Details

analyze613.0ms (0.1%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample41.0ms (0%)

Algorithm

1×

intervals

Results

9.0ms	175×	body	128	valid
8.0ms	37×	body	2048	valid
7.0ms	20×	body	1024	valid
2.0ms	9×	body	4096	valid
1.0ms	11×	body	512	valid
1.0ms	29×	body	128	nan
0.0ms	4×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify169.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune7.0ms (0%)

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

Merged error: 32.8b

Counts

2 → 2

Compiler

Compiled 37 to 28 computations (24.3% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite45.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 86

Calls

4 calls:

18.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series235.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

87.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
64.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
55.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
28.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify76.0ms (0%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4916	2170
1	4916	2170

prune339.0ms (0.1%)

Pruning

53 alts after pruning (52 fresh and 1 done)

	Pruned	Kept	Total
New	46	52	98
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	47	53	100

Merged error: 5.4b

Counts

100 → 53

Compiler

Compiled 2695 to 947 computations (64.9% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
21.8b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-pow1_binary64` `sqrt-div_binary64`
22×	`pow1_binary64`
11×	`pow1/2_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`sqrt-prod_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64`
5×	`pow-prod-up_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64`
2×	`associate-r/_binary64` `associate-l/_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `pow-plus_binary64` `cancel-sign-sub-inv_binary64` `pow2_binary64`

Counts

4 → 74

Calls

4 calls:

13.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series185.0ms (0%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
52.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
48.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
30.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify64.0ms (0%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4899	1441
1	4899	1441

prune511.0ms (0.1%)

Pruning

69 alts after pruning (67 fresh and 2 done)

	Pruned	Kept	Total
New	69	17	86
Fresh	1	50	51
Picked	0	1	1
Done	0	1	1
Total	70	69	139

Merged error: 5.4b

Counts

139 → 69

Compiler

Compiled 3375 to 1339 computations (60.3% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

21.8b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite33.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-div_binary64`
25×	`sqrt-pow1_binary64`
23×	`pow1_binary64`
12×	`pow1/2_binary64`
10×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
9×	`flip3--_binary64` `flip--_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`pow-prod-up_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `rem-sqrt-square_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`associate-r/_binary64` `associate-l/_binary64`
1×	`pow-plus_binary64` `pow2_binary64`

Counts

4 → 77

Calls

4 calls:

12.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series205.0ms (0%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
53.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
49.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
49.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify75.0ms (0%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5217	1524

prune738.0ms (0.2%)

Pruning

80 alts after pruning (77 fresh and 3 done)

	Pruned	Kept	Total
New	75	14	89
Fresh	3	63	66
Picked	0	1	1
Done	0	2	2
Total	78	80	158

Merged error: 5.4b

Counts

158 → 80

Compiler

Compiled 4619 to 1653 computations (64.2% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
21.8b	(sqrt.f64 (.f64 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))

rewrite27.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64` `sqrt-div_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`sqrt-pow1_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`rem-sqrt-square_binary64`
2×	`associate-*r/_binary64`
1×	`pow-prod-down_binary64`

Counts

4 → 58

Calls

4 calls:

6.0ms	(sqrt.f64 (.f64 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series315.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

154.0ms	(sqrt.f64 (.f64 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
57.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
53.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
51.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify66.0ms (0%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5202	1225

prune666.0ms (0.1%)

Pruning

90 alts after pruning (86 fresh and 4 done)

	Pruned	Kept	Total
New	58	12	70
Fresh	2	74	76
Picked	0	1	1
Done	0	3	3
Total	60	90	150

Merged error: 5.4b

Counts

150 → 90

Compiler

Compiled 2211 to 490 computations (77.8% saved)

regimes4.4s (0.9%)

Compiler: Compiled 27452 to 13662 computations (50.2% saved)

bsearch7.3min (95.2%)

Steps

Iters	Range		Point
9	6.332449214550715e-68	2.9260395472562554e-62	2.8611369787865605e-67
7	-3.502063382809275e+58	-5.227109355872948e+56	-3.442603392340609e+58

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify343.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	89	56
1	89	56

end0.0ms (0%)

sample12.9s (2.8%)

Algorithm

1×

intervals

Results

261.0ms	5230×	body	128	valid
254.0ms	1101×	body	2048	valid
132.0ms	726×	body	1024	valid
122.0ms	430×	body	4096	valid
50.0ms	349×	body	512	valid
37.0ms	747×	body	128	nan
15.0ms	164×	body	256	valid
15.0ms	293×	body	128	invalid

Compiler

Compiled 15339 to 8792 computations (42.7% saved)

Pareto

0.48560946309845243

Details

analyze613.0ms (0.1%)

sample41.0ms (0%)

simplify169.0ms (0%)

prune7.0ms (0%)

localize10.0ms (0%)

rewrite45.0ms (0%)

series235.0ms (0.1%)

simplify76.0ms (0%)

prune339.0ms (0.1%)

localize11.0ms (0%)

rewrite32.0ms (0%)

series185.0ms (0%)

simplify64.0ms (0%)

prune511.0ms (0.1%)

localize16.0ms (0%)

rewrite33.0ms (0%)

series205.0ms (0%)

simplify75.0ms (0%)

prune738.0ms (0.2%)

localize14.0ms (0%)

rewrite27.0ms (0%)

series315.0ms (0.1%)

simplify66.0ms (0%)

prune666.0ms (0.1%)

regimes4.4s (0.9%)

bsearch7.3min (95.2%)

simplify343.0ms (0.1%)

end0.0ms (0%)

sample12.9s (2.8%)

Profiling