Details

analyze116.0ms (3.3%)

Algorithm

1×

Search

True	Other	False	Iter
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
25%	62.4%	12.6%	6
25%	40.6%	34.4%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample22.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 23 to 19 computations (17.4% saved)

simplify132.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	24	13
1	24	13

prune6.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.0b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 x (+.f64 x 2))
0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_7602` `*-un-lft-identity_binary64_7580`
4×	`associate-r_binary64_7520` `add-log-exp_binary64_7619` `add-cbrt-cube_binary64_7616` `pow1_binary64_7641` `add-cube-cbrt_binary64_7615` `add-exp-log_binary64_7618`
3×	`associate-l_binary64_7521`
2×	`distribute-lft-in_binary64_7529` `flip-+_binary64_7554` `distribute-rgt-in_binary64_7530` `associate-*r/_binary64_7522` `associate-+l+_binary64_7513` `flip3-+_binary64_7583`
1×	`pow-prod-down_binary64_7651` `unswap-sqr_binary64_7548` `+-commutative_binary64_7510` `distribute-lft-out_binary64_7531` `cbrt-unprod_binary64_7613` `prod-exp_binary64_7629` `sum-log_binary64_7671` `*-commutative_binary64_7511`

Counts

2 → 36

Calls

2 calls:

16.0ms	(*.f64 x (+.f64 x 2))
13.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))

series50.0ms (1.4%)

Counts

2 → 6

Calls

2 calls:

28.0ms	(*.f64 x (+.f64 x 2))
22.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))

simplify102.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5006	509

prune41.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	4	43

Error

Counts

43 → 4

Compiler

Compiled 642 to 357 computations (44.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
0.0b	(sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
0.0b	(sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
0.1b	(.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y))))

rewrite69.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_7602`
24×	`sqrt-prod_binary64_7596`
21×	`pow1_binary64_7641`
16×	`sqrt-div_binary64_7597`
14×	`*-un-lft-identity_binary64_7580` `add-cube-cbrt_binary64_7615`
10×	`sqrt-pow1_binary64_7598` `pow1/2_binary64_7660`
9×	`flip-+_binary64_7554` `flip3-+_binary64_7583`
8×	`swap-sqr_binary64_7547`
6×	`associate-r_binary64_7520` `add-log-exp_binary64_7619` `add-cbrt-cube_binary64_7616` `associate-l_binary64_7521` `add-exp-log_binary64_7618`
5×	`pow-prod-up_binary64_7650`
4×	`unswap-sqr_binary64_7548` `frac-times_binary64_7590` `rem-sqrt-square_binary64_7593`
3×	`pow-prod-down_binary64_7651` `pow-sqr_binary64_7553`
2×	`associate-r/_binary64_7522` `associate-+l+_binary64_7513` `associate-l/_binary64_7523`
1×	`distribute-lft-in_binary64_7529` `pow-plus_binary64_7643` `pow2_binary64_7661` `+-commutative_binary64_7510` `sqrt-unprod_binary64_7600` `rem-square-sqrt_binary64_7592` `cbrt-unprod_binary64_7613` `prod-exp_binary64_7629` `distribute-rgt-in_binary64_7530` `sum-log_binary64_7671` `*-commutative_binary64_7511` `sqr-abs_binary64_7595`

Counts

4 → 101

Calls

4 calls:

18.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y))))
14.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
10.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
6.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))

series222.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
74.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
37.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
25.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y))))

simplify111.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4973	2138
1	4973	2138

prune186.0ms (5.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	113	4	117

Error

Counts

117 → 4

Compiler

Compiled 2706 to 1556 computations (42.5% saved)

localize29.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (-.f64 (.f64 2 2) (*.f64 x 2)))
0.0b	(+.f64 (/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2)))) (*.f64 y y))
0.0b	(*.f64 x (+.f64 (pow.f64 x 3) 8))
10.4b	(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2))))

rewrite107.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-log-exp_binary64_7619` `add-cbrt-cube_binary64_7616` `add-exp-log_binary64_7618`
10×	`add-sqr-sqrt_binary64_7602` `*-un-lft-identity_binary64_7580`
8×	`add-cube-cbrt_binary64_7615`
6×	`pow1_binary64_7641`
5×	`flip-+_binary64_7554` `flip3-+_binary64_7583`
4×	`associate-r_binary64_7520` `associate-*r/_binary64_7522`
3×	`times-frac_binary64_7586` `associate-/r_binary64_7524` `sum-log_binary64_7671` `associate-l*_binary64_7521`
2×	`associate-+r+_binary64_7512` `associate-/l/_binary64_7527` `+-commutative_binary64_7510` `associate-/r/_binary64_7526` `cbrt-unprod_binary64_7613` `prod-exp_binary64_7629` `cbrt-undiv_binary64_7614` `div-exp_binary64_7631`
1×	`distribute-lft-in_binary64_7529` `pow-prod-down_binary64_7651` `unswap-sqr_binary64_7548` `frac-2neg_binary64_7591` `associate-+r-_binary64_7514` `div-inv_binary64_7577` `clear-num_binary64_7579` `associate-/l_binary64_7525` `diff-log_binary64_7672` `distribute-lft-out_binary64_7531` `sub-neg_binary64_7573` `distribute-rgt-in_binary64_7530` `-commutative_binary64_7511` `cancel-sign-sub-inv_binary64_7546`

Counts

4 → 74

Calls

4 calls:

31.0ms	(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2))))
30.0ms	(+.f64 (/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2)))) (*.f64 y y))
19.0ms	(*.f64 x (+.f64 (pow.f64 x 3) 8))
13.0ms	(+.f64 (.f64 x x) (-.f64 (.f64 2 2) (*.f64 x 2)))

series347.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

154.0ms	(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2))))
110.0ms	(*.f64 x (+.f64 (pow.f64 x 3) 8))
66.0ms	(+.f64 (/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 (.f64 x x) (-.f64 (.f64 2 2) (.f64 x 2)))) (*.f64 y y))
17.0ms	(+.f64 (.f64 x x) (-.f64 (.f64 2 2) (*.f64 x 2)))

simplify81.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4985	1710
1	4985	1710

prune160.0ms (4.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	86	4	90

Error

Counts

90 → 4

Compiler

Compiled 2341 to 1530 computations (34.6% saved)

localize22.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
0.1b	(.f64 (.f64 x (+.f64 x 2)) (*.f64 x (+.f64 x 2)))
1.7b	(-.f64 (.f64 (.f64 x (+.f64 x 2)) (*.f64 x (+.f64 x 2))) (pow.f64 y 4))
26.3b	(/.f64 (-.f64 (.f64 (.f64 x (+.f64 x 2)) (.f64 x (+.f64 x 2))) (pow.f64 y 4)) (-.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)))

rewrite102.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`pow1_binary64_7641`
27×	`add-sqr-sqrt_binary64_7602`
18×	`add-cbrt-cube_binary64_7616` `times-frac_binary64_7586` `add-exp-log_binary64_7618`
17×	`pow-prod-down_binary64_7651` `*-un-lft-identity_binary64_7580` `add-cube-cbrt_binary64_7615`
15×	`difference-of-squares_binary64_7549`
14×	`associate-*r/_binary64_7522`
9×	`distribute-lft-in_binary64_7529` `distribute-rgt-in_binary64_7530`
8×	`add-log-exp_binary64_7619` `unpow-prod-down_binary64_7659` `cbrt-unprod_binary64_7613` `prod-exp_binary64_7629` `cancel-sign-sub-inv_binary64_7546`
6×	`associate-/l*_binary64_7525` `flip-+_binary64_7554` `associate--l+_binary64_7517` `sqr-pow_binary64_7552` `flip3-+_binary64_7583`
4×	`frac-times_binary64_7590` `flip--_binary64_7555` `pow-prod-up_binary64_7650` `pow-sqr_binary64_7553` `flip3--_binary64_7584`
3×	`associate-/r*_binary64_7524`
2×	`pow-plus_binary64_7643` `associate-/l/_binary64_7527` `diff-log_binary64_7672` `associate-/r/_binary64_7526` `sub-neg_binary64_7573` `associate-*l/_binary64_7523`
1×	`associate-r_binary64_7520` `frac-2neg_binary64_7591` `pow2_binary64_7661` `div-inv_binary64_7577` `clear-num_binary64_7579` `swap-sqr_binary64_7547` `cbrt-undiv_binary64_7614` `div-exp_binary64_7631` `-commutative_binary64_7511` `div-sub_binary64_7585` `associate-l*_binary64_7521`

Counts

4 → 129

Calls

4 calls:

30.0ms	(-.f64 (.f64 (.f64 x (+.f64 x 2)) (*.f64 x (+.f64 x 2))) (pow.f64 y 4))
25.0ms	(/.f64 (-.f64 (.f64 (.f64 x (+.f64 x 2)) (.f64 x (+.f64 x 2))) (pow.f64 y 4)) (-.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)))
16.0ms	(.f64 (.f64 x (+.f64 x 2)) (*.f64 x (+.f64 x 2)))
7.0ms	(-.f64 (.f64 x (+.f64 x 2)) (.f64 y y))

series211.0ms (6%)

Counts

4 → 12

Calls

4 calls:

85.0ms	(/.f64 (-.f64 (.f64 (.f64 x (+.f64 x 2)) (.f64 x (+.f64 x 2))) (pow.f64 y 4)) (-.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)))
73.0ms	(-.f64 (.f64 (.f64 x (+.f64 x 2)) (*.f64 x (+.f64 x 2))) (pow.f64 y 4))
27.0ms	(-.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
25.0ms	(.f64 (.f64 x (+.f64 x 2)) (*.f64 x (+.f64 x 2)))

simplify113.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4955	3194
1	4955	3194

prune292.0ms (8.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	141	4	145

Error

Counts

145 → 4

Compiler

Compiled 4103 to 2553 computations (37.8% saved)

regimes150.0ms (4.3%)

Accuracy

Total 0.0b remaining (79%)

Threshold costs 0.0b (79%)

Compiler

Compiled 1146 to 852 computations (25.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

end0.0ms (0%)

sample804.0ms (22.8%)

Algorithm

1×

intervals

Results

339.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 252 to 188 computations (25.4% saved)

Details

analyze116.0ms (3.3%)

sample22.0ms (0.6%)

simplify132.0ms (3.7%)

prune6.0ms (0.2%)

localize11.0ms (0.3%)

rewrite33.0ms (0.9%)

series50.0ms (1.4%)

simplify102.0ms (2.9%)

prune41.0ms (1.2%)

localize8.0ms (0.2%)

rewrite69.0ms (2%)

series222.0ms (6.3%)

simplify111.0ms (3.1%)

prune186.0ms (5.3%)

localize29.0ms (0.8%)

rewrite107.0ms (3%)

series347.0ms (9.8%)

simplify81.0ms (2.3%)

prune160.0ms (4.5%)

localize22.0ms (0.6%)

rewrite102.0ms (2.9%)

series211.0ms (6%)

simplify113.0ms (3.2%)

prune292.0ms (8.3%)

regimes150.0ms (4.3%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample804.0ms (22.8%)

Profiling