Details

sample99.0ms

Algorithm

intervals

Results

58.0ms	146×	body	1280	valid
16.0ms	69×	body	640	valid
12.0ms	14×	body	2560	valid
3.0ms	18×	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: 42.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.3b	(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))

series68.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(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

prune108.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
2.1b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite23.0ms

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:

4.0ms	(+ (* (sin x) (sin eps)) (cos x))
4.0ms	(* (cos x) (cos eps))
4.0ms	(* (sin x) (sin eps))
10.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* (sin x) (sin eps)) (cos x))
38.0ms	(* (cos x) (cos eps))
46.0ms	(* (sin x) (sin eps))
127.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (36.0ms)

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

prune248.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 14.9b

localize13.0ms

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))

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:

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))

series288.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos x) (cos eps))
81.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
43.0ms	(* (sin x) (sin eps))
122.0ms	(- (- (* (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

prune261.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 14.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
0.3b	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
0.3b	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
3.4b	(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

82×	`pow1`
34×	`pow-prod-down`
30×	`add-exp-log` `add-cbrt-cube`
23×	`cos-mult` `sin-mult`
18×	`add-sqr-sqrt`
16×	`prod-exp` `cbrt-unprod` `associate-/l/`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `times-frac`
12×	`associate-r/` `associate-l/`
10×	`frac-times`
9×	`frac-sub`
8×	`pow-sqr` `pow-prod-up`
6×	`add-log-exp` `difference-of-squares`
5×	`sub-div`
4×	`pow-plus` `associate-/l*`
3×	`associate-/r*` `associate-/r/`
2×	`pow2` `flip3--` `div-sub` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip--`
1×	`cbrt-undiv` `associate--l-` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `frac-add` `clear-num` `flip-+` `div-inv` `distribute-lft-out--`

Counts

4 → 141

Calls

4 calls:

16.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
46.0ms	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
13.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
117.0ms	(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

series650.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
197.0ms	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
51.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
353.0ms	(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

simplify91.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	620	2413
1	3209	2129
2	5001	2123

prune420.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 14.8b

regimes240.0ms

Accuracy

84.1% (1.6b remaining)

Error of 16.0b against oracle of 14.4b and baseline of 24.3b

bsearch158.0ms

Steps

Iters	Range		Point
11	1.951179291618044e-19	5702493.407928515	3.291024564528541e-08
9	-2.526286952290626e-15	-1.2437801318881542e-20	-2.4957789297588313e-15

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	52
1	53	52
2	53	52

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.7s	4529×	body	1280	valid
581.0ms	631×	body	2560	valid
429.0ms	1815×	body	640	valid
109.0ms	656×	body	320	valid
34.0ms	298×	body	160	valid
4.0ms	71×	body	80	valid