Details

Time bar (total: 2.5s)

analyze6.0ms (0.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
25%25%50%4
37.5%12.5%50%5
43.7%6.2%50%6
46.9%3.1%50%7
48.4%1.6%50%8
49.2%0.8%50%9
49.6%0.4%50%10
49.8%0.2%50%11
49.9%0.1%50%12
49.9%0%50.1%13
49.9%0%50.1%14
Compiler

Compiled 22 to 17 computations (22.7% saved)

sample1.2s (46.2%)

Results
1.0s8256×body128valid
0.0msbody128invalid
Compiler

Compiled 65 to 50 computations (23.1% saved)

simplify116.0ms (4.6%)

Algorithm
egg-herbie
Rules
1332×fma-def_binary64
889×associate-/r*_binary64
605×neg-sub0_binary64
599×neg-mul-1_binary64
576×fma-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01731
14228
210226
326126
468426
5108824
6180124
7354124
8391424
9400224
10441624
11440924
12441524
13515924

prune5.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.0b
(/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
1.0b
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
Compiler

Compiled 113 to 85 computations (24.8% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
0.0b
(*.f64 (PI.f64) (fma.f64 v v -1))
1.0b
(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))

series50.0ms (2%)

Counts
3 → 36
Calls

3 calls:

40.0ms
(/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
6.0ms
(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
3.0ms
(*.f64 (PI.f64) (fma.f64 v v -1))

rewrite61.0ms (2.4%)

Algorithm
batch-egg-rewrite
Rules
251×expm1-udef_binary64
251×log1p-udef_binary64
216×log-pow_binary64
151×log-div_binary64
142×add-sqr-sqrt_binary64
Counts
3 → 80
Calls

3 calls:

59.0ms
(/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
59.0ms
(*.f64 (PI.f64) (fma.f64 v v -1))
59.0ms
(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01445
129345
2350445
3488945

simplify97.0ms (3.9%)

Algorithm
egg-herbie
Rules
672×fma-def_binary64
660×times-frac_binary64
581×fma-neg_binary64
252×cancel-sign-sub-inv_binary64
132×sub-neg_binary64
Counts
116 → 124
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01781475
15651444
220051340
347171334
450801334

prune149.0ms (5.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1222124
Fresh101
Picked011
Done000
Total1233126
Error
0b
Counts
126 → 3
Alt Table
StatusErrorProgram
0.0b
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) -4/3) -1) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
0.0b
(/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
0.5b
(/.f64 (fma.f64 4/3 (/.f64 (*.f64 v v) (PI.f64)) (/.f64 4/3 (PI.f64))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
Compiler

Compiled 3549 to 2685 computations (24.3% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (/.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) -4/3) -1)
0.0b
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) -4/3) -1) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
0.0b
(/.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) -4/3)
0.0b
(*.f64 (PI.f64) (fma.f64 v v -1))

series35.0ms (1.4%)

Counts
3 → 36
Calls

3 calls:

21.0ms
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) -4/3) -1) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
9.0ms
(pow.f64 (/.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) -4/3) -1)
4.0ms
(/.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) -4/3)

rewrite65.0ms (2.6%)

Algorithm
batch-egg-rewrite
Rules
265×expm1-udef_binary64
265×log1p-udef_binary64
234×log-pow_binary64
153×add-sqr-sqrt_binary64
144×log1p-expm1-u_binary64
Counts
3 → 95
Calls

3 calls:

63.0ms
(pow.f64 (/.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) -4/3) -1)
63.0ms
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) -4/3) -1) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
63.0ms
(/.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) -4/3)
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01554
131848
2365248
3479348

simplify70.0ms (2.8%)

Algorithm
egg-herbie
Rules
682×fma-def_binary64
660×times-frac_binary64
578×fma-neg_binary64
268×cancel-sign-sub-inv_binary64
134×sub-neg_binary64
Counts
131 → 138
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01811509
15791478
220481392
347251386
450861386

prune178.0ms (7.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1621163
Fresh101
Picked101
Done011
Total1642166
Error
0b
Counts
166 → 2
Alt Table
StatusErrorProgram
0.0b
(/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
0.0b
(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
Compiler

Compiled 4400 to 3323 computations (24.5% saved)

localize13.0ms (0.5%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
0.0b
(/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))
1.0b
(/.f64 -4/3 (PI.f64))

series28.0ms (1.1%)

Counts
3 → 24
Calls

3 calls:

22.0ms
(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
6.0ms
(/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))
0.0ms
(/.f64 -4/3 (PI.f64))

rewrite68.0ms (2.7%)

Algorithm
batch-egg-rewrite
Rules
259×expm1-udef_binary64
259×log1p-udef_binary64
222×log-pow_binary64
146×add-sqr-sqrt_binary64
137×add-cbrt-cube_binary64
Counts
3 → 101
Calls

3 calls:

66.0ms
(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
66.0ms
(/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))
66.0ms
(/.f64 -4/3 (PI.f64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01441
129941
2375341
3494741

simplify83.0ms (3.3%)

Algorithm
egg-herbie
Rules
669×fma-def_binary64
660×times-frac_binary64
600×fma-neg_binary64
252×cancel-sign-sub-inv_binary64
130×associate-/r*_binary64
Counts
125 → 139
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01751347
15591325
219941239
347651233
451511233

prune146.0ms (5.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1390139
Fresh000
Picked011
Done011
Total1392141
Error
0b
Counts
141 → 2
Alt Table
StatusErrorProgram
0.0b
(/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
0.0b
(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
Compiler

Compiled 3906 to 2961 computations (24.2% saved)

regimes104.0ms (4.1%)

Accuracy

Total 0.0b remaining (33.4%)

Threshold costs 0.0b (33.4%)

Counts
13 → 1
Compiler

Compiled 940 to 746 computations (20.6% saved)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01424
11524
21524

end55.0ms (2.2%)

Compiler

Compiled 68 to 52 computations (23.5% saved)

Profiling

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