Details

sample55.0ms

Algorithm

intervals

Results

24.0ms	271×	body	80	valid
7.0ms	85×	body	80	nan

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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 (100.0%)

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: 20.9b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
1.2b	(- (* b b) (* (* 4.0 a) c))
26.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite15.0ms

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 → 54

Calls

4 calls:

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

series48.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify81.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	147	474
1	570	446
2	2550	444
3	5001	442

prune148.0ms

Filtered

66 candidates to 50 candidates (24.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	60	6	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	6	67

Merged error: 9.9b

Counts

67 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

6.9b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
26.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

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))))))
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)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	227	677
1	876	574
2	3665	562
3	5003	558

prune202.0ms

Filtered

70 candidates to 59 candidates (15.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	70	6	76

Merged error: 9.9b

Counts

76 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

26.0b	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
26.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

16.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series95.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
25.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
27.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify229.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	364	1885
1	978	1835
2	4976	1803
3	5001	1803

prune281.0ms

Filtered

101 candidates to 68 candidates (32.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	100	7	107

Merged error: 9.9b

Counts

107 → 7

localize32.0ms

Local error

Found 4 expressions with local error:

26.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

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

series82.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	218	606
1	674	574
2	2668	560
3	5001	542

prune257.0ms

Filtered

68 candidates to 58 candidates (14.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	68	7	75

Merged error: 9.9b

Counts

75 → 7

regimes241.0ms

Accuracy

91.6% (1.0b remaining)

Error of 9.4b against oracle of 8.4b and baseline of 20.2b

bsearch67.0ms

Steps

Iters	Range		Point
7	1.5733488064158731e+78	9.799352262304037e+79	9.109874728808996e+79
9	-8.657529771733274e+163	-9.656827315989575e+158	-9.79759349843333e+158

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	72
1	55	72

end0.0ms

sample1.3s

Algorithm

intervals

Results

759.0ms	8553×	body	80	valid
226.0ms	2609×	body	80	nan

Details

sample55.0ms

simplify16.0ms

prune4.0ms

localize26.0ms

rewrite15.0ms

series48.0ms

simplify81.0ms

prune148.0ms

localize26.0ms

rewrite16.0ms

series64.0ms

simplify113.0ms

prune202.0ms

localize26.0ms

rewrite33.0ms

series95.0ms

simplify229.0ms

prune281.0ms

localize32.0ms

rewrite15.0ms

series82.0ms

simplify80.0ms

prune257.0ms

regimes241.0ms

bsearch67.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling