Details

sample44.0ms

Algorithm

intervals

Results

20.0ms	277×	body	80	valid
7.0ms	104×	body	80	nan

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	18
1	79	18
2	136	18
3	161	18
4	173	18
5	177	18
6	177	18

prune4.0ms

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: 19.2b

Counts

2 → 1

localize120.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.1b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `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 → 63

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify118.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	246	646
1	890	606
2	3702	588
3	5001	584

prune288.0ms

Filtered

75 candidates to 60 candidates (80.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	67	8	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	8	76

Merged error: 7.2b

Counts

76 → 8

localize120.0ms

Local error

Found 4 expressions with local error:

10.8b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

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)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify115.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	232	680
1	883	574
2	3567	559
3	5001	555

prune285.0ms

Filtered

70 candidates to 59 candidates (84.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	70	8	78

Merged error: 7.2b

Counts

78 → 8

localize121.0ms

Local error

Found 4 expressions with local error:

7.6b	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite21.0ms

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` `flip3--` `add-cbrt-cube` `flip--`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 55

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)))
8.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
96.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
99.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	363	835
1	1402	760
2	5001	731

prune335.0ms

Filtered

67 candidates to 59 candidates (88.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	67	8	75

Merged error: 7.2b

Counts

75 → 8

localize125.0ms

Local error

Found 4 expressions with local error:

21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

3.0ms	(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)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	129	544
1	469	520
2	1914	516
3	5002	508

prune287.0ms

Filtered

72 candidates to 60 candidates (83.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	72	8	80

Merged error: 7.2b

Counts

80 → 8

regimes161.0ms

Accuracy

92.4% (0.9b remaining)

Error of 8.5b against oracle of 7.6b and baseline of 20.1b

bsearch196.0ms

Steps

Iters	Range		Point
8	4.1433580792185867e+68	2.4413096282015733e+73	2.397673767055932e+73
10	-3.534121238636866e+113	-9.206374310818687e+98	-3.461275927006126e+113

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	60
1	50	60

end0.0ms

sample1.1s

Algorithm

intervals

Results

635.0ms	8684×	body	80	valid
205.0ms	2973×	body	80	nan

Details

sample44.0ms

simplify15.0ms

prune4.0ms

localize120.0ms

rewrite29.0ms

series303.0ms

simplify118.0ms

prune288.0ms

localize120.0ms

rewrite17.0ms

series292.0ms

simplify115.0ms

prune285.0ms

localize121.0ms

rewrite21.0ms

series352.0ms

simplify52.0ms

prune335.0ms

localize125.0ms

rewrite16.0ms

series283.0ms

simplify68.0ms

prune287.0ms

regimes161.0ms

bsearch196.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling