Details

sample43.0ms

Algorithm

intervals

Results

9.0ms	191×	body	80	valid
8.0ms	25×	body	2560	valid
6.0ms	24×	body	1280	valid
5.0ms	256×	pre	80	true
2.0ms	9×	body	640	valid
1.0ms	7×	body	320	valid

simplify10.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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: 13.6b

Counts

2 → 1

localize15.0ms

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)))))
14.6b	(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:

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

series233.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
33.0ms	(+ (* (* 4.0 p) p) (* x x))
80.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify149.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	278	822
1	1014	772
2	4246	757
3	5001	757

prune253.0ms

Filtered

91 candidates to 67 candidates (73.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	79	12	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	12	92

Merged error: 13.3b

Counts

92 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.5b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
22×	`times-frac`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
14×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
5×	`unswap-sqr`
4×	`flip3-+` `sqrt-div` `prod-exp` `flip-+`
3×	`associate-l`
2×	`+-commutative` `div-exp` `sum-log` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 86

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
14.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* (* 4.0 p) p) (* x x))
53.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
79.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify54.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	387	817
1	1913	734
2	5002	700

prune253.0ms

Filtered

98 candidates to 69 candidates (70.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	93	5	98
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	98	12	110

Merged error: 13.3b

Counts

110 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.3b	(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
2.5b	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

26×	`log-pow`
24×	`exp-prod`
23×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`times-frac`
12×	`sqrt-prod`
7×	`pow1` `add-log-exp`
6×	`log-prod`
4×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+`
3×	`associate-+r+`
2×	`+-commutative` `sum-log` `associate-/r/` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `div-inv`

Counts

4 → 78

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
17.0ms	(+ 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)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* (* 4.0 p) p) (* x x))
73.0ms	(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
65.0ms	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify99.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	303	736
1	957	675
2	3385	662
3	5001	662

prune244.0ms

Filtered

90 candidates to 69 candidates (76.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	90	12	102

Merged error: 13.3b

Counts

102 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

2.6b	(log (sqrt (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
2.6b	(log (sqrt (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.6b	(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:

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)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(log (sqrt (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
126.0ms	(log (sqrt (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify110.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 4 (98.0ms)

Iter	Nodes	Cost
0	218	1114
1	499	1028
2	1322	1008
3	3216	1008
4	5001	1006

prune429.0ms

Filtered

124 candidates to 94 candidates (75.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	124	12	136

Merged error: 13.3b

Counts

136 → 12

regimes193.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	11
1	21	11

end0.0ms

sample1.1s

Algorithm

intervals

Results

304.0ms	6021×	body	80	valid
240.0ms	785×	body	2560	valid
164.0ms	641×	body	1280	valid
140.0ms	8000×	pre	80	true
66.0ms	314×	body	640	valid
20.0ms	143×	body	320	valid
9.0ms	96×	body	160	valid