Details

sample86.0ms

Algorithm

intervals

Results

39.0ms	96×	body	1280	valid
14.0ms	17×	body	2560	valid
14.0ms	62×	body	640	valid
5.0ms	34×	body	320	valid
2.0ms	34×	body	80	valid
1.0ms	13×	body	160	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: 38.1b

localize8.0ms

Local error

Found 2 expressions with local error:

2.2b	(- (sin (+ x eps)) (sin x))
2.5b	(sin (+ x eps))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

44.0ms	(- (sin (+ x eps)) (sin x))
9.0ms	(sin (+ x eps))

series52.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(- (sin (+ x eps)) (sin x))
16.0ms	(sin (+ x eps))

simplify145.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	133	175
1	301	166
2	937	164
3	3445	164
4	5001	164

prune90.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (cos eps))
4.6b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

13.0ms	(* (cos x) (sin eps))
14.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
11.0ms	(* (sin x) (cos eps))
50.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series249.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (cos x) (sin eps))
77.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
38.0ms	(* (sin x) (cos eps))
97.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify44.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	308	589
1	1168	555
2	5001	543

prune231.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (- (cos eps) 1))
1.6b	(- (cos eps) 1)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

11.0ms	(* (cos x) (sin eps))
20.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
29.0ms	(* (sin x) (- (cos eps) 1))
7.0ms	(- (cos eps) 1)

series201.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos x) (sin eps))
98.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
39.0ms	(* (sin x) (- (cos eps) 1))
19.0ms	(- (cos eps) 1)

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	337	548
1	1280	501
2	5002	499

prune270.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (log (exp (- (cos eps) 1)))) (* (cos x) (sin eps)))
0.1b	(* (sin x) (log (exp (- (cos eps) 1))))
1.5b	(log (exp (- (cos eps) 1)))
1.6b	(- (cos eps) 1)

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`log-prod`
22×	`*-un-lft-identity`
16×	`log-pow`
14×	`exp-prod`
13×	`add-cube-cbrt`
11×	`associate-r`
10×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `exp-sum`
8×	`pow1` `add-log-exp`
6×	`add-exp-log` `sub-neg` `add-cbrt-cube` `difference-of-squares`
3×	`difference-of-sqr-1` `associate-l` `distribute-lft-out--`
1×	`+-commutative` `log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

29.0ms	(+ (* (sin x) (log (exp (- (cos eps) 1)))) (* (cos x) (sin eps)))
56.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
17.0ms	(log (exp (- (cos eps) 1)))
7.0ms	(- (cos eps) 1)

series177.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (* (sin x) (log (exp (- (cos eps) 1)))) (* (cos x) (sin eps)))
39.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
21.0ms	(log (exp (- (cos eps) 1)))
18.0ms	(- (cos eps) 1)

simplify43.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	331	784
1	1197	665
2	5001	655

prune328.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes109.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	17
1	31	17
2	31	17

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.3s	3242×	body	1280	valid
582.0ms	660×	body	2560	valid
438.0ms	1876×	body	640	valid
114.0ms	760×	body	320	valid
54.0ms	1128×	body	80	valid
34.0ms	334×	body	160	valid