Details

sample47.0ms

Algorithm

intervals

Results

10.0ms	192×	body	80	valid
9.0ms	29×	body	2560	valid
9.0ms	20×	body	1280	valid
5.0ms	256×	pre	80	true
1.0ms	9×	body	320	valid
1.0ms	5×	body	640	valid
0.0ms	1×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	9
1	34	9
2	38	9
3	40	9
4	41	9
5	41	9

prune2.0ms

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: 13.1b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* (* 4.0 p) p) (* x x))
281.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
78.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify92.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	242	529
1	853	492
2	2977	488
3	5002	487

prune167.0ms

Filtered

63 candidates to 52 candidates (82.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	55	8	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	8	64

Merged error: 12.9b

Counts

64 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
0.8b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
9×	`pow1`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`log-pow`
4×	`add-exp-log` `log-prod` `exp-prod` `sqrt-prod` `add-cbrt-cube`
3×	`sqrt-pow1`
2×	`flip3-+` `pow1/2` `sqrt-div` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `rem-log-exp` `exp-sum` `pow-prod-down` `sum-log`

Counts

4 → 55

Calls

4 calls:

13.0ms	(sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
13.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

277.0ms	(sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
80.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
86.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify108.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	214	565
1	600	511
2	1473	510
3	3520	510
4	5001	510

prune213.0ms

Filtered

67 candidates to 56 candidates (83.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	61	6	67
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	64	11	75

Merged error: 12.9b

Counts

75 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(log (exp (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
0.8b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `log-pow`
9×	`add-cube-cbrt`
8×	`exp-prod`
7×	`pow1` `log-prod`
6×	`add-log-exp`
4×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
2×	`flip3-+` `sqrt-div` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `exp-sum` `sum-log`

Counts

4 → 60

Calls

4 calls:

2.0ms	(log (exp (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
13.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
17.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(log (exp (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
80.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
78.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify120.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	234	706
1	625	621
2	1501	620
3	3573	620
4	5001	620

prune271.0ms

Filtered

72 candidates to 62 candidates (86.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	72	11	83

Merged error: 12.9b

Counts

83 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

8.1b	(log (exp (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
8.1b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`sqrt-prod` `add-log-exp`
5×	`log-pow`
4×	`add-exp-log` `log-prod` `exp-prod` `sqrt-div` `add-cbrt-cube`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out`
1×	`+-commutative` `rem-log-exp` `exp-sum` `sum-log`

Counts

4 → 59

Calls

4 calls:

12.0ms	(log (exp (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
10.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
6.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(log (exp (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
79.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify139.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	198	873
1	629	785
2	1806	762
3	4882	762
4	5003	762

prune292.0ms

Filtered

71 candidates to 61 candidates (85.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	73	9	82

Merged error: 12.9b

Counts

82 → 9

regimes269.0ms

Accuracy

0% (1.3b remaining)

Error of 14.2b against oracle of 12.9b and baseline of 14.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms

sample1.1s

Algorithm

intervals

Results

300.0ms	6012×	body	80	valid
256.0ms	845×	body	2560	valid
154.0ms	616×	body	1280	valid
148.0ms	8000×	pre	80	true
56.0ms	294×	body	640	valid
24.0ms	168×	body	320	valid
6.0ms	65×	body	160	valid