Details

analyze420.0ms

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

sample42.0ms

Algorithm

intervals

Results

8.0ms	171×	body	80	valid
8.0ms	20×	body	2560	valid
7.0ms	33×	body	1280	valid
3.0ms	19×	body	640	valid
1.0ms	25×	body	80	nan
1.0ms	7×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	11×	body	80	invalid
0.0ms	4×	body	160	valid

simplify478.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune11.0ms

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: 33.1b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
7.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
13.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
26.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5748	1393

prune115.0ms

Filtered

72 candidates to 94 candidates (-30.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	87	7	94
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	87	8	95

Merged error: 6.5b

Counts

95 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.8b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
10.7b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
21.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

210×	`times-frac_binary64`
154×	`*-un-lft-identity_binary64`
93×	`add-sqr-sqrt_binary64`
92×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
31×	`distribute-lft-out_binary64`
21×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r/_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `neg-sub0_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_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 → 216

Calls

4 calls:

5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
14.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
9.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.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)))

series137.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
48.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
64.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5864	5180

prune180.0ms

Filtered

174 candidates to 228 candidates (-31.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	228	8	236

Merged error: 6.5b

Counts

236 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
0.4b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
21.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite25.0ms

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-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_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:

8.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
6.0ms	(+.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))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
14.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
7.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
15.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify54.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5326	1103

prune79.0ms

Filtered

65 candidates to 83 candidates (-27.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	83	8	91

Merged error: 6.5b

Counts

91 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 160

Calls

4 calls:

15.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
7.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
7.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
13.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
16.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5111	3271

prune100.0ms

Filtered

104 candidates to 172 candidates (-65.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	171	9	180

Merged error: 6.5b

Counts

180 → 9

regimes246.0ms

Accuracy

93% (1.7b remaining)

Error of 7.2b against oracle of 5.5b and baseline of 29.4b

bsearch81.0ms

Steps

Iters	Range		Point
8	6497523160246914.0	6.885563644766171e+18	2.8065521681772785e+18
7	-1.685469550775479e-305	-2.9189873276785382e-307	-1.243685732710164e-305
10	-6.291459953144265e+77	-1.9066222415164845e+66	-9.563637545141128e+76

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	100	53
1	100	53

end0.0ms

sample1.1s

Algorithm

intervals

Results

274.0ms	1082×	body	2560	valid
227.0ms	5055×	body	80	valid
189.0ms	922×	body	1280	valid
80.0ms	473×	body	640	valid
37.0ms	123×	body	5120	valid
32.0ms	771×	body	80	nan
30.0ms	220×	body	320	valid
11.0ms	247×	body	80	invalid
10.0ms	125×	body	160	valid

Details

analyze420.0ms

sample42.0ms

simplify478.0ms

prune11.0ms

localize20.0ms

rewrite34.0ms

series78.0ms

simplify57.0ms

prune115.0ms

localize10.0ms

rewrite43.0ms

series137.0ms

simplify72.0ms

prune180.0ms

localize9.0ms

rewrite25.0ms

series75.0ms

simplify54.0ms

prune79.0ms

localize9.0ms

rewrite42.0ms

series74.0ms

simplify73.0ms

prune100.0ms

regimes246.0ms

bsearch81.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling