Details

Time bar (total: 2.1s)

analyze95.0ms (4.5%)

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%74.9%0.1%5
37.5%50%12.6%6
50%37.5%12.6%7
56.2%25%18.8%8
62.4%18.7%18.8%9
65.6%12.5%22%10
68.7%9.4%22%11
70.2%6.2%23.5%12
71.8%4.7%23.5%13
72.6%3.1%24.3%14
Compiler

Compiled 10 to 7 computations (30% saved)

sample13.0ms (0.6%)

Algorithm
intervals
Results
5.0ms256×body128valid
0.0msbody128invalid
Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify16.0ms (0.8%)

Algorithm
egg-herbie
Rules
35×distribute-rgt-in_binary64
25×unsub-neg_binary64 sub-neg_binary64
22×distribute-lft-in_binary64
21×associate-*r*_binary64
20×associate-*l*_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
11610
23110
35610
411510
513710
615110
721810
823110
922810
1022710
1118410

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
0.1b
Counts
1 → 1
Alt Table
StatusErrorProgram
0.1b
(*.f64 x (-.f64 1 (*.f64 x y)))
Compiler

Compiled 18 to 12 computations (33.3% saved)

localize9.0ms (0.4%)

Local error

Found 1 expressions with local error:

0.1b
(*.f64 x (-.f64 1 (*.f64 x y)))

rewrite28.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
add-sqr-sqrt_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64 associate-*l*_binary64 associate-*r*_binary64
sub-neg_binary64 distribute-rgt-in_binary64 cancel-sign-sub-inv_binary64 distribute-lft-in_binary64 associate-*r/_binary64
pow-prod-down_binary64 prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 flip3--_binary64 flip--_binary64 *-commutative_binary64
Counts
1 → 24
Calls

1 calls:

6.0ms
(*.f64 x (-.f64 1 (*.f64 x y)))
Compiler

Compiled 324 to 167 computations (48.5% saved)

series27.0ms (1.2%)

Error
0.0b
Counts
1 → 12
Calls

1 calls:

23.0ms
(*.f64 x (-.f64 1 (*.f64 x y)))
Compiler

Compiled 167 to 115 computations (31.1% saved)

simplify53.0ms (2.5%)

Algorithm
egg-herbie
Rules
554×unsub-neg_binary64
551×distribute-neg-out_binary64
330×distribute-rgt-neg-out_binary64
313×associate-*l*_binary64
293×unswap-sqr_binary64
Counts
36 → 28
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
056441
1132399
2387398
31158396
42006396
55040396

prune18.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New23528
Fresh000
Picked011
Done000
Total23629
Error
0.0b
Counts
29 → 6
Alt Table
StatusErrorProgram
6.5b
(-.f64 x (*.f64 (*.f64 x x) y))
32.4b
(*.f64 (sqrt.f64 x) (*.f64 (-.f64 1 (*.f64 x y)) (sqrt.f64 x)))
23.2b
(/.f64 (-.f64 x (*.f64 (pow.f64 x 3) (*.f64 y y))) (+.f64 1 (*.f64 x y)))
7.7b
(*.f64 (*.f64 (cbrt.f64 (-.f64 x (*.f64 (*.f64 x x) y))) (cbrt.f64 (-.f64 x (*.f64 (*.f64 x x) y)))) (cbrt.f64 (-.f64 x (*.f64 (*.f64 x x) y))))
0.1b
(*.f64 x (-.f64 1 (*.f64 x y)))
12.1b
(/.f64 (*.f64 x (-.f64 1 (pow.f64 (*.f64 x y) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 1 (*.f64 x y)))))
Compiler

Compiled 387 to 164 computations (57.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(-.f64 x (*.f64 (*.f64 x x) y))
9.1b
(*.f64 (*.f64 x x) y)

rewrite38.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
add-log-exp_binary64 add-sqr-sqrt_binary64
pow-prod-down_binary64 prod-exp_binary64 add-cube-cbrt_binary64 cbrt-unprod_binary64 *-un-lft-identity_binary64 associate-*r*_binary64
unswap-sqr_binary64 associate-*l*_binary64 *-commutative_binary64 diff-log_binary64 flip3--_binary64 sub-neg_binary64 flip--_binary64 cancel-sign-sub-inv_binary64
Counts
2 → 31
Calls

2 calls:

6.0ms
(*.f64 (*.f64 x x) y)
3.0ms
(-.f64 x (*.f64 (*.f64 x x) y))
Compiler

Compiled 402 to 107 computations (73.4% saved)

series39.0ms (1.8%)

Error
0.0b
Counts
2 → 18
Calls

2 calls:

22.0ms
(-.f64 x (*.f64 (*.f64 x x) y))
14.0ms
(*.f64 (*.f64 x x) y)
Compiler

Compiled 275 to 187 computations (32% saved)

simplify105.0ms (5%)

Algorithm
egg-herbie
Rules
466×associate-*r*_binary64
377×unsub-neg_binary64
366×distribute-rgt-neg-in_binary64
337×distribute-lft-neg-in_binary64
309×unswap-sqr_binary64
Counts
49 → 28
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
063530
1147503
2462503
31383503
43774503
54291503
64951503
74705503

prune13.0ms (0.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New28028
Fresh044
Picked011
Done011
Total28634
Error
0.0b
Counts
34 → 6
Alt Table
StatusErrorProgram
6.5b
(-.f64 x (*.f64 (*.f64 x x) y))
32.4b
(*.f64 (sqrt.f64 x) (*.f64 (-.f64 1 (*.f64 x y)) (sqrt.f64 x)))
23.2b
(/.f64 (-.f64 x (*.f64 (pow.f64 x 3) (*.f64 y y))) (+.f64 1 (*.f64 x y)))
7.7b
(*.f64 (*.f64 (cbrt.f64 (-.f64 x (*.f64 (*.f64 x x) y))) (cbrt.f64 (-.f64 x (*.f64 (*.f64 x x) y)))) (cbrt.f64 (-.f64 x (*.f64 (*.f64 x x) y))))
0.1b
(*.f64 x (-.f64 1 (*.f64 x y)))
12.1b
(/.f64 (*.f64 x (-.f64 1 (pow.f64 (*.f64 x y) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 1 (*.f64 x y)))))
Compiler

Compiled 310 to 143 computations (53.9% saved)

localize12.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (-.f64 x (*.f64 (*.f64 x x) y)))
9.1b
(*.f64 (*.f64 x x) y)
9.1b
(*.f64 (*.f64 x x) y)
9.1b
(*.f64 (*.f64 x x) y)

rewrite62.0ms (2.9%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
19×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
11×add-sqr-sqrt_binary64
pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 associate-*r*_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64
add-log-exp_binary64
Counts
4 → 70
Calls

4 calls:

6.0ms
(*.f64 (*.f64 x x) y)
6.0ms
(*.f64 (*.f64 x x) y)
6.0ms
(*.f64 (*.f64 x x) y)
2.0ms
(cbrt.f64 (-.f64 x (*.f64 (*.f64 x x) y)))
Compiler

Compiled 2088 to 255 computations (87.8% saved)

series109.0ms (5.2%)

Error
0.0b
Counts
4 → 32
Calls

4 calls:

44.0ms
(cbrt.f64 (-.f64 x (*.f64 (*.f64 x x) y)))
17.0ms
(*.f64 (*.f64 x x) y)
16.0ms
(*.f64 (*.f64 x x) y)
16.0ms
(*.f64 (*.f64 x x) y)
Compiler

Compiled 2604 to 1385 computations (46.8% saved)

simplify157.0ms (7.4%)

Algorithm
egg-herbie
Rules
481×unswap-sqr_binary64
352×times-frac_binary64
349×prod-exp_binary64
324×sub-neg_binary64
275×associate-/r*_binary64
Counts
102 → 63
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01311574
13301529
29951501
333051357
448551354
543111330
645891330
751751330

prune21.0ms (1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New63063
Fresh033
Picked011
Done022
Total63669
Error
0.0b
Counts
69 → 6
Alt Table
StatusErrorProgram
6.5b
(-.f64 x (*.f64 (*.f64 x x) y))
32.4b
(*.f64 (sqrt.f64 x) (*.f64 (-.f64 1 (*.f64 x y)) (sqrt.f64 x)))
23.2b
(/.f64 (-.f64 x (*.f64 (pow.f64 x 3) (*.f64 y y))) (+.f64 1 (*.f64 x y)))
7.7b
(*.f64 (*.f64 (cbrt.f64 (-.f64 x (*.f64 (*.f64 x x) y))) (cbrt.f64 (-.f64 x (*.f64 (*.f64 x x) y)))) (cbrt.f64 (-.f64 x (*.f64 (*.f64 x x) y))))
0.1b
(*.f64 x (-.f64 1 (*.f64 x y)))
12.1b
(/.f64 (*.f64 x (-.f64 1 (pow.f64 (*.f64 x y) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 1 (*.f64 x y)))))
Compiler

Compiled 1023 to 234 computations (77.1% saved)

localize14.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.3b
(pow.f64 (*.f64 x y) 3)
0.3b
(*.f64 (*.f64 x y) (*.f64 x y))
0.7b
(*.f64 x (-.f64 1 (pow.f64 (*.f64 x y) 3)))
10.9b
(/.f64 (*.f64 x (-.f64 1 (pow.f64 (*.f64 x y) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 1 (*.f64 x y)))))

rewrite210.0ms (9.9%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
48×pow1_binary64
26×add-exp-log_binary64 add-cbrt-cube_binary64
19×pow-prod-down_binary64
17×add-sqr-sqrt_binary64 *-un-lft-identity_binary64
16×cancel-sign-sub-inv_binary64
Counts
4 → 126
Calls

4 calls:

17.0ms
(/.f64 (*.f64 x (-.f64 1 (pow.f64 (*.f64 x y) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 1 (*.f64 x y)))))
9.0ms
(*.f64 x (-.f64 1 (pow.f64 (*.f64 x y) 3)))
6.0ms
(*.f64 (*.f64 x y) (*.f64 x y))
3.0ms
(pow.f64 (*.f64 x y) 3)
Compiler

Compiled 3990 to 1997 computations (49.9% saved)

series155.0ms (7.3%)

Error
0.0b
Counts
4 → 36
Calls

4 calls:

53.0ms
(/.f64 (*.f64 x (-.f64 1 (pow.f64 (*.f64 x y) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 1 (*.f64 x y)))))
48.0ms
(*.f64 x (-.f64 1 (pow.f64 (*.f64 x y) 3)))
23.0ms
(pow.f64 (*.f64 x y) 3)
21.0ms
(*.f64 (*.f64 x y) (*.f64 x y))
Compiler

Compiled 1522 to 996 computations (34.6% saved)

simplify122.0ms (5.7%)

Algorithm
egg-herbie
Rules
428×exp-prod_binary64
343×distribute-rgt-neg-in_binary64
338×unswap-sqr_binary64
316×associate-*l*_binary64
314×log-prod_binary64
Counts
162 → 130
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01882521
14622214
221372196
342022196
449582196

prune78.0ms (3.7%)

Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New1282130
Fresh112
Picked011
Done033
Total1297136
Error
0.0b
Counts
136 → 7
Alt Table
StatusErrorProgram
6.5b
(-.f64 x (*.f64 (*.f64 x x) y))
23.2b
(/.f64 (-.f64 x (*.f64 (pow.f64 x 3) (*.f64 y y))) (+.f64 1 (*.f64 x y)))
7.7b
(*.f64 (*.f64 (cbrt.f64 (-.f64 x (*.f64 (*.f64 x x) y))) (cbrt.f64 (-.f64 x (*.f64 (*.f64 x x) y)))) (cbrt.f64 (-.f64 x (*.f64 (*.f64 x x) y))))
33.2b
(/.f64 (*.f64 x (-.f64 1 (*.f64 (pow.f64 (*.f64 x y) 3/2) (pow.f64 (*.f64 x y) 3/2)))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 1 (*.f64 x y)))))
0.1b
(*.f64 x (-.f64 1 (*.f64 x y)))
12.1b
(/.f64 (*.f64 x (-.f64 1 (pow.f64 (*.f64 x y) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 1 (*.f64 x y)))))
10.4b
(/.f64 x (/.f64 (+.f64 (pow.f64 (*.f64 x y) 2) (+.f64 1 (*.f64 x y))) (-.f64 1 (pow.f64 (*.f64 x y) 3))))
Compiler

Compiled 1884 to 1033 computations (45.2% saved)

regimes178.0ms (8.4%)

Accuracy

Total 0.1b remaining (74.4%)

Threshold costs 0.1b (74.4%)

Compiler

Compiled 3138 to 1805 computations (42.5% saved)

simplify4.0ms (0.2%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
sub-neg_binary64 +-commutative_binary64
neg-mul-1_binary64 neg-sub0_binary64
cancel-sign-sub-inv_binary64 distribute-rgt-neg-in_binary64
1-exp_binary64 distribute-lft-neg-out_binary64 distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
11610
22510
33110
43510
53610
63510

end1.0ms (0%)

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample539.0ms (25.4%)

Algorithm
intervals
Results
190.0ms8000×body128valid
2.0ms77×body128invalid
Compiler

Compiled 171 to 96 computations (43.9% saved)

Profiling

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