Details

analyze328.0ms (6.8%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample34.0ms (0.7%)

Algorithm

1×

intervals

Results

12.0ms	191×	body	128	valid
5.0ms	22×	body	2048	valid
5.0ms	17×	body	4096	valid
2.0ms	12×	body	1024	valid
1.0ms	11×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify95.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 38.8b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
1.1b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_2504` `pow1_binary64_2526`
7×	`*-un-lft-identity_binary64_2465`
6×	`add-sqr-sqrt_binary64_2487`
5×	`add-cube-cbrt_binary64_2500`
4×	`flip3-+_binary64_2468` `sqrt-prod_binary64_2481` `flip-+_binary64_2439` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqrt-div_binary64_2482`
3×	`sqrt-pow1_binary64_2483`
2×	`+-commutative_binary64_2395` `sum-log_binary64_2556` `pow1/2_binary64_2545` `associate-*r/_binary64_2407`
1×	`rem-sqrt-square_binary64_2478` `pow-prod-down_binary64_2536` `distribute-lft-out_binary64_2416`

Counts

4 → 51

Calls

4 calls:

13.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

series186.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
27.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
23.0ms	(+.f64 (.f64 re re) (.f64 im im))
23.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify78.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4937	1040
1	4937	1040

prune81.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	55	8	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	9	64

Merged error: 19.1b

Counts

64 → 9

Compiler

Compiled 1366 to 632 computations (53.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

11.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite48.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2487`
9×	`sqrt-prod_binary64_2481`
7×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `pow1_binary64_2526`
6×	`add-log-exp_binary64_2504` `sqrt-div_binary64_2482`
4×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
3×	`pow1/2_binary64_2545` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`
1×	`+-commutative_binary64_2395` `sum-log_binary64_2556`

Counts

4 → 56

Calls

4 calls:

27.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series104.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
24.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
23.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
21.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify73.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4979	928
1	4979	928

prune87.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	69	8	77

Merged error: 19.1b

Counts

77 → 8

Compiler

Compiled 2593 to 753 computations (71% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

15.7b	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) re)
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite45.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2487`
9×	`sqrt-prod_binary64_2481`
7×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `pow1_binary64_2526`
6×	`add-log-exp_binary64_2504` `sqrt-div_binary64_2482`
4×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
3×	`pow1/2_binary64_2545` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`
1×	`+-commutative_binary64_2395` `sum-log_binary64_2556`

Counts

4 → 56

Calls

4 calls:

24.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series209.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

139.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) re)
25.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
23.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
21.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify112.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4916	946
1	4916	946

prune87.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	68	8	76

Merged error: 19.1b

Counts

76 → 8

Compiler

Compiled 2681 to 784 computations (70.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.0b	(sqrt.f64 (.f64 (.f64 im im) 2))
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite43.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64_2487`
50×	`sqrt-prod_binary64_2481`
38×	`*-un-lft-identity_binary64_2465`
36×	`times-frac_binary64_2471`
26×	`add-cube-cbrt_binary64_2500`
12×	`difference-of-squares_binary64_2434`
11×	`pow1_binary64_2526`
9×	`associate-/r*_binary64_2409`
6×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `distribute-lft-out--_binary64_2417` `add-cbrt-cube_binary64_2501`
4×	`sqrt-div_binary64_2482` `sqrt-pow1_binary64_2483` `associate-/l*_binary64_2410`
3×	`cancel-sign-sub-inv_binary64_2431` `pow-prod-down_binary64_2536`
2×	`flip--_binary64_2440` `pow1/2_binary64_2545` `associate-/r/_binary64_2411` `flip3--_binary64_2469`
1×	`flip3-+_binary64_2468` `sqrt-undiv_binary64_2486` `flip-+_binary64_2439` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `sub-neg_binary64_2458` `div-exp_binary64_2516` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `frac-2neg_binary64_2476`

Counts

4 → 108

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series164.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

87.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
29.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
22.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

simplify72.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5054	3621

prune139.0ms (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	3	2	5
Picked	1	0	1
Done	1	1	2
Total	119	9	128

Merged error: 11.5b

Counts

128 → 9

Compiler

Compiled 3518 to 1216 computations (65.4% saved)

regimes1.0s (21.6%)

Compiler: Compiled 6355 to 4257 computations (33% saved)

bsearch88.0ms (1.8%)

Steps

Iters	Range	Point
9	5.099845210261379e+143	6.7117829996739365e+149	2.1575500997764812e+145
9	-8.040575062053447e-242	-4.0825037230347986e-250	-4.1578241603242444e-250
9	-6.788873956149692e+162	-2.64180144851557e+157	-2.6658846711910334e+157

Iters

Range

Point

5.099845210261379e+143

6.7117829996739365e+149

2.1575500997764812e+145

-8.040575062053447e-242

-4.0825037230347986e-250

-4.1578241603242444e-250

-6.788873956149692e+162

-2.64180144851557e+157

-2.6658846711910334e+157

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	103
1	62	103

end0.0ms (0%)

sample1.6s (33.3%)

Algorithm

1×

intervals

Results

305.0ms	6059×	body	128	valid
161.0ms	650×	body	2048	valid
148.0ms	503×	body	4096	valid
83.0ms	433×	body	1024	valid
34.0ms	239×	body	512	valid
11.0ms	116×	body	256	valid

Compiler

Compiled 904 to 598 computations (33.8% saved)

Details

analyze328.0ms (6.8%)

sample34.0ms (0.7%)

simplify95.0ms (2%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite33.0ms (0.7%)

series186.0ms (3.9%)

simplify78.0ms (1.6%)

prune81.0ms (1.7%)

localize15.0ms (0.3%)

rewrite48.0ms (1%)

series104.0ms (2.2%)

simplify73.0ms (1.5%)

prune87.0ms (1.8%)

localize20.0ms (0.4%)

rewrite45.0ms (0.9%)

series209.0ms (4.3%)

simplify112.0ms (2.3%)

prune87.0ms (1.8%)

localize12.0ms (0.3%)

rewrite43.0ms (0.9%)

series164.0ms (3.4%)

simplify72.0ms (1.5%)

prune139.0ms (2.9%)

regimes1.0s (21.6%)

bsearch88.0ms (1.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.6s (33.3%)

Profiling