Details

sample97.0ms

Algorithm

intervals

Results

48.0ms	113×	body	1280	valid
16.0ms	13×	body	2560	valid
15.0ms	59×	body	640	valid
4.0ms	22×	body	320	valid
2.0ms	35×	body	80	valid
2.0ms	14×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize9.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (sin (+ x eps)) (sin x))
3.5b	(sin (+ x eps))

rewrite63.0ms

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:

52.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series55.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (sin (+ x eps)) (sin x))
17.0ms	(sin (+ x eps))

simplify77.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (72.0ms)

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

prune115.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(- (* (cos x) (sin eps)) (sin x))
0.2b	(* (sin x) (cos eps))
2.8b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `prod-diff`
5×	`associate-+r+`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sin-cos-mult`
2×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `fma-def` `flip3-+` `fma-neg` `flip-+`

Counts

4 → 82

Calls

4 calls:

12.0ms	(* (cos x) (sin eps))
14.0ms	(- (* (cos x) (sin eps)) (sin x))
11.0ms	(* (sin x) (cos eps))
34.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos x) (sin eps))
60.0ms	(- (* (cos x) (sin eps)) (sin x))
40.0ms	(* (sin x) (cos eps))
107.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	414	729
1	1617	662
2	5002	648

prune303.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
1.3b	(- (cos eps) 1)

rewrite21.0ms

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:

12.0ms	(* (cos x) (sin eps))
0.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
8.0ms	(- (cos eps) 1)

series167.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* (cos x) (sin eps))
104.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
22.0ms	(- (cos eps) 1)

simplify98.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (93.0ms)

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

prune233.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

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))
1.3b	(- (cos eps) 1)

rewrite84.0ms

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:

25.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
11.0ms	(* (cos x) (sin eps))
33.0ms	(* (sin x) (- (cos eps) 1))
9.0ms	(- (cos eps) 1)

series213.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
41.0ms	(* (cos x) (sin eps))
46.0ms	(* (sin x) (- (cos eps) 1))
20.0ms	(- (cos eps) 1)

simplify60.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (42.0ms)

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

prune395.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes111.0ms

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	15	9
1	15	9

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.5s	3434×	body	1280	valid
592.0ms	648×	body	2560	valid
466.0ms	1746×	body	640	valid
127.0ms	748×	body	320	valid
57.0ms	1086×	body	80	valid
38.0ms	338×	body	160	valid