Details

analyze425.0ms

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample44.0ms

Algorithm

intervals

Results

9.0ms	25×	body	1280	valid
8.0ms	31×	body	2560	valid
8.0ms	172×	body	80	valid
2.0ms	15×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	24×	body	80	nan
1.0ms	6×	body	320	valid
0.0ms	9×	body	80	invalid
0.0ms	3×	body	160	valid

simplify483.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	713	13
1	713	13

prune5.0ms

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: 30.5b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.6b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
21.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`sqrt-prod_binary64`
7×	`associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 89

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
9.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
16.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
25.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4936	1587
1	4936	1587

prune125.0ms

Filtered

72 candidates to 101 candidates (-40.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	91	10	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	10	102

Merged error: 5.5b

Counts

102 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.6b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
21.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac_binary64`
130×	`add-sqr-sqrt_binary64`
129×	`*-un-lft-identity_binary64`
77×	`add-cube-cbrt_binary64`
27×	`associate-/r*_binary64`
26×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
16×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-rgt-neg-in_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
7×	`flip3--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`diff-log_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `neg-log_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 175

Calls

4 calls:

17.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
9.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
16.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
15.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5176	3699

prune130.0ms

Filtered

102 candidates to 187 candidates (-83.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	182	5	187
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	187	10	197

Merged error: 5.5b

Counts

197 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.8b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
13.6b	(/.f64 (*.f64 a c) a)
21.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

4 → 62

Calls

4 calls:

4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
11.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
5.0ms	(/.f64 (*.f64 a c) a)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
16.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
2.0ms	(/.f64 (*.f64 a c) a)
15.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5179	644

prune84.0ms

Filtered

57 candidates to 74 candidates (-29.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	74	10	84

Merged error: 5.4b

Counts

84 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.8b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
21.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `times-frac_binary64`
10×	`add-log-exp_binary64` `distribute-lft-out_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r*_binary64` `pow1_binary64` `distribute-rgt-neg-in_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64`

Counts

4 → 78

Calls

4 calls:

10.0ms	(/.f64 c (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series99.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/.f64 c (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
16.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
15.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5677	1193

prune66.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	2	6	8
Picked	0	1	1
Done	1	0	1
Total	91	9	100

Merged error: 5.4b

Counts

100 → 9

regimes274.0ms

Accuracy

93.8% (1.5b remaining)

Error of 7.1b against oracle of 5.6b and baseline of 29.5b

bsearch79.0ms

Steps

Iters	Range		Point
7	19273454904189.21	1041603463041951.4	1028948765099707.4
8	1.4006328130161814e-259	8.060327091088768e-255	1.2852416291713516e-256
8	-2.0168463992321823e+147	-1.049047891908715e+143	-1.1144738873289328e+144

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	116	55
1	116	55

end0.0ms

sample1.1s

Algorithm

intervals

Results

262.0ms	1052×	body	2560	valid
234.0ms	5131×	body	80	valid
196.0ms	925×	body	1280	valid
72.0ms	452×	body	640	valid
34.0ms	834×	body	80	nan
32.0ms	107×	body	5120	valid
28.0ms	232×	body	320	valid
11.0ms	270×	body	80	invalid
8.0ms	101×	body	160	valid

Details

analyze425.0ms

sample44.0ms

simplify483.0ms

prune5.0ms

localize21.0ms

rewrite35.0ms

series75.0ms

simplify61.0ms

prune125.0ms

localize10.0ms

rewrite43.0ms

series80.0ms

simplify59.0ms

prune130.0ms

localize11.0ms

rewrite25.0ms

series43.0ms

simplify60.0ms

prune84.0ms

localize9.0ms

rewrite29.0ms

series99.0ms

simplify57.0ms

prune66.0ms

regimes274.0ms

bsearch79.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling