Details

analyze499.0ms (9.3%)

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 (0.7%)

Algorithm

1×

intervals

Results

10.0ms	185×	body	128	valid
7.0ms	26×	body	2048	valid
4.0ms	17×	body	1024	valid
3.0ms	9×	body	4096	valid
2.0ms	15×	body	512	valid
1.0ms	27×	body	128	nan
1.0ms	17×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify223.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (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: 31.5b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_751`
15×	`add-sqr-sqrt_binary64_772`
14×	`add-cube-cbrt_binary64_783`
12×	`times-frac_binary64_757`
8×	`add-log-exp_binary64_787`
6×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
5×	`distribute-lft-out_binary64_704` `pow1_binary64_809`
4×	`associate-/l*_binary64_698`
3×	`associate-/r*_binary64_697` `sqrt-prod_binary64_766`
2×	`flip3-+_binary64_754` `associate-/l/_binary64_700` `flip--_binary64_726` `sqrt-div_binary64_767` `flip3--_binary64_755` `flip-+_binary64_725`
1×	`+-commutative_binary64_683` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `div-inv_binary64_748` `diff-log_binary64_840` `cbrt-undiv_binary64_782` `sum-log_binary64_839` `frac-2neg_binary64_762` `clear-num_binary64_750` `sub-neg_binary64_744` `sqrt-pow1_binary64_768` `div-exp_binary64_799`

Counts

4 → 71

Calls

4 calls:

9.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series460.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

145.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
132.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
123.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
60.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify68.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5412	2012

prune121.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	74	9	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	9	84

Merged error: 6.4b

Counts

84 → 9

Compiler

Compiled 2173 to 1186 computations (45.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_772`
18×	`*-un-lft-identity_binary64_751`
13×	`add-cube-cbrt_binary64_783` `add-exp-log_binary64_786` `associate-r_binary64_693`
11×	`times-frac_binary64_757`
9×	`add-cbrt-cube_binary64_784`
8×	`add-log-exp_binary64_787`
7×	`pow1_binary64_809`
4×	`prod-exp_binary64_797` `associate-l_binary64_694`
3×	`unswap-sqr_binary64_719` `flip3-+_binary64_754` `sqrt-prod_binary64_766` `flip-+_binary64_725`
2×	`frac-times_binary64_761` `distribute-lft-out_binary64_704` `flip--_binary64_726` `sqrt-div_binary64_767` `cbrt-unprod_binary64_781` `associate-*l/_binary64_696` `flip3--_binary64_755` `div-exp_binary64_799`
1×	`1-exp_binary64_792` `+-commutative_binary64_683` `rec-exp_binary64_798` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `un-div-inv_binary64_749` `pow-prod-down_binary64_819` `-commutative_binary64_684` `div-inv_binary64_748` `associate-r/_binary64_695` `diff-log_binary64_840` `cbrt-undiv_binary64_782` `sum-log_binary64_839` `sub-neg_binary64_744` `sqrt-pow1_binary64_768`

Counts

4 → 79

Calls

4 calls:

15.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series476.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

154.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
130.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
67.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4910	2052
1	4910	2052

prune107.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	92	8	100

Merged error: 6.4b

Counts

100 → 8

Compiler

Compiled 2323 to 1334 computations (42.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
15.0b	(/.f64 (.f64 4 (.f64 a c)) a)
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
12×	`add-sqr-sqrt_binary64_772`
9×	`*-un-lft-identity_binary64_751`
8×	`add-log-exp_binary64_787`
7×	`add-cube-cbrt_binary64_783`
5×	`pow1_binary64_809`
4×	`sqrt-prod_binary64_766`
3×	`prod-exp_binary64_797` `associate-/r*_binary64_697` `flip--_binary64_726` `times-frac_binary64_757` `cbrt-undiv_binary64_782` `cbrt-unprod_binary64_781` `flip3--_binary64_755` `div-exp_binary64_799`
2×	`sqrt-div_binary64_767` `diff-log_binary64_840` `sub-neg_binary64_744` `difference-of-squares_binary64_720`
1×	`distribute-lft-out--_binary64_705` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `div-inv_binary64_748` `frac-2neg_binary64_762` `clear-num_binary64_750` `associate-/l*_binary64_698` `sqrt-pow1_binary64_768`

Counts

4 → 63

Calls

4 calls:

9.0ms	(/.f64 (.f64 4 (.f64 a c)) a)
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series343.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

139.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
19.0ms	(/.f64 (.f64 4 (.f64 a c)) a)

simplify55.0ms (1%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5123	1242

prune93.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	75	8	83

Merged error: 6.3b

Counts

83 → 8

Compiler

Compiled 2103 to 1162 computations (44.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 4 c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_772`
13×	`*-un-lft-identity_binary64_751`
9×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
8×	`add-log-exp_binary64_787`
7×	`add-cube-cbrt_binary64_783`
6×	`associate-/r*_binary64_697` `times-frac_binary64_757` `sqrt-prod_binary64_766` `difference-of-squares_binary64_720`
5×	`pow1_binary64_809`
4×	`flip--_binary64_726` `flip3--_binary64_755`
3×	`distribute-lft-out--_binary64_705`
2×	`sqrt-div_binary64_767` `associate-/r/_binary64_699` `diff-log_binary64_840` `cbrt-undiv_binary64_782` `sub-neg_binary64_744` `div-exp_binary64_799`
1×	`prod-exp_binary64_797` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `div-inv_binary64_748` `frac-2neg_binary64_762` `cbrt-unprod_binary64_781` `clear-num_binary64_750` `associate-/l*_binary64_698` `sqrt-pow1_binary64_768`

Counts

4 → 69

Calls

4 calls:

11.0ms	(/.f64 (.f64 4 c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series719.0ms (13.4%)

Counts

4 → 12

Calls

4 calls:

393.0ms	(/.f64 (.f64 4 c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
135.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
66.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify96.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4892	1927
1	4892	1927

prune93.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	81	8	89

Merged error: 6.3b

Counts

89 → 8

Compiler

Compiled 2044 to 1159 computations (43.3% saved)

regimes169.0ms (3.1%)

Compiler: Compiled 408 to 348 computations (14.7% saved)

bsearch58.0ms (1.1%)

Steps

Iters	Range	Point
8	1.926398635008391e+97	1.2558611526501326e+101	1.7352320966708498e+98
0	-9.223598178820025e-299	-9.131643782654936e-299	-9.177620980737481e-299
6	-2.6124887179107254e+101	-3.952717462715973e+100	-2.1036730520568813e+101

Iters

Range

Point

1.926398635008391e+97

1.2558611526501326e+101

1.7352320966708498e+98

-9.223598178820025e-299

-9.131643782654936e-299

-9.177620980737481e-299

-2.6124887179107254e+101

-3.952717462715973e+100

-2.1036730520568813e+101

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	98	92
1	98	92

end0.0ms (0%)

sample1.5s (27.6%)

Algorithm

1×

intervals

Results

302.0ms	1111×	body	2048	valid
298.0ms	5197×	body	128	valid
151.0ms	725×	body	1024	valid
131.0ms	380×	body	4096	valid
61.0ms	376×	body	512	valid
39.0ms	695×	body	128	nan
22.0ms	211×	body	256	valid
21.0ms	374×	body	128	invalid

Compiler

Compiled 256 to 199 computations (22.3% saved)

Details

analyze499.0ms (9.3%)

sample39.0ms (0.7%)

simplify223.0ms (4.1%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite32.0ms (0.6%)

series460.0ms (8.6%)

simplify68.0ms (1.3%)

prune121.0ms (2.3%)

localize13.0ms (0.2%)

rewrite39.0ms (0.7%)

series476.0ms (8.9%)

simplify72.0ms (1.3%)

prune107.0ms (2%)

localize13.0ms (0.2%)

rewrite33.0ms (0.6%)

series343.0ms (6.4%)

simplify55.0ms (1%)

prune93.0ms (1.7%)

localize13.0ms (0.2%)

rewrite35.0ms (0.6%)

series719.0ms (13.4%)

simplify96.0ms (1.8%)

prune93.0ms (1.7%)

regimes169.0ms (3.1%)

bsearch58.0ms (1.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.5s (27.6%)

Profiling