Details

sample104.0ms

Algorithm

intervals

Results

46.0ms	105×	body	1280	valid
28.0ms	30×	body	2560	valid
12.0ms	44×	body	640	valid
6.0ms	32×	body	320	valid
2.0ms	31×	body	80	valid
2.0ms	14×	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: 40.8b

localize9.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (sin (+ x eps)) (sin x))
4.2b	(sin (+ x eps))

rewrite35.0ms

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:

29.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series56.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify75.0ms

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

prune109.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.0b

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))
0.1b	(* (sin x) (cos eps))
3.1b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite39.0ms

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:

4.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
4.0ms	(* (cos x) (sin eps))
7.0ms	(* (sin x) (cos eps))
22.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series285.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
47.0ms	(* (cos x) (sin eps))
41.0ms	(* (sin x) (cos eps))
110.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify51.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	373	918
1	1424	763
2	5001	741

prune287.0ms

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	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.9b	(- (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:

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

series175.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
43.0ms	(* (cos x) (sin eps))
19.0ms	(- (cos eps) 1)

simplify99.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (94.0ms)

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

prune235.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow (cos eps) 3) 1) (fma (cos eps) (+ (cos eps) 1) 1))
0.4b	(+ (cos eps) 1)
0.4b	(pow (cos eps) 3)
0.8b	(- (pow (cos eps) 3) 1)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
85×	`*-un-lft-identity`
53×	`add-cube-cbrt`
48×	`times-frac`
40×	`difference-of-squares`
36×	`prod-diff`
30×	`unpow-prod-down` `cube-prod`
20×	`difference-of-sqr-1` `sqr-pow`
16×	`associate-/l*`
12×	`fma-neg`
9×	`add-exp-log`
8×	`add-log-exp`
7×	`add-cbrt-cube`
5×	`pow1` `cube-mult` `unpow3` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `expm1-def` `fma-def` `associate-/r*`
2×	`pow-to-exp` `flip3--` `pow-exp` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `flip-+` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 204

Calls

4 calls:

32.0ms	(/ (- (pow (cos eps) 3) 1) (fma (cos eps) (+ (cos eps) 1) 1))
3.0ms	(+ (cos eps) 1)
2.0ms	(pow (cos eps) 3)
14.0ms	(- (pow (cos eps) 3) 1)

series196.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (- (pow (cos eps) 3) 1) (fma (cos eps) (+ (cos eps) 1) 1))
10.0ms	(+ (cos eps) 1)
35.0ms	(pow (cos eps) 3)
46.0ms	(- (pow (cos eps) 3) 1)

simplify83.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	544	2069
1	2349	1758
2	5001	1700

prune507.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

regimes147.0ms

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	16
1	23	16
2	23	16

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	3335×	body	1280	valid
601.0ms	627×	body	2560	valid
522.0ms	1811×	body	640	valid
146.0ms	768×	body	320	valid
66.0ms	1119×	body	80	valid
49.0ms	340×	body	160	valid