Details

sample157.0ms

Algorithm

intervals

Results

78.0ms	133×	body	1280	valid
31.0ms	23×	body	2560	valid
27.0ms	68×	body	640	valid
5.0ms	21×	body	320	valid
2.0ms	9×	body	160	valid
0.0ms	2×	body	80	valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize39.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (cos (+ x eps)) (cos x))
3.3b	(cos (+ x eps))

rewrite28.0ms

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:

15.0ms	(- (cos (+ x eps)) (cos x))
12.0ms	(cos (+ x eps))

series81.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

simplify108.0ms

Counts: 30 → 30

prune93.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.1b

localize16.0ms

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))
2.7b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite112.0ms

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:

11.0ms	(* (cos x) (cos eps))
19.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
15.0ms	(* (sin x) (sin eps))
66.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series339.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos x) (cos eps))
93.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
51.0ms	(* (sin x) (sin eps))
146.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify108.0ms

Counts: 82 → 82

prune241.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos eps) (cos x))
0.2b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.6b	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite70.0ms

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:

11.0ms	(* (cos eps) (cos x))
17.0ms	(+ (* (sin x) (sin eps)) (cos x))
12.0ms	(* (sin x) (sin eps))
28.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cos eps) (cos x))
55.0ms	(+ (* (sin x) (sin eps)) (cos x))
55.0ms	(* (sin x) (sin eps))
150.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

simplify40.0ms

Counts: 77 → 77

prune299.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 14.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
0.4b	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
0.4b	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
3.1b	(- (/ (- (* (* (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))

rewrite517.0ms

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:

47.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
138.0ms	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
43.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
282.0ms	(- (/ (- (* (* (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))

series798.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
238.0ms	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
66.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
428.0ms	(- (/ (- (* (* (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))

simplify94.0ms

Counts: 153 → 153

prune480.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 14.8b

regimes269.0ms

Accuracy

86.9% (1.3b remaining)

Error of 16.1b against oracle of 14.8b and baseline of 24.8b

bsearch164.0ms

Steps

Iters	Range		Point
8	3.575792316059662e-18	1.649898981639998e-13	1.6156583390350057e-13
9	-0.00011609448734148344	-5.303706873968246e-11	-2.0905327211684276e-05

simplify1.0ms

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.5s	4496×	body	1280	valid
985.0ms	624×	body	2560	valid
660.0ms	1860×	body	640	valid
197.0ms	664×	body	320	valid
76.0ms	291×	body	160	valid
4.0ms	65×	body	80	valid