Details

analyze823.0ms

Algorithm: search

sample42.0ms

Algorithm

intervals

Results

11.0ms	202×	body	80	valid
7.0ms	21×	body	2560	valid
5.0ms	12×	body	640	valid
5.0ms	256×	pre	80	true
4.0ms	16×	body	1280	valid
0.0ms	3×	body	320	valid
0.0ms	2×	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: 10.8b

Counts

2 → 1

localize13.0ms

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)))))
17.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite31.0ms

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))))
12.0ms	(+ 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:

8.0ms	(+ (* (* 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)))

simplify147.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (26.0ms)

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

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: 10.6b

Counts

92 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b	(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.8b	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
17.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite43.0ms

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)))))))
10.0ms	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify68.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 3 (57.0ms)

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

prune270.0ms

Filtered

87 candidates to 120 candidates (-37.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	119	11	130

Merged error: 10.6b

Counts

130 → 11

localize28.0ms

Local error

Found 4 expressions with local error:

1.8b	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
17.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

10.0ms	(log (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)))

series34.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
9.0ms	(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)))

simplify107.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 4 (98.0ms)

Iter	Nodes	Cost
0	203	697
1	496	648
2	1346	638
3	3288	638
4	5001	637

prune668.0ms

Filtered

73 candidates to 93 candidates (-27.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	93	11	104

Merged error: 10.6b

Counts

104 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

1.9b	(log (sqrt (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.9b	(log (sqrt (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
17.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite38.0ms

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:

12.0ms	(log (sqrt (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(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:

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

simplify104.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 4 (93.0ms)

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

prune431.0ms

Filtered

94 candidates to 124 candidates (-31.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	9	1	10
Picked	0	1	1
Done	0	0	0
Total	131	4	135

Merged error: 10.6b

Counts

135 → 4

regimes292.0ms

Accuracy

0% (0.3b remaining)

Error of 13.6b against oracle of 13.4b and baseline of 13.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	22
1	24	22

end0.0ms

analyze816.0ms

Algorithm: search

sample1.2s

Algorithm

intervals

Results

322.0ms	5987×	body	80	valid
282.0ms	849×	body	2560	valid
168.0ms	636×	body	1280	valid
143.0ms	8000×	pre	80	true
65.0ms	309×	body	640	valid
22.0ms	143×	body	320	valid
8.0ms	76×	body	160	valid

Details

analyze823.0ms

sample42.0ms

simplify9.0ms

prune3.0ms

localize13.0ms

rewrite31.0ms

series37.0ms

simplify147.0ms

prune199.0ms

localize17.0ms

rewrite43.0ms

series42.0ms

simplify68.0ms

prune270.0ms

localize28.0ms

rewrite28.0ms

series34.0ms

simplify107.0ms

prune668.0ms

localize18.0ms

rewrite38.0ms

series62.0ms

simplify104.0ms

prune431.0ms

regimes292.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze816.0ms

sample1.2s

Profiling