Details

sample97.0ms

Algorithm

intervals

Results

49.0ms	148×	body	1280	valid
25.0ms	29×	body	2560	valid
11.0ms	54×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	8×	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: 42.8b

localize8.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (cos (+ x eps)) (cos x))
2.9b	(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))
5.0ms	(cos (+ x eps))

series69.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify108.0ms

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

prune92.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 19.2b

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))
3.3b	(- (- (* (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))

series290.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos x) (cos eps))
81.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
43.0ms	(* (sin x) (sin eps))
127.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify116.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

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

prune260.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
3.3b	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))
3.3b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite62.0ms

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))
30.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))
20.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series385.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
48.0ms	(* (sin x) (sin eps))
125.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))
130.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify96.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	300	825
1	968	767
2	3673	746
3	5002	745

prune314.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 19.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
0.4b	(pow (cos x) 3)
0.6b	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
3.1b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite115.0ms

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:

58.0ms	(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
1.0ms	(pow (cos x) 3)
7.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
44.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series949.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
29.0ms	(pow (cos x) 3)
109.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
610.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify184.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	809	2240
1	4804	2061
2	5001	2061

prune551.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 18.9b

regimes383.0ms

Accuracy

83.3% (1.6b remaining)

Error of 16.4b against oracle of 14.8b and baseline of 24.5b

bsearch104.0ms

Steps

Iters	Range		Point
8	1.7888545263047805e-09	1.4320063078422164e-06	9.257973088560005e-08
7	-6.670553018524384e-09	-5.401657461917285e-11	-6.569641051506792e-09

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	17
1	35	17

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4461×	body	1280	valid
555.0ms	663×	body	2560	valid
407.0ms	1865×	body	640	valid
101.0ms	680×	body	320	valid
30.0ms	252×	body	160	valid
4.0ms	79×	body	80	valid