Details

sample82.0ms

Algorithm

intervals

Results

41.0ms	101×	body	1280	valid
14.0ms	60×	body	640	valid
10.0ms	12×	body	2560	valid
4.0ms	28×	body	320	valid
2.0ms	40×	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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.5b

localize9.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (sin (+ x eps)) (sin x))
3.5b	(sin (+ x eps))

rewrite59.0ms

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:

49.0ms	(- (sin (+ x eps)) (sin x))
9.0ms	(sin (+ x eps))

series51.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(- (sin (+ x eps)) (sin x))
16.0ms	(sin (+ x eps))

simplify74.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (70.0ms)

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

prune155.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.2b	(* (sin x) (cos eps))
3.8b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite98.0ms

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:

17.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
11.0ms	(* (cos x) (sin eps))
11.0ms	(* (sin x) (cos eps))
57.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series257.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
42.0ms	(* (cos x) (sin eps))
38.0ms	(* (sin x) (cos eps))
99.0ms	(- (+ (* (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	5001	741

prune452.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
1.9b	(- (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:

0.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
11.0ms	(* (cos x) (sin eps))
8.0ms	(- (cos eps) 1)

series156.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
42.0ms	(* (cos x) (sin eps))
17.0ms	(- (cos eps) 1)

simplify98.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (92.0ms)

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

prune383.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.3b	(cbrt (pow (- (cos eps) 1) 3))
0.4b	(pow (- (cos eps) 1) 3)
1.9b	(- (cos eps) 1)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
20×	`cbrt-prod`
19×	`add-cube-cbrt`
14×	`unpow-prod-down` `cube-prod`
10×	`difference-of-squares`
9×	`prod-diff`
8×	`add-exp-log`
7×	`pow1` `add-cbrt-cube`
6×	`add-log-exp`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `flip3--` `fma-neg` `associate-r` `associate-l` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `expm1-def` `pow-pow` `pow1/3` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

11.0ms	(* (cos x) (sin eps))
9.0ms	(cbrt (pow (- (cos eps) 1) 3))
10.0ms	(pow (- (cos eps) 1) 3)
10.0ms	(- (cos eps) 1)

series118.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos x) (sin eps))
17.0ms	(cbrt (pow (- (cos eps) 1) 3))
43.0ms	(pow (- (cos eps) 1) 3)
17.0ms	(- (cos eps) 1)

simplify47.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	388	675
1	1487	601
2	5002	592

prune513.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes192.0ms

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	20	14
1	20	14

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3301×	body	1280	valid
563.0ms	609×	body	2560	valid
447.0ms	1842×	body	640	valid
124.0ms	726×	body	320	valid
71.0ms	1161×	body	80	valid
39.0ms	361×	body	160	valid