Details

sample98.0ms

Algorithm

intervals

Results

52.0ms	154×	body	1280	valid
17.0ms	19×	body	2560	valid
12.0ms	55×	body	640	valid
6.0ms	20×	body	320	valid
0.0ms	4×	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: 40.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (cos (+ x eps)) (cos x))
2.4b	(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))

series72.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(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

prune89.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.8b

localize19.0ms

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))
2.6b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite25.0ms

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

series304.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos x) (cos eps))
85.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
50.0ms	(* (sin x) (sin eps))
129.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify117.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (32.0ms)

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

prune238.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos eps) (cos x))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.6b	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite28.0ms

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

series276.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos eps) (cos x))
48.0ms	(+ (* (sin x) (sin eps)) (cos x))
49.0ms	(* (sin x) (sin eps))
136.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

simplify40.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	329	606
1	1247	575
2	5002	567

prune246.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
0.2b	(* (sin x) (sin eps))
2.6b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.6b	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

10.0ms	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
5.0ms	(* (sin x) (sin eps))
9.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
6.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
50.0ms	(* (sin x) (sin eps))
127.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
133.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

simplify74.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	239	889
1	734	805
2	2890	794
3	5001	794

prune245.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 14.6b

regimes172.0ms

Accuracy

85.7% (1.5b remaining)

Error of 15.9b against oracle of 14.5b and baseline of 24.8b

bsearch127.0ms

Steps

Iters	Range		Point
8	8.67121852713505e-19	2.3324237763646973e-15	2.2931718725747495e-15
11	-402.67606408878214	-3.387926217419311e-22	-0.0003904334551807754

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	29
1	38	29

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	4481×	body	1280	valid
561.0ms	634×	body	2560	valid
420.0ms	1845×	body	640	valid
110.0ms	669×	body	320	valid
29.0ms	285×	body	160	valid
5.0ms	86×	body	80	valid