Details

sample90.0ms

Algorithm

intervals

Results

49.0ms	136×	body	1280	valid
16.0ms	18×	body	2560	valid
13.0ms	64×	body	640	valid
3.0ms	22×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	4×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.2b

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (cos (+ x eps)) (cos x))
4.5b	(cos (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `cos-sum` `add-cbrt-cube`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

7.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify112.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	134	176
1	281	167
2	840	164
3	2958	164
4	5002	164

prune94.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
3.1b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
3×	`cos-mult`
2×	`flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip--` `sin-mult` `associate--r+`

Counts

4 → 65

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
4.0ms	(+ (* (sin x) (sin eps)) (cos x))
4.0ms	(* (sin x) (sin eps))
9.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos x) (cos eps))
51.0ms	(+ (* (sin x) (sin eps)) (cos x))
48.0ms	(* (sin x) (sin eps))
128.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	332	607
1	1284	576
2	5002	567

prune253.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.5b	(+ (+ (* (sin x) (sin eps)) (cos x)) (* (cos x) (cos eps)))
0.6b	(pow (* (cos x) (cos eps)) 3)
2.9b	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
19×	`add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down`
15×	`add-sqr-sqrt`
11×	`add-log-exp`
9×	`prod-exp` `cos-mult` `cbrt-unprod`
8×	`difference-of-squares`
7×	`*-un-lft-identity` `sqr-pow`
5×	`cube-div` `add-cube-cbrt`
4×	`pow-sqr` `pow-prod-up`
3×	`unpow-prod-down` `pow-unpow` `flip3-+` `cube-prod` `sum-log` `flip-+`
2×	`pow-pow` `pow-plus` `frac-add` `pow-exp` `frac-sub` `rem-cube-cbrt`
1×	`difference-cubes` `+-commutative` `pow2` `cube-mult` `frac-times` `pow-to-exp` `sub-neg` `associate-+l+` `flip3--` `diff-log` `unpow3` `associate-r/` `swap-sqr` `associate-r` `associate-l` `associate-l/` `*-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 99

Calls

4 calls:

13.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
19.0ms	(+ (+ (* (sin x) (sin eps)) (cos x)) (* (cos x) (cos eps)))
3.0ms	(pow (* (cos x) (cos eps)) 3)
24.0ms	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

series619.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
96.0ms	(+ (+ (* (sin x) (sin eps)) (cos x)) (* (cos x) (cos eps)))
61.0ms	(pow (* (cos x) (cos eps)) 3)
403.0ms	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

simplify91.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	591	1157
1	2882	1092
2	5002	1089

prune472.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 12.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (* (cos x) (cos eps)) 3)
0.6b	(pow (* (cos x) (cos eps)) 3)
2.9b	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))
3.1b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`*-un-lft-identity` `difference-of-squares` `sqr-pow`
6×	`cube-div` `add-cube-cbrt` `pow-unpow` `cos-mult`
4×	`unpow-prod-down` `pow-pow` `cube-prod` `pow-exp` `frac-sub` `rem-cube-cbrt`
3×	`diff-log`
2×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `flip3-+` `unpow3` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `flip-+`
1×	`difference-cubes` `sum-log` `associate--r+` `distribute-lft-out--`

Counts

4 → 86

Calls

4 calls:

3.0ms	(pow (* (cos x) (cos eps)) 3)
3.0ms	(pow (* (cos x) (cos eps)) 3)
28.0ms	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))
10.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (* (cos x) (cos eps)) 3)
57.0ms	(pow (* (cos x) (cos eps)) 3)
410.0ms	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))
129.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify67.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	480	1144
1	2064	1073
2	5001	1069

prune438.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 12.5b

regimes379.0ms

Accuracy

83.4% (1.7b remaining)

Error of 16.2b against oracle of 14.6b and baseline of 24.7b

bsearch148.0ms

Steps

Iters	Range		Point
9	7.507640222675324e-06	0.4954286465087044	7.567295649667433e-06
8	-3.3551436115377164e-08	-2.0275543903092447e-11	-1.1888021786142176e-08

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	60
1	59	60
2	59	60

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4552×	body	1280	valid
553.0ms	636×	body	2560	valid
391.0ms	1793×	body	640	valid
94.0ms	677×	body	320	valid
27.0ms	271×	body	160	valid
4.0ms	71×	body	80	valid