Details

sample3.9s

Algorithm

intervals

sampling

Space saved by range analysis: 51.314837%

Space saved by search: 51.314837%

Guaranteed chance to sample good point: 74.54834%

Results

10.0ms	195×	body	80	valid
8.0ms	256×	pre	80	true
6.0ms	24×	body	1280	valid
5.0ms	17×	body	2560	valid
2.0ms	10×	body	640	valid
2.0ms	9×	body	320	valid
0.0ms	1×	body	160	valid

simplify9.0ms

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

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: 13.2b

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))))
0.5b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite30.0ms

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:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
11.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
11.0ms	(/ 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)))

simplify145.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	278	822
1	1014	772
2	4232	757
3	5001	757

prune199.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	80	11	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	11	92

Merged error: 12.9b

Counts

92 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.5b	(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
3.0b	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
36×	`add-sqr-sqrt` `times-frac`
35×	`add-cube-cbrt`
26×	`log-pow`
24×	`exp-prod` `sqrt-prod`
7×	`pow1`
6×	`add-exp-log` `log-prod` `sqrt-div` `associate-/r*` `add-cbrt-cube`
5×	`add-log-exp`
4×	`flip3-+` `associate-/r/` `flip-+`
3×	`associate-+r+` `associate-/l*`
2×	`div-inv` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `sum-log`

Counts

4 → 108

Calls

4 calls:

7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
16.0ms	(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
9.0ms	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
14.0ms	(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
9.0ms	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify71.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	308	1094
1	803	1021
2	2268	1001
3	5002	998

prune246.0ms

Filtered

87 candidates to 120 candidates (-37.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	120	11	131

Merged error: 12.9b

Counts

131 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

3.0b	(log (sqrt (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
3.0b	(log (sqrt (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

54×	`log-pow`
52×	`sqrt-pow1`
48×	`exp-prod`
38×	`add-sqr-sqrt`
36×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
30×	`sqrt-prod`
12×	`log-prod`
10×	`pow1`
8×	`sqrt-div`
6×	`add-exp-log`
4×	`flip3-+` `pow1/2` `associate-/r/` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp` `div-inv`

Counts

4 → 112

Calls

4 calls:

11.0ms	(log (sqrt (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
11.0ms	(log (sqrt (exp (/ 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)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(log (sqrt (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
22.0ms	(log (sqrt (exp (/ x (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)))

simplify109.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 4 (97.0ms)

Iter	Nodes	Cost
0	218	1116
1	499	1028
2	1322	1008
3	3216	1008
4	5001	1006

prune407.0ms

Filtered

94 candidates to 124 candidates (-31.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	123	12	135

Merged error: 12.9b

Counts

135 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

3.0b	(log (sqrt (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

28×	`sqrt-pow1`
27×	`log-pow`
25×	`add-sqr-sqrt`
24×	`exp-prod`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`sqrt-prod`
18×	`times-frac`
9×	`pow1`
8×	`sqrt-div`
6×	`log-prod`
5×	`add-exp-log`
4×	`flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square`
2×	`associate-/r/`
1×	`rem-log-exp` `div-inv`

Counts

4 → 86

Calls

4 calls:

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

series45.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(log (sqrt (exp (/ x (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)))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify106.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 4 (97.0ms)

Iter	Nodes	Cost
0	218	808
1	499	756
2	1322	744
3	3216	744
4	5001	743

prune332.0ms

Filtered

77 candidates to 98 candidates (-27.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	3	7	10
Picked	0	1	1
Done	1	0	1
Total	99	11	110

Merged error: 12.9b

Counts

110 → 11

regimes251.0ms

Accuracy

0% (0.5b remaining)

Error of 13.2b against oracle of 12.7b and baseline of 13.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	29
1	34	29

end0.0ms

sample5.3s

Algorithm

intervals

sampling

Space saved by range analysis: 51.314837%

Space saved by search: 51.314837%

Guaranteed chance to sample good point: 74.54834%

Results

320.0ms	6049×	body	80	valid
259.0ms	788×	body	2560	valid
165.0ms	627×	body	1280	valid
144.0ms	8000×	pre	80	true
59.0ms	284×	body	640	valid
26.0ms	175×	body	320	valid
8.0ms	77×	body	160	valid

Details

sample3.9s

simplify9.0ms

prune3.0ms

localize11.0ms

rewrite30.0ms

series37.0ms

simplify145.0ms

prune199.0ms

localize14.0ms

rewrite41.0ms

series39.0ms

simplify71.0ms

prune246.0ms

localize21.0ms

rewrite37.0ms

series62.0ms

simplify109.0ms

prune407.0ms

localize24.0ms

rewrite31.0ms

series45.0ms

simplify106.0ms

prune332.0ms

regimes251.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample5.3s

Profiling