Details

Time bar (total: 5.1s)

analyze8.0ms (0.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%25%25%4
62.5%12.5%25%5
62.5%6.2%31.3%6
65.6%3.1%31.3%7
65.6%1.6%32.8%8
66.4%0.8%32.8%9
66.4%0.4%33.2%10
66.6%0.2%33.2%11
66.6%0.1%33.3%12
66.6%0%33.3%13
66.6%0%33.3%14
Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.6s (31.9%)

Results
1.4s8256×body128valid
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify177.0ms (3.5%)

Algorithm
egg-herbie
Rules
1355×fma-neg_binary64
877×fma-def_binary64
720×distribute-rgt-neg-in_binary64
564×cancel-sign-sub-inv_binary64
530×sqr-pow_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0916
12111
24911
310711
417011
529111
651611
7100211
8149211
9212811
10273411
11315411
12335811
13353511
14410611
15309911
16352811
17466811
18473211

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.2b
(*.f64 x (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))
0.2b
(-.f64 (*.f64 238732414637843/250000000000000 x) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))
Compiler

Compiled 62 to 40 computations (35.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 238732414637843/250000000000000 x) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))
0.1b
(*.f64 238732414637843/250000000000000 x)
0.2b
(*.f64 (*.f64 x x) x)
0.2b
(*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x))

series24.0ms (0.5%)

Counts
4 → 36
Calls

4 calls:

10.0ms
(*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x))
6.0ms
(-.f64 (*.f64 238732414637843/250000000000000 x) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))
5.0ms
(*.f64 (*.f64 x x) x)
3.0ms
(*.f64 238732414637843/250000000000000 x)

rewrite204.0ms (4%)

Algorithm
batch-egg-rewrite
Rules
459×log-prod_binary64
403×fma-def_binary64
239×pow2_binary64
227×egg-rr
178×fma-neg_binary64
Counts
4 → 227
Calls

4 calls:

192.0ms
(-.f64 (*.f64 238732414637843/250000000000000 x) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))
192.0ms
(*.f64 238732414637843/250000000000000 x)
192.0ms
(*.f64 (*.f64 x x) x)
192.0ms
(*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0928
120026
2234926
3486926
000
100

simplify235.0ms (4.6%)

Algorithm
egg-herbie
Rules
1274×fma-def_binary64
875×fma-neg_binary64
818×unswap-sqr_binary64
685×cube-prod_binary64
665×cancel-sign-sub-inv_binary64
Counts
263 → 233
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
011267
127249
264249
3155249
4313249
5728249
61078249
71590249
82988249
94112249
104092249
114547249
124019249
134022249
143466249
154267249
164642249
174931249
184727249

prune440.0ms (8.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2258233
Fresh101
Picked101
Done000
Total2278235
Error
0.0b
Counts
235 → 8
Alt Table
StatusErrorProgram
37.6b
(/.f64 (+.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000)) 3) (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))) 3)) (+.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000)) 2) (-.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))) 2) (*.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000)) (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))))))
1.2b
(-.f64 (pow.f64 (cbrt.f64 (*.f64 x 238732414637843/250000000000000)) 3) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))
29.5b
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 238732414637843/250000000000000) (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
29.3b
(fma.f64 (*.f64 -6450306886639899/50000000000000000 (pow.f64 x 3/2)) (pow.f64 x 3/2) (*.f64 x 238732414637843/250000000000000))
0.2b
(fma.f64 x (-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (*.f64 x x))) (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))))
26.0b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 x 238732414637843/250000000000000) 3)) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))
0.1b
(fma.f64 x 238732414637843/250000000000000 (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
28.4b
(*.f64 (-.f64 (*.f64 (*.f64 x x) 56993165798814994692847692649/62500000000000000000000000000) (*.f64 41606458931834106848498498730201/2500000000000000000000000000000000 (pow.f64 x 6))) (/.f64 1 (fma.f64 6450306886639899/50000000000000000 (pow.f64 x 3) (*.f64 x 238732414637843/250000000000000))))
Compiler

Compiled 5090 to 3926 computations (22.9% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 x 238732414637843/250000000000000 (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
0.2b
(*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000)

series13.0ms (0.3%)

Counts
2 → 24
Calls

2 calls:

7.0ms
(fma.f64 x 238732414637843/250000000000000 (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
6.0ms
(*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000)

rewrite82.0ms (1.6%)

Algorithm
batch-egg-rewrite
Rules
651×log1p-expm1-u_binary64
651×expm1-log1p-u_binary64
305×log-prod_binary64
134×expm1-udef_binary64
134×log1p-udef_binary64
Counts
2 → 45
Calls

2 calls:

80.0ms
(fma.f64 x 238732414637843/250000000000000 (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
80.0ms
(*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0818
116718
2169718
3512218
000
100

simplify226.0ms (4.5%)

Algorithm
egg-herbie
Rules
1274×fma-def_binary64
875×fma-neg_binary64
818×unswap-sqr_binary64
685×cube-prod_binary64
665×cancel-sign-sub-inv_binary64
Counts
69 → 50
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
011219
127201
264201
3155201
4313201
5728201
61078201
71590201
82988201
94112201
104092201
114547201
124019201
134022201
143466201
154267201
164642201
174931201
184727201

prune93.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New50050
Fresh077
Picked011
Done000
Total50858
Error
0.0b
Counts
58 → 8
Alt Table
StatusErrorProgram
37.6b
(/.f64 (+.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000)) 3) (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))) 3)) (+.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000)) 2) (-.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))) 2) (*.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000)) (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))))))
1.2b
(-.f64 (pow.f64 (cbrt.f64 (*.f64 x 238732414637843/250000000000000)) 3) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))
29.5b
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 238732414637843/250000000000000) (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
29.3b
(fma.f64 (*.f64 -6450306886639899/50000000000000000 (pow.f64 x 3/2)) (pow.f64 x 3/2) (*.f64 x 238732414637843/250000000000000))
0.2b
(fma.f64 x (-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (*.f64 x x))) (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))))
26.0b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 x 238732414637843/250000000000000) 3)) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))
0.1b
(fma.f64 x 238732414637843/250000000000000 (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
28.4b
(*.f64 (-.f64 (*.f64 (*.f64 x x) 56993165798814994692847692649/62500000000000000000000000000) (*.f64 41606458931834106848498498730201/2500000000000000000000000000000000 (pow.f64 x 6))) (/.f64 1 (fma.f64 6450306886639899/50000000000000000 (pow.f64 x 3) (*.f64 x 238732414637843/250000000000000))))
Compiler

Compiled 989 to 792 computations (19.9% saved)

localize34.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 6450306886639899/50000000000000000 (*.f64 x x))
0.2b
(fma.f64 x (-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (*.f64 x x))) (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))))
0.2b
(*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))
33.7b
(fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))

series72.0ms (1.4%)

Counts
4 → 36
Calls

4 calls:

52.0ms
(fma.f64 x (-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (*.f64 x x))) (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))))
10.0ms
(fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
5.0ms
(*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))
4.0ms
(*.f64 6450306886639899/50000000000000000 (*.f64 x x))

rewrite162.0ms (3.2%)

Algorithm
batch-egg-rewrite
Rules
370×prod-diff_binary64
272×fma-udef_binary64
258×fma-def_binary64
228×expm1-udef_binary64
228×log1p-udef_binary64
Counts
4 → 80
Calls

4 calls:

159.0ms
(*.f64 6450306886639899/50000000000000000 (*.f64 x x))
159.0ms
(fma.f64 x (-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (*.f64 x x))) (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))))
159.0ms
(*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))
159.0ms
(fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01355
128341
2305939
3481639
4492139
5480739
000
100

simplify109.0ms (2.2%)

Algorithm
egg-herbie
Rules
978×fma-def_binary64
596×distribute-rgt-neg-in_binary64
566×fma-neg_binary64
540×distribute-lft-neg-in_binary64
396×neg-mul-1_binary64
Counts
116 → 88
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
015231
135213
277213
3209213
4578213
5973213
61784213
72820213
84708213
94928213
104859213

prune199.0ms (3.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New88088
Fresh066
Picked011
Done011
Total88896
Error
0.0b
Counts
96 → 8
Alt Table
StatusErrorProgram
37.6b
(/.f64 (+.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000)) 3) (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))) 3)) (+.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000)) 2) (-.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))) 2) (*.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000)) (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))))))
1.2b
(-.f64 (pow.f64 (cbrt.f64 (*.f64 x 238732414637843/250000000000000)) 3) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))
29.5b
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 238732414637843/250000000000000) (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
29.3b
(fma.f64 (*.f64 -6450306886639899/50000000000000000 (pow.f64 x 3/2)) (pow.f64 x 3/2) (*.f64 x 238732414637843/250000000000000))
0.2b
(fma.f64 x (-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (*.f64 x x))) (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))))
26.0b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 x 238732414637843/250000000000000) 3)) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))
0.1b
(fma.f64 x 238732414637843/250000000000000 (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
28.4b
(*.f64 (-.f64 (*.f64 (*.f64 x x) 56993165798814994692847692649/62500000000000000000000000000) (*.f64 41606458931834106848498498730201/2500000000000000000000000000000000 (pow.f64 x 6))) (/.f64 1 (fma.f64 6450306886639899/50000000000000000 (pow.f64 x 3) (*.f64 x 238732414637843/250000000000000))))
Compiler

Compiled 2066 to 1498 computations (27.5% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 x x) x)
0.2b
(*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x))
0.6b
(cbrt.f64 (*.f64 x 238732414637843/250000000000000))
0.7b
(pow.f64 (cbrt.f64 (*.f64 x 238732414637843/250000000000000)) 3)

series197.0ms (3.9%)

Counts
2 → 24
Calls

2 calls:

131.0ms
(pow.f64 (cbrt.f64 (*.f64 x 238732414637843/250000000000000)) 3)
66.0ms
(cbrt.f64 (*.f64 x 238732414637843/250000000000000))

rewrite108.0ms (2.1%)

Algorithm
batch-egg-rewrite
Rules
928×log1p-udef_binary64
496×log1p-expm1-u_binary64
496×expm1-log1p-u_binary64
440×unpow-prod-down_binary64
247×log-prod_binary64
Counts
2 → 104
Calls

2 calls:

105.0ms
(cbrt.f64 (*.f64 x 238732414637843/250000000000000))
105.0ms
(pow.f64 (cbrt.f64 (*.f64 x 238732414637843/250000000000000)) 3)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
112910
2131610
3494510
4640310
000
100

simplify159.0ms (3.1%)

Algorithm
egg-herbie
Rules
1252×sqr-pow_binary64
710×cube-prod_binary64
698×pow-sqr_binary64
694×fabs-mul_binary64
416×unswap-sqr_binary64
Counts
128 → 107
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
014152
128152
245152
377152
4161152
5409152
6548152
7911152
8932152
91091152
101281152
111546152
121829152
132247152
142719152
153382152
163670152
173966152
184176152
194264152
204364152
215372152

prune190.0ms (3.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1401141
Fresh235
Picked011
Done022
Total1427149
Error
0.0b
Counts
149 → 7
Alt Table
StatusErrorProgram
37.6b
(/.f64 (+.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000)) 3) (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))) 3)) (+.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000)) 2) (-.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))) 2) (*.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000)) (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))))))
1.2b
(-.f64 (pow.f64 (cbrt.f64 (*.f64 x 238732414637843/250000000000000)) 3) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))
26.0b
(-.f64 (cbrt.f64 (*.f64 (pow.f64 x 3) 13606116089006033875034270860295875508316107/15625000000000000000000000000000000000000000)) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))
29.3b
(fma.f64 (*.f64 -6450306886639899/50000000000000000 (pow.f64 x 3/2)) (pow.f64 x 3/2) (*.f64 x 238732414637843/250000000000000))
0.2b
(fma.f64 x (-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (*.f64 x x))) (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))))
26.0b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 x 238732414637843/250000000000000) 3)) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))
0.1b
(fma.f64 x 238732414637843/250000000000000 (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
Compiler

Compiled 2777 to 1887 computations (32% saved)

regimes367.0ms (7.3%)

Accuracy

Total 0.1b remaining (60.8%)

Threshold costs 0.1b (60.8%)

Counts
92 → 1
Compiler

Compiled 2950 to 2246 computations (23.9% saved)

simplify4.0ms (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
0913
11413
21613
31713
41713

end294.0ms (5.8%)

Compiler

Compiled 175 to 137 computations (21.7% saved)

Profiling

Loading profile data...