Details

sample90.0ms

Algorithm

intervals

Results

41.0ms	103×	body	1280	valid
17.0ms	57×	body	640	valid
14.0ms	16×	body	2560	valid
5.0ms	31×	body	320	valid
2.0ms	40×	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: 36.0b

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (sin (+ x eps)) (sin x))
4.5b	(sin (+ x eps))

rewrite64.0ms

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:

53.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series51.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(- (sin (+ x eps)) (sin x))
17.0ms	(sin (+ x eps))

simplify73.0ms

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

prune111.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.7b

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

rewrite105.0ms

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:

16.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
12.0ms	(* (sin x) (cos eps))
13.0ms	(* (cos x) (sin eps))
61.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series253.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
38.0ms	(* (sin x) (cos eps))
40.0ms	(* (cos x) (sin eps))
98.0ms	(- (+ (* (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

prune261.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize16.0ms

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)

rewrite22.0ms

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)))
12.0ms	(* (cos x) (sin eps))
8.0ms	(- (cos eps) 1)

series156.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
41.0ms	(* (cos x) (sin eps))
17.0ms	(- (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

prune211.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow (cos eps) 3) 1) (fma (cos eps) (+ (cos eps) 1) 1))
0.4b	(pow (cos eps) 3)
0.4b	(+ (cos eps) 1)
1.7b	(- (pow (cos eps) 3) 1)

rewrite96.0ms

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:

50.0ms	(/ (- (pow (cos eps) 3) 1) (fma (cos eps) (+ (cos eps) 1) 1))
3.0ms	(pow (cos eps) 3)
7.0ms	(+ (cos eps) 1)
26.0ms	(- (pow (cos eps) 3) 1)

series173.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- (pow (cos eps) 3) 1) (fma (cos eps) (+ (cos eps) 1) 1))
25.0ms	(pow (cos eps) 3)
13.0ms	(+ (cos eps) 1)
41.0ms	(- (pow (cos eps) 3) 1)

simplify81.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (61.0ms)

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

prune493.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes129.0ms

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	23	22
1	23	22

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	3252×	body	1280	valid
559.0ms	635×	body	2560	valid
468.0ms	1846×	body	640	valid
128.0ms	791×	body	320	valid
62.0ms	1121×	body	80	valid
37.0ms	355×	body	160	valid