Details

analyze693.0ms

Algorithm

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

sample43.0ms

Algorithm

intervals

Results

11.0ms	34×	body	2560	valid
8.0ms	156×	body	80	valid
7.0ms	27×	body	1280	valid
3.0ms	15×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	160	valid
1.0ms	13×	body	80	nan
1.0ms	10×	body	80	invalid

simplify329.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (320.0ms)

Iter	Nodes	Cost
0	1835	24
1	1835	24

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 35.7b

Counts

2 → 1

localize12.0ms

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 (.f64 b b) (.f64 (*.f64 4 a) c))
2.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_575`
13×	`*-un-lft-identity_binary64_590`
9×	`add-cbrt-cube_binary64_562` `add-exp-log_binary64_554`
8×	`add-log-exp_binary64_555`
7×	`add-cube-cbrt_binary64_561`
6×	`difference-of-squares_binary64_619` `times-frac_binary64_585` `sqrt-prod_binary64_569` `associate-/l*_binary64_654`
5×	`pow1_binary64_532`
4×	`flip--_binary64_616` `flip3--_binary64_589`
3×	`distribute-lft-out--_binary64_635`
2×	`sub-neg_binary64_594` `cbrt-undiv_binary64_560` `associate-/l/_binary64_656` `sqrt-div_binary64_570` `diff-log_binary64_501` `div-exp_binary64_539`
1×	`cbrt-unprod_binary64_559` `rem-sqrt-square_binary64_578` `div-inv_binary64_591` `prod-exp_binary64_537` `frac-2neg_binary64_583` `div-sub_binary64_584` `pow1/2_binary64_522` `sqrt-pow1_binary64_571` `associate-/r*_binary64_653` `clear-num_binary64_593`

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))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
8.0ms	(-.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)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
60.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify88.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4988	1963
1	4988	1963

prune101.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 6.2b

Counts

83 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.3b	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
11.1b	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_562` `add-exp-log_binary64_554`
22×	`times-frac_binary64_585`
21×	`*-un-lft-identity_binary64_590`
17×	`cbrt-undiv_binary64_560` `div-exp_binary64_539`
13×	`cbrt-unprod_binary64_559` `prod-exp_binary64_537`
12×	`add-sqr-sqrt_binary64_575`
11×	`add-cube-cbrt_binary64_561` `associate-/l*_binary64_654`
6×	`add-log-exp_binary64_555` `associate-/r/_binary64_655`
5×	`distribute-lft-out_binary64_634` `pow1_binary64_532` `associate-/r*_binary64_653`
4×	`flip-+_binary64_615` `div-inv_binary64_591` `flip3-+_binary64_588`
3×	`sqrt-prod_binary64_569`
2×	`frac-2neg_binary64_583` `sqrt-div_binary64_570` `clear-num_binary64_593`
1×	`rem-sqrt-square_binary64_578` `+-commutative_binary64_657` `flip--_binary64_616` `flip3--_binary64_589` `pow1/2_binary64_522` `associate-/l/_binary64_656` `sqrt-pow1_binary64_571` `sum-log_binary64_500`

Counts

4 → 102

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
15.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
11.0ms	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
154.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
200.0ms	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4935	3094
1	4935	3094

prune110.0ms

Filtered

78 candidates to 114 candidates (-46.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	115	6	121

Merged error: 6.1b

Counts

121 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_590`
20×	`add-sqr-sqrt_binary64_575`
18×	`associate-r_binary64_649`
14×	`add-cube-cbrt_binary64_561`
13×	`times-frac_binary64_585`
9×	`add-cbrt-cube_binary64_562` `add-exp-log_binary64_554`
8×	`add-log-exp_binary64_555`
7×	`pow1_binary64_532`
4×	`distribute-lft-out_binary64_634`
3×	`sqrt-prod_binary64_569` `associate-l_binary64_650`
2×	`cbrt-unprod_binary64_559` `flip-+_binary64_615` `flip--_binary64_616` `unswap-sqr_binary64_618` `prod-exp_binary64_537` `flip3--_binary64_589` `associate-/r/_binary64_655` `sqrt-div_binary64_570` `flip3-+_binary64_588`
1×	`rem-sqrt-square_binary64_578` `pow-prod-down_binary64_513` `sub-neg_binary64_594` `+-commutative_binary64_657` `div-inv_binary64_591` `cbrt-undiv_binary64_560` `-commutative_binary64_658` `pow1/2_binary64_522` `sqrt-pow1_binary64_571` `diff-log_binary64_501` `associate-r/_binary64_651` `sum-log_binary64_500` `div-exp_binary64_539`

Counts

4 → 75

Calls

4 calls:

12.0ms	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
59.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
64.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5194	1901

prune97.0ms

Filtered

66 candidates to 87 candidates (-31.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	86	7	93

Merged error: 6.1b

Counts

93 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
2.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_575`
17×	`*-un-lft-identity_binary64_590`
13×	`add-cube-cbrt_binary64_561` `associate-r_binary64_649`
10×	`times-frac_binary64_585`
9×	`add-cbrt-cube_binary64_562` `add-exp-log_binary64_554`
8×	`add-log-exp_binary64_555`
7×	`pow1_binary64_532`
6×	`associate-l_binary64_650`
5×	`flip--_binary64_616` `sqrt-prod_binary64_569` `flip3--_binary64_589`
4×	`difference-of-squares_binary64_619`
2×	`cbrt-unprod_binary64_559` `sub-neg_binary64_594` `unswap-sqr_binary64_618` `prod-exp_binary64_537` `frac-times_binary64_582` `distribute-lft-out--_binary64_635` `sqrt-div_binary64_570` `associate-*l/_binary64_652` `diff-log_binary64_501`
1×	`rem-sqrt-square_binary64_578` `pow-prod-down_binary64_513` `div-inv_binary64_591` `cbrt-undiv_binary64_560` `-commutative_binary64_658` `pow1/2_binary64_522` `sqrt-pow1_binary64_571` `associate-r/_binary64_651` `div-exp_binary64_539`

Counts

4 → 79

Calls

4 calls:

14.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
59.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4957	2223
1	4957	2223

prune75.0ms

Filtered

68 candidates to 91 candidates (-33.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	91	7	98

Merged error: 6.1b

Counts

98 → 7

regimes128.0ms

Accuracy

94.9% (1.2b remaining)

Error of 7.0b against oracle of 5.7b and baseline of 29.7b

bsearch97.0ms

Steps

Iters	Range	Point
8	4.058381416021372e+99	2.0399551007354747e+102	2.020343938322325e+102
6	-3.1187755358924823e-208	-3.671783466640133e-209	-3.965802121632277e-209
10	-1.6079749874000203e+96	-1.2215557721803615e+85	-2.744341717572267e+94

Iters

Range

Point

4.058381416021372e+99

2.0399551007354747e+102

2.020343938322325e+102

-3.1187755358924823e-208

-3.671783466640133e-209

-3.965802121632277e-209

-1.6079749874000203e+96

-1.2215557721803615e+85

-2.744341717572267e+94

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	102	82
1	102	82

end0.0ms

sample1.3s

Algorithm

intervals

Results

330.0ms	1092×	body	2560	valid
275.0ms	5104×	body	80	valid
230.0ms	909×	body	1280	valid
84.0ms	422×	body	640	valid
41.0ms	111×	body	5120	valid
37.0ms	252×	body	320	valid
31.0ms	616×	body	80	nan
19.0ms	339×	body	80	invalid
11.0ms	110×	body	160	valid

Details

analyze693.0ms

sample43.0ms

simplify329.0ms

prune8.0ms

localize12.0ms

rewrite31.0ms

series255.0ms

simplify88.0ms

prune101.0ms

localize15.0ms

rewrite41.0ms

series474.0ms

simplify113.0ms

prune110.0ms

localize12.0ms

rewrite29.0ms

series338.0ms

simplify65.0ms

prune97.0ms

localize11.0ms

rewrite35.0ms

series255.0ms

simplify69.0ms

prune75.0ms

regimes128.0ms

bsearch97.0ms

simplify4.0ms

end0.0ms

sample1.3s

Profiling