Details

sample99.0ms

Algorithm

intervals

Results

48.0ms	115×	body	1280	valid
22.0ms	24×	body	2560	valid
13.0ms	54×	body	640	valid
3.0ms	18×	body	320	valid
2.0ms	34×	body	80	valid
1.0ms	11×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 37.6b

localize10.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (sin (+ x eps)) (sin x))
3.7b	(sin (+ x eps))

rewrite18.0ms

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:

7.0ms	(- (sin (+ x eps)) (sin x))
9.0ms	(sin (+ x eps))

series57.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(- (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

prune116.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.9b

localize15.0ms

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))
3.3b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite29.0ms

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:

6.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
4.0ms	(* (sin x) (cos eps))
4.0ms	(* (cos x) (sin eps))
9.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series288.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
48.0ms	(* (sin x) (cos eps))
41.0ms	(* (cos x) (sin eps))
109.0ms	(- (+ (* (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

prune280.0ms

Pruning

10 alts after pruning (10 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)))
0.2b	(* (cos x) (sin eps))
1.0b	(- (cos eps) 1)

rewrite12.0ms

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:

1.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
5.0ms	(* (cos x) (sin eps))
5.0ms	(- (cos eps) 1)

series174.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
42.0ms	(* (cos x) (sin eps))
18.0ms	(- (cos eps) 1)

simplify97.0ms

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

prune235.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (sin eps))
0.4b	(pow (cos eps) 3)
0.4b	(+ (cos eps) 1)
0.9b	(- (pow (cos eps) 3) 1)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
18×	`unpow-prod-down` `cube-prod`
12×	`fma-neg`
9×	`add-exp-log`
8×	`add-log-exp` `difference-of-squares` `sqr-pow`
7×	`pow1` `add-cbrt-cube`
5×	`cube-mult` `unpow3`
4×	`expm1-log1p-u` `difference-of-sqr-1` `log1p-expm1-u`
3×	`pow-unpow` `expm1-def` `fma-def` `associate-r` `associate-l`
2×	`pow-to-exp` `pow-exp`
1×	`+-commutative` `sub-neg` `flip3--` `pow-pow` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 140

Calls

4 calls:

4.0ms	(* (cos x) (sin eps))
3.0ms	(pow (cos eps) 3)
4.0ms	(+ (cos eps) 1)
9.0ms	(- (pow (cos eps) 3) 1)

series134.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos x) (sin eps))
28.0ms	(pow (cos eps) 3)
9.0ms	(+ (cos eps) 1)
50.0ms	(- (pow (cos eps) 3) 1)

simplify58.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	417	861
1	1759	594
2	5003	578

prune383.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes128.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

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

1.6s	3309×	body	1280	valid
624.0ms	676×	body	2560	valid
453.0ms	1765×	body	640	valid
141.0ms	764×	body	320	valid
69.0ms	1119×	body	80	valid
42.0ms	367×	body	160	valid