Details

analyze572.0ms

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
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

sample39.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
1.0ms	14×	body	80	nan
1.0ms	7×	body	80	invalid

simplify666.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (267.0ms)

Iter	Nodes	Cost
0	3270	37
1	3270	37

prune24.0ms

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: 19.3b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
1.6b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
22.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
22.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
8×	`sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64` `sqrt-div_binary64`
3×	`diff-log_binary64` `distribute-lft-out--_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`associate--l-_binary64` `neg-sub0_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64`

Counts

4 → 61

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
9.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

series75.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
12.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
22.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
27.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

simplify60.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5567	1069

prune140.0ms

Filtered

59 candidates to 73 candidates (-23.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	6	74

Merged error: 7.1b

Counts

74 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

1.6b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
3.2b	(exp.f64 (log.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)))
22.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
22.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
7×	`pow1_binary64`
6×	`log-prod_binary64` `exp-sum_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64` `sqrt-div_binary64` `exp-prod_binary64`
3×	`distribute-lft-out--_binary64`
2×	`pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `exp-diff_binary64` `rem-sqrt-square_binary64` `log-div_binary64`
1×	`sub-neg_binary64` `associate--l-_binary64` `neg-sub0_binary64` `log-pow_binary64` `rem-exp-log_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64`

Counts

4 → 67

Calls

4 calls:

9.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
9.0ms	(exp.f64 (log.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
14.0ms	(exp.f64 (log.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

simplify61.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4892	1157
1	4892	1157

prune127.0ms

Filtered

61 candidates to 79 candidates (-29.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	78	7	85

Merged error: 7.1b

Counts

85 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
4.0b	(/.f64 (.f64 2.0 c) (-.f64 (neg.f64 b) (-.f64 b (.f64 2.0 (/.f64 (*.f64 c a) b)))))
4.5b	(/.f64 (*.f64 c a) b)
22.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-/r*_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`cbrt-undiv_binary64` `difference-of-squares_binary64` `div-exp_binary64` `sqrt-prod_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `associate-/r/_binary64` `distribute-rgt-neg-in_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 79

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
10.0ms	(/.f64 (.f64 2.0 c) (-.f64 (neg.f64 b) (-.f64 b (.f64 2.0 (/.f64 (*.f64 c a) b)))))
5.0ms	(/.f64 (*.f64 c a) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
31.0ms	(/.f64 (.f64 2.0 c) (-.f64 (neg.f64 b) (-.f64 b (.f64 2.0 (/.f64 (*.f64 c a) b)))))
6.0ms	(/.f64 (*.f64 c a) b)
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

simplify44.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5381	1179

prune134.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	90	8	98

Merged error: 6.5b

Counts

98 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
4.0b	(/.f64 (.f64 2.0 c) (-.f64 (neg.f64 b) (-.f64 b (.f64 2.0 (*.f64 c (/.f64 a b))))))
6.6b	(*.f64 c (/.f64 a b))
22.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
16×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-r_binary64`
7×	`pow1_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64`
5×	`distribute-lft-out--_binary64`
4×	`difference-of-squares_binary64` `sqrt-prod_binary64`
3×	`flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `prod-exp_binary64` `div-exp_binary64` `flip--_binary64`
2×	`associate-/r/_binary64` `unswap-sqr_binary64` `distribute-rgt-neg-in_binary64` `div-inv_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `*-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
10.0ms	(/.f64 (.f64 2.0 c) (-.f64 (neg.f64 b) (-.f64 b (.f64 2.0 (*.f64 c (/.f64 a b))))))
7.0ms	(*.f64 c (/.f64 a b))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
28.0ms	(/.f64 (.f64 2.0 c) (-.f64 (neg.f64 b) (-.f64 b (.f64 2.0 (*.f64 c (/.f64 a b))))))
5.0ms	(*.f64 c (/.f64 a b))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

simplify45.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5127	1264

prune121.0ms

Filtered

75 candidates to 102 candidates (-36.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	103	7	110

Merged error: 6.2b

Counts

110 → 7

regimes255.0ms

Accuracy

94% (0.9b remaining)

Error of 6.9b against oracle of 5.9b and baseline of 21.1b

bsearch105.0ms

Steps

Iters	Range	Point
9	1.1832726428531494e+121	1.4545663394930315e+128	2.838341990170196e+126
9	-1.1435203403412755e-293	-2.7481330108391266e-300	-2.780192689850507e-300
10	-2.9936197355724482e+134	-2.185187917165607e+122	-4.1275090717025735e+127

Iters

Range

Point

1.1832726428531494e+121

1.4545663394930315e+128

2.838341990170196e+126

-1.1435203403412755e-293

-2.7481330108391266e-300

-2.780192689850507e-300

-2.9936197355724482e+134

-2.185187917165607e+122

-4.1275090717025735e+127

simplify15.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	706	144
1	706	144

end0.0ms

sample1.0s

Algorithm

intervals

Results

718.0ms	8000×	body	80	valid
58.0ms	708×	body	80	nan
34.0ms	398×	body	80	invalid

Details

analyze572.0ms

sample39.0ms

simplify666.0ms

prune24.0ms

localize23.0ms

rewrite31.0ms

series75.0ms

simplify60.0ms

prune140.0ms

localize27.0ms

rewrite28.0ms

series60.0ms

simplify61.0ms

prune127.0ms

localize27.0ms

rewrite29.0ms

series68.0ms

simplify44.0ms

prune134.0ms

localize25.0ms

rewrite31.0ms

series66.0ms

simplify45.0ms

prune121.0ms

regimes255.0ms

bsearch105.0ms

simplify15.0ms

end0.0ms

sample1.0s

Profiling