Details

Time bar (total: 5.2s)

analyze218.0ms (4.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%68.7%6.3%5
25%65.6%9.5%6
37.5%39%23.5%7
37.5%36.7%25.9%8
43.7%20.7%35.6%9
43.7%19.3%37%10
46.8%10.6%42.5%11
46.8%9.9%43.3%12
48.4%5.4%46.2%13
48.4%5%46.6%14
Compiler

Compiled 19 to 17 computations (10.5% saved)

sample55.0ms (1.1%)

Algorithm
intervals
Results
25.0ms256×body128valid
2.0ms21×body128nan
Compiler

Compiled 39 to 35 computations (10.3% saved)

simplify9.0ms (0.2%)

Algorithm
egg-herbie
Rules
16×fma-def_binary64
sub-neg_binary64
*-commutative_binary64
+-commutative_binary64
div-sub_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01526
12623
24021
34921
45621
56321
67421
77321
86221

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
1.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
1.0b
(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
Compiler

Compiled 61 to 49 computations (19.7% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
1.0b
(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
1.0b
(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))

series36.0ms (0.7%)

Counts
3 → 72
Calls

3 calls:

22.0ms
(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
8.0ms
(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
5.0ms
(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

rewrite6.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
11×add-cube-cbrt_binary64
times-frac_binary64
add-cbrt-cube_binary64
Counts
3 → 51
Calls

3 calls:

2.0ms
(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
1.0ms
(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
0.0ms
(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))

simplify127.0ms (2.5%)

Algorithm
egg-herbie
Rules
516×distribute-rgt-in_binary64
515×fma-neg_binary64
508×associate-/l/_binary64
495×distribute-lft-in_binary64
420×distribute-rgt-out_binary64
Counts
123 → 97
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01052186
11502070
22462070
34112070
48742070
521992070
646842070
751092070

prune131.0ms (2.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New93497
Fresh000
Picked101
Done000
Total94498
Error
1.0b
Counts
98 → 4
Alt Table
StatusErrorProgram
1.5b
(*.f64 2 (cbrt.f64 (*.f64 (*.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
1.0b
(*.f64 2 (-.f64 (*.f64 (cos.f64 (*.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (*.f64 (sin.f64 (*.f64 (PI.f64) 2/3)) (sin.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))
1.0b
(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
1.0b
(*.f64 2 (cos.f64 (cbrt.f64 (*.f64 (*.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
Compiler

Compiled 2237 to 1273 computations (43.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.0b
(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
1.0b
(cos.f64 (cbrt.f64 (*.f64 (*.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))
1.0b
(cbrt.f64 (*.f64 (*.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
1.0b
(*.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))

series51.0ms (1%)

Counts
3 → 72
Calls

3 calls:

23.0ms
(cos.f64 (cbrt.f64 (*.f64 (*.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))
20.0ms
(*.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
9.0ms
(cbrt.f64 (*.f64 (*.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

rewrite10.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
10×pow1_binary64
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
3 → 50
Calls

3 calls:

3.0ms
(cbrt.f64 (*.f64 (*.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
3.0ms
(*.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
1.0ms
(cos.f64 (cbrt.f64 (*.f64 (*.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

simplify160.0ms (3.1%)

Algorithm
egg-herbie
Rules
548×unswap-sqr_binary64
439×distribute-rgt-in_binary64
434×distribute-lft-in_binary64
420×exp-prod_binary64
341×fma-def_binary64
Counts
122 → 81
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0753601
11182693
23512383
39652357
431082258
543162258
646652258
748972258

prune342.0ms (6.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2520252
Fresh033
Picked011
Done000
Total2524256
Error
1.0b
Counts
256 → 4
Alt Table
StatusErrorProgram
1.5b
(*.f64 2 (cbrt.f64 (*.f64 (*.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
1.0b
(*.f64 2 (-.f64 (*.f64 (cos.f64 (*.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (*.f64 (sin.f64 (*.f64 (PI.f64) 2/3)) (sin.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))
1.0b
(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
1.0b
(*.f64 2 (cos.f64 (cbrt.f64 (*.f64 (*.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
Compiler

Compiled 10936 to 5600 computations (48.8% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.0b
(expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
1.0b
(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
1.0b
(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
1.0b
(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

series50.0ms (1%)

Counts
2 → 48
Calls

2 calls:

27.0ms
(expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
22.0ms
(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

rewrite2.0ms (0%)

Algorithm
rewrite-expression-head
Rules
log1p-expm1-u_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
2 → 22
Calls

2 calls:

0.0ms
(expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
0.0ms
(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

simplify246.0ms (4.8%)

Algorithm
egg-herbie
Rules
1392×sqr-pow_binary64
724×unswap-sqr_binary64
592×cube-prod_binary64
500×fabs-mul_binary64
470×pow-sqr_binary64
Counts
70 → 42
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0451455
1591377
2741377
3871377
41001377
51221377
61701377
72701377
86141377
912101377
1013491377
1116121377
1219171377
1322111377
1426131377
1529671377
1631501377
1734071377
1835461377
1936251377
2037051377
2144631377
2248551377

prune163.0ms (3.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1172119
Fresh112
Picked011
Done011
Total1185123
Error
0.9b
Counts
123 → 5
Alt Table
StatusErrorProgram
1.0b
(*.f64 2 (log1p.f64 (log.f64 (exp.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))))
1.0b
(*.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3)))
1.0b
(*.f64 2 (-.f64 (*.f64 (cos.f64 (*.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (*.f64 (sin.f64 (*.f64 (PI.f64) 2/3)) (sin.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))
1.0b
(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
1.0b
(*.f64 2 (cos.f64 (cbrt.f64 (*.f64 (*.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
Compiler

Compiled 2844 to 1738 computations (38.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.0b
(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)
1.0b
(cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
1.0b
(cbrt.f64 (pow.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3))
1.0b
(pow.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3)

series101.0ms (2%)

Counts
4 → 96
Calls

4 calls:

52.0ms
(pow.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3)
22.0ms
(cbrt.f64 (pow.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3))
21.0ms
(cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
6.0ms
(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)

rewrite11.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity_binary64
18×add-sqr-sqrt_binary64
18×add-cube-cbrt_binary64
12×cbrt-prod_binary64
times-frac_binary64
Counts
4 → 89
Calls

4 calls:

3.0ms
(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)
2.0ms
(pow.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3)
2.0ms
(cbrt.f64 (pow.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3))
1.0ms
(cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))

simplify206.0ms (4%)

Algorithm
egg-herbie
Rules
580×fma-def_binary64
459×*-commutative_binary64
441×log-prod_binary64
384×exp-prod_binary64
358×sqr-pow_binary64
Counts
185 → 125
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01373920
12093650
24443634
313803634
426273631
542303631
646233631
748073631

prune136.0ms (2.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1232125
Fresh112
Picked101
Done022
Total1255130
Error
0.0b
Counts
130 → 5
Alt Table
StatusErrorProgram
1.0b
(*.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3)) (sqrt.f64 3)))) 3)))
1.0b
(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
0.0b
(*.f64 2 (*.f64 (cbrt.f64 (*.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))) (cbrt.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))
1.0b
(*.f64 2 (log1p.f64 (log.f64 (exp.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))))
1.0b
(*.f64 2 (cos.f64 (cbrt.f64 (*.f64 (*.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
Compiler

Compiled 3139 to 1954 computations (37.8% saved)

regimes1.8s (34.2%)

Accuracy

Total 0.0b remaining (72.8%)

Threshold costs 0.0b (72.8%)

Counts
163 → 1
Compiler

Compiled 38025 to 30365 computations (20.1% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01865
12665
23065
33365
43465
53465

end1.0ms (0%)

Compiler

Compiled 41 to 27 computations (34.1% saved)

sample1.3s (24.6%)

Algorithm
intervals
Results
840.0ms8000×body128valid
47.0ms550×body128nan
Compiler

Compiled 199 to 149 computations (25.1% saved)

Profiling

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