Details

analyze325.0ms (7.3%)

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
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)

sample29.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	202×	body	128	valid
5.0ms	21×	body	2048	valid
4.0ms	12×	body	4096	valid
2.0ms	13×	body	1024	valid
1.0ms	6×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify169.0ms (3.8%)

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: 37.9b

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	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.9b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`pow1_binary64_3168` `add-log-exp_binary64_3146`
7×	`*-un-lft-identity_binary64_3110`
6×	`add-sqr-sqrt_binary64_3131`
5×	`add-cube-cbrt_binary64_3142`
4×	`sqrt-prod_binary64_3125` `add-exp-log_binary64_3145` `sqrt-div_binary64_3126` `flip3-+_binary64_3113` `add-cbrt-cube_binary64_3143` `flip-+_binary64_3084`
3×	`sqrt-pow1_binary64_3127`
2×	`+-commutative_binary64_3042` `associate-*r/_binary64_3054` `sum-log_binary64_3198` `pow1/2_binary64_3187`
1×	`distribute-lft-out_binary64_3063` `pow-prod-down_binary64_3178` `rem-sqrt-square_binary64_3123`

Counts

4 → 51

Calls

4 calls:

9.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))

series358.0ms (8%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
56.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
49.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
40.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify55.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5113	1040

prune77.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	7	64

Merged error: 15.3b

Counts

64 → 7

Compiler

Compiled 1313 to 601 computations (54.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
3.4b	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
21.4b	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite44.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_3131`
13×	`*-un-lft-identity_binary64_3110`
9×	`add-exp-log_binary64_3145` `add-cbrt-cube_binary64_3143`
8×	`pow1_binary64_3168`
7×	`sqrt-prod_binary64_3125` `add-cube-cbrt_binary64_3142`
6×	`times-frac_binary64_3116` `difference-of-squares_binary64_3079` `add-log-exp_binary64_3146` `associate-/r*_binary64_3056`
3×	`sqrt-pow1_binary64_3127` `sqrt-div_binary64_3126` `distribute-lft-out--_binary64_3064`
2×	`cbrt-undiv_binary64_3141` `div-exp_binary64_3158` `associate-/r/_binary64_3058` `pow1/2_binary64_3187` `flip3--_binary64_3114` `flip--_binary64_3085`
1×	`sub-neg_binary64_3103` `prod-exp_binary64_3156` `pow-prod-down_binary64_3178` `cbrt-unprod_binary64_3140` `rem-sqrt-square_binary64_3123` `clear-num_binary64_3109` `associate-r/_binary64_3054` `flip3-+_binary64_3113` `diff-log_binary64_3199` `frac-2neg_binary64_3121` `flip-+_binary64_3084` `associate-/l_binary64_3057` `div-inv_binary64_3107`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
12.0ms	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series383.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

184.0ms	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
100.0ms	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
56.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
44.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify68.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	6110	1721

prune91.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	80	9	89

Merged error: 11.6b

Counts

89 → 9

Compiler

Compiled 2196 to 794 computations (63.8% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) im)
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
3.4b	(sqrt.f64 (.f64 2 (/.f64 im (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re) im))))
29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite51.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_3131`
26×	`*-un-lft-identity_binary64_3110`
18×	`times-frac_binary64_3116`
16×	`add-cube-cbrt_binary64_3142`
10×	`difference-of-squares_binary64_3079`
9×	`sqrt-prod_binary64_3125`
8×	`pow1_binary64_3168`
6×	`add-exp-log_binary64_3145` `add-log-exp_binary64_3146` `add-cbrt-cube_binary64_3143` `associate-/l*_binary64_3057`
5×	`distribute-lft-out--_binary64_3064`
3×	`sqrt-pow1_binary64_3127` `sqrt-div_binary64_3126` `associate-/r*_binary64_3056`
2×	`associate-/l/_binary64_3059` `pow1/2_binary64_3187` `flip3--_binary64_3114` `flip--_binary64_3085`
1×	`sub-neg_binary64_3103` `pow-prod-down_binary64_3178` `cbrt-undiv_binary64_3141` `div-sub_binary64_3115` `div-exp_binary64_3158` `rem-sqrt-square_binary64_3123` `clear-num_binary64_3109` `associate-*r/_binary64_3054` `flip3-+_binary64_3113` `diff-log_binary64_3199` `frac-2neg_binary64_3121` `flip-+_binary64_3084` `div-inv_binary64_3107`

Counts

4 → 83

Calls

4 calls:

17.0ms	(sqrt.f64 (.f64 2 (/.f64 im (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re) im))))
12.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) im)
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series367.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

171.0ms	(sqrt.f64 (.f64 2 (/.f64 im (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re) im))))
102.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) im)
52.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
42.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify54.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4969	2236
1	4969	2236

prune105.0ms (2.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	90	5	95
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	94	10	104

Merged error: 9.9b

Counts

104 → 10

Compiler

Compiled 2634 to 967 computations (63.3% 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)))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.2b	(sqrt.f64 (.f64 (.f64 im im) 2))
29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite49.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`sqrt-prod_binary64_3125` `add-sqr-sqrt_binary64_3131`
37×	`*-un-lft-identity_binary64_3110`
36×	`times-frac_binary64_3116`
25×	`add-cube-cbrt_binary64_3142`
12×	`difference-of-squares_binary64_3079`
11×	`pow1_binary64_3168`
9×	`associate-/r*_binary64_3056`
6×	`add-exp-log_binary64_3145` `add-log-exp_binary64_3146` `distribute-lft-out--_binary64_3064` `add-cbrt-cube_binary64_3143`
4×	`sqrt-pow1_binary64_3127` `sqrt-div_binary64_3126` `associate-/l*_binary64_3057`
3×	`pow-prod-down_binary64_3178`
2×	`associate-/r/_binary64_3058` `pow1/2_binary64_3187` `flip3--_binary64_3114` `flip--_binary64_3085`
1×	`sub-neg_binary64_3103` `cbrt-undiv_binary64_3141` `div-exp_binary64_3158` `rem-sqrt-square_binary64_3123` `clear-num_binary64_3109` `sqrt-undiv_binary64_3130` `flip3-+_binary64_3113` `diff-log_binary64_3199` `frac-2neg_binary64_3121` `flip-+_binary64_3084` `div-inv_binary64_3107`

Counts

4 → 105

Calls

4 calls:

16.0ms	(/.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)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

series342.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

189.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
63.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
46.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
43.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify109.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4923	3604
1	4923	3604

prune130.0ms (2.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	112	5	117
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	115	12	127

Merged error: 7.7b

Counts

127 → 12

Compiler

Compiled 3449 to 1196 computations (65.3% saved)

regimes326.0ms (7.3%)

Compiler: Compiled 1734 to 1234 computations (28.8% saved)

bsearch76.0ms (1.7%)

Steps

Iters	Range	Point
7	1.0783879871995089e+121	6.321203557273547e+122	5.6392861707035385e+122
7	-9.089728099399469e-302	-5.2137122067099377e-303	-5.2611073750173795e-303
9	-7.879764341688507e+170	-2.5496100832393085e+162	-2.5991937408382053e+162

Iters

Range

Point

1.0783879871995089e+121

6.321203557273547e+122

5.6392861707035385e+122

-9.089728099399469e-302

-5.2137122067099377e-303

-5.2611073750173795e-303

-7.879764341688507e+170

-2.5496100832393085e+162

-2.5991937408382053e+162

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	103
1	62	103

end0.0ms (0%)

sample1.2s (26.1%)

Algorithm

1×

intervals

Results

303.0ms	6143×	body	128	valid
149.0ms	495×	body	4096	valid
147.0ms	623×	body	2048	valid
72.0ms	368×	body	1024	valid
36.0ms	247×	body	512	valid
11.0ms	124×	body	256	valid

Compiler

Compiled 348 to 241 computations (30.7% saved)

Details

analyze325.0ms (7.3%)

sample29.0ms (0.6%)

simplify169.0ms (3.8%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite31.0ms (0.7%)

series358.0ms (8%)

simplify55.0ms (1.2%)

prune77.0ms (1.7%)

localize14.0ms (0.3%)

rewrite44.0ms (1%)

series383.0ms (8.6%)

simplify68.0ms (1.5%)

prune91.0ms (2%)

localize13.0ms (0.3%)

rewrite51.0ms (1.1%)

series367.0ms (8.2%)

simplify54.0ms (1.2%)

prune105.0ms (2.4%)

localize12.0ms (0.3%)

rewrite49.0ms (1.1%)

series342.0ms (7.7%)

simplify109.0ms (2.4%)

prune130.0ms (2.9%)

regimes326.0ms (7.3%)

bsearch76.0ms (1.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (26.1%)

Profiling