Details

Time bar (total: 11.6min)

analyze432.0ms (0.1%)

Algorithm
1×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
31.2%68.6%0.1%9
35.9%55.4%8.7%10
42.9%47.6%9.5%11
51.5%38.2%10.3%12
55%30%15%13
59.5%25.3%15.3%14
Compiler

Compiled 14 to 13 computations (7.1% saved)

sample24.0ms (0%)

Algorithm
1×intervals
Results
9.0ms238×body128valid
1.0ms8×body512valid
1.0ms6×body1024valid
1.0ms14×body128invalid
0.0ms4×body256valid
Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify346.0ms (0%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (251.0ms)

IterNodesCost
0242616
1242616

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.4b
Counts
2 → 2
Compiler

Compiled 11 to 10 computations (9.1% saved)

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (*.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
0.0b
(+.f64 x (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
0.0b
(-.f64 (/.f64 2 3) z)
0.0b
(*.f64 (-.f64 y x) 6)
0.0b
(*.f64 (-.f64 y x) 6)
0.0b
(+.f64 x (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
0.0b
(-.f64 (/.f64 2 3) z)
0.3b
(*.f64 (*.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))

rewrite49.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
26×add-sqr-sqrt_binary64_10671
18×*-un-lft-identity_binary64_10649
15×cancel-sign-sub-inv_binary64_10615
12×add-cube-cbrt_binary64_10684
11×pow1_binary64_10710 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687
10×associate-*l/_binary64_10592
9×associate-*r*_binary64_10589
8×add-log-exp_binary64_10688 distribute-rgt-in_binary64_10599 distribute-lft-in_binary64_10598 flip3--_binary64_10653 flip--_binary64_10624 associate-+r+_binary64_10581
6×associate-*l*_binary64_10590
5×difference-of-squares_binary64_10618 sub-neg_binary64_10642
4×prod-exp_binary64_10698 cbrt-unprod_binary64_10682 pow-prod-down_binary64_10720 frac-times_binary64_10659
3×distribute-lft-out--_binary64_10601
2×*-commutative_binary64_10580 times-frac_binary64_10655 associate-*r/_binary64_10591
1×sum-log_binary64_10740 unswap-sqr_binary64_10617 +-commutative_binary64_10579 flip-+_binary64_10623 flip3-+_binary64_10652 diff-log_binary64_10741
Counts
4 → 95
Calls

8 calls:

16.0ms
(*.f64 (*.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
11.0ms
(-.f64 (/.f64 2 3) z)
6.0ms
(*.f64 (-.f64 y x) 6)
6.0ms
(+.f64 x (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
0.0ms
(*.f64 (-.f64 y x) 6)

series589.0ms (0.1%)

Counts
4 → 54
Calls

4 calls:

289.0ms
(+.f64 x (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
203.0ms
(*.f64 (*.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
76.0ms
(*.f64 (-.f64 y x) 6)
20.0ms
(-.f64 (/.f64 2 3) z)
Compiler

Compiled 1219 to 1076 computations (11.7% saved)

simplify93.0ms (0%)

Algorithm
1×egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
050661963

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z))
0.0b
(+.f64 x (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)))
0.0b
(-.f64 2/3 z)
0.0b
(*.f64 (-.f64 y x) 6)
0.0b
(*.f64 (-.f64 y x) 6)
0.0b
(+.f64 x (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)))
0.0b
(-.f64 2/3 z)
0.3b
(*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z))

rewrite38.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64_10671
18×*-un-lft-identity_binary64_10649
15×cancel-sign-sub-inv_binary64_10615
12×add-cube-cbrt_binary64_10684
11×pow1_binary64_10710 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687
10×associate-*l/_binary64_10592
8×add-log-exp_binary64_10688 distribute-rgt-in_binary64_10599 distribute-lft-in_binary64_10598 flip3--_binary64_10653 flip--_binary64_10624 associate-*r*_binary64_10589 associate-+r+_binary64_10581
6×associate-*l*_binary64_10590
5×sub-neg_binary64_10642
4×prod-exp_binary64_10698 cbrt-unprod_binary64_10682 pow-prod-down_binary64_10720 frac-times_binary64_10659
3×difference-of-squares_binary64_10618 distribute-lft-out--_binary64_10601
2×*-commutative_binary64_10580 associate-*r/_binary64_10591
1×sum-log_binary64_10740 unswap-sqr_binary64_10617 +-commutative_binary64_10579 flip-+_binary64_10623 flip3-+_binary64_10652 diff-log_binary64_10741
Counts
4 → 93
Calls

8 calls:

12.0ms
(*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z))
7.0ms
(*.f64 (-.f64 y x) 6)
5.0ms
(+.f64 x (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)))
4.0ms
(-.f64 2/3 z)
0.0ms
(*.f64 (-.f64 y x) 6)

series598.0ms (0.1%)

Counts
4 → 54
Calls

4 calls:

306.0ms
(+.f64 x (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)))
200.0ms
(*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z))
71.0ms
(*.f64 (-.f64 y x) 6)
20.0ms
(-.f64 2/3 z)
Compiler

Compiled 1183 to 1040 computations (12.1% saved)

simplify124.0ms (0%)

Algorithm
1×egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 0 (95.0ms)

IterNodesCost
049461915
149461915

prune1.1s (0.2%)

Pruning

86 alts after pruning (84 fresh and 2 done)

PrunedKeptTotal
New21284296
Fresh000
Picked000
Done022
Total21286298
Error
0.0b
Counts
298 → 86
Compiler

Compiled 3687 to 2531 computations (31.4% saved)

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 (*.f64 (-.f64 y x) 6) (*.f64 (neg.f64 1) z))
0.0b
(+.f64 (+.f64 x (*.f64 (-.f64 y x) 4)) (*.f64 (*.f64 (-.f64 y x) 6) (*.f64 (neg.f64 1) z)))
0.0b
(+.f64 x (*.f64 (-.f64 y x) 4))
0.0b
(*.f64 (-.f64 y x) 6)
0.0b
(*.f64 (-.f64 y x) 6)
0.0b
(+.f64 (+.f64 x (*.f64 (-.f64 y x) 4)) (*.f64 (*.f64 (-.f64 y x) 6) (*.f64 (neg.f64 1) z)))
0.0b
(+.f64 x (*.f64 (-.f64 y x) 4))
0.2b
(*.f64 (*.f64 (-.f64 y x) 6) (*.f64 (neg.f64 1) z))

rewrite39.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
18×pow1_binary64_10710 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687
14×associate-*l/_binary64_10592
11×add-log-exp_binary64_10688
10×add-sqr-sqrt_binary64_10671
9×prod-exp_binary64_10698 cbrt-unprod_binary64_10682 pow-prod-down_binary64_10720
8×*-un-lft-identity_binary64_10649
6×add-cube-cbrt_binary64_10684 associate-*l*_binary64_10590
4×sum-log_binary64_10740 frac-add_binary64_10657 flip-+_binary64_10623 flip3--_binary64_10653 flip--_binary64_10624 flip3-+_binary64_10652 associate-*r*_binary64_10589
2×distribute-rgt-neg-out_binary64_10609 +-commutative_binary64_10579 *-commutative_binary64_10580 distribute-lft-neg-out_binary64_10608
1×difference-of-squares_binary64_10618 unswap-sqr_binary64_10617 associate-+l+_binary64_10582 unsub-neg_binary64_10643 distribute-lft-out--_binary64_10601
Counts
4 → 76
Calls

8 calls:

10.0ms
(*.f64 (*.f64 (-.f64 y x) 6) (*.f64 (neg.f64 1) z))
9.0ms
(*.f64 (-.f64 y x) 6)
9.0ms
(+.f64 (+.f64 x (*.f64 (-.f64 y x) 4)) (*.f64 (*.f64 (-.f64 y x) 6) (*.f64 (neg.f64 1) z)))
4.0ms
(+.f64 x (*.f64 (-.f64 y x) 4))
0.0ms
(*.f64 (-.f64 y x) 6)

series607.0ms (0.1%)

Counts
4 → 57
Calls

4 calls:

296.0ms
(+.f64 (+.f64 x (*.f64 (-.f64 y x) 4)) (*.f64 (*.f64 (-.f64 y x) 6) (*.f64 (neg.f64 1) z)))
148.0ms
(*.f64 (*.f64 (-.f64 y x) 6) (*.f64 (neg.f64 1) z))
89.0ms
(+.f64 x (*.f64 (-.f64 y x) 4))
72.0ms
(*.f64 (-.f64 y x) 6)
Compiler

Compiled 1455 to 1246 computations (14.4% saved)

simplify118.0ms (0%)

Algorithm
1×egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 0 (93.0ms)

IterNodesCost
049431941
149431941

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 x (-.f64 (*.f64 6 z) 3))
0.0b
(-.f64 (*.f64 6 z) 3)
0.0b
(-.f64 (*.f64 6 z) 3)
0.1b
(*.f64 x (-.f64 (*.f64 6 z) 3))

rewrite14.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
9×cancel-sign-sub-inv_binary64_10615 add-sqr-sqrt_binary64_10671
7×*-un-lft-identity_binary64_10649 add-cube-cbrt_binary64_10684
4×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
3×sub-neg_binary64_10642 associate-*r*_binary64_10589 associate-*l*_binary64_10590
2×flip3--_binary64_10653 flip--_binary64_10624 associate-*r/_binary64_10591
1×prod-exp_binary64_10698 cbrt-unprod_binary64_10682 pow-prod-down_binary64_10720 unswap-sqr_binary64_10617 *-commutative_binary64_10580 diff-log_binary64_10741
Counts
2 → 42
Calls

4 calls:

7.0ms
(*.f64 x (-.f64 (*.f64 6 z) 3))
4.0ms
(-.f64 (*.f64 6 z) 3)
0.0ms
(-.f64 (*.f64 6 z) 3)
0.0ms
(*.f64 x (-.f64 (*.f64 6 z) 3))

series121.0ms (0%)

Counts
2 → 15
Calls

2 calls:

92.0ms
(*.f64 x (-.f64 (*.f64 6 z) 3))
29.0ms
(-.f64 (*.f64 6 z) 3)
Compiler

Compiled 164 to 184 computations (-12.2% saved)

simplify57.0ms (0%)

Algorithm
1×egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
04980582
14980582

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 x (/.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 4/9 (*.f64 z z))) (+.f64 (/.f64 2 3) z)))
0.0b
(-.f64 4/9 (*.f64 z z))
0.0b
(*.f64 (-.f64 y x) 6)
0.0b
(+.f64 (/.f64 2 3) z)
0.0b
(-.f64 4/9 (*.f64 z z))
0.0b
(+.f64 x (/.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 4/9 (*.f64 z z))) (+.f64 (/.f64 2 3) z)))
2.2b
(*.f64 (*.f64 (-.f64 y x) 6) (-.f64 4/9 (*.f64 z z)))
7.7b
(/.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 4/9 (*.f64 z z))) (+.f64 (/.f64 2 3) z))

rewrite55.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
18×add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687
16×associate-*l/_binary64_10592
13×*-un-lft-identity_binary64_10649 flip3--_binary64_10653 flip--_binary64_10624
9×pow1_binary64_10710 add-sqr-sqrt_binary64_10671
8×add-log-exp_binary64_10688 associate-/l/_binary64_10596 frac-times_binary64_10659
7×add-cube-cbrt_binary64_10684
6×prod-exp_binary64_10698 cbrt-unprod_binary64_10682
4×associate-/r*_binary64_10593 times-frac_binary64_10655 associate-*r*_binary64_10589 associate-*r/_binary64_10591
3×pow-prod-down_binary64_10720 sub-neg_binary64_10642 cancel-sign-sub-inv_binary64_10615 div-exp_binary64_10700 cbrt-undiv_binary64_10683 distribute-lft-out_binary64_10600
2×difference-of-squares_binary64_10618 associate-/r/_binary64_10595 distribute-rgt-in_binary64_10599 distribute-lft-in_binary64_10598 flip-+_binary64_10623 flip3-+_binary64_10652
1×sum-log_binary64_10740 clear-num_binary64_10648 associate-/l*_binary64_10594 +-commutative_binary64_10579 *-commutative_binary64_10580 frac-2neg_binary64_10660 div-inv_binary64_10646 associate-*l*_binary64_10590 diff-log_binary64_10741
Counts
4 → 91
Calls

8 calls:

18.0ms
(/.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 4/9 (*.f64 z z))) (+.f64 (/.f64 2 3) z))
13.0ms
(+.f64 x (/.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 4/9 (*.f64 z z))) (+.f64 (/.f64 2 3) z)))
11.0ms
(*.f64 (*.f64 (-.f64 y x) 6) (-.f64 4/9 (*.f64 z z)))
3.0ms
(-.f64 4/9 (*.f64 z z))
0.0ms
(+.f64 (/.f64 2 3) z)

series1.5s (0.2%)

Counts
4 → 60
Calls

4 calls:

821.0ms
(+.f64 x (/.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 4/9 (*.f64 z z))) (+.f64 (/.f64 2 3) z)))
418.0ms
(/.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 4/9 (*.f64 z z))) (+.f64 (/.f64 2 3) z))
267.0ms
(*.f64 (*.f64 (-.f64 y x) 6) (-.f64 4/9 (*.f64 z z)))
39.0ms
(-.f64 4/9 (*.f64 z z))
Compiler

Compiled 2364 to 1996 computations (15.6% saved)

simplify105.0ms (0%)

Algorithm
1×egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
049883559
149883559

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(-.f64 (/.f64 2 3) z)
0.0b
(*.f64 (-.f64 y x) 6)
0.0b
(+.f64 x (*.f64 (log.f64 (exp.f64 (*.f64 (-.f64 y x) 6))) (-.f64 (/.f64 2 3) z)))
0.0b
(exp.f64 (*.f64 (-.f64 y x) 6))
0.0b
(+.f64 x (*.f64 (log.f64 (exp.f64 (*.f64 (-.f64 y x) 6))) (-.f64 (/.f64 2 3) z)))
0.0b
(-.f64 (/.f64 2 3) z)
0.0b
(*.f64 (log.f64 (exp.f64 (*.f64 (-.f64 y x) 6))) (-.f64 (/.f64 2 3) z))
5.4b
(log.f64 (exp.f64 (*.f64 (-.f64 y x) 6)))

rewrite38.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
24×add-sqr-sqrt_binary64_10671
16×*-un-lft-identity_binary64_10649
15×cancel-sign-sub-inv_binary64_10615
14×add-log-exp_binary64_10688
12×add-cube-cbrt_binary64_10684
8×log-pow_binary64_10738 pow1_binary64_10710 distribute-rgt-in_binary64_10599 distribute-lft-in_binary64_10598 associate-+r+_binary64_10581
7×associate-*l*_binary64_10590
6×add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687 associate-*r*_binary64_10589
5×sub-neg_binary64_10642
4×difference-of-squares_binary64_10618 exp-to-pow_binary64_10711
3×log-prod_binary64_10735 diff-log_binary64_10741
2×exp-prod_binary64_10701 distribute-lft-out--_binary64_10601 times-frac_binary64_10655 flip3--_binary64_10653 flip--_binary64_10624 associate-*r/_binary64_10591
1×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 flip-+_binary64_10623 rem-log-exp_binary64_10690 flip3-+_binary64_10652
Counts
4 → 86
Calls

8 calls:

13.0ms
(*.f64 (log.f64 (exp.f64 (*.f64 (-.f64 y x) 6))) (-.f64 (/.f64 2 3) z))
8.0ms
(-.f64 (/.f64 2 3) z)
6.0ms
(+.f64 x (*.f64 (log.f64 (exp.f64 (*.f64 (-.f64 y x) 6))) (-.f64 (/.f64 2 3) z)))
3.0ms
(log.f64 (exp.f64 (*.f64 (-.f64 y x) 6)))
0.0ms
(exp.f64 (*.f64 (-.f64 y x) 6))

series1.6s (0.2%)

Counts
4 → 44
Calls

4 calls:

855.0ms
(+.f64 x (*.f64 (log.f64 (exp.f64 (*.f64 (-.f64 y x) 6))) (-.f64 (/.f64 2 3) z)))
463.0ms
(*.f64 (log.f64 (exp.f64 (*.f64 (-.f64 y x) 6))) (-.f64 (/.f64 2 3) z))
229.0ms
(log.f64 (exp.f64 (*.f64 (-.f64 y x) 6)))
25.0ms
(-.f64 (/.f64 2 3) z)
Compiler

Compiled 1191 to 1054 computations (11.5% saved)

simplify94.0ms (0%)

Algorithm
1×egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
051661622

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(-.f64 2/3 z)
0.0b
(-.f64 2/3 z)
0.0b
(-.f64 2/3 z)
0.0b
(*.f64 (-.f64 y x) 6)
0.3b
(*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z))
0.8b
(*.f64 (-.f64 y x) (*.f64 (*.f64 6 (-.f64 2/3 z)) (-.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) x)))
12.5b
(+.f64 (*.f64 216 (pow.f64 (*.f64 (-.f64 y x) (-.f64 2/3 z)) 3)) (pow.f64 x 3))
40.9b
(/.f64 (+.f64 (*.f64 216 (pow.f64 (*.f64 (-.f64 y x) (-.f64 2/3 z)) 3)) (pow.f64 x 3)) (+.f64 (*.f64 x x) (*.f64 (-.f64 y x) (*.f64 (*.f64 6 (-.f64 2/3 z)) (-.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) x)))))

rewrite107.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
68×distribute-rgt-in_binary64_10599 distribute-lft-in_binary64_10598
42×cancel-sign-sub-inv_binary64_10615
34×associate-*r/_binary64_10591
33×flip3--_binary64_10653 flip--_binary64_10624
32×associate--l+_binary64_10586 *-un-lft-identity_binary64_10649 add-sqr-sqrt_binary64_10671 frac-times_binary64_10659
28×add-cube-cbrt_binary64_10684
20×add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687
18×pow1_binary64_10710
16×associate-*l/_binary64_10592
14×sub-neg_binary64_10642
9×prod-exp_binary64_10698 cbrt-unprod_binary64_10682 pow-prod-down_binary64_10720 times-frac_binary64_10655
6×add-log-exp_binary64_10688 associate-*r*_binary64_10589 associate-*l*_binary64_10590
3×associate-/r*_binary64_10593 associate-/l*_binary64_10594 flip-+_binary64_10623 flip3-+_binary64_10652
2×difference-of-squares_binary64_10618 associate-/r/_binary64_10595 *-commutative_binary64_10580 distribute-lft-out--_binary64_10601 associate-/l/_binary64_10596
1×sum-log_binary64_10740 clear-num_binary64_10648 +-commutative_binary64_10579 div-exp_binary64_10700 cbrt-undiv_binary64_10683 frac-2neg_binary64_10660 div-inv_binary64_10646
Counts
4 → 175
Calls

8 calls:

34.0ms
(*.f64 (-.f64 y x) (*.f64 (*.f64 6 (-.f64 2/3 z)) (-.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) x)))
17.0ms
(/.f64 (+.f64 (*.f64 216 (pow.f64 (*.f64 (-.f64 y x) (-.f64 2/3 z)) 3)) (pow.f64 x 3)) (+.f64 (*.f64 x x) (*.f64 (-.f64 y x) (*.f64 (*.f64 6 (-.f64 2/3 z)) (-.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) x)))))
14.0ms
(*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z))
11.0ms
(+.f64 (*.f64 216 (pow.f64 (*.f64 (-.f64 y x) (-.f64 2/3 z)) 3)) (pow.f64 x 3))
0.0ms
(*.f64 (-.f64 y x) 6)

series9.1s (1.3%)

Counts
4 → 99
Calls

4 calls:

6.8s
(/.f64 (+.f64 (*.f64 216 (pow.f64 (*.f64 (-.f64 y x) (-.f64 2/3 z)) 3)) (pow.f64 x 3)) (+.f64 (*.f64 x x) (*.f64 (-.f64 y x) (*.f64 (*.f64 6 (-.f64 2/3 z)) (-.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) x)))))
1.1s
(+.f64 (*.f64 216 (pow.f64 (*.f64 (-.f64 y x) (-.f64 2/3 z)) 3)) (pow.f64 x 3))
929.0ms
(*.f64 (-.f64 y x) (*.f64 (*.f64 6 (-.f64 2/3 z)) (-.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) x)))
218.0ms
(*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z))
Compiler

Compiled 19686 to 15221 computations (22.7% saved)

simplify184.0ms (0%)

Algorithm
1×egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
0563920534

prune13.0s (1.9%)

Pruning

374 alts after pruning (369 fresh and 5 done)

PrunedKeptTotal
New447298745
Fresh87179
Picked000
Done257
Total457374831
Error
0b
Counts
831 → 374
Compiler

Compiled 34262 to 21585 computations (37% saved)

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 (*.f64 (-.f64 y x) 6) (*.f64 (neg.f64 1) z))
0.0b
(+.f64 (-.f64 (*.f64 y 4) (*.f64 x 3)) (*.f64 (*.f64 (-.f64 y x) 6) (*.f64 (neg.f64 1) z)))
0.0b
(*.f64 (-.f64 y x) 6)
0.0b
(-.f64 (*.f64 y 4) (*.f64 x 3))
0.0b
(-.f64 (*.f64 y 4) (*.f64 x 3))
0.0b
(*.f64 (-.f64 y x) 6)
0.0b
(+.f64 (-.f64 (*.f64 y 4) (*.f64 x 3)) (*.f64 (*.f64 (-.f64 y x) 6) (*.f64 (neg.f64 1) z)))
0.2b
(*.f64 (*.f64 (-.f64 y x) 6) (*.f64 (neg.f64 1) z))

rewrite39.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
18×pow1_binary64_10710 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687
14×associate-*l/_binary64_10592
11×add-log-exp_binary64_10688
10×add-sqr-sqrt_binary64_10671
9×prod-exp_binary64_10698 cbrt-unprod_binary64_10682 pow-prod-down_binary64_10720
8×*-un-lft-identity_binary64_10649
7×flip3--_binary64_10653 flip--_binary64_10624
6×add-cube-cbrt_binary64_10684 associate-*l*_binary64_10590
4×frac-add_binary64_10657 associate-*r*_binary64_10589
2×sum-log_binary64_10740 distribute-rgt-neg-out_binary64_10609 sub-neg_binary64_10642 cancel-sign-sub-inv_binary64_10615 *-commutative_binary64_10580 distribute-lft-neg-out_binary64_10608 associate-+l+_binary64_10582 diff-log_binary64_10741
1×associate-+l-_binary64_10584 difference-of-squares_binary64_10618 unswap-sqr_binary64_10617 +-commutative_binary64_10579 unsub-neg_binary64_10643 distribute-lft-out--_binary64_10601 flip-+_binary64_10623 flip3-+_binary64_10652
Counts
4 → 79
Calls

8 calls:

11.0ms
(*.f64 (*.f64 (-.f64 y x) 6) (*.f64 (neg.f64 1) z))
9.0ms
(+.f64 (-.f64 (*.f64 y 4) (*.f64 x 3)) (*.f64 (*.f64 (-.f64 y x) 6) (*.f64 (neg.f64 1) z)))
7.0ms
(*.f64 (-.f64 y x) 6)
4.0ms
(-.f64 (*.f64 y 4) (*.f64 x 3))
0.0ms
(-.f64 (*.f64 y 4) (*.f64 x 3))

series607.0ms (0.1%)

Counts
4 → 57
Calls

4 calls:

295.0ms
(+.f64 (-.f64 (*.f64 y 4) (*.f64 x 3)) (*.f64 (*.f64 (-.f64 y x) 6) (*.f64 (neg.f64 1) z)))
146.0ms
(*.f64 (*.f64 (-.f64 y x) 6) (*.f64 (neg.f64 1) z))
90.0ms
(-.f64 (*.f64 y 4) (*.f64 x 3))
76.0ms
(*.f64 (-.f64 y x) 6)
Compiler

Compiled 1455 to 1292 computations (11.2% saved)

simplify94.0ms (0%)

Algorithm
1×egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
050902047

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify8.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
000

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

37.2b
(cbrt.f64 (pow.f64 (*.f64 x (-.f64 (*.f64 6 z) 3)) 3))
0.2b
(pow.f64 (*.f64 x (-.f64 (*.f64 6 z) 3)) 3)
0.1b
(*.f64 x (-.f64 (*.f64 6 z) 3))
0.0b
(-.f64 (*.f64 6 z) 3)
0.0b
(-.f64 (*.f64 6 z) 3)
0.1b
(*.f64 x (-.f64 (*.f64 6 z) 3))
0.2b
(pow.f64 (*.f64 x (-.f64 (*.f64 6 z) 3)) 3)
37.2b
(cbrt.f64 (pow.f64 (*.f64 x (-.f64 (*.f64 6 z) 3)) 3))

rewrite28.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
13×add-sqr-sqrt_binary64_10671
11×*-un-lft-identity_binary64_10649 add-cube-cbrt_binary64_10684
9×pow1_binary64_10710 cancel-sign-sub-inv_binary64_10615 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687
8×cbrt-prod_binary64_10680
6×add-log-exp_binary64_10688 associate-*r/_binary64_10591
4×cube-div_binary64_10678 distribute-rgt-in_binary64_10599 distribute-lft-in_binary64_10598 flip3--_binary64_10653 flip--_binary64_10624
3×sub-neg_binary64_10642 pow-unpow_binary64_10726 associate-*r*_binary64_10589 associate-*l*_binary64_10590
2×prod-exp_binary64_10698 cbrt-unprod_binary64_10682 unpow3_binary64_10715 pow-prod-down_binary64_10720 rem-cube-cbrt_binary64_10672 cbrt-div_binary64_10681 sqr-pow_binary64_10621 pow-pow_binary64_10721 pow-exp_binary64_10717 cube-prod_binary64_10677 unpow-prod-down_binary64_10728 cube-mult_binary64_10679
1×unswap-sqr_binary64_10617 *-commutative_binary64_10580 pow1/3_binary64_10731 pow-to-exp_binary64_10718 diff-log_binary64_10741 rem-cbrt-cube_binary64_10673
Counts
4 → 85
Calls

8 calls:

7.0ms
(*.f64 x (-.f64 (*.f64 6 z) 3))
7.0ms
(pow.f64 (*.f64 x (-.f64 (*.f64 6 z) 3)) 3)
4.0ms
(-.f64 (*.f64 6 z) 3)
3.0ms
(cbrt.f64 (pow.f64 (*.f64 x (-.f64 (*.f64 6 z) 3)) 3))
0.0ms
(-.f64 (*.f64 6 z) 3)

series385.0ms (0.1%)

Counts
4 → 39
Calls

4 calls:

152.0ms
(pow.f64 (*.f64 x (-.f64 (*.f64 6 z) 3)) 3)
112.0ms
(cbrt.f64 (pow.f64 (*.f64 x (-.f64 (*.f64 6 z) 3)) 3))
86.0ms
(*.f64 x (-.f64 (*.f64 6 z) 3))
35.0ms
(-.f64 (*.f64 6 z) 3)
Compiler

Compiled 704 to 722 computations (-2.6% saved)

simplify100.0ms (0%)

Algorithm
1×egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
049341653
149341653

localize32.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 (pow.f64 y 3) 64)
0.0b
(+.f64 (*.f64 (*.f64 x x) 21) (*.f64 (*.f64 y y) 16))
0.0b
(+.f64 (*.f64 (pow.f64 x 3) 63) (*.f64 192 (*.f64 x (*.f64 y y))))
0.0b
(+.f64 (*.f64 (pow.f64 y 3) 64) (*.f64 192 (*.f64 y (*.f64 x x))))
6.3b
(*.f64 y (*.f64 x x))
7.1b
(-.f64 (+.f64 (*.f64 (pow.f64 y 3) 64) (*.f64 192 (*.f64 y (*.f64 x x)))) (+.f64 (*.f64 (pow.f64 x 3) 63) (*.f64 192 (*.f64 x (*.f64 y y)))))
7.3b
(*.f64 x (*.f64 y y))
39.1b
(/.f64 (-.f64 (+.f64 (*.f64 (pow.f64 y 3) 64) (*.f64 192 (*.f64 y (*.f64 x x)))) (+.f64 (*.f64 (pow.f64 x 3) 63) (*.f64 192 (*.f64 x (*.f64 y y))))) (-.f64 (+.f64 (*.f64 (*.f64 x x) 21) (*.f64 (*.f64 y y) 16)) (*.f64 36 (*.f64 y x))))

rewrite75.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
29×add-sqr-sqrt_binary64_10671
27×*-un-lft-identity_binary64_10649
17×add-cube-cbrt_binary64_10684
16×add-log-exp_binary64_10688 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687
15×times-frac_binary64_10655
14×pow1_binary64_10710
8×frac-sub_binary64_10658 flip-+_binary64_10623 flip3-+_binary64_10652
6×prod-exp_binary64_10698 cbrt-unprod_binary64_10682 pow-prod-down_binary64_10720 associate-/l/_binary64_10596 associate-*l*_binary64_10590
5×difference-of-squares_binary64_10618 associate-/l*_binary64_10594 distribute-lft-out--_binary64_10601
4×sum-log_binary64_10740 diff-log_binary64_10741
3×associate-/r*_binary64_10593 cancel-sign-sub-inv_binary64_10615 flip3--_binary64_10653 flip--_binary64_10624
2×unswap-sqr_binary64_10617 associate-/r/_binary64_10595 *-commutative_binary64_10580 associate-*r*_binary64_10589
1×clear-num_binary64_10648 sub-neg_binary64_10642 div-sub_binary64_10654 div-exp_binary64_10700 associate--r+_binary64_10585 associate--l+_binary64_10586 cbrt-undiv_binary64_10683 frac-2neg_binary64_10660 div-inv_binary64_10646
Counts
4 → 107
Calls

8 calls:

29.0ms
(/.f64 (-.f64 (+.f64 (*.f64 (pow.f64 y 3) 64) (*.f64 192 (*.f64 y (*.f64 x x)))) (+.f64 (*.f64 (pow.f64 x 3) 63) (*.f64 192 (*.f64 x (*.f64 y y))))) (-.f64 (+.f64 (*.f64 (*.f64 x x) 21) (*.f64 (*.f64 y y) 16)) (*.f64 36 (*.f64 y x))))
15.0ms
(-.f64 (+.f64 (*.f64 (pow.f64 y 3) 64) (*.f64 192 (*.f64 y (*.f64 x x)))) (+.f64 (*.f64 (pow.f64 x 3) 63) (*.f64 192 (*.f64 x (*.f64 y y)))))
6.0ms
(*.f64 y (*.f64 x x))
6.0ms
(*.f64 x (*.f64 y y))
0.0ms
(+.f64 (*.f64 (pow.f64 y 3) 64) (*.f64 192 (*.f64 y (*.f64 x x))))

series749.0ms (0.1%)

Counts
4 → 48
Calls

4 calls:

458.0ms
(/.f64 (-.f64 (+.f64 (*.f64 (pow.f64 y 3) 64) (*.f64 192 (*.f64 y (*.f64 x x)))) (+.f64 (*.f64 (pow.f64 x 3) 63) (*.f64 192 (*.f64 x (*.f64 y y))))) (-.f64 (+.f64 (*.f64 (*.f64 x x) 21) (*.f64 (*.f64 y y) 16)) (*.f64 36 (*.f64 y x))))
146.0ms
(-.f64 (+.f64 (*.f64 (pow.f64 y 3) 64) (*.f64 192 (*.f64 y (*.f64 x x)))) (+.f64 (*.f64 (pow.f64 x 3) 63) (*.f64 192 (*.f64 x (*.f64 y y)))))
72.0ms
(*.f64 y (*.f64 x x))
72.0ms
(*.f64 x (*.f64 y y))
Compiler

Compiled 2010 to 1608 computations (20% saved)

simplify103.0ms (0%)

Algorithm
1×egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
051426793

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(-.f64 (/.f64 2 3) z)
0.0b
(+.f64 x (*.f64 (*.f64 (*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6)) (*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6))) (-.f64 (/.f64 2 3) z)))
0.0b
(sqrt.f64 (-.f64 y x))
0.0b
(sqrt.f64 (-.f64 y x))
0.1b
(*.f64 (*.f64 (*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6)) (*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6))) (-.f64 (/.f64 2 3) z))
0.3b
(*.f64 (*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6)) (*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6)))
0.3b
(*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6))
0.3b
(*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6))

rewrite99.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
85×pow1_binary64_10710
68×associate-*l/_binary64_10592
54×pow-prod-down_binary64_10720
52×sqrt-div_binary64_10666
41×add-sqr-sqrt_binary64_10671
38×add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687
35×flip3--_binary64_10653 flip--_binary64_10624
32×frac-times_binary64_10659
24×sqrt-prod_binary64_10665
23×prod-exp_binary64_10698 cbrt-unprod_binary64_10682
21×*-un-lft-identity_binary64_10649
20×sqrt-pow1_binary64_10667 pow1/2_binary64_10729
19×associate-*r*_binary64_10589
18×associate-*l*_binary64_10590
15×add-cube-cbrt_binary64_10684
10×associate-*r/_binary64_10591
9×unswap-sqr_binary64_10617
8×pow-prod-up_binary64_10719
7×sqrt-unprod_binary64_10669
6×pow-sqr_binary64_10622 cancel-sign-sub-inv_binary64_10615
4×add-log-exp_binary64_10688 difference-of-squares_binary64_10618 *-commutative_binary64_10580 distribute-rgt-in_binary64_10599 distribute-lft-in_binary64_10598
3×distribute-lft-out--_binary64_10601
2×pow-plus_binary64_10712 sub-neg_binary64_10642
1×times-frac_binary64_10655 pow2_binary64_10730 rem-square-sqrt_binary64_10661 swap-sqr_binary64_10616
Counts
4 → 185
Calls

8 calls:

38.0ms
(*.f64 (*.f64 (*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6)) (*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6))) (-.f64 (/.f64 2 3) z))
17.0ms
(*.f64 (*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6)) (*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6)))
10.0ms
(*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6))
10.0ms
(*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6))
0.0ms
(sqrt.f64 (-.f64 y x))

series728.0ms (0.1%)

Counts
4 → 46
Calls

4 calls:

374.0ms
(*.f64 (*.f64 (*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6)) (*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6))) (-.f64 (/.f64 2 3) z))
159.0ms
(*.f64 (*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6)) (*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6)))
99.0ms
(*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6))
95.0ms
(*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 6))
Compiler

Compiled 2143 to 1909 computations (10.9% saved)

simplify112.0ms (0%)

Algorithm
1×egg-herbie
Counts
231 → 231
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049693856
149693856

prune23.2s (3.3%)

Pruning

542 alts after pruning (532 fresh and 10 done)

PrunedKeptTotal
New443203646
Fresh35329364
Picked000
Done01010
Total4785421020
Error
0b
Counts
1020 → 542
Compiler

Compiled 35504 to 23418 computations (34% saved)

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 (*.f64 (-.f64 y x) 6) z)
0.0b
(+.f64 (-.f64 (*.f64 y 4) (*.f64 x 3)) (neg.f64 (*.f64 (*.f64 (-.f64 y x) 6) z)))
0.0b
(*.f64 (-.f64 y x) 6)
0.0b
(-.f64 (*.f64 y 4) (*.f64 x 3))
0.0b
(-.f64 (*.f64 y 4) (*.f64 x 3))
0.0b
(*.f64 (-.f64 y x) 6)
0.0b
(+.f64 (-.f64 (*.f64 y 4) (*.f64 x 3)) (neg.f64 (*.f64 (*.f64 (-.f64 y x) 6) z)))
0.2b
(*.f64 (*.f64 (-.f64 y x) 6) z)

rewrite36.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
16×add-log-exp_binary64_10688
14×associate-*l/_binary64_10592
11×pow1_binary64_10710 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687 *-un-lft-identity_binary64_10649 add-sqr-sqrt_binary64_10671
7×flip3--_binary64_10653 flip--_binary64_10624 add-cube-cbrt_binary64_10684
6×associate-*r*_binary64_10589 associate-*l*_binary64_10590
4×prod-exp_binary64_10698 cbrt-unprod_binary64_10682 sum-log_binary64_10740 frac-add_binary64_10657 pow-prod-down_binary64_10720 distribute-neg-frac_binary64_10613
3×diff-log_binary64_10741
2×sub-neg_binary64_10642 cancel-sign-sub-inv_binary64_10615 *-commutative_binary64_10580 associate-+l+_binary64_10582 neg-log_binary64_10742
1×associate-+l-_binary64_10584 difference-of-squares_binary64_10618 unswap-sqr_binary64_10617 +-commutative_binary64_10579 unsub-neg_binary64_10643 neg-sub0_binary64_10644 distribute-lft-out--_binary64_10601 flip-+_binary64_10623 flip3-+_binary64_10652 distribute-lft-out_binary64_10600 associate-+r-_binary64_10583
Counts
4 → 78
Calls

8 calls:

10.0ms
(+.f64 (-.f64 (*.f64 y 4) (*.f64 x 3)) (neg.f64 (*.f64 (*.f64 (-.f64 y x) 6) z)))
9.0ms
(*.f64 (*.f64 (-.f64 y x) 6) z)
7.0ms
(*.f64 (-.f64 y x) 6)
4.0ms
(-.f64 (*.f64 y 4) (*.f64 x 3))
0.0ms
(-.f64 (*.f64 y 4) (*.f64 x 3))

series638.0ms (0.1%)

Counts
4 → 57
Calls

4 calls:

320.0ms
(+.f64 (-.f64 (*.f64 y 4) (*.f64 x 3)) (neg.f64 (*.f64 (*.f64 (-.f64 y x) 6) z)))
150.0ms
(*.f64 (*.f64 (-.f64 y x) 6) z)
91.0ms
(-.f64 (*.f64 y 4) (*.f64 x 3))
76.0ms
(*.f64 (-.f64 y x) 6)
Compiler

Compiled 1407 to 1244 computations (11.6% saved)

simplify88.0ms (0%)

Algorithm
1×egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
053692076

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify8.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
000

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (*.f64 x (-.f64 (*.f64 6 z) 3)))
0.1b
(sqrt.f64 (*.f64 x (-.f64 (*.f64 6 z) 3)))
0.0b
(-.f64 (*.f64 6 z) 3)
0.0b
(-.f64 (*.f64 6 z) 3)
0.1b
(sqrt.f64 (*.f64 x (-.f64 (*.f64 6 z) 3)))
0.1b
(*.f64 x (-.f64 (*.f64 6 z) 3))
0.1b
(*.f64 x (-.f64 (*.f64 6 z) 3))
0.2b
(*.f64 (sqrt.f64 (*.f64 x (-.f64 (*.f64 6 z) 3))) (sqrt.f64 (*.f64 x (-.f64 (*.f64 6 z) 3))))

rewrite49.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
60×pow1_binary64_10710
30×sqrt-pow1_binary64_10667
23×pow-prod-down_binary64_10720
22×add-sqr-sqrt_binary64_10671
20×associate-*r/_binary64_10591
16×*-un-lft-identity_binary64_10649 add-cube-cbrt_binary64_10684
14×sqrt-div_binary64_10666
12×cancel-sign-sub-inv_binary64_10615
11×pow1/2_binary64_10729
10×pow-prod-up_binary64_10719 add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687 associate-*r*_binary64_10589 associate-*l*_binary64_10590
9×flip3--_binary64_10653 flip--_binary64_10624
8×distribute-rgt-in_binary64_10599 distribute-lft-in_binary64_10598
6×pow-sqr_binary64_10622
5×sqrt-prod_binary64_10665
4×add-log-exp_binary64_10688 sub-neg_binary64_10642 frac-times_binary64_10659 swap-sqr_binary64_10616
3×prod-exp_binary64_10698 cbrt-unprod_binary64_10682 unswap-sqr_binary64_10617 *-commutative_binary64_10580
2×associate-*l/_binary64_10592
1×pow-plus_binary64_10712 pow2_binary64_10730 rem-square-sqrt_binary64_10661 sqrt-unprod_binary64_10669
Counts
4 → 126
Calls

8 calls:

17.0ms
(*.f64 (sqrt.f64 (*.f64 x (-.f64 (*.f64 6 z) 3))) (sqrt.f64 (*.f64 x (-.f64 (*.f64 6 z) 3))))
8.0ms
(*.f64 x (-.f64 (*.f64 6 z) 3))
7.0ms
(*.f64 x (-.f64 (*.f64 6 z) 3))
5.0ms
(sqrt.f64 (*.f64 x (-.f64 (*.f64 6 z) 3)))
0.0ms
(-.f64 (*.f64 6 z) 3)

series379.0ms (0.1%)

Counts
4 → 34
Calls

4 calls:

99.0ms
(*.f64 x (-.f64 (*.f64 6 z) 3))
98.0ms
(*.f64 (sqrt.f64 (*.f64 x (-.f64 (*.f64 6 z) 3))) (sqrt.f64 (*.f64 x (-.f64 (*.f64 6 z) 3))))
97.0ms
(*.f64 x (-.f64 (*.f64 6 z) 3))
84.0ms
(sqrt.f64 (*.f64 x (-.f64 (*.f64 6 z) 3)))
Compiler

Compiled 1128 to 1021 computations (9.5% saved)

simplify95.0ms (0%)

Algorithm
1×egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
049071997
149071997

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 (*.f64 (-.f64 y x) (*.f64 (cbrt.f64 6) (cbrt.f64 6))) (cbrt.f64 6))
0.1b
(*.f64 (-.f64 y x) (*.f64 (cbrt.f64 6) (cbrt.f64 6)))
0.0b
(+.f64 x (*.f64 (*.f64 (*.f64 (-.f64 y x) (*.f64 (cbrt.f64 6) (cbrt.f64 6))) (cbrt.f64 6)) (-.f64 (/.f64 2 3) z)))
0.0b
(-.f64 (/.f64 2 3) z)
0.2b
(*.f64 (*.f64 (*.f64 (-.f64 y x) (*.f64 (cbrt.f64 6) (cbrt.f64 6))) (cbrt.f64 6)) (-.f64 (/.f64 2 3) z))
1.0b
(cbrt.f64 6)
1.0b
(cbrt.f64 6)
1.0b
(cbrt.f64 6)

rewrite36.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
18×pow1_binary64_10710 add-exp-log_binary64_10687
15×add-sqr-sqrt_binary64_10671
14×associate-*l/_binary64_10592
13×add-cbrt-cube_binary64_10685
12×*-un-lft-identity_binary64_10649
10×prod-exp_binary64_10698 cbrt-unprod_binary64_10682 pow-prod-down_binary64_10720 add-cube-cbrt_binary64_10684
9×cbrt-prod_binary64_10680
6×cancel-sign-sub-inv_binary64_10615 flip3--_binary64_10653 flip--_binary64_10624 associate-*r*_binary64_10589
4×add-log-exp_binary64_10688 distribute-rgt-in_binary64_10599 distribute-lft-in_binary64_10598 frac-times_binary64_10659
3×pow1/3_binary64_10731
2×difference-of-squares_binary64_10618 sub-neg_binary64_10642 associate-*r/_binary64_10591
1×*-commutative_binary64_10580 distribute-lft-out--_binary64_10601 times-frac_binary64_10655 associate-*l*_binary64_10590
Counts
4 → 76
Calls

8 calls:

23.0ms
(*.f64 (*.f64 (*.f64 (-.f64 y x) (*.f64 (cbrt.f64 6) (cbrt.f64 6))) (cbrt.f64 6)) (-.f64 (/.f64 2 3) z))
2.0ms
(cbrt.f64 6)
1.0ms
(cbrt.f64 6)
1.0ms
(cbrt.f64 6)
0.0ms
(-.f64 (/.f64 2 3) z)

series446.0ms (0.1%)

Counts
4 → 18
Calls

4 calls:

445.0ms
(*.f64 (*.f64 (*.f64 (-.f64 y x) (*.f64 (cbrt.f64 6) (cbrt.f64 6))) (cbrt.f64 6)) (-.f64 (/.f64 2 3) z))
0.0ms
(cbrt.f64 6)
0.0ms
(cbrt.f64 6)
0.0ms
(cbrt.f64 6)
Compiler

Compiled 784 to 710 computations (9.4% saved)

simplify64.0ms (0%)

Algorithm
1×egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
057501255

localize46.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(-.f64 2/3 z)
0.0b
(*.f64 (-.f64 y x) 6)
0.0b
(*.f64 (-.f64 y x) 6)
0.0b
(*.f64 (-.f64 y x) 6)
10.3b
(+.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) x))
12.5b
(+.f64 (*.f64 216 (pow.f64 (*.f64 (-.f64 y x) (-.f64 2/3 z)) 3)) (pow.f64 x 3))
39.9b
(/.f64 (*.f64 (-.f64 y x) (*.f64 (*.f64 (-.f64 2/3 z) 6) (-.f64 (pow.f64 (*.f64 (-.f64 y x) (*.f64 (-.f64 2/3 z) 6)) 3) (pow.f64 x 3)))) (+.f64 (*.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z))) (+.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) x))))
40.9b
(/.f64 (+.f64 (*.f64 216 (pow.f64 (*.f64 (-.f64 y x) (-.f64 2/3 z)) 3)) (pow.f64 x 3)) (+.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 y x) (*.f64 (*.f64 (-.f64 2/3 z) 6) (-.f64 (pow.f64 (*.f64 (-.f64 y x) (*.f64 (-.f64 2/3 z) 6)) 3) (pow.f64 x 3)))) (+.f64 (*.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z))) (+.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) x))))))

rewrite333.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
330×associate-*l/_binary64_10592
300×frac-times_binary64_10659
243×flip3--_binary64_10653 flip--_binary64_10624
164×associate-/r/_binary64_10595
160×frac-add_binary64_10657
102×associate-*r/_binary64_10591
85×flip-+_binary64_10623 flip3-+_binary64_10652
28×associate-/l/_binary64_10596
20×add-cbrt-cube_binary64_10685 add-exp-log_binary64_10687
14×*-un-lft-identity_binary64_10649 add-sqr-sqrt_binary64_10671 add-cube-cbrt_binary64_10684
12×times-frac_binary64_10655
8×add-log-exp_binary64_10688
6×prod-exp_binary64_10698 cbrt-unprod_binary64_10682 associate-/r*_binary64_10593
5×div-exp_binary64_10700 cbrt-undiv_binary64_10683
4×pow1_binary64_10710 associate-/l*_binary64_10594
2×sum-log_binary64_10740 clear-num_binary64_10648 +-commutative_binary64_10579 frac-2neg_binary64_10660 div-inv_binary64_10646
1×distribute-rgt-out_binary64_10602
Counts
4 → 267
Calls

8 calls:

94.0ms
(/.f64 (*.f64 (-.f64 y x) (*.f64 (*.f64 (-.f64 2/3 z) 6) (-.f64 (pow.f64 (*.f64 (-.f64 y x) (*.f64 (-.f64 2/3 z) 6)) 3) (pow.f64 x 3)))) (+.f64 (*.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z))) (+.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) x))))
90.0ms
(/.f64 (+.f64 (*.f64 216 (pow.f64 (*.f64 (-.f64 y x) (-.f64 2/3 z)) 3)) (pow.f64 x 3)) (+.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 y x) (*.f64 (*.f64 (-.f64 2/3 z) 6) (-.f64 (pow.f64 (*.f64 (-.f64 y x) (*.f64 (-.f64 2/3 z) 6)) 3) (pow.f64 x 3)))) (+.f64 (*.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z))) (+.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) x))))))
12.0ms
(+.f64 (*.f64 216 (pow.f64 (*.f64 (-.f64 y x) (-.f64 2/3 z)) 3)) (pow.f64 x 3))
5.0ms
(+.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) x))
0.0ms
(*.f64 (-.f64 y x) 6)

series7.7min (66.2%)

Counts
4 → 99
Calls

4 calls:

7.2min
(/.f64 (+.f64 (*.f64 216 (pow.f64 (*.f64 (-.f64 y x) (-.f64 2/3 z)) 3)) (pow.f64 x 3)) (+.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 y x) (*.f64 (*.f64 (-.f64 2/3 z) 6) (-.f64 (pow.f64 (*.f64 (-.f64 y x) (*.f64 (-.f64 2/3 z) 6)) 3) (pow.f64 x 3)))) (+.f64 (*.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z))) (+.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) x))))))
28.5s
(/.f64 (*.f64 (-.f64 y x) (*.f64 (*.f64 (-.f64 2/3 z) 6) (-.f64 (pow.f64 (*.f64 (-.f64 y x) (*.f64 (-.f64 2/3 z) 6)) 3) (pow.f64 x 3)))) (+.f64 (*.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z))) (+.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) x))))
1.2s
(+.f64 (*.f64 216 (pow.f64 (*.f64 (-.f64 y x) (-.f64 2/3 z)) 3)) (pow.f64 x 3))
527.0ms
(+.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 (-.f64 y x) 6) (-.f64 2/3 z)) x))
Compiler

Compiled 213436 to 167832 computations (21.4% saved)

simplify805.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
366 → 366
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
05147116419

prune1.1min (9.2%)

Pruning

848 alts after pruning (834 fresh and 14 done)

PrunedKeptTotal
New426329755
Fresh22505527
Picked000
Done11415
Total4498481297
Error
0b
Counts
1297 → 848
Compiler

Compiled 91948 to 52112 computations (43.3% saved)

simplify2.2s (0.3%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
07794181806

regimes27.1s (3.9%)

Compiler

Compiled 361140 to 228405 computations (36.8% saved)

bsearch0.0ms (0%)

regimes258.0ms (0%)

Compiler

Compiled 1722 to 1722 computations (0% saved)

bsearch0.0ms (0%)

regimes166.0ms (0%)

Compiler

Compiled 852 to 927 computations (-8.8% saved)

bsearch0.0ms (0%)

regimes154.0ms (0%)

Compiler

Compiled 786 to 867 computations (-10.3% saved)

bsearch0.0ms (0%)

regimes290.0ms (0%)

Compiler

Compiled 753 to 837 computations (-11.2% saved)

bsearch38.0ms (0%)

Steps
ItersRangePoint
7
0.10715923520712735
19.928167835426866
0.5781135423820416
10
-250706.46781315652
-1.0990526403159329e-07
-0.6617380995883639
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes282.0ms (0%)

Compiler

Compiled 723 to 810 computations (-12% saved)

bsearch40.0ms (0%)

Steps
ItersRangePoint
7
0.10715923520712735
19.928167835426866
0.5781135423820416
10
-250706.46781315652
-1.0990526403159329e-07
-0.5614723910915681
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes206.0ms (0%)

Compiler

Compiled 135 to 198 computations (-46.7% saved)

bsearch122.0ms (0%)

Steps
ItersRangePoint
7
0.10715923520712735
19.928167835426866
19.457482665026856
9
1.844252992611734e-106
9.087551736297304e-101
6.849124482767209e-102
10
-7.498118472994925e-247
-3.127992860671832e-259
-5.7471583799886725e-254
6
-1.125911850769328e-192
-2.1216512211693492e-193
-6.555100999375592e-193
9
-1.6060396800775168e-112
-1.4945441922238658e-118
-4.671310924749331e-115
8
-2.4131126039262908e-46
-4.150965911355492e-49
-5.446531970662387e-48
7
-1.0990526403159329e-07
-8.694145375809736e-10
-1.0828083935718329e-07
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes193.0ms (0%)

Compiler

Compiled 114 to 177 computations (-55.3% saved)

bsearch128.0ms (0%)

Steps
ItersRangePoint
7
0.10715923520712735
19.928167835426866
19.457482665026856
9
1.844252992611734e-106
9.087551736297304e-101
5.9262544907659085e-102
10
-7.498118472994925e-247
-3.127992860671832e-259
-8.167864008949096e-252
6
-1.125911850769328e-192
-2.1216512211693492e-193
-8.646031249717085e-193
9
-1.6060396800775168e-112
-1.4945441922238658e-118
-4.178277989252238e-113
8
-2.4131126039262908e-46
-4.150965911355492e-49
-1.8872563064995598e-48
7
-1.0990526403159329e-07
-8.694145375809736e-10
-1.0828083935718329e-07
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes517.0ms (0.1%)

Compiler

Compiled 72 to 132 computations (-83.3% saved)

bsearch118.0ms (0%)

Steps
ItersRangePoint
7
0.10715923520712735
19.928167835426866
0.49493003646601996
9
1.844252992611734e-106
9.087551736297304e-101
3.721297174862834e-106
10
-7.498118472994925e-247
-3.127992860671832e-259
-3.860770922513212e-253
6
-1.125911850769328e-192
-2.1216512211693492e-193
-4.94669311449752e-193
9
-1.6060396800775168e-112
-1.4945441922238658e-118
-2.519457736207247e-118
8
-2.4131126039262908e-46
-4.150965911355492e-49
-2.426125580152609e-48
7
-1.0990526403159329e-07
-8.694145375809736e-10
-1.0828083935718329e-07
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes145.0ms (0%)

Compiler

Compiled 51 to 111 computations (-117.6% saved)

bsearch125.0ms (0%)

Steps
ItersRangePoint
10
19.928167835426866
88631507097.69885
20.17851352049041
9
1.844252992611734e-106
9.087551736297304e-101
3.409795255460514e-105
10
-7.498118472994925e-247
-3.127992860671832e-259
-6.011515358352692e-251
6
-1.125911850769328e-192
-2.1216512211693492e-193
-1.0454914565254245e-192
9
-1.6060396800775168e-112
-1.4945441922238658e-118
-3.632746662456877e-117
8
-2.4131126039262908e-46
-4.150965911355492e-49
-5.62032163658667e-47
7
-1.0990526403159329e-07
-8.694145375809736e-10
-1.0828083935718329e-07
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes123.0ms (0%)

Compiler

Compiled 36 to 93 computations (-158.3% saved)

bsearch57.0ms (0%)

Steps
ItersRangePoint
6
1.7115772798229812e-13
2.1144583037917035e-12
4.462371963252473e-13
6
-5.20481454207247e-128
-5.0491010516879424e-129
-5.083000400705727e-128
9
-1.0404837475734025e-112
-5.4274354485444925e-118
-5.495717977092104e-118
5
-1.4559927757417296e+36
-5.011783952568722e+35
-5.4238416061398306e+35
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes32.0ms (0%)

Compiler

Compiled 27 to 78 computations (-188.9% saved)

bsearch0.0ms (0%)

regimes29.0ms (0%)

Accuracy

Total 0.2b remaining (99.6%)

Threshold costs 0.2b (99.6%)

Compiler

Compiled 18 to 63 computations (-250% saved)

bsearch19.0ms (0%)

Compiler

Compiled 397 to 305 computations (23.2% saved)

simplify39.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
0750561
1750561

end0.0ms (0%)

sample1.3min (11.4%)

Algorithm
1×intervals
Results
304.0ms7351×body128valid
36.0ms228×body1024valid
26.0ms242×body512valid
23.0ms590×body128invalid
13.0ms179×body256valid
Compiler

Compiled 121559 to 77045 computations (36.6% saved)

Pareto

0.3847394974125431

Profiling

Loading profile data...