Details

sample132.0ms

Algorithm

intervals

Results

69.0ms	51×	body	2560	valid
35.0ms	84×	body	1280	valid
13.0ms	59×	body	640	valid
4.0ms	30×	body	320	valid
2.0ms	22×	body	160	valid
1.0ms	10×	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: 29.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.4b	(- 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))

series62.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
21.0ms	(- 1.0 (cos x))

simplify81.0ms

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

prune154.0ms

Pruning

13 alts after pruning (13 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))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.5b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.4b	(- 1.0 (cos x))

rewrite42.0ms

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)))
16.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series144.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
42.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
41.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify90.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (21.0ms)

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

prune316.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
0.3b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
2.2b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`flip3-+` `associate-*l/` `flip-+`
1×	`difference-cubes` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

19.0ms	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
1.0ms	(pow (cos x) 3)
3.0ms	(+ (cos x) 1.0)
15.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series178.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
28.0ms	(pow (cos x) 3)
10.0ms	(+ (cos x) 1.0)
53.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify65.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	434	706
1	1921	654
2	5003	650

prune285.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
0.4b	(+ (cos x) 1.0)
0.4b	(+ (cos x) 1.0)
2.4b	(- 1.0 (cos x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`flip3-+` `associate-r` `associate-l` `flip-+`
2×	`+-commutative` `associate-*l/` `sum-log` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

19.0ms	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
3.0ms	(+ (cos x) 1.0)
3.0ms	(+ (cos x) 1.0)
3.0ms	(- 1.0 (cos x))

series131.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
15.0ms	(+ (cos x) 1.0)
10.0ms	(+ (cos x) 1.0)
19.0ms	(- 1.0 (cos x))

simplify40.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	295	451
1	1190	399
2	5001	399

prune180.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

regimes364.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 29.8b

bsearch96.0ms

Steps

Iters	Range		Point
9	0.004380743253548005	488.5072251079851	0.02290180043346201
9	-3.9934486818618	-6.3299436832828755e-06	-0.022842957444596936

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	49
1	61	49

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.0s	1546×	body	2560	valid
1.2s	2704×	body	1280	valid
455.0ms	1935×	body	640	valid
140.0ms	949×	body	320	valid
62.0ms	512×	body	160	valid
29.0ms	351×	body	80	valid
16.0ms	3×	body	5120	valid