Details

analyze1.3s

Algorithm

sampling

Space saved by range analysis: 51.36237%

Space saved by search: 51.36237%

Guaranteed chance to sample good point: 74.54834%

sample42.0ms

Algorithm

intervals

Results

10.0ms	191×	body	80	valid
9.0ms	27×	body	2560	valid
7.0ms	25×	body	1280	valid
4.0ms	256×	pre	80	true
1.0ms	5×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify8.0ms

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

prune6.0ms

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	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

12.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 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)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
9.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
11.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify71.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	280	888
1	816	840
2	2486	828
3	5001	827

prune198.0ms

Filtered

71 candidates to 93 candidates (-31.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	83	10	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	10	94

Merged error: 13.0b

Counts

94 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)
0.0b	(cbrt (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
1.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
14×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
8×	`unpow-prod-down` `cube-prod`
6×	`pow1` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
4×	`cube-div` `flip3-+` `flip-+`
3×	`pow-unpow` `sqrt-prod`
2×	`cube-mult` `cbrt-div` `sqrt-div` `unpow3` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `sum-log` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 79

Calls

4 calls:

12.0ms	(pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)
12.0ms	(cbrt (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
11.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)
12.0ms	(cbrt (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
11.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
9.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	271	923
1	1077	868
2	5002	862

prune181.0ms

Filtered

61 candidates to 91 candidates (-49.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	92	9	101

Merged error: 13.0b

Counts

101 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ 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)))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite26.0ms

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:

11.0ms	(+ 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)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series34.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify103.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	167	517
1	465	490
2	1264	489
3	3249	489
4	5001	489

prune260.0ms

Filtered

61 candidates to 69 candidates (-13.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	69	9	78

Merged error: 13.0b

Counts

78 → 9

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)))
13.8b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
13.8b	(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

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

series59.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	179	576
1	478	546
2	1655	542
3	5002	524

prune273.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	68	9	77

Merged error: 13.0b

Counts

77 → 9

regimes206.0ms

Accuracy

0% (0.5b remaining)

Error of 13.4b against oracle of 12.9b and baseline of 13.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	36
1	32	36

end0.0ms

analyze1.3s

Algorithm

sampling

Space saved by range analysis: 51.36237%

Space saved by search: 51.36237%

Guaranteed chance to sample good point: 74.54834%

sample1.1s

Algorithm

intervals

Results

321.0ms	6045×	body	80	valid
249.0ms	781×	body	2560	valid
173.0ms	654×	body	1280	valid
145.0ms	8000×	pre	80	true
61.0ms	302×	body	640	valid
22.0ms	148×	body	320	valid
7.0ms	70×	body	160	valid

Details

analyze1.3s

sample42.0ms

simplify8.0ms

prune6.0ms

localize11.0ms

rewrite37.0ms

series60.0ms

simplify71.0ms

prune198.0ms

localize14.0ms

rewrite42.0ms

series55.0ms

simplify41.0ms

prune181.0ms

localize15.0ms

rewrite26.0ms

series34.0ms

simplify103.0ms

prune260.0ms

localize28.0ms

rewrite21.0ms

series59.0ms

simplify60.0ms

prune273.0ms

regimes206.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.3s

sample1.1s

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