Details

sample98.0ms

Algorithm

intervals

Results

45.0ms	110×	body	1280	valid
25.0ms	25×	body	2560	valid
11.0ms	44×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	42×	body	80	valid
1.0ms	10×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize9.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (sin (+ x eps)) (sin x))
3.7b	(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))
5.0ms	(sin (+ x eps))

series65.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify141.0ms

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

prune81.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.9b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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×	`sin-cos-mult`
2×	`sub-neg` `associate-+r+` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 66

Calls

4 calls:

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

series268.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* (cos x) (sin eps)) (sin x))
48.0ms	(* (sin x) (cos eps))
45.0ms	(* (cos x) (sin eps))
115.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	348	614
1	1352	581
2	5002	565

prune240.0ms

Filtered

78 candidates to 55 candidates (70.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (- (cos eps) 1))
2.0b	(- (cos eps) 1)

rewrite29.0ms

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)))
4.0ms	(* (cos x) (sin eps))
10.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(- (cos eps) 1)

series224.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
47.0ms	(* (cos x) (sin eps))
45.0ms	(* (sin x) (- (cos eps) 1))
20.0ms	(- (cos eps) 1)

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (39.0ms)

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

prune259.0ms

Filtered

89 candidates to 57 candidates (64.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (log (exp (- (cos eps) 1))))
2.0b	(- (cos eps) 1)
2.0b	(log (exp (- (cos eps) 1)))

rewrite25.0ms

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))
9.0ms	(* (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:

44.0ms	(* (cos x) (sin eps))
49.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
19.0ms	(- (cos eps) 1)
20.0ms	(log (exp (- (cos eps) 1)))

simplify140.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (30.0ms)

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

prune284.0ms

Filtered

104 candidates to 67 candidates (64.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes129.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.5s	3298×	body	1280	valid
612.0ms	672×	body	2560	valid
467.0ms	1826×	body	640	valid
133.0ms	762×	body	320	valid
65.0ms	1100×	body	80	valid
39.0ms	342×	body	160	valid