Details

sample90.0ms

Algorithm

intervals

Results

39.0ms	97×	body	1280	valid
19.0ms	22×	body	2560	valid
16.0ms	68×	body	640	valid
3.0ms	21×	body	320	valid
2.0ms	39×	body	80	valid
1.0ms	9×	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: 38.3b

localize13.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (sin (+ x eps)) (sin x))
2.9b	(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:

48.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series61.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify72.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (68.0ms)

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

prune106.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (cos eps))
0.2b	(* (cos x) (sin eps))
2.0b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite97.0ms

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:

15.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
13.0ms	(* (sin x) (cos eps))
11.0ms	(* (cos x) (sin eps))
56.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series297.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
44.0ms	(* (sin x) (cos eps))
48.0ms	(* (cos x) (sin 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

prune272.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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))
1.9b	(- (cos eps) 1)

rewrite20.0ms

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)

series182.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
49.0ms	(* (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

prune240.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos eps))
0.3b	(cbrt (cos eps))
0.3b	(cbrt (cos eps))
1.7b	(fma (* (cbrt (cos eps)) (cbrt (cos eps))) (cbrt (cos eps)) (- 1))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (cos eps))
1.0ms	(cbrt (cos eps))
1.0ms	(cbrt (cos eps))
0.0ms	(fma (* (cbrt (cos eps)) (cbrt (cos eps))) (cbrt (cos eps)) (- 1))

series634.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (cos eps))
99.0ms	(cbrt (cos eps))
100.0ms	(cbrt (cos eps))
328.0ms	(fma (* (cbrt (cos eps)) (cbrt (cos eps))) (cbrt (cos eps)) (- 1))

simplify40.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	88	331
1	248	292
2	918	277
3	5002	277

prune257.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes129.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	19
1	20	19

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.3s	3230×	body	1280	valid
583.0ms	653×	body	2560	valid
462.0ms	1897×	body	640	valid
130.0ms	778×	body	320	valid
54.0ms	1118×	body	80	valid
34.0ms	324×	body	160	valid