Details

Time bar (total: 4.7s)

analyze763.0ms (16.4%)

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
0%99.9%0.1%5
0%99.9%0.1%6
12.5%87.4%0.1%7
18.7%81.1%0.1%8
18.7%81.1%0.1%9
42.1%57.7%0.1%10
49.1%50.7%0.1%11
49.1%50.7%0.1%12
66.9%33%0.1%13
71.7%28.2%0.1%14
Compiler

Compiled 25 to 19 computations (24% saved)

sample1.3s (27.3%)

Results
1.2s8256×body128valid
Compiler

Compiled 74 to 56 computations (24.3% saved)

simplify25.0ms (0.5%)

Algorithm
egg-herbie
Rules
722×fma-def_binary64
94×distribute-rgt-out_binary64
88×associate-/l*_binary64
66×associate-*l*_binary64
65×*-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01925
13925
27123
313423
424723
538923
656723
767023
883123
991423
1097423
1197523
1297223

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
15.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
15.9b
(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)
21.4b
(+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)))
Compiler

Compiled 129 to 93 computations (27.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)
0.1b
(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)
0.3b
(fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)
15.4b
(/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000))

series94.0ms (2%)

Counts
4 → 72
Calls

4 calls:

87.0ms
(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)
3.0ms
(/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000))
2.0ms
(fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)
2.0ms
(fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)

rewrite5.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
times-frac_binary64
add-cbrt-cube_binary64
Counts
4 → 59
Calls

4 calls:

2.0ms
(/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000))
0.0ms
(fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)
0.0ms
(fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)
0.0ms
(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)

simplify133.0ms (2.9%)

Algorithm
egg-herbie
Rules
701×fma-neg_binary64
357×associate-/l*_binary64
357×times-frac_binary64
331×fma-def_binary64
198×associate-/l/_binary64
Counts
131 → 117
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01733421
14012901
210262870
329872573
449862571
552782571

prune147.0ms (3.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1116117
Fresh011
Picked101
Done000
Total1127119
Error
0.1b
Counts
119 → 7
Alt Table
StatusErrorProgram
12.8b
(fma.f64 692910599291889/10000000000000000 y x)
13.0b
(fma.f64 y 279195317918525/3350343815022304 x)
41.2b
(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)) (sqrt.f64 (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)))
15.9b
(+.f64 (*.f64 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (*.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000))) (fma.f64 11167812716741/40000000000000 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x))
21.8b
(fma.f64 y (/.f64 (fma.f64 z (cbrt.f64 (pow.f64 (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 3)) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)
16.0b
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000))) (/.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000))) x)
21.4b
(+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)))
Compiler

Compiled 2915 to 2025 computations (30.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 692910599291889/10000000000000000 y x)

series3.0ms (0.1%)

Counts
1 → 24
Calls

1 calls:

3.0ms
(fma.f64 692910599291889/10000000000000000 y x)

rewrite1.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
1 → 10
Calls

1 calls:

0.0ms
(fma.f64 692910599291889/10000000000000000 y x)

simplify86.0ms (1.8%)

Algorithm
egg-herbie
Rules
645×distribute-rgt-in_binary64
623×distribute-lft-out_binary64
494×distribute-lft-in_binary64
445×distribute-rgt-out_binary64
412×*-commutative_binary64
Counts
34 → 14
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
016193
119182
242182
3103182
4282182
5916182
61568182
72166182
82356182
92900182
103204182
113902182
125196182

prune18.0ms (0.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New11314
Fresh156
Picked011
Done000
Total12921
Error
0.0b
Counts
21 → 9
Alt Table
StatusErrorProgram
12.8b
(fma.f64 692910599291889/10000000000000000 y x)
13.0b
(fma.f64 y 279195317918525/3350343815022304 x)
21.8b
(fma.f64 y (/.f64 (fma.f64 z (cbrt.f64 (pow.f64 (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 3)) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)
16.0b
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000))) (/.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000))) x)
41.1b
(*.f64 (sqrt.f64 (fma.f64 692910599291889/10000000000000000 y x)) (sqrt.f64 (fma.f64 692910599291889/10000000000000000 y x)))
13.7b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x))) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)))
46.6b
(cbrt.f64 (pow.f64 (fma.f64 692910599291889/10000000000000000 y x) 3))
15.9b
(+.f64 (*.f64 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (*.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000))) (fma.f64 11167812716741/40000000000000 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x))
21.4b
(+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)))
Compiler

Compiled 443 to 315 computations (28.9% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 y 279195317918525/3350343815022304 x)

series3.0ms (0.1%)

Counts
1 → 24
Calls

1 calls:

3.0ms
(fma.f64 y 279195317918525/3350343815022304 x)

rewrite1.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
1 → 10
Calls

1 calls:

0.0ms
(fma.f64 y 279195317918525/3350343815022304 x)

simplify87.0ms (1.9%)

Algorithm
egg-herbie
Rules
645×distribute-rgt-in_binary64
623×distribute-lft-out_binary64
494×distribute-lft-in_binary64
445×distribute-rgt-out_binary64
411×associate-*l*_binary64
Counts
34 → 21
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
017193
120182
242182
3103182
4282182
5916182
61568182
72166182
82356182
92900182
103204182
113902182
125196182

prune22.0ms (0.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New21021
Fresh077
Picked011
Done011
Total21930
Error
0.0b
Counts
30 → 9
Alt Table
StatusErrorProgram
12.8b
(fma.f64 692910599291889/10000000000000000 y x)
13.0b
(fma.f64 y 279195317918525/3350343815022304 x)
21.8b
(fma.f64 y (/.f64 (fma.f64 z (cbrt.f64 (pow.f64 (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 3)) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)
16.0b
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000))) (/.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000))) x)
41.1b
(*.f64 (sqrt.f64 (fma.f64 692910599291889/10000000000000000 y x)) (sqrt.f64 (fma.f64 692910599291889/10000000000000000 y x)))
13.7b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x))) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)))
46.6b
(cbrt.f64 (pow.f64 (fma.f64 692910599291889/10000000000000000 y x) 3))
15.9b
(+.f64 (*.f64 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (*.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000))) (fma.f64 11167812716741/40000000000000 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x))
21.4b
(+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)))
Compiler

Compiled 493 to 347 computations (29.6% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 692910599291889/10000000000000000 y x)
0.3b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x))) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)))
0.5b
(*.f64 (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)))
0.6b
(cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x))

series53.0ms (1.1%)

Counts
3 → 72
Calls

3 calls:

28.0ms
(*.f64 (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)))
20.0ms
(cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x))
4.0ms
(*.f64 (*.f64 (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x))) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)))

rewrite19.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
29×pow1_binary64
24×add-sqr-sqrt_binary64
23×cbrt-prod_binary64
16×pow1/3_binary64
14×*-un-lft-identity_binary64
Counts
3 → 93
Calls

3 calls:

6.0ms
(*.f64 (*.f64 (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x))) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)))
4.0ms
(*.f64 (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)))
1.0ms
(cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x))

simplify123.0ms (2.6%)

Algorithm
egg-herbie
Rules
849×times-frac_binary64
648×fma-def_binary64
254×fma-neg_binary64
228×cancel-sign-sub-inv_binary64
196×associate-*r*_binary64
Counts
165 → 210
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02703559
17023353
221723016
349693016
450713016

prune300.0ms (6.4%)

Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New3735378
Fresh156
Picked011
Done022
Total37413387
Error
0.0b
Counts
387 → 13
Alt Table
StatusErrorProgram
41.5b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 692910599291889/10000000000000000 y x))) (cbrt.f64 (sqrt.f64 (fma.f64 692910599291889/10000000000000000 y x)))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 692910599291889/10000000000000000 y x))) (cbrt.f64 (sqrt.f64 (fma.f64 692910599291889/10000000000000000 y x))))) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)))
21.8b
(fma.f64 y (/.f64 (fma.f64 z (cbrt.f64 (pow.f64 (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 3)) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)
12.8b
(fma.f64 692910599291889/10000000000000000 y x)
13.0b
(fma.f64 y 279195317918525/3350343815022304 x)
15.8b
(*.f64 (expm1.f64 (log1p.f64 (*.f64 (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x))))) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)))
15.9b
(+.f64 (*.f64 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (*.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000))) (fma.f64 11167812716741/40000000000000 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x))
21.4b
(+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)))
14.2b
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y 692910599291889/10000000000000000 x))) 6) (cbrt.f64 (fma.f64 y 692910599291889/10000000000000000 x)))
14.0b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y 692910599291889/10000000000000000 x))) 6)) (cbrt.f64 (cbrt.f64 (fma.f64 y 692910599291889/10000000000000000 x)))))
16.0b
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000))) (/.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000))) x)
38.8b
(*.f64 (cbrt.f64 (*.f64 (fma.f64 692910599291889/10000000000000000 y x) (fma.f64 692910599291889/10000000000000000 y x))) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)))
41.1b
(*.f64 (sqrt.f64 (fma.f64 692910599291889/10000000000000000 y x)) (sqrt.f64 (fma.f64 692910599291889/10000000000000000 y x)))
13.7b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x))) (cbrt.f64 (fma.f64 692910599291889/10000000000000000 y x)))
Compiler

Compiled 11174 to 7990 computations (28.5% saved)

regimes1.1s (24.6%)

Accuracy

Total 0.6b remaining (86.2%)

Threshold costs 0.6b (86.2%)

Counts
106 → 3
Compiler

Compiled 12063 to 8928 computations (26% saved)

bsearch60.0ms (1.3%)

Steps
ItersRangePoint
9
4.867051807925935e-16
4.854481376535082e-9
4.770054248343753e-9
10
-43739.185400016395
-1.9770681382042597e-8
-5.35837927315707
Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.2%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64
*-commutative_binary64
distribute-neg-frac_binary64
neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02775
13175
23975
34175
44275
54175

end263.0ms (5.6%)

Compiler

Compiled 399 to 286 computations (28.3% saved)

Profiling

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