Details

sample97.0ms

Algorithm

intervals

Results

52.0ms	141×	body	1280	valid
19.0ms	22×	body	2560	valid
13.0ms	62×	body	640	valid
3.0ms	20×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	1×	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: 40.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (cos (+ x eps)) (cos x))
3.4b	(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))

series71.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (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

prune81.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.5b

localize14.0ms

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))
1.1b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite27.0ms

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))
7.0ms	(- (* (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))

series293.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos x) (cos eps))
77.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
47.0ms	(* (sin x) (sin eps))
126.0ms	(- (- (* (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	632
1	1061	601
2	4487	583
3	5002	583

prune239.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
0.4b	(pow (cos x) 3)
0.5b	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
1.0b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
18×	`unpow-prod-down` `cube-prod`
16×	`difference-of-squares`
12×	`add-cube-cbrt`
10×	`sqr-pow`
8×	`pow1` `add-exp-log` `frac-times` `cos-mult` `add-cbrt-cube` `sin-mult`
6×	`pow-unpow` `add-log-exp`
5×	`flip3--` `flip3-+` `flip--` `flip-+` `distribute-lft-out--`
4×	`cube-div` `associate-r` `associate-*l/` `frac-sub` `sub-div`
3×	`associate-l`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `associate-*r/` `pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

15.0ms	(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
2.0ms	(pow (cos x) 3)
7.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
19.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series945.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
28.0ms	(pow (cos x) 3)
115.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
602.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify180.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	809	2265
1	4798	2078
2	5002	2078

prune582.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.2b

localize22.0ms

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))
1.1b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
1.2b	(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))
7.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
44.0ms	(* (sin x) (sin eps))
132.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
130.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

simplify75.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (19.0ms)

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

prune244.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 16.2b

regimes223.0ms

Accuracy

83.7% (1.6b remaining)

Error of 15.9b against oracle of 14.3b and baseline of 24.1b

bsearch164.0ms

Steps

Iters	Range		Point
11	3.318030725202088e-29	4.9177062248324165e-05	3.284559791012932e-07
11	-358284796.04772377	-9.565599748882727e-17	-1.133154992718873e-10

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	37
1	43	37

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4393×	body	1280	valid
554.0ms	632×	body	2560	valid
412.0ms	1898×	body	640	valid
113.0ms	708×	body	320	valid
29.0ms	286×	body	160	valid
4.0ms	83×	body	80	valid