Details

analyze468.0ms

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

sample46.0ms

Algorithm

intervals

Results

14.0ms	50×	body	2560	valid
7.0ms	142×	body	80	valid
7.0ms	30×	body	1280	valid
3.0ms	18×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	25×	body	80	nan
1.0ms	15×	body	80	invalid
1.0ms	6×	body	160	valid
0.0ms	1×	body	5120	valid

simplify356.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (347.0ms)

Iter	Nodes	Cost
0	1835	24
1	1835	24

prune4.0ms

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: 39.1b

Counts

2 → 1

localize11.0ms

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)
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
26.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

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 (.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))))

series244.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
35.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
65.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify85.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4945	2018
1	4945	2018

prune108.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

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: 5.8b

Counts

84 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.6b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.7b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
10.7b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
26.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
13×	`associate-/l*_binary64`
10×	`cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64` `sqrt-prod_binary64`
9×	`associate-/r*_binary64`
7×	`flip3--_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `div-inv_binary64`
5×	`pow1_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 130

Calls

4 calls:

8.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
16.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
16.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.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))))

series544.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
184.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
232.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify82.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5245	4840

prune158.0ms

Filtered

106 candidates to 142 candidates (-34.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	145	6	151

Merged error: 5.7b

Counts

151 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.6b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
26.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac_binary64`
121×	`add-sqr-sqrt_binary64`
94×	`*-un-lft-identity_binary64`
68×	`add-cube-cbrt_binary64`
26×	`difference-of-squares_binary64`
22×	`associate-/r*_binary64`
16×	`sqrt-prod_binary64`
13×	`distribute-lft-out--_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
5×	`pow1_binary64` `div-inv_binary64`
3×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 146

Calls

4 calls:

13.0ms	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
10.0ms	(-.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))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
36.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
72.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify103.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4957	5651
1	4957	5651

prune173.0ms

Filtered

113 candidates to 158 candidates (-39.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	157	7	164

Merged error: 5.7b

Counts

164 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.7b	(/.f64 (/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a c))) a)
11.0b	(/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a c))
26.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

303×	`times-frac_binary64`
172×	`add-sqr-sqrt_binary64`
141×	`*-un-lft-identity_binary64`
111×	`add-cube-cbrt_binary64`
41×	`associate-/l*_binary64`
30×	`difference-of-squares_binary64`
23×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`div-inv_binary64` `sqrt-prod_binary64`
15×	`distribute-lft-out--_binary64`
11×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64`
4×	`associate-/r*_binary64` `associate-/r/_binary64`
3×	`associate-/l/_binary64` `flip3--_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64`

Counts

4 → 221

Calls

4 calls:

11.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
21.0ms	(/.f64 (/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a c))) a)
12.0ms	(/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series360.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
124.0ms	(/.f64 (/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a c))) a)
105.0ms	(/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a c))
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify165.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4936	9602
1	4936	9602

prune301.0ms

Filtered

178 candidates to 233 candidates (-30.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	233	0	233
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	233	7	240

Merged error: 5.7b

Counts

240 → 7

regimes100.0ms

Accuracy

92.4% (1.8b remaining)

Error of 7.6b against oracle of 5.8b and baseline of 29.4b

bsearch92.0ms

Steps

Iters	Range		Point
6	34121940725.3485	379128542044.51965	371841908308.4654
7	8.374909980274751e-238	2.0581579040773618e-235	3.772087380287071e-236
9	-1.0549617536863574e+96	-5.0296565417525773e+89	-2.2136550152753833e+95

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	100	113
1	100	113

end0.0ms

sample1.3s

Algorithm

intervals

Results

316.0ms	1078×	body	2560	valid
263.0ms	5054×	body	80	valid
229.0ms	929×	body	1280	valid
92.0ms	466×	body	640	valid
42.0ms	106×	body	5120	valid
41.0ms	251×	body	320	valid
36.0ms	683×	body	80	nan
19.0ms	382×	body	80	invalid
11.0ms	116×	body	160	valid

Details

analyze468.0ms

sample46.0ms

simplify356.0ms

prune4.0ms

localize11.0ms

rewrite30.0ms

series244.0ms

simplify85.0ms

prune108.0ms

localize13.0ms

rewrite50.0ms

series544.0ms

simplify82.0ms

prune158.0ms

localize13.0ms

rewrite41.0ms

series294.0ms

simplify103.0ms

prune173.0ms

localize14.0ms

rewrite63.0ms

series360.0ms

simplify165.0ms

prune301.0ms

regimes100.0ms

bsearch92.0ms

simplify5.0ms

end0.0ms

sample1.3s

Profiling