Details

analyze532.0ms

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
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

sample39.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
2.0ms	22×	body	80	nan
1.0ms	13×	body	80	invalid

simplify265.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (262.0ms)

Iter	Nodes	Cost
0	2747	36
1	2747	36

prune9.0ms

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: 21.7b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 53

Calls

4 calls:

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

series66.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
18.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4969	853
1	4969	853

prune124.0ms

Filtered

52 candidates to 65 candidates (-25.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	59	6	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	6	66

Merged error: 9.6b

Counts

66 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

5.9b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) b)
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cbrt-prod_binary64`
5×	`pow1_binary64`
4×	`cbrt-div_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`sqrt-prod_binary64`
2×	`pow1/3_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 52

Calls

4 calls:

9.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) b)
20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
27.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
29.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5000	1099

prune150.0ms

Filtered

58 candidates to 64 candidates (-10.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	62	8	70

Merged error: 9.6b

Counts

70 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify36.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4953	924
1	4953	924

prune163.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	72	8	80

Merged error: 9.6b

Counts

80 → 8

localize32.0ms

Local error

Found 4 expressions with local error:

14.2b	(-.f64 (.f64 (fabs.f64 (exp.f64 (log.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) b)
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cbrt-prod_binary64`
5×	`pow1_binary64`
4×	`cbrt-div_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`sqrt-prod_binary64`
2×	`pow1/3_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 52

Calls

4 calls:

10.0ms	(-.f64 (.f64 (fabs.f64 (exp.f64 (log.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series107.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(-.f64 (.f64 (fabs.f64 (exp.f64 (log.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) b)
20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5036	1099

prune125.0ms

Filtered

57 candidates to 64 candidates (-12.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	64	8	72

Merged error: 9.6b

Counts

72 → 8

regimes254.0ms

Accuracy

90.2% (1.2b remaining)

Error of 8.9b against oracle of 7.7b and baseline of 19.7b

bsearch51.0ms

Steps

Iters	Range		Point
8	6.093467662767075e+66	1.6571798933176391e+69	1.6435099743363113e+69
6	-1.7832963248470996e+80	-3.612699187479539e+79	-1.7621272729921349e+80

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	128	125
1	128	125

end0.0ms

sample1.1s

Algorithm

intervals

Results

806.0ms	8000×	body	80	valid
61.0ms	657×	body	80	nan
37.0ms	367×	body	80	invalid

Details

analyze532.0ms

sample39.0ms

simplify265.0ms

prune9.0ms

localize21.0ms

rewrite25.0ms

series66.0ms

simplify48.0ms

prune124.0ms

localize27.0ms

rewrite24.0ms

series113.0ms

simplify53.0ms

prune150.0ms

localize29.0ms

rewrite20.0ms

series74.0ms

simplify36.0ms

prune163.0ms

localize32.0ms

rewrite24.0ms

series107.0ms

simplify53.0ms

prune125.0ms

regimes254.0ms

bsearch51.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling