Details

analyze720.0ms

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

sample38.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
2.0ms	24×	body	80	nan
1.0ms	8×	body	80	invalid

simplify648.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (215.0ms)

Iter	Nodes	Cost
0	3270	37
1	3270	37

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 19.4b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
0.6b	(- (* b b) (* (* 4.0 a) c))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 52

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
32.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify37.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5017	824

prune179.0ms

Filtered

54 candidates to 64 candidates (-18.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	55	9	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	9	65

Merged error: 6.9b

Counts

65 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

11.4b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `neg-log` `flip-+`

Counts

4 → 58

Calls

4 calls:

4.0ms	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4959	931
1	4959	931

prune215.0ms

Filtered

60 candidates to 70 candidates (-16.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	70	9	79

Merged error: 6.9b

Counts

79 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

9.1b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 59

Calls

4 calls:

4.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4873	981
1	4873	981

prune206.0ms

Filtered

61 candidates to 71 candidates (-16.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	71	9	80

Merged error: 6.9b

Counts

80 → 9

localize32.0ms

Local error

Found 4 expressions with local error:

10.1b	(+ (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.9b	(cbrt (- (* b b) (* 4.0 (* a c))))
24.9b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `add-cbrt-cube`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`pow1/3` `sqrt-div` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 54

Calls

4 calls:

4.0ms	(+ (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
26.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify66.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4959	1157
1	4959	1157

prune190.0ms

Filtered

55 candidates to 66 candidates (-20.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	66	9	75

Merged error: 6.9b

Counts

75 → 9

regimes329.0ms

Accuracy

93.8% (0.9b remaining)

Error of 6.5b against oracle of 5.6b and baseline of 19.6b

bsearch68.0ms

Steps

Iters	Range		Point
8	3.999740121244286e+107	1.2599723971826903e+112	6.946117005702196e+108
10	-3.990078447059155e+148	-6.826166648164365e+136	-5.361260385010324e+145

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	144	129
1	144	129

end0.0ms

sample987.0ms

Algorithm

intervals

Results

701.0ms	8000×	body	80	valid
58.0ms	690×	body	80	nan
33.0ms	371×	body	80	invalid

Details

analyze720.0ms

sample38.0ms

simplify648.0ms

prune13.0ms

localize23.0ms

rewrite20.0ms

series64.0ms

simplify37.0ms

prune179.0ms

localize30.0ms

rewrite18.0ms

series63.0ms

simplify49.0ms

prune215.0ms

localize28.0ms

rewrite18.0ms

series60.0ms

simplify47.0ms

prune206.0ms

localize32.0ms

rewrite17.0ms

series97.0ms

simplify66.0ms

prune190.0ms

regimes329.0ms

bsearch68.0ms

simplify3.0ms

end0.0ms

sample987.0ms

Profiling