-.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))))
(/.f64 (*.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) #s(literal 1/4 binary64))) x) (neg.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64))) x) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))))))
(/.f64 (*.f64 x (-.f64 #s(literal 1/4 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))))
(/.f64 (*.f64 x (neg.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(/.f64 (*.f64 x (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (/.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))))) (fma.f64 #s(literal 1/576 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))) (/.f64 (*.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))))) (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))))) (-.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))))))
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(fma.f64 x (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))
(-.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))) (/.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))))
(-.f64 (/.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))))
(-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) (*.f64 #s(literal -1/2 binary64) x))
(-.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))))) x) (*.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))))) x))
(+.f64 (*.f64 x (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x)))))) (*.f64 x (/.f64 #s(literal 1/8 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x)))))))
(+.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))) (/.f64 (*.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))))
(+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))))
(+.f64 (/.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (/.f64 (neg.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))))
(+.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) (*.f64 (neg.f64 x) #s(literal -1/2 binary64)))
(+.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(*.f64 (fabs.f64 (*.f64 #s(literal -1/24 binary64) x)) x)
(*.f64 (fabs.f64 (*.f64 #s(literal 1/24 binary64) x)) x)
(*.f64 (*.f64 #s(literal -1/24 binary64) x) (neg.f64 x))
(*.f64 (*.f64 #s(literal 1/24 binary64) x) x)
(*.f64 (neg.f64 x) (*.f64 #s(literal -1/24 binary64) x))
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
(*.f64 x (fabs.f64 (*.f64 #s(literal -1/24 binary64) x)))
(*.f64 x (fabs.f64 (*.f64 #s(literal 1/24 binary64) x)))
(*.f64 x (*.f64 #s(literal 1/24 binary64) x))
(neg.f64 (*.f64 #s(literal -1/24 binary64) (*.f64 x x)))
(sqrt.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)))
(fabs.f64 (*.f64 #s(literal -1/24 binary64) (*.f64 x x)))
(fabs.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(+.f64 (cosh.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(fabs.f64 (*.f64 #s(literal -1/2 binary64) x))
(fabs.f64 (*.f64 #s(literal 1/2 binary64) x))

eval38.0ms (0.6%)

Memory
-7.1MiB live, 50.3MiB allocated
Compiler

Compiled 6 762 to 771 computations (88.6% saved)

prune8.0ms (0.1%)

Memory
-32.3MiB live, 13.6MiB allocated
Pruning

7 alts after pruning (1 fresh and 6 done)

PrunedKeptTotal
New1981199
Fresh000
Picked112
Done055
Total1997206
Accuracy
100.0%
Counts
206 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.2%
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
50.3%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
50.2%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
50.2%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
4.5%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x)) x))
50.3%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
100.0%
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
Compiler

Compiled 127 to 91 computations (28.3% saved)

simplify114.0ms (1.9%)

Memory
9.9MiB live, 101.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (*.f64 #s(literal 1/24 binary64) x) x)
cost-diff0
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x))
cost-diff0
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x)) x)
cost-diff0
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x)) x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01661
01958
14358
28558
316758
424258
527958
633658
748358
889658
9202558
10412858
11743658
0802355
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x)) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x)) x)
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x))
(*.f64 (*.f64 #s(literal 1/24 binary64) x) x)
(*.f64 #s(literal 1/24 binary64) x)
#s(literal 1/24 binary64)
x
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x)) x)
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) x)
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x))
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))
(*.f64 (*.f64 #s(literal 1/24 binary64) x) x)
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
(*.f64 #s(literal 1/24 binary64) x)
#s(literal 1/24 binary64)
x

localize122.0ms (2%)

Memory
-8.0MiB live, 90.7MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.11328125
(*.f64 (*.f64 #s(literal 1/24 binary64) x) x)
accuracy0.33203125
(*.f64 #s(literal 1/24 binary64) x)
accuracy30.85882979033244
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x))
accuracy31.88256610824091
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x)) x))
Samples
75.0ms72×2valid
21.0ms134×0valid
9.0ms22×3valid
5.0ms28×1valid
Compiler

Compiled 35 to 16 computations (54.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 100.0ms
adjust: 43.0ms (43.2% of total)
ival-cos: 21.0ms (21.1% of total)
const: 16.0ms (16.1% of total)
ival-mult: 7.0ms (7% of total)
ival-sin: 5.0ms (5% of total)
ival-div: 3.0ms (3% of total)
ival-sub: 3.0ms (3% of total)
ival-add: 1.0ms (1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory
5.7MiB live, 5.7MiB allocated
Counts
5 → 12
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x)) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x)) x)
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x))
(*.f64 (*.f64 #s(literal 1/24 binary64) x) x)
(*.f64 #s(literal 1/24 binary64) x)
Outputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(* 1/24 (pow x 2))
(* 1/24 x)
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* (* 1/24 x) x) (* 1/24 x))
1.0ms
x
@inf
((/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* (* 1/24 x) x) (* 1/24 x))
1.0ms
x
@0
((/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* (* 1/24 x) x) (* 1/24 x))

simplify162.0ms (2.7%)

Memory
27.5MiB live, 115.1MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03789
114189
241989
3163689
4526889
0836680
Stop Event
iter limit
node limit
Counts
12 → 12
Calls
Call 1
Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(* 1/24 (pow x 2))
(* 1/24 x)
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(* 1/24 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 #s(literal 1/24 binary64) x)
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 1/24 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))

rewrite162.0ms (2.7%)

Memory
4.1MiB live, 144.3MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01659
01956
17556
247856
3460156
0829853
Stop Event
iter limit
node limit
iter limit
Counts
5 → 20
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x)) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x)) x)
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x))
(*.f64 (*.f64 #s(literal 1/24 binary64) x) x)
(*.f64 #s(literal 1/24 binary64) x)
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) x)
(*.f64 x #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))
(*.f64 (fabs.f64 (*.f64 #s(literal -1/24 binary64) x)) x)
(*.f64 (fabs.f64 (*.f64 #s(literal 1/24 binary64) x)) x)
(*.f64 (*.f64 #s(literal -1/24 binary64) x) (neg.f64 x))
(*.f64 (neg.f64 x) (*.f64 #s(literal -1/24 binary64) x))
(*.f64 (*.f64 #s(literal 1/24 binary64) x) x)
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
(*.f64 x (fabs.f64 (*.f64 #s(literal -1/24 binary64) x)))
(*.f64 x (fabs.f64 (*.f64 #s(literal 1/24 binary64) x)))
(*.f64 x (*.f64 #s(literal 1/24 binary64) x))
(neg.f64 (*.f64 #s(literal -1/24 binary64) (*.f64 x x)))
(sqrt.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))))
(fabs.f64 (*.f64 #s(literal -1/24 binary64) (*.f64 x x)))
(fabs.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 x #s(literal 1/24 binary64))

eval3.0ms (0.1%)

Memory
4.0MiB live, 4.0MiB allocated
Compiler

Compiled 704 to 133 computations (81.1% saved)

prune5.0ms (0.1%)

Memory
5.6MiB live, 5.6MiB allocated
Pruning

7 alts after pruning (0 fresh and 7 done)

PrunedKeptTotal
New31031
Fresh000
Picked011
Done066
Total31738
Accuracy
100.0%
Counts
38 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.2%
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
50.3%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
50.2%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
50.2%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
4.5%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x)) x))
50.3%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
100.0%
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
Compiler

Compiled 284 to 140 computations (50.7% saved)

regimes6.0ms (0.1%)

Memory
6.5MiB live, 6.5MiB allocated
Counts
9 → 1
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
Calls

2 calls:

3.0ms
x
3.0ms
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Results
AccuracySegmentsBranch
100.0%1(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
100.0%1x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes32.0ms (0.5%)

Memory
-37.4MiB live, 8.8MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
Calls

2 calls:

29.0ms
x
2.0ms
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Results
AccuracySegmentsBranch
50.3%1(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
50.3%1x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes5.0ms (0.1%)

Memory
8.9MiB live, 8.9MiB allocated
Accuracy

Total -29.4b remaining (-92.4%)

Threshold costs -29.4b (-92.4%)

Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(literal 1/24 binary64) x) x)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
Calls

2 calls:

2.0ms
x
2.0ms
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Results
AccuracySegmentsBranch
50.3%1(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
50.3%1x
Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify73.0ms (1.2%)

Memory
-6.7MiB live, 46.2MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02040
13440
24440
35440
47040
510840
619040
739140
8102740
9319140
10698140
Stop Event
node limit
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

soundness350.0ms (5.8%)

Memory
-7.0MiB live, 228.3MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079202
1266202
2777196
33247196
47420196
08622178
Stop Event
done
iter limit
node limit
Compiler

Compiled 74 to 37 computations (50% saved)

preprocess33.0ms (0.5%)

Memory
1.1MiB live, 47.0MiB allocated
Remove

(negabs x)

Compiler

Compiled 144 to 80 computations (44.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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