Details

sample128.0ms

Algorithm

intervals

Results

59.0ms	47×	body	2560	valid
38.0ms	86×	body	1280	valid
16.0ms	74×	body	640	valid
3.0ms	21×	body	320	valid
1.0ms	13×	body	160	valid
1.0ms	15×	body	80	valid

simplify7.0ms

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: 27.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.8b	(- 1.0 (cos x))

rewrite27.0ms

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:

17.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series64.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (- 1.0 (cos x)) (sin x))
21.0ms	(- 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

prune181.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.8b	(- 1.0 (cos x))

rewrite30.0ms

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:

21.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series56.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ (- 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

prune170.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite52.0ms

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:

17.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
19.0ms	(/ (sin x) (- 1.0 (cos x)))
7.0ms	(- 1.0 (cos x))

series100.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
43.0ms	(/ (sin x) (- 1.0 (cos x)))
21.0ms	(- 1.0 (cos x))

simplify67.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (52.0ms)

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

prune291.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

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)))
1.2b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.8b	(- 1.0 (cos x))

rewrite75.0ms

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:

18.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
25.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
7.0ms	(- 1.0 (cos x))

series147.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (- 1.0 (cos x)) (sin x))
44.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
37.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
24.0ms	(- 1.0 (cos x))

simplify42.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (33.0ms)

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

prune325.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

regimes158.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.3b

bsearch60.0ms

Steps

Iters	Range		Point
8	0.002806896206153352	41.96612619086958	0.021731898587967143
7	-0.5149414008252181	-0.002950799818357885	-0.01849382956573876

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	33
1	52	33
2	52	33

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	1642×	body	2560	valid
1.2s	2775×	body	1280	valid
388.0ms	1830×	body	640	valid
136.0ms	914×	body	320	valid
49.0ms	481×	body	160	valid
21.0ms	355×	body	80	valid
13.0ms	3×	body	5120	valid