Details

sample122.0ms

Algorithm

intervals

Results

55.0ms	48×	body	2560	valid
39.0ms	90×	body	1280	valid
15.0ms	66×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	18×	body	160	valid
1.0ms	8×	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: 30.9b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.2b	(- 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))

series55.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify36.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

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

prune191.0ms

Filtered

74 candidates to 51 candidates (68.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	56	18	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	18	75

Merged error: 0.1b

Counts

75 → 18

localize14.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))

series57.0ms

Counts

1 → 3

Calls

1 calls:

57.0ms

(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))

simplify32.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	50	89
1	151	78
2	862	78
3	5001	78

prune69.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	13	18	31

Merged error: 0.1b

Counts

31 → 18

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.2b	(- 1.0 (cos x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

12.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
5.0ms	(exp (log (- 1.0 (cos x))))
4.0ms	(log (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series159.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
19.0ms	(exp (log (- 1.0 (cos x))))
81.0ms	(log (- 1.0 (cos x)))
20.0ms	(- 1.0 (cos x))

simplify46.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	354	1019
1	1045	861
2	5001	817

prune255.0ms

Filtered

130 candidates to 76 candidates (58.5%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	124	6	130
Fresh	4	12	16
Picked	1	0	1
Done	0	1	1
Total	129	19	148

Merged error: 0.1b

Counts

148 → 19

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.4b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.2b	(- 1.0 (cos x))

rewrite33.0ms

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))

series142.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (- 1.0 (cos x)) (sin x))
49.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
20.0ms	(- 1.0 (cos x))

simplify43.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (31.0ms)

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

prune279.0ms

Filtered

144 candidates to 99 candidates (68.8%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	138	6	144
Fresh	5	12	17
Picked	1	0	1
Done	0	1	1
Total	144	19	163

Merged error: 0.1b

Counts

163 → 19

regimes200.0ms

Accuracy

98.9% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.8b

bsearch73.0ms

Steps

Iters	Range		Point
7	0.00999808388340962	0.475758948552502	0.024621020206448203
9	-164485.30314980465	-0.009598081335721272	-0.023734893863066063

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	25
1	36	25

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	1616×	body	2560	valid
1.2s	2725×	body	1280	valid
443.0ms	1917×	body	640	valid
154.0ms	946×	body	320	valid
62.0ms	429×	body	160	valid
23.0ms	5×	body	5120	valid
23.0ms	362×	body	80	valid