Details

sample48.0ms

Algorithm

intervals

Results

24.0ms	286×	body	80	valid
6.0ms	93×	body	80	nan

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	18
1	67	18
2	123	18
3	160	18
4	175	18
5	177	18
6	177	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: 20.2b

Counts

2 → 1

localize115.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (* b b) (* (* 4.0 a) c))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

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` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

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

series235.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 4.0 a) c))
43.0ms	(- (* b b) (* (* 4.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify92.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	170	540
1	665	506
2	2968	498
3	5001	488

prune301.0ms

Filtered

78 candidates to 62 candidates (79.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	70	8	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	8	79

Merged error: 6.0b

Counts

79 → 8

localize118.0ms

Local error

Found 4 expressions with local error:

6.5b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

5.0ms	(- (- 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)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
72.0ms	(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)))

simplify191.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	283	1391
1	998	1121
2	4723	1013
3	5001	1013

prune393.0ms

Filtered

100 candidates to 83 candidates (83.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	100	8	108

Merged error: 6.0b

Counts

108 → 8

localize123.0ms

Local error

Found 4 expressions with local error:

14.3b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

5.0ms	(+ (- 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)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify119.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	249	756
1	969	641
2	4038	626
3	5001	624

prune384.0ms

Filtered

88 candidates to 79 candidates (89.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	88	8	96

Merged error: 6.0b

Counts

96 → 8

localize123.0ms

Local error

Found 4 expressions with local error:

7.5b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

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)))
4.0ms	(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))))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
95.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (42.0ms)

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

prune404.0ms

Filtered

95 candidates to 79 candidates (83.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	95	8	103

Merged error: 6.0b

Counts

103 → 8

regimes226.0ms

Accuracy

93.3% (0.9b remaining)

Error of 8.8b against oracle of 7.9b and baseline of 20.6b

bsearch236.0ms

Steps

Iters	Range		Point
10	1.5450168366677492e+128	2.0521185469434633e+142	1.026832803109243e+130
11	-3.334524116472281e+99	-2.3662890435539516e+79	-1.599359189869806e+99

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	58
1	48	58

end0.0ms

sample1.1s

Algorithm

intervals

Results

636.0ms	8703×	body	80	valid
205.0ms	2967×	body	80	nan