Details

sample148.0ms

Algorithm

intervals

Results

78.0ms	60×	body	2560	valid
40.0ms	86×	body	1280	valid
15.0ms	58×	body	640	valid
4.0ms	23×	body	320	valid
3.0ms	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))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series59.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify80.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373

prune159.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

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))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `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 → 112

Calls

4 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
12.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series138.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
41.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
39.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify87.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	303	818
1	799	768
2	2970	766
3	5001	766

prune307.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
0.4b	(+ (cos x) 1.0)
0.4b	(pow (cos x) 3)
1.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
48×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
15×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
3×	`difference-cubes` `pow-unpow`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-*l/` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 139

Calls

4 calls:

50.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
3.0ms	(+ (cos x) 1.0)
1.0ms	(pow (cos x) 3)
15.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series257.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
9.0ms	(+ (cos x) 1.0)
28.0ms	(pow (cos x) 3)
51.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify79.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	566	1663
1	2538	1547
2	5001	1503

prune357.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- 1.0 (cos x)) (/ 1 (sin x)))
0.2b	(exp (* (- 1.0 (cos x)) (/ 1 (sin x))))
0.9b	(log (exp (* (- 1.0 (cos x)) (/ 1 (sin x)))))
1.5b	(- 1.0 (cos x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-r` `add-log-exp`
11×	`times-frac`
9×	`add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`exp-to-pow` `prod-exp` `log-pow`
3×	`log-prod` `flip3--` `diff-log` `flip--` `unswap-sqr`
2×	`frac-times` `exp-prod` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `un-div-inv` `-commutative` `div-inv` `rem-exp-log`

Counts

4 → 82

Calls

4 calls:

18.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
3.0ms	(exp (* (- 1.0 (cos x)) (/ 1 (sin x))))
2.0ms	(log (exp (* (- 1.0 (cos x)) (/ 1 (sin x)))))
3.0ms	(- 1.0 (cos x))

series132.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
47.0ms	(exp (* (- 1.0 (cos x)) (/ 1 (sin x))))
34.0ms	(log (exp (* (- 1.0 (cos x)) (/ 1 (sin x)))))
18.0ms	(- 1.0 (cos x))

simplify40.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	335	613
1	1367	532
2	5001	520

prune201.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

regimes167.0ms

Accuracy

97.7% (0.7b remaining)

Error of 0.9b against oracle of 0.2b and baseline of 30.3b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	32
1	33	32

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.4s	1612×	body	2560	valid
1.3s	2718×	body	1280	valid
499.0ms	1921×	body	640	valid
164.0ms	904×	body	320	valid
70.0ms	511×	body	160	valid
29.0ms	329×	body	80	valid
24.0ms	5×	body	5120	valid