Details

sample90.0ms

Algorithm

intervals

Results

53.0ms	150×	body	1280	valid
12.0ms	64×	body	640	valid
11.0ms	13×	body	2560	valid
2.0ms	17×	body	320	valid
1.0ms	12×	body	160	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:

1.2b	(- (cos (+ x eps)) (cos x))
3.7b	(cos (+ x eps))

rewrite24.0ms

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))

series62.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(- (cos (+ x eps)) (cos x))
13.0ms	(cos (+ x eps))

simplify114.0ms

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

prune88.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.5b

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))
2.2b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite105.0ms

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))
17.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
14.0ms	(* (sin x) (sin eps))
62.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series277.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (cos x) (cos eps))
76.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
47.0ms	(* (sin x) (sin eps))
119.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify116.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (32.0ms)

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

prune241.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
2.2b	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
27.3b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`cbrt-prod` `add-cube-cbrt`
3×	`pow-unpow` `diff-log` `associate-r` `associate-l` `sin-mult`
2×	`cube-div` `cube-mult` `sub-neg` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `associate--l+` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `cbrt-div` `flip3--` `pow1/3` `*-commutative` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

12.0ms	(* (sin x) (sin eps))
9.0ms	(pow (* (sin x) (sin eps)) 3)
90.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
5.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series264.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sin x) (sin eps))
61.0ms	(pow (* (sin x) (sin eps)) 3)
116.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
46.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify42.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	293	634
1	1142	580
2	5001	565

prune286.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 12.4b

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))
2.3b	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite68.0ms

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:

10.0ms	(* (cos eps) (cos x))
16.0ms	(+ (* (sin x) (sin eps)) (cos x))
12.0ms	(* (sin x) (sin eps))
28.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos eps) (cos x))
45.0ms	(+ (* (sin x) (sin eps)) (cos x))
48.0ms	(* (sin x) (sin eps))
123.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (35.0ms)

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

prune198.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.3b

regimes206.0ms

Accuracy

86.8% (1.3b remaining)

Error of 16.0b against oracle of 14.7b and baseline of 24.3b

bsearch135.0ms

Steps

Iters	Range		Point
9	2.15302222000921e-20	1.638622225374179e-14	1.6114711274948726e-14
10	-12786724.3536924	-3.489101517161873e-08	-8.194833237230457e-08

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	52
1	51	52

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4550×	body	1280	valid
543.0ms	648×	body	2560	valid
368.0ms	1796×	body	640	valid
91.0ms	659×	body	320	valid
30.0ms	259×	body	160	valid
4.0ms	88×	body	80	valid