Details

Time bar (total: 5.4s)

analyze89.0ms (1.6%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%50%0%4
50%50%0%5
81.2%18.7%0%6
100%0%0%7
Compiler

Compiled 175 to 47 computations (73.1% saved)

sample89.0ms (1.6%)

Algorithm
intervals
Results
81.0ms256×body128valid
Compiler

Compiled 350 to 94 computations (73.1% saved)

simplify70.0ms (1.3%)

Algorithm
egg-herbie
Rules
755×unswap-sqr_binary64
705×fma-def_binary64
691×distribute-rgt-out_binary64
576×+-commutative_binary64
488×*-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
046256
1133150
2549101
3242790
4370584
5452984
6487484
7588784

prune9.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
30.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
30.9b
(*.f64 (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (*.f64 1049934947/10000000000 (*.f64 x x))) (*.f64 106015151/2500000000 (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 36322091/5000000000 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)))) (*.f64 2532017/5000000000 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)))) (*.f64 1789971/10000000000 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (*.f64 7715471019/10000000000 (*.f64 x x))) (*.f64 2909738639/10000000000 (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 694555761/10000000000 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)))) (*.f64 70002721/5000000000 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)))) (*.f64 1665589/2000000000 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)))) (*.f64 (*.f64 2 1789971/10000000000) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x))))) x)
30.9b
(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
Compiler

Compiled 704 to 274 computations (61.1% saved)

localize35.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))
0.5b
(fma.f64 1049934947/10000000000 (*.f64 x x) 1)
14.1b
(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
30.3b
(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1)))))))

series22.0ms (0.4%)

Counts
4 → 48
Calls

4 calls:

9.0ms
(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1)))))))
6.0ms
(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
4.0ms
(fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))
3.0ms
(fma.f64 1049934947/10000000000 (*.f64 x x) 1)

rewrite20.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64
20×*-un-lft-identity_binary64
20×add-cube-cbrt_binary64
19×times-frac_binary64
13×associate-*r*_binary64
Counts
4 → 83
Calls

4 calls:

6.0ms
(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
2.0ms
(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1)))))))
0.0ms
(fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))
0.0ms
(fma.f64 1049934947/10000000000 (*.f64 x x) 1)

simplify205.0ms (3.8%)

Algorithm
egg-herbie
Rules
552×associate-*l*_binary64
479×associate-*r*_binary64
410×fma-def_binary64
236×associate-*r/_binary64
217×distribute-rgt-in_binary64
Counts
131 → 190
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02108288
14697376
213677368
349187368
449617368

prune437.0ms (8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1882190
Fresh101
Picked011
Done000
Total1893192
Error
0b
Counts
192 → 3
Alt Table
StatusErrorProgram
33.6b
(*.f64 x (-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1) (fma.f64 833192009/1250000000 (*.f64 x x) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6)))))
30.2b
(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
30.9b
(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
Compiler

Compiled 15139 to 11251 computations (25.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
0.4b
(/.f64 600041/2386628 (pow.f64 x 3))

series7.0ms (0.1%)

Counts
2 → 12
Calls

2 calls:

3.0ms
(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
3.0ms
(/.f64 600041/2386628 (pow.f64 x 3))

rewrite42.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
47×times-frac_binary64
40×*-un-lft-identity_binary64
34×add-sqr-sqrt_binary64
34×add-cube-cbrt_binary64
13×fma-def_binary64
Counts
2 → 96
Calls

2 calls:

29.0ms
(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
4.0ms
(/.f64 600041/2386628 (pow.f64 x 3))

simplify123.0ms (2.3%)

Algorithm
egg-herbie
Rules
683×associate-*l*_binary64
353×associate-/l*_binary64
342×associate-*r/_binary64
342×associate-*l/_binary64
272×associate-/l/_binary64
Counts
108 → 112
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01291319
12421280
29651242
347061242
449471242

prune127.0ms (2.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1120112
Fresh011
Picked011
Done011
Total1123115
Error
0b
Counts
115 → 3
Alt Table
StatusErrorProgram
33.6b
(*.f64 x (-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1) (fma.f64 833192009/1250000000 (*.f64 x x) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6)))))
30.2b
(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
30.9b
(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
Compiler

Compiled 1932 to 1496 computations (22.6% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))
0.1b
(fma.f64 833192009/1250000000 (*.f64 x x) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6)))
0.1b
(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)
24.4b
(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1) (fma.f64 833192009/1250000000 (*.f64 x x) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))))

series29.0ms (0.5%)

Counts
4 → 36
Calls

4 calls:

10.0ms
(fma.f64 833192009/1250000000 (*.f64 x x) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6)))
7.0ms
(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1) (fma.f64 833192009/1250000000 (*.f64 x x) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))))
6.0ms
(*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))
6.0ms
(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)

rewrite25.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt_binary64
17×*-un-lft-identity_binary64
15×add-cube-cbrt_binary64
add-exp-log_binary64
prod-diff_binary64
Counts
4 → 79
Calls

4 calls:

9.0ms
(*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))
7.0ms
(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1) (fma.f64 833192009/1250000000 (*.f64 x x) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))))
1.0ms
(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)
1.0ms
(fma.f64 833192009/1250000000 (*.f64 x x) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6)))

simplify209.0ms (3.8%)

Algorithm
egg-herbie
Rules
615×fma-neg_binary64
406×fma-def_binary64
336×distribute-rgt-in_binary64
335×distribute-lft-in_binary64
334×exp-prod_binary64
Counts
115 → 127
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01432226
12602014
28021804
327771749
443421734
549561734
648601734

prune319.0ms (5.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1270127
Fresh000
Picked011
Done022
Total1273130
Error
0b
Counts
130 → 3
Alt Table
StatusErrorProgram
33.6b
(*.f64 x (-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1) (fma.f64 833192009/1250000000 (*.f64 x x) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6)))))
30.2b
(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
30.9b
(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
Compiler

Compiled 3874 to 2783 computations (28.2% saved)

regimes337.0ms (6.2%)

Accuracy

Total 0.0b remaining (38.3%)

Threshold costs 0.0b (38.3%)

Counts
37 → 3
Compiler

Compiled 2460 to 1530 computations (37.8% saved)

bsearch56.0ms (1%)

Steps
ItersRangePoint
3
24.798164135285973
14154284214998436.0
8107458.540103673
3
-25438.21571874868
-15.247968665141558
-10008.959366090668
Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
1-exp_binary64
if-if-or-not_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
052111
159111
258111

end4.0ms (0.1%)

Compiler

Compiled 79 to 60 computations (24.1% saved)

sample3.1s (57.8%)

Algorithm
intervals
Results
2.6s8000×body128valid
Compiler

Compiled 346 to 177 computations (48.8% saved)

Profiling

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