Details

sample135.0ms

Algorithm

intervals

Results

67.0ms	50×	body	2560	valid
41.0ms	95×	body	1280	valid
12.0ms	54×	body	640	valid
5.0ms	33×	body	320	valid
1.0ms	11×	body	160	valid
1.0ms	13×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

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: 30.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
2.1b	(- 1.0 (cos x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series60.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	292	569
1	965	460
2	5002	460

prune168.0ms

Filtered

74 candidates to 51 candidates (68.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	62	12	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	12	75

Merged error: 0.1b

Counts

75 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.7b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.1b	(- 1.0 (cos x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
40×	`add-cube-cbrt`
38×	`exp-prod`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`prod-diff`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 132

Calls

4 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series138.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
40.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
40.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 1.0 (cos x))

simplify43.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	368	1009
1	1099	873
2	5002	871

prune303.0ms

Filtered

144 candidates to 101 candidates (70.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	144	12	156

Merged error: 0.1b

Counts

156 → 12

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.1b	(/ (sin x) (- 1.0 (cos x)))
2.1b	(- 1.0 (cos x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
112×	`add-sqr-sqrt` `*-un-lft-identity`
78×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
9×	`prod-diff`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 177

Calls

3 calls:

9.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
7.0ms	(/ (sin x) (- 1.0 (cos x)))
5.0ms	(- 1.0 (cos x))

series96.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
34.0ms	(/ (sin x) (- 1.0 (cos x)))
22.0ms	(- 1.0 (cos x))

simplify70.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	572	1779
1	2636	1549
2	5001	1441

prune245.0ms

Filtered

186 candidates to 98 candidates (52.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	183	3	186
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	184	14	198

Merged error: 0.1b

Counts

198 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (- 1.0 (cos x)))
0.1b	(/ (expm1 (log1p (- 1.0 (cos x)))) (sin x))
0.2b	(expm1 (log1p (- 1.0 (cos x))))
2.1b	(- 1.0 (cos x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
9×	`times-frac` `prod-diff`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`expm1-log1p-u`
4×	`pow1` `log1p-expm1-u`
3×	`fma-neg` `associate-/r` `associate-/l`
2×	`expm1-udef`
1×	`cbrt-undiv` `sub-neg` `log1p-udef` `expm1-log1p` `flip3--` `frac-2neg` `diff-log` `div-sub` `log1p-expm1` `div-exp` `clear-num` `flip--` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 80

Calls

4 calls:

1.0ms	(log1p (- 1.0 (cos x)))
3.0ms	(/ (expm1 (log1p (- 1.0 (cos x)))) (sin x))
1.0ms	(expm1 (log1p (- 1.0 (cos x))))
4.0ms	(- 1.0 (cos x))

series437.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(log1p (- 1.0 (cos x)))
168.0ms	(/ (expm1 (log1p (- 1.0 (cos x)))) (sin x))
151.0ms	(expm1 (log1p (- 1.0 (cos x))))
18.0ms	(- 1.0 (cos x))

simplify161.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (153.0ms)

Iter	Nodes	Cost
0	290	669
1	877	520
2	4660	491
3	5001	488

prune163.0ms

Filtered

92 candidates to 65 candidates (70.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	92	14	106

Merged error: 0.1b

Counts

106 → 14

regimes139.0ms

Accuracy

97.6% (0.7b remaining)

Error of 0.9b against oracle of 0.2b and baseline of 30.3b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	24
1	31	24

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.1s	1634×	body	2560	valid
1.4s	2734×	body	1280	valid
424.0ms	1853×	body	640	valid
146.0ms	930×	body	320	valid
52.0ms	476×	body	160	valid
23.0ms	368×	body	80	valid
16.0ms	5×	body	5120	valid