Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	192×	body	80	valid
5.0ms	21×	body	2560	valid
4.0ms	22×	body	1280	valid
4.0ms	256×	pre	80	true
1.0ms	11×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	4×	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

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: 14.0b

Counts

2 → 1

localize11.0ms

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)))))))
1.0b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite39.0ms

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))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* (* 4.0 p) p) (* x x))
292.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
77.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify88.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (81.0ms)

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

prune202.0ms

Filtered

63 candidates to 52 candidates (82.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	53	10	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	10	64

Merged error: 13.7b

Counts

64 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

1.6b	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
1.6b	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
12×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*`
7×	`sqrt-prod`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `unpow2` `sqr-pow`
3×	`flip3-+` `div-exp` `associate-/r*` `flip-+` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-exp` `clear-num` `flip--` `div-inv` `distribute-lft-out--`

Counts

4 → 97

Calls

4 calls:

8.0ms	(/ (pow x 2) (+ (* (* 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)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
80.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify54.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	325	1030
1	1289	956
2	5001	954

prune517.0ms

Filtered

109 candidates to 81 candidates (74.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	109	10	119

Merged error: 13.7b

Counts

119 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite25.0ms

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` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify81.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	98	500
1	283	484
2	827	484
3	2050	484
4	5001	484

prune533.0ms

Filtered

72 candidates to 64 candidates (88.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	71	11	82

Merged error: 13.7b

Counts

82 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.6b	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
1.0b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

12.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
2.0ms	(log (exp (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)))

series724.0ms

Counts

4 → 12

Calls

4 calls:

292.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
292.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
81.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify125.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	234	637
1	607	590
2	1618	589
3	4163	589
4	5001	589

prune233.0ms

Filtered

68 candidates to 60 candidates (88.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	66	13	79

Merged error: 13.7b

Counts

79 → 13

regimes473.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	11
1	22	11

end0.0ms

sample826.0ms

Algorithm

intervals

Results

216.0ms	6044×	body	80	valid
174.0ms	791×	body	2560	valid
108.0ms	8000×	pre	80	true
107.0ms	613×	body	1280	valid
41.0ms	303×	body	640	valid
17.0ms	171×	body	320	valid
5.0ms	78×	body	160	valid