Details

sample79.0ms

Algorithm

intervals

Results

34.0ms	51×	body	2560	valid
14.0ms	40×	body	1280	valid
9.0ms	41×	body	640	valid
6.0ms	33×	body	320	valid
4.0ms	79×	body	80	valid
1.0ms	12×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize7.0ms

Local error

Found 2 expressions with local error:

1.7b	(- 1.0 (cos x))
14.2b	(/ (- 1.0 (cos x)) (* x x))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

8.0ms	(- 1.0 (cos x))
37.0ms	(/ (- 1.0 (cos x)) (* x x))

series83.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(- 1.0 (cos x))
55.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify45.0ms

Counts: 48 → 48

prune140.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.2b	(* 1/24 (pow x 2))
13.6b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 66

Calls

3 calls:

19.0ms	(* 1/720 (pow x 4))
21.0ms	(* 1/24 (pow x 2))
81.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series127.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* 1/720 (pow x 4))
30.0ms	(* 1/24 (pow x 2))
50.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify137.0ms

Counts: 75 → 75

prune239.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.2b	(* 1/24 (pow x 2))
13.6b	(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `associate-+r+` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod` `unpow2`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `flip-+`

Counts

3 → 67

Calls

3 calls:

23.0ms	(* 1/720 (pow x 4))
19.0ms	(* 1/24 (pow x 2))
26.0ms	(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

series162.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(* 1/720 (pow x 4))
42.0ms	(* 1/24 (pow x 2))
64.0ms	(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

simplify141.0ms

Counts: 76 → 76

prune219.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) x)
0.1b	(/ (/ (- 1.0 (cos x)) x) x)
1.7b	(- 1.0 (cos x))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
103×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 147

Calls

3 calls:

26.0ms	(/ (- 1.0 (cos x)) x)
30.0ms	(/ (/ (- 1.0 (cos x)) x) x)
7.0ms	(- 1.0 (cos x))

series141.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- 1.0 (cos x)) x)
69.0ms	(/ (/ (- 1.0 (cos x)) x) x)
21.0ms	(- 1.0 (cos x))

simplify36.0ms

Counts: 156 → 156

prune352.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.4b

bsearch72.0ms

Steps

Iters	Range		Point
9	3.244205803610274e-06	1902.9075791774285	0.029443367970699307
8	-45.38980787391071	-0.005411406272604966	-0.03306643978524941

simplify46.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	1640×	body	2560	valid
763.0ms	1251×	body	1280	valid
572.0ms	1452×	body	640	valid
152.0ms	947×	body	320	valid
105.0ms	2232×	body	80	valid
50.0ms	478×	body	160	valid