Details

sample89.0ms

Algorithm

intervals

Results

51.0ms	142×	body	1280	valid
14.0ms	64×	body	640	valid
11.0ms	13×	body	2560	valid
3.0ms	18×	body	320	valid
1.0ms	16×	body	160	valid
0.0ms	3×	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: 38.6b

localize8.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (cos (+ x eps)) (cos x))
4.5b	(cos (+ x eps))

rewrite12.0ms

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:

7.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify113.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

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

prune95.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.3b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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:

5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms	(* (cos x) (cos eps))
4.0ms	(* (sin x) (sin eps))
24.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series303.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
39.0ms	(* (cos x) (cos eps))
50.0ms	(* (sin x) (sin eps))
129.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify114.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	304	633
1	1061	602
2	4488	583
3	5001	583

prune255.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.1b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
4.0ms	(+ (* (sin x) (sin eps)) (cos x))
8.0ms	(* (sin x) (sin eps))
10.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos x) (cos eps))
51.0ms	(+ (* (sin x) (sin eps)) (cos x))
50.0ms	(* (sin x) (sin eps))
132.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	332	607
1	1284	576
2	5002	567

prune250.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

6.0ms	(+ (log (exp (* (sin x) (sin eps)))) (cos x))
4.0ms	(* (sin x) (sin eps))
1.0ms	(log (exp (* (sin x) (sin eps))))
11.0ms	(- (* (cos x) (cos eps)) (+ (log (exp (* (sin x) (sin eps)))) (cos x)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ (log (exp (* (sin x) (sin eps)))) (cos x))
51.0ms	(* (sin x) (sin eps))
45.0ms	(log (exp (* (sin x) (sin eps))))
138.0ms	(- (* (cos x) (cos eps)) (+ (log (exp (* (sin x) (sin eps)))) (cos x)))

simplify118.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	309	701
1	1065	625
2	4315	609
3	5001	609

prune227.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.0b

regimes188.0ms

Accuracy

82.8% (1.7b remaining)

Error of 16.5b against oracle of 14.8b and baseline of 24.7b

bsearch100.0ms

Steps

Iters	Range		Point
7	0.00013951198456185504	0.004380743253548005	0.00014188596036111877
8	-8.894349585236044e-09	-1.0921156594031797e-11	-8.189106507089701e-09

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	17
1	36	17

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4453×	body	1280	valid
555.0ms	632×	body	2560	valid
376.0ms	1853×	body	640	valid
95.0ms	690×	body	320	valid
26.0ms	283×	body	160	valid
5.0ms	89×	body	80	valid