Details

sample98.0ms

Algorithm

intervals

Results

46.0ms	106×	body	1280	valid
22.0ms	25×	body	2560	valid
14.0ms	61×	body	640	valid
3.0ms	20×	body	320	valid
2.0ms	32×	body	80	valid
1.0ms	12×	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: 36.6b

localize8.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (sin (+ x eps)) (sin x))
3.6b	(sin (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `sin-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

7.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series58.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- (sin (+ x eps)) (sin x))
17.0ms	(sin (+ x eps))

simplify72.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	192	386
1	538	285
2	2616	275
3	5002	220

prune107.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (cos eps))
0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
1.6b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`add-log-exp`
9×	`prod-diff`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg`
2×	`diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `fma-def` `flip3-+` `associate--l+` `sin-cos-mult` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (sin x) (cos eps))
6.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
4.0ms	(* (cos x) (sin eps))
9.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series277.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (sin x) (cos eps))
84.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
45.0ms	(* (cos x) (sin eps))
106.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify49.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	373	918
1	1424	763
2	5002	741

prune271.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
1.4b	(- (cos eps) 1)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`prod-diff`
6×	`add-exp-log`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-r` `associate-l` `log1p-expm1-u`
2×	`difference-of-squares`
1×	`sub-neg` `expm1-def` `flip3--` `diff-log` `difference-of-sqr-1` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

1.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
5.0ms	(* (cos x) (sin eps))
5.0ms	(- (cos eps) 1)

series166.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
44.0ms	(* (cos x) (sin eps))
18.0ms	(- (cos eps) 1)

simplify96.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	276	442
1	932	347
2	3460	325
3	5001	303

prune223.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (- (cos eps) 1))
0.2b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
1.4b	(- (cos eps) 1)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
45×	`*-un-lft-identity` `prod-diff`
39×	`add-cube-cbrt`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
10×	`associate-r`
9×	`add-exp-log`
8×	`pow1` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
5×	`sub-neg`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`fma-neg`
2×	`flip3--` `difference-of-sqr-1` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `expm1-def` `fma-def` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 135

Calls

4 calls:

13.0ms	(* (sin x) (- (cos eps) 1))
11.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
4.0ms	(* (cos x) (sin eps))
5.0ms	(- (cos eps) 1)

series214.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin x) (- (cos eps) 1))
111.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
41.0ms	(* (cos x) (sin eps))
18.0ms	(- (cos eps) 1)

simplify51.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	446	1178
1	1727	907
2	5001	882

prune370.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes119.0ms

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	17	9
1	19	9
2	19	9

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3284×	body	1280	valid
592.0ms	636×	body	2560	valid
431.0ms	1789×	body	640	valid
141.0ms	810×	body	320	valid
56.0ms	1119×	body	80	valid
38.0ms	362×	body	160	valid