Details

sample96.0ms

Algorithm

intervals

Results

51.0ms	149×	body	1280	valid
21.0ms	24×	body	2560	valid
12.0ms	62×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	2×	body	80	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: 40.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (cos (+ x eps)) (cos x))
3.7b	(cos (+ x eps))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `cos-sum` `add-cbrt-cube`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

6.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify111.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	134	176
1	281	167
2	840	164
3	2958	164
4	5002	164

prune87.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
1.9b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`diff-log`
3×	`sub-neg` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 70

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms	(* (sin x) (sin eps))
9.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series295.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos x) (cos eps))
83.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
49.0ms	(* (sin x) (sin eps))
125.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify112.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	304	633
1	1061	602
2	4487	583
3	5002	583

prune230.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
1.9b	(- (- (* (cos x) (cos eps)) (* (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (sin x)) (sin eps)))) (cos x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
7×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3` `diff-log`
2×	`sub-neg` `associate--l+`
1×	`associate--l-` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 51

Calls

4 calls:

4.0ms	(cbrt (sin x))
1.0ms	(cbrt (sin x))
1.0ms	(cbrt (sin x))
10.0ms	(- (- (* (cos x) (cos eps)) (* (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (sin x)) (sin eps)))) (cos x))

series415.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (sin x))
95.0ms	(cbrt (sin x))
95.0ms	(cbrt (sin x))
124.0ms	(- (- (* (cos x) (cos eps)) (* (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (sin x)) (sin eps)))) (cos x))

simplify59.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	187	622
1	481	552
2	1873	502
3	5002	476

prune230.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 16.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.4b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.5b	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
1.7b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
18×	`unpow-prod-down` `cube-prod`
16×	`difference-of-squares`
11×	`add-log-exp`
10×	`add-cube-cbrt` `sqr-pow`
6×	`pow1` `add-exp-log` `pow-unpow` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`cube-div`
2×	`cube-mult` `pow-to-exp` `sub-neg` `associate-+l+` `flip3--` `pow-pow` `diff-log` `unpow3` `pow-exp` `sum-log` `cos-mult` `flip--` `sin-mult` `rem-cube-cbrt`
1×	`difference-cubes` `+-commutative` `associate-+l-` `flip3-+` `frac-sub` `flip-+` `distribute-lft-out` `sub-div`

Counts

4 → 100

Calls

4 calls:

2.0ms	(pow (cos x) 3)
8.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
6.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
16.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series828.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (cos x) 3)
96.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
108.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
597.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify103.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	599	1433
1	2889	1321
2	5002	1280

prune338.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 16.7b

regimes255.0ms

Accuracy

82.3% (1.8b remaining)

Error of 16.8b against oracle of 15.0b and baseline of 25.0b

bsearch143.0ms

Steps

Iters	Range		Point
9	1.2358748968334836e-07	0.23288488004633429	3.239422419785483e-07
10	-9.963366173383092e-17	-1.5200352594837407e-30	-9.839040800040512e-17

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	57
1	53	57
2	53	57

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4491×	body	1280	valid
577.0ms	676×	body	2560	valid
393.0ms	1793×	body	640	valid
100.0ms	680×	body	320	valid
30.0ms	296×	body	160	valid
3.0ms	64×	body	80	valid