Details

sample98.0ms

Algorithm

intervals

Results

42.0ms	100×	body	1280	valid
25.0ms	22×	body	2560	valid
14.0ms	57×	body	640	valid
3.0ms	17×	body	320	valid
2.0ms	45×	body	80	valid
2.0ms	15×	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: 34.2b

localize8.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (sin (+ x eps)) (sin x))
3.5b	(sin (+ x eps))

rewrite11.0ms

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:

6.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series62.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify148.0ms

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

prune78.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
0.2b	(* (sin x) (cos eps))
2.5b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite26.0ms

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:

6.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
5.0ms	(* (cos x) (sin eps))
5.0ms	(* (sin x) (cos eps))
9.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series293.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
47.0ms	(* (cos x) (sin eps))
42.0ms	(* (sin x) (cos eps))
114.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify39.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (33.0ms)

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

prune215.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
0.2b	(* (sin x) (- (cos eps) 1))
1.1b	(- (cos eps) 1)

rewrite31.0ms

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:

9.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
5.0ms	(* (cos x) (sin eps))
8.0ms	(* (sin x) (- (cos eps) 1))
8.0ms	(- (cos eps) 1)

series221.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
48.0ms	(* (cos x) (sin eps))
44.0ms	(* (sin x) (- (cos eps) 1))
19.0ms	(- (cos eps) 1)

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	337	548
1	1280	501
2	5001	499

prune248.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (sin eps))
0.2b	(* (sin x) (log (exp (- (cos eps) 1))))
1.1b	(- (cos eps) 1)
1.1b	(log (exp (- (cos eps) 1)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

4.0ms	(* (cos x) (sin eps))
11.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
4.0ms	(- (cos eps) 1)
5.0ms	(log (exp (- (cos eps) 1)))

series133.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos x) (sin eps))
45.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
23.0ms	(- (cos eps) 1)
19.0ms	(log (exp (- (cos eps) 1)))

simplify131.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	287	592
1	1044	493
2	4516	482
3	5002	482

prune283.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

regimes129.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	13
1	20	13

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3279×	body	1280	valid
605.0ms	663×	body	2560	valid
445.0ms	1809×	body	640	valid
133.0ms	761×	body	320	valid
54.0ms	1110×	body	80	valid
45.0ms	378×	body	160	valid