Details

sample90.0ms

Algorithm

intervals

Results

47.0ms	140×	body	1280	valid
18.0ms	22×	body	2560	valid
11.0ms	58×	body	640	valid
3.0ms	23×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	4×	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: 40.3b

localize8.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
2.8b	(cos (+ x eps))

rewrite23.0ms

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:

14.0ms	(- (cos (+ x eps)) (cos x))
9.0ms	(cos (+ x eps))

series73.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify109.0ms

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

prune86.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.2b

localize13.0ms

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))
2.0b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite97.0ms

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:

10.0ms	(* (cos x) (cos eps))
16.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
12.0ms	(* (sin x) (sin eps))
57.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series326.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos x) (cos eps))
89.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
48.0ms	(* (sin x) (sin eps))
143.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify113.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	601
2	4487	583
3	5002	583

prune240.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos eps) (cos x))
0.1b	(- (* (cos eps) (cos x)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
2.0b	(- (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (cos x))

rewrite97.0ms

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:

10.0ms	(* (cos eps) (cos x))
16.0ms	(- (* (cos eps) (cos x)) (* (sin x) (sin eps)))
12.0ms	(* (sin x) (sin eps))
58.0ms	(- (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (cos x))

series332.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos eps) (cos x))
89.0ms	(- (* (cos eps) (cos x)) (* (sin x) (sin eps)))
48.0ms	(* (sin x) (sin eps))
148.0ms	(- (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (cos x))

simplify132.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	299	631
1	1027	600
2	4493	593
3	5001	593

prune236.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos eps) (cos x)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
1.9b	(log (exp (- (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (cos x))))
2.0b	(- (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (cos x))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

16.0ms	(- (* (cos eps) (cos x)) (* (sin x) (sin eps)))
11.0ms	(* (sin x) (sin eps))
65.0ms	(log (exp (- (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (cos x))))
57.0ms	(- (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (cos x))

series422.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- (* (cos eps) (cos x)) (* (sin x) (sin eps)))
52.0ms	(* (sin x) (sin eps))
140.0ms	(log (exp (- (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (cos x))))
141.0ms	(- (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (cos x))

simplify110.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	290	823
1	971	765
2	3826	758
3	5002	758

prune230.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 16.0b

regimes172.0ms

Accuracy

87.9% (1.2b remaining)

Error of 15.6b against oracle of 14.4b and baseline of 24.4b

bsearch87.0ms

Steps

Iters	Range		Point
5	1.317141247235427e-05	4.932692811293218e-05	1.3396711044516438e-05
9	-3096.4512561506854	-5.8848704152608634e-05	-0.00018949125417145804

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	51
1	47	51

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	4420×	body	1280	valid
748.0ms	653×	body	2560	valid
381.0ms	1863×	body	640	valid
98.0ms	703×	body	320	valid
29.0ms	263×	body	160	valid
5.0ms	98×	body	80	valid