Details

Time bar (total: 5.8s)

analyze777.0ms (13.3%)

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 (21.7%)

Results
1.2s8256×body128valid
Compiler

Compiled 74 to 56 computations (24.3% saved)

simplify23.0ms (0.4%)

Algorithm
egg-herbie
Rules
722×fma-def_binary64
94×distribute-rgt-out_binary64
88×associate-/l*_binary64
68×associate-*l*_binary64
64×*-commutative_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01925
13925
27423
317523
434923
560723
687823
7101023
8125623
9167123
10173523
11173623
Stop Event
saturated
Counts
1 → 2

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
17.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
23.4b
(+.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)))
17.6b
(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)
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)
0.2b
(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)
0.2b
(fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)
17.1b
(/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000))

series83.0ms (1.4%)

Counts
4 → 72
Calls

4 calls:

76.0ms
(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)
1.0ms
(fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)

rewrite73.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
285×expm1-udef_binary64
285×log1p-udef_binary64
160×add-sqr-sqrt_binary64
159×prod-diff_binary64
152×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01556
132356
2388656
Stop Event
node limit
Counts
4 → 102
Calls

4 calls:

71.0ms
(fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)
71.0ms
(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)
71.0ms
(fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)
71.0ms
(/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000))

simplify65.0ms (1.1%)

Algorithm
egg-herbie
Rules
611×cancel-sign-sub-inv_binary64
508×associate-*l*_binary64
322×fma-neg_binary64
300×fma-def_binary64
183×associate-/r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0961961
12801748
27671567
322871270
Stop Event
node limit
Counts
174 → 151

prune183.0ms (3.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1447151
Fresh101
Picked101
Done000
Total1467153
Error
0.1b
Counts
153 → 7
Alt Table
StatusErrorProgram
18.4b
(+.f64 x (fma.f64 11167812716741/40000000000000 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (*.f64 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (*.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)))))
18.5b
(pow.f64 (cbrt.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)) 3)
17.7b
(fma.f64 y (/.f64 (fma.f64 z (pow.f64 (cbrt.f64 (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)) 3) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)
37.9b
(pow.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)) 2)
23.4b
(+.f64 (*.f64 307332350656623/625000000000000 (/.f64 (*.f64 y z) (+.f64 104698244219447/31250000000000 (+.f64 (pow.f64 z 2) (*.f64 6012459259764103/1000000000000000 z))))) (+.f64 (*.f64 11167812716741/40000000000000 (/.f64 y (+.f64 104698244219447/31250000000000 (+.f64 (pow.f64 z 2) (*.f64 6012459259764103/1000000000000000 z))))) (+.f64 (*.f64 692910599291889/10000000000000000 (/.f64 (*.f64 y (pow.f64 z 2)) (+.f64 104698244219447/31250000000000 (+.f64 (pow.f64 z 2) (*.f64 6012459259764103/1000000000000000 z))))) x)))
11.6b
(fma.f64 y 692910599291889/10000000000000000 x)
17.8b
(fma.f64 y (pow.f64 (pow.f64 (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) 3) 1/3) x)
Compiler

Compiled 3588 to 2516 computations (29.9% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.1%)

Counts
1 → 24
Calls

1 calls:

4.0ms
(fma.f64 y 692910599291889/10000000000000000 x)

rewrite33.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
416×log1p-expm1-u_binary64
416×expm1-log1p-u_binary64
365×pow1_binary64
210×unpow-prod-down_binary64
202×log-prod_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
055
11005
211145
Stop Event
node limit
Counts
1 → 39
Calls

1 calls:

32.0ms
(fma.f64 y 692910599291889/10000000000000000 x)

simplify9.0ms (0.1%)

Algorithm
egg-herbie
Rules
fma-def_binary64
+-commutative_binary64
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06105
19105
210105
Stop Event
saturated
Counts
63 → 43

prune37.0ms (0.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New39443
Fresh246
Picked011
Done000
Total41950
Error
0.1b
Counts
50 → 9
Alt Table
StatusErrorProgram
17.7b
(fma.f64 y (/.f64 (fma.f64 z (pow.f64 (cbrt.f64 (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)) 3) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)
13.1b
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y 692910599291889/10000000000000000 x))) 2) 3) (cbrt.f64 (fma.f64 y 692910599291889/10000000000000000 x)))
18.4b
(+.f64 x (fma.f64 11167812716741/40000000000000 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (*.f64 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (*.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)))))
18.5b
(pow.f64 (cbrt.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)) 3)
17.8b
(fma.f64 y (pow.f64 (pow.f64 (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) 3) 1/3) x)
12.5b
(pow.f64 (cbrt.f64 (fma.f64 y 692910599291889/10000000000000000 x)) 3)
47.6b
(cbrt.f64 (pow.f64 (fma.f64 y 692910599291889/10000000000000000 x) 3))
11.6b
(fma.f64 y 692910599291889/10000000000000000 x)
35.7b
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y 692910599291889/10000000000000000 x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y 692910599291889/10000000000000000 x))) 3))
Compiler

Compiled 747 to 548 computations (26.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 y 692910599291889/10000000000000000 x)
0.6b
(cbrt.f64 (fma.f64 y 692910599291889/10000000000000000 x))
0.8b
(pow.f64 (cbrt.f64 (fma.f64 y 692910599291889/10000000000000000 x)) 3)

series1.0s (17.6%)

Counts
2 → 48
Calls

2 calls:

1.0s
(pow.f64 (cbrt.f64 (fma.f64 y 692910599291889/10000000000000000 x)) 3)
17.0ms
(cbrt.f64 (fma.f64 y 692910599291889/10000000000000000 x))

rewrite42.0ms (0.7%)

Algorithm
batch-egg-rewrite
Rules
584×log1p-expm1-u_binary64
584×expm1-log1p-u_binary64
271×log-prod_binary64
169×pow2_binary64
120×expm1-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0812
116112
2161512
Stop Event
node limit
Counts
2 → 65
Calls

2 calls:

41.0ms
(cbrt.f64 (fma.f64 y 692910599291889/10000000000000000 x))
41.0ms
(pow.f64 (cbrt.f64 (fma.f64 y 692910599291889/10000000000000000 x)) 3)

simplify44.0ms (0.7%)

Algorithm
egg-herbie
Rules
592×times-frac_binary64
474×associate-*l*_binary64
401×associate-/l*_binary64
362×fma-def_binary64
317×associate-/r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01441633
14311577
213811399
Stop Event
node limit
Counts
113 → 123

prune107.0ms (1.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1624166
Fresh257
Picked011
Done011
Total16411175
Error
0.0b
Counts
175 → 11
Alt Table
StatusErrorProgram
12.0b
(+.f64 (*.f64 (pow.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000 1/3) y) (*.f64 10000000000000000/692910599291889 (*.f64 (pow.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000 1/3) x)))
17.7b
(fma.f64 y (/.f64 (fma.f64 z (pow.f64 (cbrt.f64 (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)) 3) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)
18.4b
(+.f64 x (fma.f64 11167812716741/40000000000000 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (*.f64 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (*.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)))))
18.5b
(pow.f64 (cbrt.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)) 3)
17.8b
(fma.f64 y (pow.f64 (pow.f64 (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) 3) 1/3) x)
12.5b
(pow.f64 (cbrt.f64 (fma.f64 y 692910599291889/10000000000000000 x)) 3)
37.7b
(fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) 692910599291889/10000000000000000) x)
11.8b
(fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) 692910599291889/10000000000000000) x)
48.0b
(pow.f64 (cbrt.f64 (/.f64 (+.f64 (*.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000 (pow.f64 y 3)) (pow.f64 x 3)) (+.f64 (pow.f64 (*.f64 y 692910599291889/10000000000000000) 2) (-.f64 (*.f64 x x) (*.f64 (*.f64 y 692910599291889/10000000000000000) x))))) 3)
47.6b
(cbrt.f64 (pow.f64 (fma.f64 y 692910599291889/10000000000000000 x) 3))
11.6b
(fma.f64 y 692910599291889/10000000000000000 x)
Compiler

Compiled 3131 to 2399 computations (23.4% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) 692910599291889/10000000000000000) x)
0.5b
(pow.f64 (cbrt.f64 y) 2)
0.5b
(*.f64 (cbrt.f64 y) 692910599291889/10000000000000000)
0.5b
(cbrt.f64 y)

series248.0ms (4.2%)

Counts
4 → 60
Calls

4 calls:

140.0ms
(fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) 692910599291889/10000000000000000) x)
40.0ms
(pow.f64 (cbrt.f64 y) 2)
35.0ms
(*.f64 (cbrt.f64 y) 692910599291889/10000000000000000)
33.0ms
(cbrt.f64 y)

rewrite48.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
694×log1p-expm1-u_binary64
694×expm1-log1p-u_binary64
146×expm1-udef_binary64
146×log1p-udef_binary64
85×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0930
118122
2196822
Stop Event
node limit
Counts
4 → 77
Calls

4 calls:

46.0ms
(fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) 692910599291889/10000000000000000) x)
46.0ms
(pow.f64 (cbrt.f64 y) 2)
46.0ms
(*.f64 (cbrt.f64 y) 692910599291889/10000000000000000)
46.0ms
(cbrt.f64 y)

simplify91.0ms (1.6%)

Algorithm
egg-herbie
Rules
508×fma-def_binary64
488×sqr-pow_binary64
412×unswap-sqr_binary64
343×*-commutative_binary64
243×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
020379
150379
299379
3266379
41014379
51879379
62017379
72227379
82524379
92883379
103378379
113982379
124712379
Stop Event
node limit
Counts
137 → 92

prune122.0ms (2.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New1153118
Fresh088
Picked011
Done112
Total11613129
Error
0.0b
Counts
129 → 13
Alt Table
StatusErrorProgram
12.0b
(+.f64 (*.f64 (pow.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000 1/3) y) (*.f64 10000000000000000/692910599291889 (*.f64 (pow.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000 1/3) x)))
17.7b
(fma.f64 y (/.f64 (fma.f64 z (pow.f64 (cbrt.f64 (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)) 3) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)
18.4b
(+.f64 x (fma.f64 11167812716741/40000000000000 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (*.f64 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (*.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)))))
18.5b
(pow.f64 (cbrt.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)) 3)
17.9b
(fma.f64 (pow.f64 (*.f64 (sqrt.f64 (cbrt.f64 (*.f64 y (cbrt.f64 y)))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 y)) 2))) 2) (*.f64 (cbrt.f64 y) 692910599291889/10000000000000000) x)
37.7b
(fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) 692910599291889/10000000000000000) x)
11.8b
(fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) 692910599291889/10000000000000000) x)
11.9b
(fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 y)) 3) 692910599291889/10000000000000000) x)
48.0b
(pow.f64 (cbrt.f64 (/.f64 (+.f64 (*.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000 (pow.f64 y 3)) (pow.f64 x 3)) (+.f64 (pow.f64 (*.f64 y 692910599291889/10000000000000000) 2) (-.f64 (*.f64 x x) (*.f64 (*.f64 y 692910599291889/10000000000000000) x))))) 3)
47.6b
(cbrt.f64 (pow.f64 (fma.f64 y 692910599291889/10000000000000000 x) 3))
11.6b
(fma.f64 y 692910599291889/10000000000000000 x)
17.8b
(fma.f64 y (pow.f64 (pow.f64 (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) 3) 1/3) x)
11.9b
(fma.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 y)) 2) (*.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 y))) (*.f64 (cbrt.f64 y) 692910599291889/10000000000000000) x)
Compiler

Compiled 1704 to 1044 computations (38.7% saved)

regimes1.2s (21.3%)

Accuracy

Total 0.1b remaining (72.3%)

Threshold costs 0.1b (72.3%)

Counts
123 → 3
Compiler

Compiled 12228 to 8968 computations (26.7% saved)

bsearch45.0ms (0.8%)

Steps
ItersRangePoint
10
0.25684162106722397
51844314701.5997
2092713.5458700638
5
-1.5541873432777608e+32
-5255274192941128000.0
-14193016526032128000.0
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03795
14595
25295
35495
45595
Stop Event
saturated

end234.0ms (4%)

Compiler

Compiled 387 to 277 computations (28.4% saved)

Profiling

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