Details

sample43.0ms

Algorithm

intervals

Results

10.0ms	192×	body	80	valid
9.0ms	29×	body	2560	valid
5.0ms	20×	body	1280	valid
5.0ms	256×	pre	80	true
1.0ms	9×	body	320	valid
1.0ms	5×	body	640	valid
0.0ms	1×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	40	9
2	48	9
3	50	9
4	52	9
5	53	9
6	53	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: 13.1b

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)))))))
0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `*-un-lft-identity` `add-log-exp`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
4×	`add-exp-log` `expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 63

Calls

4 calls:

9.0ms	(+ (* (* 4.0 p) p) (* x x))
13.0ms	(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)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* (* 4.0 p) p) (* x x))
269.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
74.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify97.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	260	581
1	922	542
2	3335	537
3	5001	533

prune225.0ms

Filtered

75 candidates to 64 candidates (85.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	66	9	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	9	76

Merged error: 12.9b

Counts

76 → 9

localize20.0ms

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)))))))))
0.8b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
9×	`pow1` `add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`log-pow`
4×	`add-exp-log` `expm1-log1p-u` `log-prod` `exp-prod` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `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 → 66

Calls

4 calls:

16.0ms	(sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
14.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
13.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

277.0ms	(sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
77.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
77.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify118.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 4 (110.0ms)

Iter	Nodes	Cost
0	231	632
1	667	576
2	1681	575
3	4254	574
4	5001	566

prune259.0ms

Filtered

78 candidates to 67 candidates (85.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	75	12	87

Merged error: 12.9b

Counts

87 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(log (exp (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
0.8b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `log-pow`
8×	`exp-prod`
7×	`pow1` `log-prod`
6×	`add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def`
2×	`flip3-+` `sqrt-div` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `exp-sum` `sum-log`

Counts

4 → 71

Calls

4 calls:

2.0ms	(log (exp (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
13.0ms	(log (exp (+ 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)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(log (exp (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
77.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
76.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify118.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 4 (109.0ms)

Iter	Nodes	Cost
0	251	777
1	692	690
2	1709	689
3	4299	688
4	5001	680

prune321.0ms

Filtered

83 candidates to 73 candidates (88.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	77	6	83
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	83	12	95

Merged error: 12.9b

Counts

95 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

8.1b	(log (exp (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
8.1b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
7×	`pow1`
6×	`sqrt-prod` `add-log-exp`
5×	`log-pow`
4×	`add-exp-log` `expm1-log1p-u` `log-prod` `exp-prod` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out`
1×	`+-commutative` `rem-log-exp` `exp-sum` `sum-log`

Counts

4 → 70

Calls

4 calls:

14.0ms	(log (exp (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
10.0ms	(+ 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)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(log (exp (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
77.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
52.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	213	966
1	693	867
2	2020	844
3	5001	834

prune344.0ms

Filtered

82 candidates to 72 candidates (87.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	84	10	94

Merged error: 12.9b

Counts

94 → 10

regimes301.0ms

Accuracy

0% (1.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms

sample1.1s

Algorithm

intervals

Results

304.0ms	6012×	body	80	valid
263.0ms	845×	body	2560	valid
152.0ms	616×	body	1280	valid
139.0ms	8000×	pre	80	true
59.0ms	294×	body	640	valid
24.0ms	168×	body	320	valid
7.0ms	65×	body	160	valid