Details

sample91.0ms

Algorithm

intervals

Results

38.0ms	51×	body	2560	valid
14.0ms	31×	body	1280	valid
14.0ms	42×	body	640	valid
6.0ms	32×	body	320	valid
5.0ms	88×	body	80	valid
2.0ms	12×	body	160	valid

simplify37.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize8.0ms

Local error

Found 2 expressions with local error:

2.3b	(- 1.0 (cos x))
15.7b	(/ (- 1.0 (cos x)) (* x x))

rewrite52.0ms

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:

27.0ms	(- 1.0 (cos x))
23.0ms	(/ (- 1.0 (cos x)) (* x x))

series113.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(- 1.0 (cos x))
78.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify886.0ms

Counts: 48 → 48

prune158.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.3b	(- 1.0 (cos x))

rewrite83.0ms

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:

47.0ms	(/ (/ (- 1.0 (cos x)) x) x)
18.0ms	(/ (- 1.0 (cos x)) x)
10.0ms	(- 1.0 (cos x))

series136.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (/ (- 1.0 (cos x)) x) x)
61.0ms	(/ (- 1.0 (cos x)) x)
27.0ms	(- 1.0 (cos x))

simplify675.0ms

Counts: 156 → 156

prune438.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) x)
0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.3b	(- 1.0 (cos x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`log-prod`
25×	`exp-sum`
24×	`add-cube-cbrt` `times-frac`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
3×	`associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 98

Calls

4 calls:

20.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
13.0ms	(exp (log (- 1.0 (cos x))))
8.0ms	(log (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series253.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
32.0ms	(exp (log (- 1.0 (cos x))))
102.0ms	(log (- 1.0 (cos x)))
41.0ms	(- 1.0 (cos x))

simplify974.0ms

Counts: 110 → 110

prune388.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
0.6b	(log (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x)))))
1.2b	(log (- (pow 1.0 3) (pow (cos x) 3)))
2.1b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
32×	`difference-of-squares`
28×	`log-prod`
26×	`*-un-lft-identity`
24×	`unpow-prod-down` `cube-prod`
16×	`sqr-pow`
10×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `add-cube-cbrt`
4×	`log-div` `add-cbrt-cube`
2×	`difference-cubes` `flip3--` `flip3-+` `rem-log-exp` `log-pow` `flip--` `flip-+`
1×	`+-commutative` `sub-neg` `sqr-cos` `associate-+l+` `distribute-rgt-out` `diff-log` `sum-log`

Counts

4 → 97

Calls

4 calls:

17.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
24.0ms	(log (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x)))))
33.0ms	(log (- (pow 1.0 3) (pow (cos x) 3)))
41.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series525.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
216.0ms	(log (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x)))))
169.0ms	(log (- (pow 1.0 3) (pow (cos x) 3)))
82.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify826.0ms

Counts: 109 → 109

prune607.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes136.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.8b

bsearch132.0ms

Steps

Iters	Range		Point
8	0.0026080803058150265	15.61478477777618	0.028278218138381377
8	-0.06705623481545048	-1.7104155354788486e-05	-0.03195107380254883

simplify926.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.8s	1636×	body	2560	valid
498.0ms	1225×	body	1280	valid
480.0ms	1419×	body	640	valid
172.0ms	940×	body	320	valid
129.0ms	2309×	body	80	valid
64.0ms	471×	body	160	valid