Details

sample59.0ms

Algorithm

intervals

Results

30.0ms	65×	body	1280	valid
12.0ms	53×	body	640	valid
3.0ms	28×	body	320	valid
2.0ms	90×	body	80	valid
2.0ms	75×	body	80	nan
1.0ms	20×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	2
1	5	2

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: 38.8b

Counts

2 → 1

localize3.0ms

Local error

Found 1 expressions with local error:

5.6b	(log (+ 1.0 x))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log-prod` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `log-div`
1×	`expm1-log1p-u` `flip3-+` `rem-log-exp` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`

Counts

1 → 17

Calls

1 calls:

3.0ms

(log (+ 1.0 x))

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

(log (+ 1.0 x))

simplify40.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	131	99
1	363	89
2	1292	86
3	5002	81

prune40.0ms

Filtered

20 candidates to 15 candidates (75.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	18	2	20
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	3	21

Merged error: 0.1b

Counts

21 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
70×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
36×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp`
4×	`pow1`
3×	`associate-l`
2×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `associate-r/` `pow-prod-down` `-commutative` `fma-udef` `div-inv`

Counts

2 → 122

Calls

2 calls:

23.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
1.0ms	(fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series98.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
43.0ms	(fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	560	763
1	2406	633
2	5001	632

prune241.0ms

Filtered

128 candidates to 81 candidates (63.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	128	3	131

Merged error: 0.1b

Counts

131 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (log (+ 1.0 x)))
5.6b	(log (+ 1.0 x))
5.6b	(log (+ 1.0 x))
5.6b	(log (+ 1.0 x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`log-prod`
8×	`pow1` `add-sqr-sqrt` `add-cube-cbrt`
7×	`add-exp-log`
6×	`log-div`
4×	`cbrt-prod` `expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`pow1/3`

Counts

4 → 65

Calls

4 calls:

1.0ms	(cbrt (log (+ 1.0 x)))
3.0ms	(log (+ 1.0 x))
3.0ms	(log (+ 1.0 x))
3.0ms	(log (+ 1.0 x))

series277.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (log (+ 1.0 x)))
42.0ms	(log (+ 1.0 x))
45.0ms	(log (+ 1.0 x))
43.0ms	(log (+ 1.0 x))

simplify117.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	321	470
1	1028	431
2	4280	399
3	5001	396

prune179.0ms

Filtered

77 candidates to 63 candidates (81.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	77	3	80

Merged error: 0.1b

Counts

80 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

2.2b	(log (exp (cbrt (log (+ 1.0 x)))))
5.6b	(log (+ 1.0 x))
5.6b	(log (+ 1.0 x))
5.6b	(log (+ 1.0 x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
15×	`log-prod`
12×	`log-pow`
10×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`pow1`
7×	`add-exp-log` `exp-prod`
6×	`log-div`
4×	`cbrt-prod` `expm1-log1p-u` `rem-log-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+` `distribute-lft-out`

Counts

4 → 72

Calls

4 calls:

3.0ms	(log (exp (cbrt (log (+ 1.0 x)))))
3.0ms	(log (+ 1.0 x))
3.0ms	(log (+ 1.0 x))
3.0ms	(log (+ 1.0 x))

series276.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(log (exp (cbrt (log (+ 1.0 x)))))
44.0ms	(log (+ 1.0 x))
41.0ms	(log (+ 1.0 x))
45.0ms	(log (+ 1.0 x))

simplify122.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	349	516
1	1066	467
2	4340	435
3	5001	432

prune216.0ms

Filtered

84 candidates to 68 candidates (81.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	84	3	87

Merged error: 0.1b

Counts

87 → 3

regimes77.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 22.1b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.0s	2236×	body	1280	valid
364.0ms	1627×	body	640	valid
95.0ms	814×	body	320	valid
75.0ms	2880×	body	80	valid
52.0ms	2821×	body	80	nan
33.0ms	443×	body	160	valid