Details

analyze1.4s (0.3%)

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)

sample150.0ms (0%)

Algorithm

1×

intervals

Results

40.0ms	34×	body	2048	valid
35.0ms	185×	body	128	valid
16.0ms	6×	body	4096	valid
6.0ms	16×	body	1024	valid
2.0ms	7×	body	512	valid
2.0ms	20×	body	128	nan
2.0ms	17×	body	128	invalid
2.0ms	8×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify963.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (656.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune11.0ms (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: 30.0b

Counts

2 → 2

Compiler

Compiled 49 to 40 computations (18.4% saved)

localize24.0ms (0%)

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))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite84.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_441`
14×	`*-un-lft-identity_binary64_419`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454`
6×	`times-frac_binary64_425` `difference-of-squares_binary64_388` `sqrt-prod_binary64_435` `associate-/l*_binary64_364`
5×	`pow1_binary64_480`
4×	`flip3--_binary64_423` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385`
3×	`distribute-lft-out--_binary64_371`
2×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `diff-log_binary64_511` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `pow1/2_binary64_499` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `associate-/r*_binary64_363` `rem-sqrt-square_binary64_432` `div-sub_binary64_424`

Counts

4 → 74

Calls

4 calls:

29.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
20.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
11.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series1.2s (0.3%)

Counts

4 → 12

Calls

4 calls:

924.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
120.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
72.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify197.0ms (0%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (154.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune855.0ms (0.2%)

Pruning

47 alts after pruning (46 fresh and 1 done)

	Pruned	Kept	Total
New	40	46	86
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	41	47	88

Merged error: 5.1b

Counts

88 → 47

Compiler

Compiled 3199 to 2062 computations (35.5% saved)

localize64.0ms (0%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.4b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite180.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-div_binary64_436` `sqrt-pow1_binary64_437`
22×	`pow1_binary64_480`
11×	`pow1/2_binary64_499`
9×	`flip3--_binary64_423` `flip--_binary64_394`
8×	`add-sqr-sqrt_binary64_441`
7×	`sqrt-prod_binary64_435`
6×	`*-un-lft-identity_binary64_419` `add-log-exp_binary64_458` `add-cube-cbrt_binary64_454`
5×	`pow-prod-up_binary64_489`
4×	`frac-times_binary64_429` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`pow-prod-down_binary64_490` `pow-sqr_binary64_392` `rem-sqrt-square_binary64_432`
2×	`associate-l/_binary64_362` `associate-r/_binary64_361`
1×	`sub-neg_binary64_412` `pow-plus_binary64_482` `diff-log_binary64_511` `cancel-sign-sub-inv_binary64_385` `pow2_binary64_500`

Counts

4 → 74

Calls

4 calls:

60.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
25.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series701.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

234.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
196.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
150.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
121.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

simplify162.0ms (0%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4951	1719
1	4951	1719

prune1.8s (0.4%)

Pruning

66 alts after pruning (64 fresh and 2 done)

	Pruned	Kept	Total
New	63	23	86
Fresh	4	41	45
Picked	0	1	1
Done	0	1	1
Total	67	66	133

Merged error: 5.1b

Counts

133 → 66

Compiler

Compiled 4707 to 3051 computations (35.2% saved)

localize36.0ms (0%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.4b	(sqrt.f64 (.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/2) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
20.4b	(pow.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)) 1/2)

rewrite57.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_441` `pow1_binary64_480`
7×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `sqrt-pow1_binary64_437`
6×	`sqrt-div_binary64_436` `add-log-exp_binary64_458`
5×	`pow1/2_binary64_499` `add-exp-log_binary64_457`
4×	`add-cbrt-cube_binary64_455` `sqrt-prod_binary64_435`
3×	`unpow-prod-down_binary64_498` `flip3--_binary64_423` `pow-unpow_binary64_496` `flip--_binary64_394`
2×	`associate-*r/_binary64_361` `pow-prod-up_binary64_489`
1×	`pow-prod-down_binary64_490` `sub-neg_binary64_412` `pow-exp_binary64_487` `sqr-pow_binary64_391` `pow-to-exp_binary64_488` `pow-pow_binary64_491` `diff-log_binary64_511` `unpow1/2_binary64_483` `pow-sqr_binary64_392` `cancel-sign-sub-inv_binary64_385` `rem-sqrt-square_binary64_432`

Counts

4 → 61

Calls

4 calls:

20.0ms	(sqrt.f64 (.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/2) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
10.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)) 1/2)
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series382.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt.f64 (.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/2) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
109.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)) 1/2)
106.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
56.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify84.0ms (0%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5099	1316

prune1.2s (0.3%)

Pruning

78 alts after pruning (75 fresh and 3 done)

	Pruned	Kept	Total
New	55	18	73
Fresh	6	57	63
Picked	0	1	1
Done	0	2	2
Total	61	78	139

Merged error: 5.1b

Counts

139 → 78

Compiler

Compiled 4751 to 3149 computations (33.7% saved)

localize33.0ms (0%)

Local error

Found 4 expressions with local error:

20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.4b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
20.4b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite280.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`sqrt-div_binary64_436`
83×	`sqrt-pow1_binary64_437`
57×	`pow1_binary64_480`
35×	`flip3--_binary64_423` `flip--_binary64_394`
32×	`pow1/2_binary64_499` `frac-times_binary64_429`
30×	`pow-prod-up_binary64_489`
16×	`associate-*r/_binary64_361`
10×	`associate-*l/_binary64_362`
8×	`pow-prod-down_binary64_490` `add-sqr-sqrt_binary64_441` `sqrt-prod_binary64_435` `pow-sqr_binary64_392`
6×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`rem-sqrt-square_binary64_432`
2×	`pow-plus_binary64_482` `pow2_binary64_500`

Counts

4 → 118

Calls

4 calls:

111.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
62.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
13.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series721.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

244.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
191.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
181.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
105.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify194.0ms (0%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4891	4243
1	4891	4243

prune3.5s (0.7%)

Pruning

101 alts after pruning (97 fresh and 4 done)

	Pruned	Kept	Total
New	101	29	130
Fresh	6	68	74
Picked	0	1	1
Done	0	3	3
Total	107	101	208

Merged error: 5.1b

Counts

208 → 101

Compiler

Compiled 5720 to 3432 computations (40% saved)

regimes13.8s (2.9%)

Compiler: Compiled 29552 to 21166 computations (28.4% saved)

bsearch6.8min (86.7%)

Steps

Iters	Range		Point
7	5.077603163681316e+86	3.0675607530650454e+88	1.0076800180697053e+87
8	1.1967310277021378e-191	8.34259427963184e-189	2.43077786380867e-190
6	-5.59945793777678e+90	-4.402997549349525e+89	-4.787296627726359e+90

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify575.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	110	129
1	110	129

end0.0ms (0%)

sample33.9s (7.2%)

Algorithm

1×

intervals

Results

739.0ms	1131×	body	2048	valid
729.0ms	5223×	body	128	valid
322.0ms	697×	body	1024	valid
302.0ms	403×	body	4096	valid
124.0ms	368×	body	512	valid
81.0ms	641×	body	128	nan
52.0ms	418×	body	128	invalid
35.0ms	178×	body	256	valid

Compiler

Compiled 14628 to 9848 computations (32.7% saved)

Pareto

0.2695072273836827

Details

analyze1.4s (0.3%)

sample150.0ms (0%)

simplify963.0ms (0.2%)

prune11.0ms (0%)

localize24.0ms (0%)

rewrite84.0ms (0%)

series1.2s (0.3%)

simplify197.0ms (0%)

prune855.0ms (0.2%)

localize64.0ms (0%)

rewrite180.0ms (0%)

series701.0ms (0.1%)

simplify162.0ms (0%)

prune1.8s (0.4%)

localize36.0ms (0%)

rewrite57.0ms (0%)

series382.0ms (0.1%)

simplify84.0ms (0%)

prune1.2s (0.3%)

localize33.0ms (0%)

rewrite280.0ms (0.1%)

series721.0ms (0.2%)

simplify194.0ms (0%)

prune3.5s (0.7%)

regimes13.8s (2.9%)

bsearch6.8min (86.7%)

simplify575.0ms (0.1%)

end0.0ms (0%)

sample33.9s (7.2%)

Profiling