Details

Time bar (total: 3.4min)

analyze70.0ms (0%)

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
40.6%59.3%0.1%6
53.1%45.3%1.7%7
62.4%32.8%4.8%8
69.5%22.6%7.9%9
74.5%16.4%9.1%10
78.2%11.1%10.6%11
80.9%8.2%10.9%12
82.8%5.5%11.7%13
84.1%4.1%11.8%14
Compiler

Compiled 8 to 6 computations (25% saved)

sample18.0ms (0%)

Algorithm
intervals
Results
11.0ms256×body128valid
0.0msbody128invalid
Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify111.0ms (0.1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (16.0ms)

IterNodesCost
025610
125610

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Compiler

Compiled 7 to 5 computations (28.6% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite9.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-log-exp_binary64_10688
diff-log_binary64_10741
sum-log_binary64_10740 pow1_binary64_10710 sub-neg_binary64_10642 cancel-sign-sub-inv_binary64_10615 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687 associate--l+_binary64_10586 *-un-lft-identity_binary64_10649 flip3--_binary64_10653 add-sqr-sqrt_binary64_10671 flip--_binary64_10624 add-cube-cbrt_binary64_10684
Counts
1 → 14
Calls

2 calls:

8.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
0.0ms
(-.f64 (+.f64 x y) (*.f64 x y))

series79.0ms (0%)

Counts
1 → 12
Calls

1 calls:

79.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
Compiler

Compiled 110 to 88 computations (20% saved)

simplify72.0ms (0%)

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
06203308

prune63.0ms (0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New111526
Fresh000
Picked000
Done101
Total121527
Error
0.0b
Counts
27 → 15
Compiler

Compiled 345 to 134 computations (61.2% saved)

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite10.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-log-exp_binary64_10688
*-un-lft-identity_binary64_10649
sum-log_binary64_10740 pow1_binary64_10710 sub-neg_binary64_10642 cancel-sign-sub-inv_binary64_10615 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687 add-sqr-sqrt_binary64_10671 add-cube-cbrt_binary64_10684 diff-log_binary64_10741 associate-+r+_binary64_10581
distribute-rgt-out--_binary64_10603 +-commutative_binary64_10579 flip-+_binary64_10623 flip3--_binary64_10653 flip--_binary64_10624 flip3-+_binary64_10652 distribute-lft-out_binary64_10600 associate-+r-_binary64_10583
Counts
2 → 29
Calls

4 calls:

5.0ms
(+.f64 x (-.f64 y (*.f64 x y)))
3.0ms
(-.f64 y (*.f64 x y))
0.0ms
(+.f64 x (-.f64 y (*.f64 x y)))
0.0ms
(-.f64 y (*.f64 x y))

series132.0ms (0.1%)

Counts
2 → 21
Calls

2 calls:

79.0ms
(+.f64 x (-.f64 y (*.f64 x y)))
53.0ms
(-.f64 y (*.f64 x y))
Compiler

Compiled 215 to 173 computations (19.5% saved)

simplify68.0ms (0%)

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
04979512
14979512

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite4.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-log-exp_binary64_10688
pow1_binary64_10710 sub-neg_binary64_10642 cancel-sign-sub-inv_binary64_10615 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687 *-un-lft-identity_binary64_10649 flip3--_binary64_10653 add-sqr-sqrt_binary64_10671 flip--_binary64_10624 add-cube-cbrt_binary64_10684 diff-log_binary64_10741
Counts
1 → 12
Calls

2 calls:

3.0ms
(-.f64 x (*.f64 x y))
0.0ms
(-.f64 x (*.f64 x y))

series55.0ms (0%)

Counts
1 → 9
Calls

1 calls:

55.0ms
(-.f64 x (*.f64 x y))
Compiler

Compiled 75 to 70 computations (6.7% saved)

simplify82.0ms (0%)

Algorithm
egg-herbie
Counts
21 → 21
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
05848200

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite8.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-log-exp_binary64_10688
diff-log_binary64_10741
sum-log_binary64_10740 pow1_binary64_10710 sub-neg_binary64_10642 cancel-sign-sub-inv_binary64_10615 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687 associate--l+_binary64_10586 *-un-lft-identity_binary64_10649 flip3--_binary64_10653 add-sqr-sqrt_binary64_10671 flip--_binary64_10624 add-cube-cbrt_binary64_10684
Counts
1 → 14
Calls

2 calls:

6.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
0.0ms
(-.f64 (+.f64 x y) (*.f64 x y))

series72.0ms (0%)

Counts
1 → 12
Calls

1 calls:

72.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
Compiler

Compiled 146 to 124 computations (15.1% saved)

simplify73.0ms (0%)

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
06203308

localize7.0ms (0%)

Local error

Found 6 expressions with local error:

5.0b
(log.f64 (exp.f64 (-.f64 (+.f64 x y) (*.f64 x y))))
0.0b
(-.f64 (+.f64 x y) (*.f64 x y))
0.0b
(exp.f64 (-.f64 (+.f64 x y) (*.f64 x y)))
0.0b
(exp.f64 (-.f64 (+.f64 x y) (*.f64 x y)))
0.0b
(-.f64 (+.f64 x y) (*.f64 x y))
5.0b
(log.f64 (exp.f64 (-.f64 (+.f64 x y) (*.f64 x y))))

rewrite22.0ms (0%)

Algorithm
rewrite-expression-head
Rules
14×add-log-exp_binary64_10688
exp-prod_binary64_10701 *-un-lft-identity_binary64_10649 add-sqr-sqrt_binary64_10671 add-cube-cbrt_binary64_10684 log-prod_binary64_10735 exp-sum_binary64_10695
log-pow_binary64_10738 pow1_binary64_10710 diff-log_binary64_10741
rem-exp-log_binary64_10689 sub-neg_binary64_10642 cancel-sign-sub-inv_binary64_10615 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687 associate--l+_binary64_10586
exp-diff_binary64_10697 sum-log_binary64_10740
flip3--_binary64_10653 rem-log-exp_binary64_10690 log-div_binary64_10736 flip--_binary64_10624
Counts
3 → 50
Calls

6 calls:

7.0ms
(exp.f64 (-.f64 (+.f64 x y) (*.f64 x y)))
6.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
6.0ms
(log.f64 (exp.f64 (-.f64 (+.f64 x y) (*.f64 x y))))
0.0ms
(exp.f64 (-.f64 (+.f64 x y) (*.f64 x y)))
0.0ms
(log.f64 (exp.f64 (-.f64 (+.f64 x y) (*.f64 x y))))

series505.0ms (0.2%)

Counts
3 → 31
Calls

3 calls:

362.0ms
(log.f64 (exp.f64 (-.f64 (+.f64 x y) (*.f64 x y))))
77.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
67.0ms
(exp.f64 (-.f64 (+.f64 x y) (*.f64 x y)))
Compiler

Compiled 644 to 476 computations (26.1% saved)

simplify87.0ms (0%)

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
049451117
149451117

localize7.0ms (0%)

Local error

Found 6 expressions with local error:

0.3b
(*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))
0.0b
(-.f64 (+.f64 x y) (*.f64 x y))
0.0b
(-.f64 (+.f64 x y) (*.f64 x y))
0.0b
(-.f64 (+.f64 x y) (*.f64 x y))
0.0b
(-.f64 (+.f64 x y) (*.f64 x y))
0.3b
(*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))

rewrite38.0ms (0%)

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64_10671
18×pow1_binary64_10710 sqrt-prod_binary64_10665
13×add-log-exp_binary64_10688
12×sqrt-div_binary64_10666
11×*-un-lft-identity_binary64_10649 add-cube-cbrt_binary64_10684
sqrt-pow1_binary64_10667 pow1/2_binary64_10729 flip3--_binary64_10653 flip--_binary64_10624 swap-sqr_binary64_10616
associate-*r*_binary64_10589 associate-*l*_binary64_10590
pow-prod-up_binary64_10719 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687
unswap-sqr_binary64_10617 frac-times_binary64_10659 diff-log_binary64_10741
pow-sqr_binary64_10622 pow-prod-down_binary64_10720
associate-*l/_binary64_10592 sum-log_binary64_10740 sub-neg_binary64_10642 cancel-sign-sub-inv_binary64_10615 associate--l+_binary64_10586 rem-sqrt-square_binary64_10662 associate-*r/_binary64_10591
prod-exp_binary64_10698 cbrt-unprod_binary64_10682 pow-plus_binary64_10712 sqr-abs_binary64_10664 *-commutative_binary64_10580 pow2_binary64_10730 rem-square-sqrt_binary64_10661 sqrt-unprod_binary64_10669
Counts
3 → 86
Calls

6 calls:

16.0ms
(*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))
6.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
6.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
0.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
0.0ms
(*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))

series236.0ms (0.1%)

Counts
3 → 36
Calls

3 calls:

81.0ms
(*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))
78.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
77.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
Compiler

Compiled 690 to 420 computations (39.1% saved)

simplify120.0ms (0.1%)

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (96.0ms)

IterNodesCost
049201733
149201733

prune2.0s (1%)

Pruning

92 alts after pruning (90 fresh and 2 done)

PrunedKeptTotal
New21486300
Fresh6410
Picked000
Done325
Total22392315
Error
0b
Counts
315 → 92
Compiler

Compiled 4091 to 1397 computations (65.9% saved)

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 x (*.f64 y (-.f64 1 x)))
0.0b
(*.f64 y (-.f64 1 x))
0.0b
(+.f64 x (*.f64 y (-.f64 1 x)))
0.0b
(*.f64 y (-.f64 1 x))

rewrite16.0ms (0%)

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt_binary64_10671
12×cancel-sign-sub-inv_binary64_10615
11×*-un-lft-identity_binary64_10649
distribute-rgt-in_binary64_10599 distribute-lft-in_binary64_10598 add-cube-cbrt_binary64_10684 associate-+r+_binary64_10581
associate-*r*_binary64_10589
add-log-exp_binary64_10688 pow1_binary64_10710 sub-neg_binary64_10642 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687
associate-*l*_binary64_10590
difference-of-squares_binary64_10618 associate-*r/_binary64_10591
prod-exp_binary64_10698 cbrt-unprod_binary64_10682 sum-log_binary64_10740 pow-prod-down_binary64_10720 unswap-sqr_binary64_10617 +-commutative_binary64_10579 *-commutative_binary64_10580 distribute-lft-out--_binary64_10601 flip-+_binary64_10623 flip3--_binary64_10653 flip--_binary64_10624 flip3-+_binary64_10652
Counts
2 → 50
Calls

4 calls:

8.0ms
(*.f64 y (-.f64 1 x))
4.0ms
(+.f64 x (*.f64 y (-.f64 1 x)))
0.0ms
(*.f64 y (-.f64 1 x))
0.0ms
(+.f64 x (*.f64 y (-.f64 1 x)))

series132.0ms (0.1%)

Counts
2 → 21
Calls

2 calls:

69.0ms
(+.f64 x (*.f64 y (-.f64 1 x)))
63.0ms
(*.f64 y (-.f64 1 x))
Compiler

Compiled 211 to 169 computations (19.9% saved)

simplify101.0ms (0%)

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 0 (87.0ms)

IterNodesCost
04922631
14922631

localize5.0ms (0%)

rewrite0.0ms (0%)

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify8.0ms (0%)

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
000

localize7.0ms (0%)

Local error

Found 6 expressions with local error:

4.5b
(log.f64 (exp.f64 (-.f64 x (*.f64 x y))))
0.0b
(-.f64 x (*.f64 x y))
0.0b
(exp.f64 (-.f64 x (*.f64 x y)))
0.0b
(exp.f64 (-.f64 x (*.f64 x y)))
0.0b
(-.f64 x (*.f64 x y))
4.5b
(log.f64 (exp.f64 (-.f64 x (*.f64 x y))))

rewrite14.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-log-exp_binary64_10688
exp-prod_binary64_10701 *-un-lft-identity_binary64_10649 add-sqr-sqrt_binary64_10671 add-cube-cbrt_binary64_10684
log-prod_binary64_10735
log-pow_binary64_10738 pow1_binary64_10710 exp-sum_binary64_10695
sub-neg_binary64_10642 cancel-sign-sub-inv_binary64_10615 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687
exp-diff_binary64_10697 rem-exp-log_binary64_10689 diff-log_binary64_10741
flip3--_binary64_10653 rem-log-exp_binary64_10690 log-div_binary64_10736 flip--_binary64_10624
Counts
3 → 45
Calls

6 calls:

4.0ms
(log.f64 (exp.f64 (-.f64 x (*.f64 x y))))
4.0ms
(exp.f64 (-.f64 x (*.f64 x y)))
3.0ms
(-.f64 x (*.f64 x y))
0.0ms
(exp.f64 (-.f64 x (*.f64 x y)))
0.0ms
(-.f64 x (*.f64 x y))

series362.0ms (0.2%)

Counts
3 → 25
Calls

3 calls:

264.0ms
(log.f64 (exp.f64 (-.f64 x (*.f64 x y))))
54.0ms
(-.f64 x (*.f64 x y))
43.0ms
(exp.f64 (-.f64 x (*.f64 x y)))
Compiler

Compiled 384 to 335 computations (12.8% saved)

simplify73.0ms (0%)

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
04926685
14926685

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 y (+.f64 (+.f64 x y) (*.f64 x y)))
0.0b
(pow.f64 (+.f64 x y) 3)
0.0b
(*.f64 (+.f64 x y) (+.f64 x y))
0.0b
(+.f64 (+.f64 x y) (*.f64 x y))
3.8b
(+.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 x (*.f64 y (+.f64 (+.f64 x y) (*.f64 x y)))))
4.6b
(*.f64 x (*.f64 y (+.f64 (+.f64 x y) (*.f64 x y))))
6.9b
(-.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (*.f64 x y) 3))
39.0b
(/.f64 (-.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (*.f64 x y) 3)) (+.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 x (*.f64 y (+.f64 (+.f64 x y) (*.f64 x y))))))

rewrite114.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
76×associate-*r/_binary64_10591
74×add-sqr-sqrt_binary64_10671
43×flip-+_binary64_10623 flip3-+_binary64_10652
40×difference-of-squares_binary64_10618
39×times-frac_binary64_10655
34×*-un-lft-identity_binary64_10649
32×frac-add_binary64_10657
31×sqr-pow_binary64_10621
24×add-cube-cbrt_binary64_10684
18×associate-/r/_binary64_10595
16×frac-times_binary64_10659
13×associate-/l*_binary64_10594
11×add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687 cube-prod_binary64_10677 unpow-prod-down_binary64_10728
pow1_binary64_10710 distribute-rgt-in_binary64_10599 distribute-lft-in_binary64_10598
associate-*l/_binary64_10592 add-log-exp_binary64_10688 cancel-sign-sub-inv_binary64_10615
difference-cubes_binary64_10651 distribute-lft-out--_binary64_10601
associate-+r+_binary64_10581
prod-exp_binary64_10698 cbrt-unprod_binary64_10682 associate-/r*_binary64_10593 pow-prod-down_binary64_10720 associate-*l*_binary64_10590
associate-+l+_binary64_10582 flip3--_binary64_10653 flip--_binary64_10624 associate-/l/_binary64_10596
sum-log_binary64_10740 unpow3_binary64_10715 clear-num_binary64_10648 sub-neg_binary64_10642 div-sub_binary64_10654 +-commutative_binary64_10579 div-exp_binary64_10700 *-commutative_binary64_10580 cbrt-undiv_binary64_10683 frac-2neg_binary64_10660 div-inv_binary64_10646 associate-*r*_binary64_10589 diff-log_binary64_10741 cube-mult_binary64_10679
Counts
4 → 174
Calls

8 calls:

32.0ms
(/.f64 (-.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (*.f64 x y) 3)) (+.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 x (*.f64 y (+.f64 (+.f64 x y) (*.f64 x y))))))
17.0ms
(-.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (*.f64 x y) 3))
16.0ms
(+.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 x (*.f64 y (+.f64 (+.f64 x y) (*.f64 x y)))))
11.0ms
(*.f64 x (*.f64 y (+.f64 (+.f64 x y) (*.f64 x y))))
0.0ms
(+.f64 (+.f64 x y) (*.f64 x y))

series1.5s (0.7%)

Counts
4 → 66
Calls

4 calls:

772.0ms
(/.f64 (-.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (*.f64 x y) 3)) (+.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 x (*.f64 y (+.f64 (+.f64 x y) (*.f64 x y))))))
377.0ms
(+.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 x (*.f64 y (+.f64 (+.f64 x y) (*.f64 x y)))))
153.0ms
(*.f64 x (*.f64 y (+.f64 (+.f64 x y) (*.f64 x y))))
152.0ms
(-.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (*.f64 x y) 3))
Compiler

Compiled 3996 to 2822 computations (29.4% saved)

simplify120.0ms (0.1%)

Algorithm
egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
0509012481

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))
0.0b
(-.f64 (+.f64 x y) (*.f64 x y))
0.0b
(-.f64 (+.f64 x y) (*.f64 x y))
0.0b
(-.f64 (+.f64 x y) (*.f64 x y))
0.0b
(-.f64 (+.f64 x y) (*.f64 x y))
0.0b
(-.f64 (+.f64 x y) (*.f64 x y))
0.3b
(*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))
0.3b
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))

rewrite88.0ms (0%)

Algorithm
rewrite-expression-head
Rules
90×sqrt-div_binary64_10666
58×pow1_binary64_10710
50×sqrt-pow1_binary64_10667
38×add-sqr-sqrt_binary64_10671
35×flip3--_binary64_10653 flip--_binary64_10624
32×frac-times_binary64_10659
31×pow-prod-up_binary64_10719
29×sqrt-prod_binary64_10665
28×pow1/2_binary64_10729
16×associate-*l/_binary64_10592
15×*-un-lft-identity_binary64_10649 add-cube-cbrt_binary64_10684
14×add-log-exp_binary64_10688
12×associate-*r*_binary64_10589
10×associate-*l*_binary64_10590 associate-*r/_binary64_10591 swap-sqr_binary64_10616
pow-sqr_binary64_10622
pow-prod-down_binary64_10720 unswap-sqr_binary64_10617 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687
pow-plus_binary64_10712
rem-sqrt-square_binary64_10662 diff-log_binary64_10741
pow2_binary64_10730
prod-exp_binary64_10698 cbrt-unprod_binary64_10682 sqr-abs_binary64_10664 sum-log_binary64_10740 sub-neg_binary64_10642 cancel-sign-sub-inv_binary64_10615 associate--l+_binary64_10586 *-commutative_binary64_10580 sqrt-unprod_binary64_10669
rem-square-sqrt_binary64_10661
Counts
4 → 164
Calls

8 calls:

31.0ms
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))
20.0ms
(*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))
7.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
6.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
0.0ms
(-.f64 (+.f64 x y) (*.f64 x y))

series341.0ms (0.2%)

Counts
4 → 48
Calls

4 calls:

89.0ms
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))
86.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
84.0ms
(*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))
82.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
Compiler

Compiled 1340 to 658 computations (50.9% saved)

simplify126.0ms (0.1%)

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 0 (80.0ms)

IterNodesCost
049294452
149294452

prune12.1s (6%)

Pruning

286 alts after pruning (282 fresh and 4 done)

PrunedKeptTotal
New380213593
Fresh166985
Picked000
Done347
Total399286685
Error
0b
Counts
685 → 286
Compiler

Compiled 23233 to 7666 computations (67% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 x (pow.f64 (*.f64 y (-.f64 1 x)) 1))
0.0b
(*.f64 y (-.f64 1 x))
0.0b
(+.f64 x (pow.f64 (*.f64 y (-.f64 1 x)) 1))
0.0b
(*.f64 y (-.f64 1 x))

rewrite16.0ms (0%)

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity_binary64_10649 add-sqr-sqrt_binary64_10671
cancel-sign-sub-inv_binary64_10615 add-cube-cbrt_binary64_10684 associate-*r*_binary64_10589
add-log-exp_binary64_10688 pow1_binary64_10710 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687 distribute-rgt-in_binary64_10599 distribute-lft-in_binary64_10598
associate-*l*_binary64_10590
difference-of-squares_binary64_10618 sub-neg_binary64_10642 associate-*r/_binary64_10591
prod-exp_binary64_10698 cbrt-unprod_binary64_10682 sum-log_binary64_10740 pow-prod-down_binary64_10720 unswap-sqr_binary64_10617 +-commutative_binary64_10579 *-commutative_binary64_10580 distribute-lft-out--_binary64_10601 flip-+_binary64_10623 flip3--_binary64_10653 flip--_binary64_10624 flip3-+_binary64_10652 distribute-lft-out_binary64_10600
Counts
2 → 43
Calls

4 calls:

8.0ms
(*.f64 y (-.f64 1 x))
4.0ms
(+.f64 x (pow.f64 (*.f64 y (-.f64 1 x)) 1))
0.0ms
(*.f64 y (-.f64 1 x))
0.0ms
(+.f64 x (pow.f64 (*.f64 y (-.f64 1 x)) 1))

series140.0ms (0.1%)

Counts
2 → 21
Calls

2 calls:

72.0ms
(+.f64 x (pow.f64 (*.f64 y (-.f64 1 x)) 1))
68.0ms
(*.f64 y (-.f64 1 x))
Compiler

Compiled 241 to 199 computations (17.4% saved)

simplify85.0ms (0%)

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
04953603
14953603

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify9.0ms (0%)

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
000

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

6.9b
(-.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (*.f64 x y) 3))
0.3b
(pow.f64 (*.f64 x y) 3)
0.0b
(pow.f64 (+.f64 x y) 3)
0.0b
(+.f64 y (+.f64 1 (*.f64 y y)))
0.3b
(pow.f64 (*.f64 x y) 3)
6.9b
(-.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (*.f64 x y) 3))
8.5b
(*.f64 (*.f64 x x) (+.f64 y (+.f64 1 (*.f64 y y))))
33.5b
(/.f64 (-.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (*.f64 x y) 3)) (*.f64 (*.f64 x x) (+.f64 y (+.f64 1 (*.f64 y y)))))

rewrite74.0ms (0%)

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt_binary64_10671
24×difference-of-squares_binary64_10618
21×add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687
20×sqr-pow_binary64_10621
17×*-un-lft-identity_binary64_10649
13×associate-/l*_binary64_10594 times-frac_binary64_10655
12×pow1_binary64_10710
add-cube-cbrt_binary64_10684
cancel-sign-sub-inv_binary64_10615 cube-prod_binary64_10677 unpow-prod-down_binary64_10728
prod-exp_binary64_10698 cbrt-unprod_binary64_10682
add-log-exp_binary64_10688
pow-prod-down_binary64_10720 associate-*r*_binary64_10589 associate-*r/_binary64_10591
difference-cubes_binary64_10651 div-exp_binary64_10700 cbrt-undiv_binary64_10683 pow-unpow_binary64_10726 distribute-lft-out--_binary64_10601
unpow3_binary64_10715 rem-cube-cbrt_binary64_10672 associate-/r/_binary64_10595 pow-pow_binary64_10721 pow-exp_binary64_10717 flip-+_binary64_10623 flip3--_binary64_10653 flip--_binary64_10624 flip3-+_binary64_10652 associate-/l/_binary64_10596 cube-mult_binary64_10679
associate-/r*_binary64_10593 clear-num_binary64_10648 sub-neg_binary64_10642 unswap-sqr_binary64_10617 div-sub_binary64_10654 *-commutative_binary64_10580 distribute-rgt-in_binary64_10599 frac-2neg_binary64_10660 distribute-lft-in_binary64_10598 div-inv_binary64_10646 pow-to-exp_binary64_10718 distribute-lft-out_binary64_10600 associate-*l*_binary64_10590 diff-log_binary64_10741
Counts
4 → 123
Calls

8 calls:

26.0ms
(/.f64 (-.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (*.f64 x y) 3)) (*.f64 (*.f64 x x) (+.f64 y (+.f64 1 (*.f64 y y)))))
15.0ms
(-.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (*.f64 x y) 3))
10.0ms
(*.f64 (*.f64 x x) (+.f64 y (+.f64 1 (*.f64 y y))))
8.0ms
(pow.f64 (*.f64 x y) 3)
0.0ms
(+.f64 y (+.f64 1 (*.f64 y y)))

series636.0ms (0.3%)

Counts
4 → 62
Calls

4 calls:

243.0ms
(/.f64 (-.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (*.f64 x y) 3)) (*.f64 (*.f64 x x) (+.f64 y (+.f64 1 (*.f64 y y)))))
165.0ms
(-.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (*.f64 x y) 3))
144.0ms
(*.f64 (*.f64 x x) (+.f64 y (+.f64 1 (*.f64 y y))))
84.0ms
(pow.f64 (*.f64 x y) 3)
Compiler

Compiled 2281 to 1734 computations (24% saved)

simplify153.0ms (0.1%)

Algorithm
egg-herbie
Counts
185 → 185
Iterations

Useful iterations: 0 (103.0ms)

IterNodesCost
051004920

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(-.f64 y (*.f64 x y))
0.0b
(sqrt.f64 (-.f64 y (*.f64 x y)))
0.0b
(-.f64 (+.f64 x y) (*.f64 x y))
0.0b
(-.f64 (+.f64 x y) (*.f64 x y))
0.0b
(-.f64 (+.f64 x y) (*.f64 x y))
0.0b
(sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 y (*.f64 x y)))))
0.2b
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 y (*.f64 x y))))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))
0.2b
(*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 y (*.f64 x y))))

rewrite82.0ms (0%)

Algorithm
rewrite-expression-head
Rules
110×sqrt-div_binary64_10666
40×flip3--_binary64_10653 flip--_binary64_10624
36×frac-times_binary64_10659
23×add-sqr-sqrt_binary64_10671
20×pow1_binary64_10710
18×associate-*l/_binary64_10592
17×sqrt-prod_binary64_10665
13×associate-*r*_binary64_10589
12×sqrt-pow1_binary64_10667 *-un-lft-identity_binary64_10649 associate-*r/_binary64_10591
11×pow-prod-down_binary64_10720 add-cube-cbrt_binary64_10684
10×associate-*l*_binary64_10590
add-log-exp_binary64_10688
add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687
pow1/2_binary64_10729
unswap-sqr_binary64_10617
prod-exp_binary64_10698 cbrt-unprod_binary64_10682 *-commutative_binary64_10580 sqrt-unprod_binary64_10669 diff-log_binary64_10741
sum-log_binary64_10740 sub-neg_binary64_10642 distribute-rgt-out--_binary64_10603 cancel-sign-sub-inv_binary64_10615 associate--l+_binary64_10586
Counts
4 → 127
Calls

8 calls:

23.0ms
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 y (*.f64 x y))))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))
16.0ms
(sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 y (*.f64 x y)))))
15.0ms
(*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 y (*.f64 x y))))
7.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
0.0ms
(-.f64 (+.f64 x y) (*.f64 x y))

series2.9s (1.4%)

Counts
4 → 52
Calls

4 calls:

2.0s
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 y (*.f64 x y))))) (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))))
448.0ms
(sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 y (*.f64 x y)))))
332.0ms
(*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 y (*.f64 x y))))
91.0ms
(-.f64 (+.f64 x y) (*.f64 x y))
Compiler

Compiled 8694 to 7009 computations (19.4% saved)

simplify121.0ms (0.1%)

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
050189801

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(-.f64 (+.f64 x y) (*.f64 x y))
0.0b
(-.f64 (+.f64 x y) (*.f64 x y))
0.0b
(+.f64 (+.f64 x y) (*.f64 x y))
0.0b
(sqrt.f64 (+.f64 (+.f64 x y) (*.f64 x y)))
5.0b
(/.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 (*.f64 x y) (*.f64 x y))))))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 x y) (*.f64 x y)))))
6.5b
(-.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 (*.f64 x y) (*.f64 x y)))
9.6b
(sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 (*.f64 x y) (*.f64 x y))))))
22.3b
(sqrt.f64 (-.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 (*.f64 x y) (*.f64 x y))))

rewrite118.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
104×sqrt-div_binary64_10666
35×flip3--_binary64_10653 flip--_binary64_10624
32×frac-times_binary64_10659
26×associate-/l/_binary64_10596
23×sqrt-prod_binary64_10665
16×associate-*r/_binary64_10591
12×add-sqr-sqrt_binary64_10671
11×*-un-lft-identity_binary64_10649 add-cube-cbrt_binary64_10684
10×associate-*l/_binary64_10592 pow1_binary64_10710
associate-/r*_binary64_10593 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687 times-frac_binary64_10655
sqrt-pow1_binary64_10667
add-log-exp_binary64_10688
pow1/2_binary64_10729
pow-prod-down_binary64_10720
difference-of-squares_binary64_10618 associate-/r/_binary64_10595 div-exp_binary64_10700 associate--l+_binary64_10586 cbrt-undiv_binary64_10683
prod-exp_binary64_10698 cbrt-unprod_binary64_10682 sqrt-undiv_binary64_10670 clear-num_binary64_10648 sub-neg_binary64_10642 associate-/l*_binary64_10594 cancel-sign-sub-inv_binary64_10615 distribute-rgt-in_binary64_10599 frac-2neg_binary64_10660 distribute-lft-in_binary64_10598 flip-+_binary64_10623 div-inv_binary64_10646 flip3-+_binary64_10652 rem-sqrt-square_binary64_10662 sqrt-unprod_binary64_10669 diff-log_binary64_10741
Counts
4 → 114
Calls

8 calls:

47.0ms
(/.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 (*.f64 x y) (*.f64 x y))))))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 x y) (*.f64 x y)))))
21.0ms
(sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 (*.f64 x y) (*.f64 x y))))))
12.0ms
(sqrt.f64 (-.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 (*.f64 x y) (*.f64 x y))))
12.0ms
(-.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 (*.f64 x y) (*.f64 x y)))
0.0ms
(sqrt.f64 (+.f64 (+.f64 x y) (*.f64 x y)))

series1.3min (37.2%)

Counts
4 → 60
Calls

4 calls:

1.2min
(/.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 (*.f64 x y) (*.f64 x y))))))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 x y) (*.f64 x y)))))
1.1s
(sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (+.f64 x y) (*.f64 x y))) (sqrt.f64 (-.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 (*.f64 x y) (*.f64 x y))))))
283.0ms
(-.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 (*.f64 x y) (*.f64 x y)))
119.0ms
(sqrt.f64 (-.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (*.f64 (*.f64 x y) (*.f64 x y))))
Compiler

Compiled 46997 to 38924 computations (17.2% saved)

simplify358.0ms (0.2%)

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
0522244667

prune30.1s (14.9%)

Pruning

594 alts after pruning (587 fresh and 7 done)

PrunedKeptTotal
New279323602
Fresh13264277
Picked000
Done279
Total294594888
Error
0b
Counts
888 → 594
Compiler

Compiled 43838 to 23491 computations (46.4% saved)

simplify1.1s (0.6%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
0597688110

regimes23.0s (11.4%)

Compiler

Compiled 163304 to 96469 computations (40.9% saved)

bsearch0.0ms (0%)

regimes52.0ms (0%)

Compiler

Compiled 120 to 132 computations (-10% saved)

bsearch0.0ms (0%)

regimes61.0ms (0%)

Compiler

Compiled 58 to 74 computations (-27.6% saved)

bsearch28.0ms (0%)

Steps
ItersRangePoint
7
0.09582668147813252
3.268946677870827
0.9902767981226298
10
-1.1569509840180279e+21
-583136590.1913133
-593851404.9764618
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes62.0ms (0%)

Compiler

Compiled 28 to 48 computations (-71.4% saved)

bsearch37.0ms (0%)

Steps
ItersRangePoint
6
2.0822606743933182e+66
1.0780099654922019e+67
2.113375967930279e+66
8
3.268946677870827
1789.244117588337
1771.0184468490431
8
-1.3055583814112207e+63
-4.224391814205669e+58
-9.418554090792549e+61
2
-4.875228123034846e+186
-4.21828461320786e+186
-4.2676434465687404e+186
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes23.0ms (0%)

Compiler

Compiled 20 to 40 computations (-100% saved)

bsearch0.0ms (0%)

regimes44.0ms (0%)

Accuracy

Total 0.0b remaining (100%)

Threshold costs 0.0b (100%)

Compiler

Compiled 14 to 34 computations (-142.9% saved)

bsearch29.0ms (0%)

Steps
ItersRangePoint
9
3.927026218737797e-69
3.011701016625198e-60
6.405195131067386e-62
9
-4.064726354951099e-44
-1.2397308971073883e-49
-1.9332129628652103e-48
Compiler

Compiled 80 to 54 computations (32.5% saved)

simplify6.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
076107
176107

end0.0ms (0%)

sample48.6s (24%)

Algorithm
intervals
Results
175.0ms7999×body128valid
2.0ms81×body128invalid
0.0msbody1024valid
Compiler

Compiled 54218 to 32118 computations (40.8% saved)

Pareto

0.360150339742176

Profiling

Loading profile data...