Details

sample34.0ms

Algorithm

intervals

Results

14.0ms	279×	body	80	valid
4.0ms	76×	body	80	nan

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	18
1	80	18
2	143	18
3	177	18
4	189	18
5	193	18
6	193	18

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 16.7b

Counts

2 → 1

localize121.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
58×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
37×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
12×	`add-log-exp`
10×	`fma-def` `fma-neg`
8×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 151

Calls

4 calls:

10.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(+ (- b) (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)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify84.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	418	3056
1	1471	2008
2	5001	1917

prune390.0ms

Filtered

163 candidates to 92 candidates (56.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	158	5	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	5	164

Merged error: 7.0b

Counts

164 → 5

localize122.0ms

Local error

Found 4 expressions with local error:

9.6b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`fma-neg` `prod-diff`
8×	`add-log-exp`
6×	`cbrt-prod` `distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`neg-mul-1` `pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 83

Calls

4 calls:

5.0ms	(- (- 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)))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
96.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
102.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	428	1492
1	1667	1341
2	5002	1297

prune427.0ms

Filtered

95 candidates to 79 candidates (83.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	94	6	100

Merged error: 7.0b

Counts

100 → 6

localize126.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 66

Calls

4 calls:

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)))
9.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify82.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	215	614
1	688	585
2	2689	580
3	5001	577

prune412.0ms

Filtered

78 candidates to 68 candidates (87.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	77	7	84

Merged error: 6.9b

Counts

84 → 7

localize132.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 62

Calls

4 calls:

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)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
94.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
96.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
96.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify81.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	215	657
1	688	619
2	2689	612
3	5001	611

prune445.0ms

Filtered

74 candidates to 68 candidates (91.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	74	7	81

Merged error: 6.9b

Counts

81 → 7

regimes169.0ms

Accuracy

89.9% (1.2b remaining)

Error of 8.6b against oracle of 7.4b and baseline of 19.4b

bsearch172.0ms

Steps

Iters	Range		Point
9	1.314833454423355e+61	1.6016599845544569e+66	1.5877733204280517e+66
7	-2.5450419946620176e+154	-3.605266790381871e+152	-1.2796758542224547e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	66
1	53	66

end0.0ms

sample923.0ms

Algorithm

intervals

Results

496.0ms	8688×	body	80	valid
151.0ms	2902×	body	80	nan