Details

sample86.0ms

Algorithm

intervals

Results

42.0ms	105×	body	1280	valid
16.0ms	61×	body	640	valid
12.0ms	13×	body	2560	valid
4.0ms	24×	body	320	valid
2.0ms	40×	body	80	valid
1.0ms	13×	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: 35.1b

localize11.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (sin (+ x eps)) (sin x))
4.3b	(sin (+ x eps))

rewrite31.0ms

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:

25.0ms	(- (sin (+ x eps)) (sin x))
5.0ms	(sin (+ x eps))

series62.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify77.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (72.0ms)

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

prune117.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.2b

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))
3.2b	(+ (* (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)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* (cos x) (sin eps)) (sin x))
44.0ms	(* (sin x) (cos eps))
47.0ms	(* (cos x) (sin eps))
111.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify54.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (47.0ms)

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

prune288.0ms

Pruning

12 alts after pruning (12 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)))
0.2b	(* (cos x) (sin eps))
2.5b	(- (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)

series176.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
47.0ms	(* (cos x) (sin eps))
19.0ms	(- (cos eps) 1)

simplify100.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (95.0ms)

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

prune223.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (sin eps))
0.4b	(cbrt (pow (- (cos eps) 1) 3))
0.4b	(pow (- (cos eps) 1) 3)
2.5b	(- (cos eps) 1)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
20×	`cbrt-prod`
19×	`add-cube-cbrt`
14×	`unpow-prod-down` `cube-prod`
10×	`difference-of-squares`
9×	`prod-diff`
8×	`add-exp-log`
7×	`pow1` `add-cbrt-cube`
6×	`add-log-exp`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `flip3--` `fma-neg` `associate-r` `associate-l` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `expm1-def` `pow-pow` `pow1/3` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

4.0ms	(* (cos x) (sin eps))
6.0ms	(cbrt (pow (- (cos eps) 1) 3))
5.0ms	(pow (- (cos eps) 1) 3)
4.0ms	(- (cos eps) 1)

series137.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos x) (sin eps))
20.0ms	(cbrt (pow (- (cos eps) 1) 3))
46.0ms	(pow (- (cos eps) 1) 3)
24.0ms	(- (cos eps) 1)

simplify50.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	392	649
1	1504	596
2	5001	589

prune324.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

regimes134.0ms

Accuracy

0% (0.4b 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	16	9
1	16	9

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	3316×	body	1280	valid
577.0ms	632×	body	2560	valid
469.0ms	1829×	body	640	valid
127.0ms	768×	body	320	valid
58.0ms	1129×	body	80	valid
41.0ms	326×	body	160	valid