Details

sample94.0ms

Algorithm

intervals

Results

48.0ms	103×	body	1280	valid
17.0ms	64×	body	640	valid
13.0ms	13×	body	2560	valid
5.0ms	24×	body	320	valid
3.0ms	44×	body	80	valid
1.0ms	8×	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: 33.2b

localize8.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (sin (+ x eps)) (sin x))
2.9b	(sin (+ x eps))

rewrite38.0ms

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:

32.0ms	(- (sin (+ x eps)) (sin x))
5.0ms	(sin (+ x eps))

series57.0ms

Counts

2 → 6

Calls

2 calls:

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

prune108.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (cos eps))
2.5b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite29.0ms

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	(* (cos x) (sin eps))
4.0ms	(* (sin x) (cos eps))
14.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* (cos x) (sin eps)) (sin x))
45.0ms	(* (cos x) (sin eps))
41.0ms	(* (sin x) (cos eps))
107.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify50.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (43.0ms)

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

prune275.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

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))
2.8b	(- (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)

series174.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
47.0ms	(* (cos x) (sin eps))
19.0ms	(- (cos eps) 1)

simplify94.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (89.0ms)

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

prune243.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (- (cos eps) 1)) (cbrt (- (cos eps) 1)))
2.8b	(- (cos eps) 1)
2.8b	(- (cos eps) 1)
2.8b	(- (cos eps) 1)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
40×	`cbrt-prod`
33×	`add-cube-cbrt`
27×	`prod-diff`
16×	`difference-of-squares`
14×	`swap-sqr`
12×	`cbrt-div`
11×	`pow1`
10×	`associate-r` `associate-l` `add-log-exp`
9×	`add-exp-log` `flip3--` `fma-neg` `difference-of-sqr-1` `flip--` `distribute-lft-out--`
6×	`pow1/3`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `expm1-def` `diff-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 159

Calls

4 calls:

28.0ms	(* (cbrt (- (cos eps) 1)) (cbrt (- (cos eps) 1)))
4.0ms	(- (cos eps) 1)
4.0ms	(- (cos eps) 1)
4.0ms	(- (cos eps) 1)

series198.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (cbrt (- (cos eps) 1)) (cbrt (- (cos eps) 1)))
18.0ms	(- (cos eps) 1)
18.0ms	(- (cos eps) 1)
18.0ms	(- (cos eps) 1)

simplify146.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 3 (134.0ms)

Iter	Nodes	Cost
0	293	1300
1	1037	1063
2	4403	961
3	5001	914

prune556.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes104.0ms

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	26	19
1	34	19
2	36	19
3	36	19

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.5s	3298×	body	1280	valid
643.0ms	663×	body	2560	valid
521.0ms	1822×	body	640	valid
141.0ms	746×	body	320	valid
74.0ms	1137×	body	80	valid
47.0ms	334×	body	160	valid