Details

analyze967.0ms

Algorithm

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

sample36.0ms

Algorithm

intervals

Results

11.0ms	208×	body	80	valid
6.0ms	20×	body	2560	valid
4.0ms	256×	pre	80	true
4.0ms	17×	body	1280	valid
2.0ms	9×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	38	17
1	38	17

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 9.9b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `flip-+`
3×	`associate-/l*`
2×	`+-commutative` `sum-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 79

Calls

4 calls:

7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
5.0ms	(+ (* (* 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)))

series34.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
6.0ms	(+ (* (* 4.0 p) p) (* x x))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify32.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4994	1385
1	4994	1385

prune194.0ms

Filtered

71 candidates to 91 candidates (-28.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	81	10	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	10	92

Merged error: 9.7b

Counts

92 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

4.0b	(+ 1.0 (* (* (cbrt x) (/ (cbrt x) (* (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x))))))) (/ (cbrt x) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
14.7b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
14.7b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
14.7b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

4.0ms	(+ 1.0 (* (* (cbrt x) (/ (cbrt x) (* (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x))))))) (/ (cbrt x) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ 1.0 (* (* (cbrt x) (/ (cbrt x) (* (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x))))))) (/ (cbrt x) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify29.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5159	810

prune206.0ms

Filtered

57 candidates to 68 candidates (-19.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	68	10	78

Merged error: 9.7b

Counts

78 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ x (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))
6.2b	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x))))) (/ x (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
14.7b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
14.7b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`associate-/r*`
8×	`sqrt-div`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 94

Calls

4 calls:

10.0ms	(/ x (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))
3.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x))))) (/ x (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ x (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))
12.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x))))) (/ x (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify67.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5019	1773

prune325.0ms

Filtered

76 candidates to 106 candidates (-39.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	105	11	116

Merged error: 9.7b

Counts

116 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

6.4b	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x))))) (* (* (cbrt x) (/ (cbrt x) (fabs (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x))))))) (/ (cbrt x) (sqrt (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))))
14.7b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
14.7b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
14.7b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

5.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x))))) (* (* (cbrt x) (/ (cbrt x) (fabs (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x))))))) (/ (cbrt x) (sqrt (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series97.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x))))) (* (* (cbrt x) (/ (cbrt x) (fabs (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x))))))) (/ (cbrt x) (sqrt (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
7.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4960	1337
1	4960	1337

prune241.0ms

Filtered

57 candidates to 68 candidates (-19.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	3	5	8
Picked	0	1	1
Done	1	1	2
Total	70	9	79

Merged error: 9.7b

Counts

79 → 9

regimes155.0ms

Accuracy

0% (0.7b remaining)

Error of 13.5b against oracle of 12.8b and baseline of 13.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	49
1	26	49

end0.0ms

sample1.1s

Algorithm

intervals

Results

325.0ms	6068×	body	80	valid
251.0ms	803×	body	2560	valid
157.0ms	602×	body	1280	valid
139.0ms	8000×	pre	80	true
60.0ms	299×	body	640	valid
28.0ms	156×	body	320	valid
7.0ms	72×	body	160	valid

Details

analyze967.0ms

sample36.0ms

simplify3.0ms

prune6.0ms

localize16.0ms

rewrite32.0ms

series34.0ms

simplify32.0ms

prune194.0ms

localize25.0ms

rewrite22.0ms

series38.0ms

simplify29.0ms

prune206.0ms

localize17.0ms

rewrite27.0ms

series57.0ms

simplify67.0ms

prune325.0ms

localize29.0ms

rewrite23.0ms

series97.0ms

simplify49.0ms

prune241.0ms

regimes155.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling