Details

analyze787.0ms

Algorithm: search

sample40.0ms

Algorithm

intervals

Results

10.0ms	194×	body	80	valid
9.0ms	28×	body	2560	valid
5.0ms	18×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	14×	body	640	valid
0.0ms	2×	body	320	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

prune5.0ms

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: 13.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

11.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(+ (* (* 4.0 p) p) (* x x))
12.0ms	(sqrt (* 0.5 (+ 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:

12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(+ (* (* 4.0 p) p) (* x x))
34.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify87.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	242	529
1	853	492
2	2977	488
3	5002	487

prune168.0ms

Filtered

52 candidates to 63 candidates (-21.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	53	10	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	10	64

Merged error: 13.3b

Counts

64 → 10

localize15.0ms

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	(exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.0b	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

12.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
2.0ms	(exp (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)))))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series144.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
70.0ms	(exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
33.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify107.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	223	645
1	568	593
2	1473	593
3	3592	593
4	5001	593

prune206.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	67	11	78

Merged error: 13.3b

Counts

78 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series30.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify79.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	98	500
1	283	484
2	827	484
3	2050	484
4	5001	484

prune405.0ms

Filtered

64 candidates to 72 candidates (-12.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	72	11	83

Merged error: 13.3b

Counts

83 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

4.2b	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
6.3b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

2.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
9.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (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)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
12.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
9.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify148.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	219	912
1	605	814
2	1797	791
3	4938	791
4	5001	791

prune239.0ms

Filtered

61 candidates to 70 candidates (-14.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	69	12	81

Merged error: 13.3b

Counts

81 → 12

regimes409.0ms

Accuracy

0% (0.2b remaining)

Error of 13.7b against oracle of 13.5b and baseline of 13.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	36
1	31	36

end0.0ms

analyze777.0ms

Algorithm: search

sample1.2s

Algorithm

intervals

Results

340.0ms	5979×	body	80	valid
279.0ms	813×	body	2560	valid
187.0ms	666×	body	1280	valid
144.0ms	8000×	pre	80	true
74.0ms	340×	body	640	valid
23.0ms	138×	body	320	valid
7.0ms	64×	body	160	valid

Details

analyze787.0ms

sample40.0ms

simplify8.0ms

prune5.0ms

localize11.0ms

rewrite34.0ms

series60.0ms

simplify87.0ms

prune168.0ms

localize15.0ms

rewrite23.0ms

series144.0ms

simplify107.0ms

prune206.0ms

localize25.0ms

rewrite20.0ms

series30.0ms

simplify79.0ms

prune405.0ms

localize17.0ms

rewrite22.0ms

series60.0ms

simplify148.0ms

prune239.0ms

regimes409.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze777.0ms

sample1.2s

Profiling