Details

sample58.0ms

Algorithm

intervals

Results

33.0ms	83×	body	10240	exit
10.0ms	271×	body	80	valid
2.0ms	3×	body	1280	valid
2.0ms	6×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	23	5
3	23	5

prune2.0ms

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: 0.3b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.3b	(log (+ 1.0 (exp x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod`
6×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-div` `fma-neg` `prod-diff` `associate--l+`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `sum-log` `flip--`

Counts

3 → 62

Calls

3 calls:

3.0ms	(+ 1.0 (exp x))
6.0ms	(- (log (+ 1.0 (exp x))) (* x y))
3.0ms	(log (+ 1.0 (exp x)))

series127.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ 1.0 (exp x))
60.0ms	(- (log (+ 1.0 (exp x))) (* x y))
60.0ms	(log (+ 1.0 (exp x)))

simplify57.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	236	404
1	702	369
2	2284	367
3	5002	340

prune164.0ms

Filtered

71 candidates to 54 candidates (76.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	3	72

Merged error: 0.2b

Counts

72 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (expm1 (log1p (log (+ 1.0 (exp x))))) (* x y))
0.0b	(+ 1.0 (exp x))
0.0b	(expm1 (log1p (log (+ 1.0 (exp x)))))
0.3b	(log (+ 1.0 (exp x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `log-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `fma-neg` `prod-diff`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out` `expm1-udef`
1×	`+-commutative` `associate--l-` `sub-neg` `expm1-log1p` `flip3--` `diff-log` `rem-log-exp` `sum-log` `log-pow` `flip--`

Counts

4 → 66

Calls

4 calls:

3.0ms	(- (expm1 (log1p (log (+ 1.0 (exp x))))) (* x y))
4.0ms	(+ 1.0 (exp x))
1.0ms	(expm1 (log1p (log (+ 1.0 (exp x)))))
3.0ms	(log (+ 1.0 (exp x)))

series507.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(- (expm1 (log1p (log (+ 1.0 (exp x))))) (* x y))
13.0ms	(+ 1.0 (exp x))
221.0ms	(expm1 (log1p (log (+ 1.0 (exp x)))))
64.0ms	(log (+ 1.0 (exp x)))

simplify88.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	309	497
1	985	433
2	3700	425
3	5001	418

prune208.0ms

Filtered

78 candidates to 60 candidates (76.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	78	3	81

Merged error: 0.2b

Counts

81 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
0.0b	(fma 1/2 (pow x 2) (+ x 2.0))
8.5b	(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `log-prod`
4×	`add-exp-log` `fma-neg` `prod-diff` `add-log-exp`
3×	`expm1-log1p-u` `associate--l+` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `fma-udef`

Counts

3 → 49

Calls

3 calls:

7.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
1.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

series143.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
17.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
50.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	229	423
1	763	380
2	3267	376
3	5001	356

prune151.0ms

Filtered

58 candidates to 46 candidates (79.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	58	3	61

Merged error: 0.2b

Counts

61 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

1.3b	(cbrt (log (fma 1/2 (pow x 2) (+ x 2.0))))
8.5b	(log (fma 1/2 (pow x 2) (+ x 2.0)))
8.5b	(log (fma 1/2 (pow x 2) (+ x 2.0)))
8.5b	(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-prod`
8×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`add-exp-log`
4×	`cbrt-prod` `expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
1×	`pow1/3`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt (log (fma 1/2 (pow x 2) (+ x 2.0))))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt (log (fma 1/2 (pow x 2) (+ x 2.0))))
49.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))
55.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))
50.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify143.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (135.0ms)

Iter	Nodes	Cost
0	307	613
1	1079	545
2	4907	517
3	5001	514

prune253.0ms

Filtered

68 candidates to 57 candidates (83.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	68	3	71

Merged error: 0.2b

Counts

71 → 3

regimes43.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	7
1	12	7

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.0s	2506×	body	10240	exit
306.0ms	8428×	body	80	valid
69.0ms	251×	body	640	valid
58.0ms	116×	body	1280	valid
28.0ms	179×	body	320	valid
10.0ms	105×	body	160	valid