Details

sample85.0ms

Algorithm

intervals

Results

45.0ms	141×	body	1280	valid
15.0ms	18×	body	2560	valid
11.0ms	53×	body	640	valid
4.0ms	28×	body	320	valid
1.0ms	13×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.1b

localize14.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (cos (+ x eps)) (cos x))
2.7b	(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:

6.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

series63.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify110.0ms

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

prune93.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.0b

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)))
0.3b	(* (sin x) (sin eps))
3.8b	(- (- (* (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))

series298.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos x) (cos eps))
83.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
43.0ms	(* (sin x) (sin eps))
128.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify115.0ms

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

prune254.0ms

Filtered

82 candidates to 57 candidates (69.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.3b	(* (sin x) (sin eps))
3.8b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
3.8b	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms	(* (sin x) (sin eps))
23.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
30.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
44.0ms	(* (sin x) (sin eps))
132.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
127.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

simplify97.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	300	825
1	970	767
2	3675	746
3	5002	745

prune297.0ms

Filtered

85 candidates to 56 candidates (65.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (- (* (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)
3.6b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

13.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
1.0ms	(pow (cos x) 3)
6.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
45.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series829.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
28.0ms	(pow (cos x) 3)
107.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
596.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify99.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	599	1433
1	2889	1321
2	5002	1280

prune351.0ms

Filtered

112 candidates to 63 candidates (56.3%)

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.7b

regimes297.0ms

Accuracy

83% (1.7b remaining)

Error of 16.0b against oracle of 14.3b and baseline of 24.4b

bsearch119.0ms

Steps

Iters	Range		Point
9	6.076487468149909e-10	0.8818080259852756	1.1618945885559161e-07
8	-1.1644421995593973e-08	-1.289801985686209e-11	-8.54115634291998e-10

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	62
1	44	62

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.5s	4498×	body	1280	valid
505.0ms	601×	body	2560	valid
405.0ms	1840×	body	640	valid
100.0ms	680×	body	320	valid
27.0ms	286×	body	160	valid
5.0ms	95×	body	80	valid