Details

sample100.0ms

Algorithm

intervals

Results

48.0ms	119×	body	1280	valid
25.0ms	29×	body	2560	valid
12.0ms	55×	body	640	valid
3.0ms	18×	body	320	valid
1.0ms	30×	body	80	valid
1.0ms	5×	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: 41.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (sin (+ x eps)) (sin x))
2.9b	(sin (+ x eps))

rewrite36.0ms

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:

30.0ms	(- (sin (+ x eps)) (sin x))
5.0ms	(sin (+ x eps))

series56.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify73.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (69.0ms)

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

prune111.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (cos eps))
2.2b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite29.0ms

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:

5.0ms	(- (* (cos x) (sin eps)) (sin x))
4.0ms	(* (cos x) (sin eps))
7.0ms	(* (sin x) (cos eps))
11.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (* (cos x) (sin eps)) (sin x))
48.0ms	(* (cos x) (sin eps))
42.0ms	(* (sin x) (cos eps))
112.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify50.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (43.0ms)

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

prune309.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.2b	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
2.9b	(- (cos eps) 1)

rewrite9.0ms

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:

4.0ms	(* (cos x) (sin eps))
0.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
4.0ms	(- (cos eps) 1)

series177.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* (cos x) (sin eps))
110.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
20.0ms	(- (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

prune279.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.2b	(fma (sin x) (log (exp (- (cos eps) 1))) (* (cos x) (sin eps)))
2.8b	(log (exp (- (cos eps) 1)))
2.9b	(- (cos eps) 1)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff`
14×	`log-prod`
11×	`exp-sum`
8×	`log-pow`
7×	`pow1` `add-exp-log` `exp-prod`
6×	`add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`fma-neg` `associate-r` `associate-l`
2×	`sub-neg` `difference-of-sqr-1` `distribute-lft-out--`
1×	`log-div` `expm1-def` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

4.0ms	(* (cos x) (sin eps))
0.0ms	(fma (sin x) (log (exp (- (cos eps) 1))) (* (cos x) (sin eps)))
9.0ms	(log (exp (- (cos eps) 1)))
4.0ms	(- (cos eps) 1)

series198.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos x) (sin eps))
112.0ms	(fma (sin x) (log (exp (- (cos eps) 1))) (* (cos x) (sin eps)))
19.0ms	(log (exp (- (cos eps) 1)))
19.0ms	(- (cos eps) 1)

simplify110.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	339	680
1	1052	506
2	3734	442
3	5001	434

prune353.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

regimes172.0ms

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	21	14
1	31	14
2	33	14
3	33	14

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.6s	3317×	body	1280	valid
596.0ms	663×	body	2560	valid
476.0ms	1852×	body	640	valid
124.0ms	746×	body	320	valid
56.0ms	1076×	body	80	valid
37.0ms	346×	body	160	valid