Details

sample87.0ms

Algorithm

intervals

Results

47.0ms	146×	body	1280	valid
14.0ms	17×	body	2560	valid
12.0ms	59×	body	640	valid
4.0ms	25×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	2×	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: 40.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
3.1b	(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))
4.0ms	(cos (+ x eps))

series70.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify111.0ms

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

prune90.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.3b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite22.0ms

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:

3.0ms	(* (cos x) (cos eps))
4.0ms	(+ (* (sin x) (sin eps)) (cos x))
4.0ms	(* (sin x) (sin eps))
9.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos x) (cos eps))
49.0ms	(+ (* (sin x) (sin eps)) (cos x))
49.0ms	(* (sin x) (sin eps))
128.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (37.0ms)

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

prune239.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.2b

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

rewrite34.0ms

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)))
4.0ms	(* (sin x) (sin eps))
20.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series302.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos x) (cos eps))
83.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
44.0ms	(* (sin x) (sin eps))
130.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify117.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (31.0ms)

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

prune263.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (+ (* (sin x) (sin eps)) (cos x)) (* (cos x) (cos eps)))
0.3b	(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
0.5b	(pow (* (cos x) (cos eps)) 3)
2.2b	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `difference-of-squares` `sqr-pow`
7×	`cube-div`
6×	`unpow-prod-down` `pow-unpow` `cube-prod`
5×	`cos-mult`
4×	`flip3-+` `flip-+`
3×	`pow-pow` `pow-exp` `sum-log` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `unpow3` `frac-add` `frac-sub`
1×	`difference-cubes` `+-commutative` `sub-neg` `associate-+l+` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 87

Calls

4 calls:

16.0ms	(+ (+ (* (sin x) (sin eps)) (cos x)) (* (cos x) (cos eps)))
6.0ms	(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
3.0ms	(pow (* (cos x) (cos eps)) 3)
27.0ms	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

series641.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(+ (+ (* (sin x) (sin eps)) (cos x)) (* (cos x) (cos eps)))
74.0ms	(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
64.0ms	(pow (* (cos x) (cos eps)) 3)
406.0ms	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

simplify90.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	531	1253
1	2604	1149
2	5002	1134

prune364.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 14.2b

regimes332.0ms

Accuracy

83.6% (1.6b remaining)

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

bsearch137.0ms

Steps

Iters	Range		Point
9	6.68940051768271e-13	7.712829756242493e-08	2.1724003884687943e-10
10	-0.00043085380315138777	-1.9028865815992217e-15	-4.951154464097428e-09

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	28
1	36	28

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.7s	4447×	body	1280	valid
520.0ms	623×	body	2560	valid
402.0ms	1889×	body	640	valid
93.0ms	674×	body	320	valid
29.0ms	299×	body	160	valid
3.0ms	68×	body	80	valid