Details

sample94.0ms

Algorithm

intervals

Results

45.0ms	137×	body	1280	valid
24.0ms	25×	body	2560	valid
13.0ms	62×	body	640	valid
3.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	4×	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: 37.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.7b	(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))

series69.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify109.0ms

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

prune88.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
0.2b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
1.2b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite36.0ms

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:

3.0ms	(* (cos x) (cos eps))
4.0ms	(* (sin x) (sin eps))
5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
22.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series294.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos x) (cos eps))
48.0ms	(* (sin x) (sin eps))
81.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
126.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify111.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	601
2	4488	583
3	5002	583

prune236.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.2b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
1.2b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
1.3b	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

rewrite59.0ms

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:

4.0ms	(* (sin x) (sin eps))
5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
20.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
29.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin x) (sin eps))
82.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
125.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
128.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

simplify95.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	300	825
1	970	767
2	3676	746
3	5001	745

prune262.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 14.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.4b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.5b	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
1.1b	(- (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:

1.0ms	(pow (cos x) 3)
14.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
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))

series832.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (cos x) 3)
98.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
106.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
594.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify98.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (86.0ms)

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

prune337.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 14.4b

regimes242.0ms

Accuracy

83.8% (1.6b remaining)

Error of 15.5b against oracle of 13.9b and baseline of 23.8b

bsearch136.0ms

Steps

Iters	Range		Point
9	4.808780483129348e-13	8.07893749493944e-05	2.6734197226084376e-08
9	-0.00013776134412608358	-1.1851374698435839e-09	-2.1400263784195043e-07

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	52
1	49	52
2	49	52

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	4441×	body	1280	valid
548.0ms	636×	body	2560	valid
379.0ms	1830×	body	640	valid
303.0ms	701×	body	320	valid
29.0ms	304×	body	160	valid
4.0ms	88×	body	80	valid