Details

sample134.0ms

Algorithm

intervals

Results

64.0ms	49×	body	2560	valid
37.0ms	83×	body	1280	valid
15.0ms	58×	body	640	valid
6.0ms	36×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	14×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.5b	(- 1.0 (cos x))

rewrite20.0ms

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:

9.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series55.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(- 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

prune204.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

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)))
0.2b	(fma 1/240 (pow x 5) (* 1/2 x))

rewrite1.0ms

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:

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

series188.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
126.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

simplify35.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (4.0ms)

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

prune111.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin x) (- 1.0 (cos x)))
0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
2.5b	(- 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:

7.0ms	(/ (sin x) (- 1.0 (cos x)))
10.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
4.0ms	(- 1.0 (cos x))

series96.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ (sin x) (- 1.0 (cos x)))
40.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
20.0ms	(- 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

prune311.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (expm1 (log1p (- 1.0 (cos x)))))
0.1b	(/ 1 (/ (sin x) (expm1 (log1p (- 1.0 (cos x))))))
0.2b	(expm1 (log1p (- 1.0 (cos x))))
2.5b	(- 1.0 (cos x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 146

Calls

4 calls:

3.0ms	(/ (sin x) (expm1 (log1p (- 1.0 (cos x)))))
6.0ms	(/ 1 (/ (sin x) (expm1 (log1p (- 1.0 (cos x))))))
0.0ms	(expm1 (log1p (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))

series540.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (sin x) (expm1 (log1p (- 1.0 (cos x)))))
180.0ms	(/ 1 (/ (sin x) (expm1 (log1p (- 1.0 (cos x))))))
159.0ms	(expm1 (log1p (- 1.0 (cos x))))
24.0ms	(- 1.0 (cos x))

simplify59.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	504	1603
1	2108	1229
2	5001	1149

prune305.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

regimes60.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.5b

bsearch92.0ms

Steps

Iters	Range		Point
9	0.00035723662727133143	33.11368705657117	0.02343065570717855
10	-29.541817090935037	-6.322351620237733e-11	-0.023342343569720127

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	19
1	33	19

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.2s	1614×	body	2560	valid
1.5s	2733×	body	1280	valid
512.0ms	1883×	body	640	valid
176.0ms	950×	body	320	valid
60.0ms	460×	body	160	valid
41.0ms	353×	body	80	valid
29.0ms	7×	body	5120	valid