Details

analyze94.0ms (1.2%)

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%	74.9%	25.1%	4
18.7%	56.2%	25.1%	5
28.1%	34.3%	37.6%	6
34.3%	28.1%	37.6%	7
39%	17.2%	43.8%	8
41%	13.7%	45.4%	9
43.1%	8.4%	48.5%	10
44%	6.7%	49.3%	11
45%	4.1%	50.8%	12
45.4%	3.3%	51.2%	13
45.9%	2.1%	52%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample29.0ms (0.4%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
0.0ms	6×	body	128	nan
0.0ms	2×	body	128	invalid

Compiler

Compiled 17 to 17 computations (0% saved)

simplify161.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	207	12
1	207	12

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 y (sqrt.f64 x))
0.0b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
0.0b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
0.2b	(*.f64 y (sqrt.f64 x))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2757`
7×	`add-log-exp_binary64_2774`
6×	`-un-lft-identity_binary64_2735` `add-cube-cbrt_binary64_2770` `associate-r*_binary64_2675`
4×	`pow1_binary64_2796` `associate-+l+_binary64_2668` `sqrt-prod_binary64_2751` `add-cbrt-cube_binary64_2771` `add-exp-log_binary64_2773`
3×	`associate-l_binary64_2676` `cancel-sign-sub-inv_binary64_2701`
2×	`sum-log_binary64_2826` `unswap-sqr_binary64_2703`
1×	`flip-+_binary64_2709` `flip3-+_binary64_2738` `sub-neg_binary64_2728` `pow-prod-down_binary64_2806` `diff-log_binary64_2827` `associate-+l-_binary64_2670` `*-commutative_binary64_2666` `prod-exp_binary64_2784` `cbrt-unprod_binary64_2768` `+-commutative_binary64_2665`

Counts

2 → 39

Calls

4 calls:

14.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
10.0ms	(*.f64 y (sqrt.f64 x))
0.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
0.0ms	(*.f64 y (sqrt.f64 x))

series180.0ms (2.3%)

Counts

2 → 15

Calls

2 calls:

93.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
86.0ms	(*.f64 y (sqrt.f64 x))

Compiler

Compiled 209 to 190 computations (9.1% saved)

simplify95.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5110	552

prune117.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	48	6	54
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	48	7	55

Error

0.0b

Counts

55 → 7

Compiler

Compiled 683 to 322 computations (52.9% saved)

localize16.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.2b	(sqrt.f64 (sqrt.f64 x))
0.2b	(sqrt.f64 (sqrt.f64 x))
0.0b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
0.2b	(sqrt.f64 (sqrt.f64 x))
0.2b	(sqrt.f64 (sqrt.f64 x))
0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

rewrite47.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`sqrt-prod_binary64_2751`
25×	`add-sqr-sqrt_binary64_2757`
18×	`associate-r_binary64_2675`
15×	`pow1_binary64_2796` `*-un-lft-identity_binary64_2735` `add-cube-cbrt_binary64_2770`
11×	`add-cbrt-cube_binary64_2771` `add-exp-log_binary64_2773`
8×	`sqrt-pow1_binary64_2753`
4×	`associate-l_binary64_2676` `pow1/2_binary64_2815` `pow-prod-down_binary64_2806` `rem-sqrt-square_binary64_2748` `prod-exp_binary64_2784` `cbrt-unprod_binary64_2768` `add-log-exp_binary64_2774`
3×	`unswap-sqr_binary64_2703`
2×	`*-commutative_binary64_2666`

Counts

4 → 88

Calls

8 calls:

17.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
11.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
4.0ms	(sqrt.f64 (sqrt.f64 x))
3.0ms	(sqrt.f64 (sqrt.f64 x))
0.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))

series532.0ms (6.9%)

Counts

4 → 18

Calls

4 calls:

251.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
99.0ms	(sqrt.f64 (sqrt.f64 x))
95.0ms	(sqrt.f64 (sqrt.f64 x))
87.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

Compiler

Compiled 459 to 393 computations (14.4% saved)

simplify153.0ms (2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	5186	879

prune178.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	104	9	113

Error

Counts

113 → 9

Compiler

Compiled 1748 to 677 computations (61.3% saved)

localize22.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4))
0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.2b	(sqrt.f64 (sqrt.f64 x))
0.0b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))
0.0b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))
0.2b	(sqrt.f64 (sqrt.f64 x))
0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4))

rewrite66.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`sqrt-prod_binary64_2751`
21×	`add-sqr-sqrt_binary64_2757`
19×	`add-exp-log_binary64_2773`
16×	`associate-r_binary64_2675`
13×	`*-un-lft-identity_binary64_2735` `add-cube-cbrt_binary64_2770`
11×	`add-cbrt-cube_binary64_2771`
10×	`prod-exp_binary64_2784`
9×	`add-log-exp_binary64_2774`
8×	`pow1_binary64_2796`
4×	`sqrt-pow1_binary64_2753` `associate-l_binary64_2676` `associate-+l+_binary64_2668` `cbrt-unprod_binary64_2768`
3×	`unpow-prod-down_binary64_2814` `unswap-sqr_binary64_2703` `cancel-sign-sub-inv_binary64_2701`
2×	`sum-log_binary64_2826` `pow-to-exp_binary64_2804` `pow1/2_binary64_2815` `rem-sqrt-square_binary64_2748` `pow-exp_binary64_2803` `*-commutative_binary64_2666`
1×	`flip-+_binary64_2709` `flip3-+_binary64_2738` `sub-neg_binary64_2728` `pow-prod-down_binary64_2806` `diff-log_binary64_2827` `associate-+l-_binary64_2670` `sqr-pow_binary64_2707` `+-commutative_binary64_2665`

Counts

4 → 86

Calls

8 calls:

18.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))
17.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4))
14.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
4.0ms	(sqrt.f64 (sqrt.f64 x))
0.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))

series581.0ms (7.5%)

Counts

4 → 24

Calls

4 calls:

237.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
134.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))
115.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4))
94.0ms	(sqrt.f64 (sqrt.f64 x))

Compiler

Compiled 511 to 451 computations (11.7% saved)

simplify138.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4907	1358
1	4907	1358

prune205.0ms (2.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	110	9	119

Error

Counts

119 → 9

Compiler

Compiled 1848 to 962 computations (47.9% saved)

localize36.0ms (0.5%)

Local error

Found 8 expressions with local error:

0.2b	(sqrt.f64 (sqrt.f64 x))
0.1b	(pow.f64 (cbrt.f64 x) 1/4)
0.1b	(pow.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 1/4)
0.0b	(+.f64 (-.f64 1 x) (.f64 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1/4)) (pow.f64 (cbrt.f64 x) 1/4)))
0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_2766`
23×	`add-sqr-sqrt_binary64_2757`
15×	`*-un-lft-identity_binary64_2735` `add-cube-cbrt_binary64_2770`
11×	`pow1_binary64_2796`
9×	`pow1/3_binary64_2817`
6×	`associate-l_binary64_2676` `associate-r_binary64_2675` `add-exp-log_binary64_2773` `swap-sqr_binary64_2702`
4×	`unswap-sqr_binary64_2703` `add-cbrt-cube_binary64_2771` `add-log-exp_binary64_2774`
2×	`pow-sqr_binary64_2708` `pow-prod-up_binary64_2805` `pow-prod-down_binary64_2806`
1×	`pow-plus_binary64_2798` `pow2_binary64_2816` `*-commutative_binary64_2666` `prod-exp_binary64_2784` `cbrt-unprod_binary64_2768`

Counts

4 → 73

Calls

8 calls:

13.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
2.0ms	(cbrt.f64 x)
2.0ms	(cbrt.f64 x)
2.0ms	(cbrt.f64 x)
0.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1/4)) (pow.f64 (cbrt.f64 x) 1/4)))

series584.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
141.0ms	(cbrt.f64 x)
135.0ms	(cbrt.f64 x)
122.0ms	(cbrt.f64 x)

Compiler

Compiled 586 to 478 computations (18.4% saved)

simplify138.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4873	548
1	4873	548

prune177.0ms (2.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	85	9	94

Error

Counts

94 → 9

Compiler

Compiled 2083 to 982 computations (52.9% saved)

simplify22.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	266	617
1	266	617

regimes248.0ms (3.2%)

Accuracy

Total 0.1b remaining (96.6%)

Threshold costs 0.1b (96.6%)

Compiler

Compiled 1193 to 892 computations (25.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms (0%)

sample3.8s (49.5%)

Algorithm

1×

intervals

Results

469.0ms	8000×	body	128	valid
7.0ms	120×	body	128	nan
4.0ms	63×	body	128	invalid

Compiler

Compiled 1182 to 880 computations (25.5% saved)

Pareto

0.5369083367545978

Details

analyze94.0ms (1.2%)

sample29.0ms (0.4%)

simplify161.0ms (2.1%)

prune4.0ms (0.1%)

localize17.0ms (0.2%)

rewrite30.0ms (0.4%)

series180.0ms (2.3%)

simplify95.0ms (1.2%)

prune117.0ms (1.5%)

localize16.0ms (0.2%)

rewrite47.0ms (0.6%)

series532.0ms (6.9%)

simplify153.0ms (2%)

prune178.0ms (2.3%)

localize22.0ms (0.3%)

rewrite66.0ms (0.9%)

series581.0ms (7.5%)

simplify138.0ms (1.8%)

prune205.0ms (2.6%)

localize36.0ms (0.5%)

rewrite34.0ms (0.4%)

series584.0ms (7.5%)

simplify138.0ms (1.8%)

prune177.0ms (2.3%)

simplify22.0ms (0.3%)

regimes248.0ms (3.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.8s (49.5%)

Profiling