Details

sample149.0ms

Algorithm

intervals

Results

76.0ms	60×	body	2560	valid
43.0ms	86×	body	1280	valid
15.0ms	58×	body	640	valid
4.0ms	23×	body	320	valid
2.0ms	20×	body	160	valid
1.0ms	9×	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: 28.3b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.5b	(- 1.0 (cos x))

rewrite14.0ms

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))

series60.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify36.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (7.0ms)

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

prune191.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
0.9b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.5b	(- 1.0 (cos x))

rewrite45.0ms

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:

9.0ms	(/ (- 1.0 (cos x)) (sin x))
15.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
13.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series134.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
46.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
34.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify41.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (31.0ms)

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

prune366.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (- 1.0 (cos x))))
0.2b	(exp (/ (expm1 (log1p (- 1.0 (cos x)))) (sin x)))
0.9b	(log (exp (/ (expm1 (log1p (- 1.0 (cos x)))) (sin x))))
1.5b	(- 1.0 (cos x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `*-un-lft-identity`
26×	`add-cube-cbrt` `exp-prod`
18×	`times-frac`
14×	`log-pow`
9×	`prod-diff`
7×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `expm1-udef`
2×	`exp-diff` `div-sub` `div-inv`
1×	`sub-neg` `log-div` `expm1-log1p` `flip3--` `diff-log` `rem-log-exp` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 91

Calls

4 calls:

0.0ms	(expm1 (log1p (- 1.0 (cos x))))
4.0ms	(exp (/ (expm1 (log1p (- 1.0 (cos x)))) (sin x)))
5.0ms	(log (exp (/ (expm1 (log1p (- 1.0 (cos x)))) (sin x))))
3.0ms	(- 1.0 (cos x))

series676.0ms

Counts

4 → 12

Calls

4 calls:

352.0ms	(expm1 (log1p (- 1.0 (cos x))))
128.0ms	(exp (/ (expm1 (log1p (- 1.0 (cos x)))) (sin x)))
172.0ms	(log (exp (/ (expm1 (log1p (- 1.0 (cos x)))) (sin x))))
23.0ms	(- 1.0 (cos x))

simplify125.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	292	779
1	798	619
2	3653	598
3	5001	591

prune320.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.5b	(- 1.0 (cos x))

rewrite15.0ms

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))
4.0ms	(- 1.0 (cos x))

series56.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify38.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (9.0ms)

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

prune115.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 0.2b

regimes194.0ms

Accuracy

98.1% (0.6b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 30.2b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	17
1	26	17

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.2s	1612×	body	2560	valid
1.3s	2718×	body	1280	valid
500.0ms	1921×	body	640	valid
157.0ms	904×	body	320	valid
63.0ms	511×	body	160	valid
24.0ms	5×	body	5120	valid
24.0ms	329×	body	80	valid