Details

sample1.3s

Algorithm

intervals

Results

11.0ms	194×	body	80	valid
9.0ms	27×	body	2560	valid
7.0ms	14×	body	1280	valid
6.0ms	10×	body	640	valid
5.0ms	256×	pre	80	true
1.0ms	6×	body	320	valid
1.0ms	5×	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: 12.6b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite38.0ms

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:

8.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 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)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
31.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify73.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (63.0ms)

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

prune196.0ms

Filtered

71 candidates to 93 candidates (-31.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	82	11	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	11	94

Merged error: 12.3b

Counts

94 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.3b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

13.0ms	(sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
11.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify106.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	214	565
1	600	511
2	1473	510
3	3520	510
4	5001	510

prune164.0ms

Filtered

57 candidates to 67 candidates (-17.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	67	11	78

Merged error: 12.3b

Counts

78 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.8b	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `*-un-lft-identity`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`sqrt-prod` `log-pow`
4×	`add-exp-log` `exp-prod` `sqrt-div` `add-cbrt-cube`
3×	`log-prod` `sqrt-pow1` `flip3-+` `flip-+`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `rem-log-exp` `pow-prod-down` `sum-log` `distribute-lft-out`

Counts

4 → 56

Calls

4 calls:

12.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
2.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ 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)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
32.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ 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)))

simplify118.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	234	637
1	607	590
2	1618	589
3	4163	589
4	5001	589

prune190.0ms

Filtered

60 candidates to 68 candidates (-13.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	66	13	79

Merged error: 12.3b

Counts

79 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

1.7b	(log (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
1.7b	(log (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

2.0ms	(log (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.0ms	(log (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series140.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(log (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
64.0ms	(log (cbrt (exp (sqrt (* 0.5 (+ 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)))

simplify149.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	163	876
1	388	786
2	1092	786
3	3154	786
4	5002	786

prune254.0ms

Filtered

60 candidates to 74 candidates (-23.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	67	7	74
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	74	13	87

Merged error: 12.3b

Counts

87 → 13

regimes716.0ms

Accuracy

0% (1.3b remaining)

Error of 14.2b against oracle of 12.9b and baseline of 14.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	53
1	34	53

end0.0ms

sample2.8s

Algorithm

intervals

Results

361.0ms	6050×	body	80	valid
275.0ms	803×	body	2560	valid
168.0ms	605×	body	1280	valid
145.0ms	8000×	pre	80	true
62.0ms	290×	body	640	valid
27.0ms	169×	body	320	valid
9.0ms	83×	body	160	valid

Details

sample1.3s

simplify9.0ms

prune3.0ms

localize11.0ms

rewrite38.0ms

series62.0ms

simplify73.0ms

prune196.0ms

localize14.0ms

rewrite45.0ms

series64.0ms

simplify106.0ms

prune164.0ms

localize14.0ms

rewrite32.0ms

series82.0ms

simplify118.0ms

prune190.0ms

localize20.0ms

rewrite34.0ms

series140.0ms

simplify149.0ms

prune254.0ms

regimes716.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.8s

Profiling