Details

analyze797.0ms

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

sample35.0ms

Algorithm

intervals

Results

11.0ms	208×	body	80	valid
4.0ms	14×	body	2560	valid
4.0ms	256×	pre	80	true
3.0ms	14×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify4.0ms

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: 10.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite36.0ms

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:

9.0ms	(+ (* (* 4.0 p) p) (* x x))
8.0ms	(/ 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)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify38.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4994	1385
1	4994	1385

prune204.0ms

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: 10.2b

Counts

92 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ x (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))
6.7b	(+ 1.0 (/ (/ x (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.5b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
30×	`add-sqr-sqrt` `*-un-lft-identity`
28×	`add-cube-cbrt`
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` `distribute-lft-out`

Counts

4 → 95

Calls

4 calls:

13.0ms	(/ x (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))
70.0ms	(+ 1.0 (/ (/ x (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify66.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5020	1779

prune279.0ms

Filtered

78 candidates to 107 candidates (-37.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	107	10	117

Merged error: 10.2b

Counts

117 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

2.8b	(+ 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)))))))
15.5b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.5b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.5b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite24.0ms

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)))

series39.0ms

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)))

simplify34.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5159	810

prune221.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	67	11	78

Merged error: 10.2b

Counts

78 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

7.2b	(+ 1.0 (/ (/ (/ x (sqrt (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.5b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.5b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite919.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `sqrt-prod`
7×	`pow1` `add-cube-cbrt`
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` `distribute-lft-out`

Counts

4 → 57

Calls

4 calls:

900.0ms	(+ 1.0 (/ (/ (/ x (sqrt (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (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)))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ 1.0 (/ (/ (/ x (sqrt (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify68.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4923	876
1	4923	876

prune203.0ms

Filtered

59 candidates to 69 candidates (-16.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	69	11	80

Merged error: 10.2b

Counts

80 → 11

regimes161.0ms

Accuracy

0% (0.8b remaining)

Error of 14.0b against oracle of 13.1b and baseline of 14.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	49
1	26	49

end0.0ms

sample1.1s

Algorithm

intervals

Results

309.0ms	5999×	body	80	valid
262.0ms	839×	body	2560	valid
158.0ms	600×	body	1280	valid
138.0ms	8000×	pre	80	true
64.0ms	324×	body	640	valid
22.0ms	152×	body	320	valid
8.0ms	86×	body	160	valid

Details

analyze797.0ms

sample35.0ms

simplify4.0ms

prune6.0ms

localize11.0ms

rewrite36.0ms

series35.0ms

simplify38.0ms

prune204.0ms

localize19.0ms

rewrite98.0ms

series56.0ms

simplify66.0ms

prune279.0ms

localize27.0ms

rewrite24.0ms

series39.0ms

simplify34.0ms

prune221.0ms

localize26.0ms

rewrite919.0ms

series39.0ms

simplify68.0ms

prune203.0ms

regimes161.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling