Details

analyze445.0ms (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
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
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	170×	body	128	valid
7.0ms	27×	body	2048	valid
5.0ms	16×	body	4096	valid
5.0ms	24×	body	1024	valid
2.0ms	13×	body	512	valid
1.0ms	18×	body	128	nan
1.0ms	6×	body	256	valid
1.0ms	11×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify224.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune3.0ms (0.1%)

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

Merged error: 34.8b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_435`
13×	`*-un-lft-identity_binary64_414`
9×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`add-log-exp_binary64_450`
7×	`add-cube-cbrt_binary64_446`
6×	`times-frac_binary64_420` `difference-of-squares_binary64_383` `sqrt-prod_binary64_429` `associate-/l*_binary64_361`
5×	`pow1_binary64_472`
4×	`flip3--_binary64_418` `flip--_binary64_389`
3×	`distribute-lft-out--_binary64_368`
2×	`sqrt-div_binary64_430` `diff-log_binary64_503` `cbrt-undiv_binary64_445` `sub-neg_binary64_407` `associate-/l/_binary64_363` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `div-inv_binary64_411` `sqrt-pow1_binary64_431` `prod-exp_binary64_460` `frac-2neg_binary64_425` `pow1/2_binary64_491` `cbrt-unprod_binary64_444` `div-sub_binary64_419` `associate-/r*_binary64_360` `rem-sqrt-square_binary64_427`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series530.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

212.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
129.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
68.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify98.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4884	1963
1	4884	1963

prune120.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Merged error: 7.4b

Counts

83 → 9

Compiler

Compiled 2117 to 1273 computations (39.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.5b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
2.4b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
11.2b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite53.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
22×	`times-frac_binary64_420`
21×	`*-un-lft-identity_binary64_414`
17×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
13×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
12×	`add-sqr-sqrt_binary64_435`
11×	`add-cube-cbrt_binary64_446` `associate-/l*_binary64_361`
6×	`associate-/r/_binary64_362` `add-log-exp_binary64_450`
5×	`pow1_binary64_472` `distribute-lft-out_binary64_367` `associate-/r*_binary64_360`
4×	`flip3-+_binary64_417` `div-inv_binary64_411` `flip-+_binary64_388`
3×	`sqrt-prod_binary64_429`
2×	`clear-num_binary64_413` `sqrt-div_binary64_430` `frac-2neg_binary64_425`
1×	`flip3--_binary64_418` `sqrt-pow1_binary64_431` `+-commutative_binary64_346` `pow1/2_binary64_491` `flip--_binary64_389` `associate-/l/_binary64_363` `sum-log_binary64_502` `rem-sqrt-square_binary64_427`

Counts

4 → 102

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series927.0ms (15.2%)

Counts

4 → 12

Calls

4 calls:

368.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
304.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
129.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
126.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

simplify92.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4940	3121
1	4940	3121

prune149.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	114	9	123

Merged error: 7.3b

Counts

123 → 9

Compiler

Compiled 3300 to 2028 computations (38.5% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.5b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_435`
9×	`sqrt-prod_binary64_429` `*-un-lft-identity_binary64_414`
7×	`pow1_binary64_472` `add-cube-cbrt_binary64_446`
6×	`sqrt-div_binary64_430` `add-log-exp_binary64_450`
4×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
3×	`flip3--_binary64_418` `sqrt-pow1_binary64_431` `pow1/2_binary64_491` `flip--_binary64_389` `rem-sqrt-square_binary64_427`
1×	`flip3-+_binary64_417` `+-commutative_binary64_346` `flip-+_binary64_388` `distribute-lft-out_binary64_367` `sum-log_binary64_502`

Counts

4 → 57

Calls

4 calls:

7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series454.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
113.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
110.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify61.0ms (1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4964	1379
1	4964	1379

prune151.0ms (2.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	68	10	78

Merged error: 7.3b

Counts

78 → 10

Compiler

Compiled 3860 to 2353 computations (39% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

4.0b	(exp.f64 (log.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_435`
11×	`*-un-lft-identity_binary64_414`
9×	`add-cube-cbrt_binary64_446` `sqrt-prod_binary64_429`
8×	`pow1_binary64_472`
6×	`sqrt-div_binary64_430`
4×	`exp-sum_binary64_457` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `add-log-exp_binary64_450` `log-prod_binary64_497` `exp-prod_binary64_463`
3×	`flip3--_binary64_418` `sqrt-pow1_binary64_431` `pow1/2_binary64_491` `flip--_binary64_389` `rem-sqrt-square_binary64_427`
2×	`exp-diff_binary64_459` `log-div_binary64_498`
1×	`log-pow_binary64_500` `flip3-+_binary64_417` `rem-exp-log_binary64_451` `flip-+_binary64_388` `distribute-lft-out_binary64_367`

Counts

4 → 63

Calls

4 calls:

8.0ms	(exp.f64 (log.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series644.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

310.0ms	(exp.f64 (log.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
106.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify49.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5174	1504

prune169.0ms (2.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	75	10	85

Merged error: 7.3b

Counts

85 → 10

Compiler

Compiled 4140 to 2553 computations (38.3% saved)

regimes158.0ms (2.6%)

Compiler: Compiled 855 to 636 computations (25.6% saved)

bsearch126.0ms (2.1%)

Steps

Iters	Range	Point
9	1.1653234244488785e+68	1.7662955524606724e+75	8.216375787380612e+73
11	-1.2558861078378803e-289	6.227874363503412e-308	1.4533084893508145e-308
7	-8.319194415650854e+137	-5.043818001310122e+136	-2.0779796988596927e+137

Iters

Range

Point

1.1653234244488785e+68

1.7662955524606724e+75

8.216375787380612e+73

-1.2558861078378803e-289

6.227874363503412e-308

1.4533084893508145e-308

-8.319194415650854e+137

-5.043818001310122e+136

-2.0779796988596927e+137

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	110	152
1	110	152

end0.0ms (0%)

sample1.5s (23.8%)

Algorithm

1×

intervals

Results

264.0ms	5180×	body	128	valid
263.0ms	1076×	body	2048	valid
149.0ms	773×	body	1024	valid
126.0ms	420×	body	4096	valid
56.0ms	387×	body	512	valid
34.0ms	643×	body	128	nan
22.0ms	378×	body	128	invalid
15.0ms	164×	body	256	valid

Compiler

Compiled 400 to 286 computations (28.5% saved)

Details

analyze445.0ms (7.3%)

sample39.0ms (0.6%)

simplify224.0ms (3.7%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite36.0ms (0.6%)

series530.0ms (8.7%)

simplify98.0ms (1.6%)

prune120.0ms (2%)

localize16.0ms (0.3%)

rewrite53.0ms (0.9%)

series927.0ms (15.2%)

simplify92.0ms (1.5%)

prune149.0ms (2.4%)

localize19.0ms (0.3%)

rewrite29.0ms (0.5%)

series454.0ms (7.4%)

simplify61.0ms (1%)

prune151.0ms (2.5%)

localize21.0ms (0.4%)

rewrite32.0ms (0.5%)

series644.0ms (10.5%)

simplify49.0ms (0.8%)

prune169.0ms (2.8%)

regimes158.0ms (2.6%)

bsearch126.0ms (2.1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.5s (23.8%)

Profiling