Details

sample98.0ms

Algorithm

intervals

Results

48.0ms	106×	body	1280	valid
17.0ms	64×	body	640	valid
13.0ms	14×	body	2560	valid
7.0ms	22×	body	320	valid
2.0ms	39×	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: 37.4b

localize9.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (sin (+ x eps)) (sin x))
3.1b	(sin (+ x eps))

rewrite30.0ms

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:

24.0ms	(- (sin (+ x eps)) (sin x))
5.0ms	(sin (+ x eps))

series63.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(- (sin (+ x eps)) (sin x))
23.0ms	(sin (+ x eps))

simplify73.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (69.0ms)

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

prune109.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (sin x) (cos eps))
0.2b	(* (cos x) (sin eps))
3.5b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `prod-diff`
5×	`associate-+r+`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sin-cos-mult`
2×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `fma-def` `flip3-+` `fma-neg` `flip-+`

Counts

4 → 82

Calls

4 calls:

4.0ms	(- (* (cos x) (sin eps)) (sin x))
4.0ms	(* (sin x) (cos eps))
4.0ms	(* (cos x) (sin eps))
11.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* (cos x) (sin eps)) (sin x))
46.0ms	(* (sin x) (cos eps))
43.0ms	(* (cos x) (sin eps))
112.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify54.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	414	729
1	1617	662
2	5002	648

prune279.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

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))
1.2b	(- (cos eps) 1)

rewrite10.0ms

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)

series171.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
43.0ms	(* (cos x) (sin eps))
22.0ms	(- (cos eps) 1)

simplify99.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (93.0ms)

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

prune206.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(expm1 (fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps))))
0.2b	(* (cos x) (sin eps))
0.2b	(log1p (expm1 (fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))))
1.2b	(- (cos eps) 1)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-exp-log`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u`
3×	`fma-neg` `associate-r` `associate-l`
2×	`difference-of-squares`
1×	`sub-neg` `expm1-def` `log1p-udef` `expm1-log1p` `flip3--` `diff-log` `difference-of-sqr-1` `log1p-expm1` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `expm1-udef` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

0.0ms	(expm1 (fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps))))
4.0ms	(* (cos x) (sin eps))
0.0ms	(log1p (expm1 (fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))))
4.0ms	(- (cos eps) 1)

series382.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(expm1 (fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps))))
46.0ms	(* (cos x) (sin eps))
157.0ms	(log1p (expm1 (fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))))
18.0ms	(- (cos eps) 1)

simplify102.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	304	606
1	998	489
2	3683	462
3	5001	448

prune228.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes99.0ms

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	17	11
1	17	11

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.6s	3322×	body	1280	valid
600.0ms	631×	body	2560	valid
519.0ms	1824×	body	640	valid
142.0ms	744×	body	320	valid
71.0ms	1099×	body	80	valid
52.0ms	380×	body	160	valid