Details

sample84.0ms

Algorithm

intervals

Results

38.0ms	96×	body	1280	valid
14.0ms	17×	body	2560	valid
14.0ms	62×	body	640	valid
5.0ms	34×	body	320	valid
2.0ms	34×	body	80	valid
1.0ms	13×	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: 38.1b

localize8.0ms

Local error

Found 2 expressions with local error:

2.2b	(- (sin (+ x eps)) (sin x))
2.5b	(sin (+ x eps))

rewrite62.0ms

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))

series63.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify75.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (71.0ms)

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

prune111.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (cos eps))
4.6b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite96.0ms

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:

12.0ms	(* (cos x) (sin eps))
14.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
11.0ms	(* (sin x) (cos eps))
57.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series298.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos x) (sin eps))
91.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
43.0ms	(* (sin x) (cos eps))
114.0ms	(- (+ (* (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

prune282.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

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)))
1.6b	(- (cos eps) 1)

rewrite25.0ms

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:

15.0ms	(* (cos x) (sin eps))
0.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
8.0ms	(- (cos eps) 1)

series177.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(* (cos x) (sin eps))
113.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
19.0ms	(- (cos eps) 1)

simplify103.0ms

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

prune209.0ms

Pruning

12 alts after pruning (12 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	(fma (sin x) (log (exp (- (cos eps) 1))) (* (cos x) (sin eps)))
1.5b	(log (exp (- (cos eps) 1)))
1.6b	(- (cos eps) 1)

rewrite42.0ms

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:

11.0ms	(* (cos x) (sin eps))
0.0ms	(fma (sin x) (log (exp (- (cos eps) 1))) (* (cos x) (sin eps)))
16.0ms	(log (exp (- (cos eps) 1)))
12.0ms	(- (cos eps) 1)

series201.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos x) (sin eps))
119.0ms	(fma (sin x) (log (exp (- (cos eps) 1))) (* (cos x) (sin eps)))
19.0ms	(log (exp (- (cos eps) 1)))
20.0ms	(- (cos eps) 1)

simplify112.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	335	702
1	1046	507
2	3728	442
3	5001	434

prune296.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes122.0ms

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	24	15
1	26	15
2	26	15

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.5s	3242×	body	1280	valid
584.0ms	660×	body	2560	valid
432.0ms	1876×	body	640	valid
113.0ms	760×	body	320	valid
59.0ms	1128×	body	80	valid
34.0ms	334×	body	160	valid