Details

sample46.0ms

Algorithm

intervals

Results

10.0ms	194×	body	80	valid
7.0ms	25×	body	2560	valid
4.0ms	256×	pre	80	true
4.0ms	17×	body	1280	valid
2.0ms	11×	body	640	valid
1.0ms	6×	body	160	valid
0.0ms	3×	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

prune4.0ms

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: 13.4b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite39.0ms

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:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* (* 4.0 p) p) (* x x))
295.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
80.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify89.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (82.0ms)

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

prune289.0ms

Filtered

63 candidates to 52 candidates (82.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	55	8	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	8	64

Merged error: 13.1b

Counts

64 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))) 3))
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))) 3)
1.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
13×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
9×	`pow1`
8×	`unpow-prod-down` `cube-prod`
7×	`sqrt-prod`
6×	`sqrt-div` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`cube-div` `pow-pow` `flip3-+` `associate-*r/` `flip-+`
3×	`pow-unpow` `sqrt-pow1`
2×	`cube-mult` `cbrt-div` `pow1/2` `unpow3` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `pow1/3` `pow-prod-down` `pow-exp` `sum-log` `sqrt-pow2` `rem-cbrt-cube` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 83

Calls

4 calls:

3.0ms	(cbrt (pow (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))) 3))
14.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))) 3)
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series979.0ms

Counts

4 → 12

Calls

4 calls:

297.0ms	(cbrt (pow (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))) 3))
537.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))) 3)
83.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	343	1068
1	1150	1033
2	5001	1025

prune373.0ms

Filtered

95 candidates to 64 candidates (67.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	89	6	95
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	92	11	103

Merged error: 13.1b

Counts

103 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (sqrt (* 0.5 (+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))) 3)
8.2b	(+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
16.2b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
16.2b	(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`pow1`
6×	`cbrt-prod` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`unpow-prod-down` `cbrt-div` `pow-pow` `flip3-+` `cube-prod` `flip-+`
3×	`pow-unpow`
2×	`cube-div` `sqrt-pow1` `pow1/3` `sqrt-div` `associate-*r/` `sqrt-prod`
1×	`+-commutative` `cube-mult` `pow-to-exp` `pow1/2` `unpow3` `pow-prod-down` `pow-exp` `sum-log` `sqrt-pow2` `distribute-lft-out` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 69

Calls

4 calls:

14.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))) 3)
6.0ms	(+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

series1.4s

Counts

4 → 12

Calls

4 calls:

961.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))) 3)
163.0ms	(+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
143.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
141.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify86.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	750	1616
1	3371	1540
2	5002	1532

prune539.0ms

Filtered

81 candidates to 64 candidates (79.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	75	6	81
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	80	12	92

Merged error: 13.1b

Counts

92 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

8.2b	(+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
8.3b	(log (exp (+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))))
16.2b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
16.2b	(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

6.0ms	(+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms	(log (exp (+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))))
5.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

series624.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
168.0ms	(log (exp (+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))))
139.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
148.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	342	1044
1	1243	938
2	5001	930

prune465.0ms

Filtered

67 candidates to 61 candidates (91.0%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	62	5	67
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	63	16	79

Merged error: 13.1b

Counts

79 → 16

regimes949.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	42
1	34	42

end0.0ms

sample1.2s

Algorithm

intervals

Results

304.0ms	6055×	body	80	valid
245.0ms	810×	body	2560	valid
143.0ms	579×	body	1280	valid
130.0ms	8000×	pre	80	true
60.0ms	315×	body	640	valid
24.0ms	155×	body	320	valid
8.0ms	86×	body	160	valid

Details

sample46.0ms

simplify8.0ms

prune4.0ms

localize11.0ms

rewrite39.0ms

series470.0ms

simplify89.0ms

prune289.0ms

localize15.0ms

rewrite37.0ms

series979.0ms

simplify44.0ms

prune373.0ms

localize19.0ms

rewrite32.0ms

series1.4s

simplify86.0ms

prune539.0ms

localize23.0ms

rewrite25.0ms

series624.0ms

simplify41.0ms

prune465.0ms

regimes949.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling