Details

sample139.0ms

Algorithm

intervals

Results

63.0ms	50×	body	2560	valid
44.0ms	86×	body	1280	valid
14.0ms	58×	body	640	valid
4.0ms	25×	body	320	valid
3.0ms	24×	body	160	valid
3.0ms	1×	body	5120	valid
1.0ms	12×	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

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.8b	(- 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:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series58.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- 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

prune178.0ms

Filtered

74 candidates to 51 candidates (68.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	58	16	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	16	75

Merged error: 0.2b

Counts

75 → 16

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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

2 → 20

Calls

2 calls:

1.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
1.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

series170.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
114.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

simplify34.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	61	148
1	188	130
2	1009	130
3	5002	130

prune92.0ms

Filtered

26 candidates to 21 candidates (80.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	26	16	42

Merged error: 0.2b

Counts

42 → 16

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
1.8b	(- 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)))
4.0ms	(- 1.0 (cos x))

series90.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
39.0ms	(/ (sin x) (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))

simplify68.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (52.0ms)

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

prune248.0ms

Filtered

186 candidates to 96 candidates (51.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	179	7	186
Fresh	7	7	14
Picked	1	0	1
Done	0	1	1
Total	187	15	202

Merged error: 0.2b

Counts

202 → 15

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2 (/ 1 x) (- (fma 1/360 (pow x 3) (* 1/6 x))))
0.1b	(fma 1/360 (pow x 3) (* 1/6 x))
0.1b	(/ 1 (fma 2 (/ 1 x) (- (fma 1/360 (pow x 3) (* 1/6 x)))))
0.4b	(* 1/6 x)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log`
9×	`times-frac`
8×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`div-exp` `fma-udef`
1×	`cbrt-undiv` `rec-exp` `pow-flip` `frac-2neg` `1-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `inv-pow` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

1.0ms	(fma 2 (/ 1 x) (- (fma 1/360 (pow x 3) (* 1/6 x))))
1.0ms	(fma 1/360 (pow x 3) (* 1/6 x))
3.0ms	(/ 1 (fma 2 (/ 1 x) (- (fma 1/360 (pow x 3) (* 1/6 x)))))
4.0ms	(* 1/6 x)

series201.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(fma 2 (/ 1 x) (- (fma 1/360 (pow x 3) (* 1/6 x))))
79.0ms	(fma 1/360 (pow x 3) (* 1/6 x))
61.0ms	(/ 1 (fma 2 (/ 1 x) (- (fma 1/360 (pow x 3) (* 1/6 x)))))
13.0ms	(* 1/6 x)

simplify71.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	235	603
1	827	541
2	2618	526
3	5001	526

prune149.0ms

Filtered

85 candidates to 55 candidates (64.7%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	85	15	100

Merged error: 0.2b

Counts

100 → 15

regimes128.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.0b

bsearch71.0ms

Steps

Iters	Range		Point
9	2.1846438371975785e-05	719.5386143167987	0.0219772417603219
10	-43540924890.08803	-0.0051836583041924315	-0.023228222164187143

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	11
1	32	11

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.1s	1541×	body	2560	valid
1.5s	2872×	body	1280	valid
449.0ms	1851×	body	640	valid
152.0ms	918×	body	320	valid
56.0ms	474×	body	160	valid
31.0ms	338×	body	80	valid
24.0ms	6×	body	5120	valid