Details

sample54.0ms

Algorithm

intervals

Results

24.0ms	53×	body	2560	valid
8.0ms	48×	body	640	valid
7.0ms	32×	body	1280	valid
3.0ms	30×	body	320	valid
2.0ms	67×	body	80	valid
2.0ms	26×	body	160	valid

simplify22.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize6.0ms

Local error

Found 2 expressions with local error:

1.6b	(- 1.0 (cos x))
16.0b	(/ (- 1.0 (cos x)) (* x x))

rewrite38.0ms

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:

6.0ms	(- 1.0 (cos x))
31.0ms	(/ (- 1.0 (cos x)) (* x x))

series61.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
43.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify738.0ms

Counts: 48 → 48

prune108.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.6b	(- 1.0 (cos x))

rewrite48.0ms

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:

19.0ms	(/ (/ (- 1.0 (cos x)) x) x)
15.0ms	(/ (- 1.0 (cos x)) x)
8.0ms	(- 1.0 (cos x))

series106.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ (/ (- 1.0 (cos x)) x) x)
41.0ms	(/ (- 1.0 (cos x)) x)
22.0ms	(- 1.0 (cos x))

simplify489.0ms

Counts: 156 → 156

prune260.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) x)
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.6b	(- 1.0 (cos x))

rewrite37.0ms

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:

18.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
6.0ms	(exp (log (- 1.0 (cos x))))
4.0ms	(log (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series154.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
18.0ms	(exp (log (- 1.0 (cos x))))
72.0ms	(log (- 1.0 (cos x)))
23.0ms	(- 1.0 (cos x))

simplify866.0ms

Counts: 110 → 110

prune215.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.5b	(+ (cos x) 1.0)
1.2b	(log (- (pow 1.0 3) (pow (cos x) 3)))
1.5b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
32×	`difference-of-squares`
30×	`*-un-lft-identity`
27×	`unpow-prod-down` `cube-prod`
25×	`log-prod`
17×	`sqr-pow`
10×	`distribute-lft-out--`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `add-exp-log`
5×	`add-cbrt-cube`
3×	`pow-unpow`
2×	`difference-cubes` `log-div` `flip3--` `flip--`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `flip3-+` `diff-log` `unpow3` `rem-log-exp` `pow-exp` `sum-log` `log-pow` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 105

Calls

4 calls:

5.0ms	(pow (cos x) 3)
6.0ms	(+ (cos x) 1.0)
17.0ms	(log (- (pow 1.0 3) (pow (cos x) 3)))
21.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series191.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (cos x) 3)
12.0ms	(+ (cos x) 1.0)
105.0ms	(log (- (pow 1.0 3) (pow (cos x) 3)))
46.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify496.0ms

Counts: 117 → 117

prune284.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.1b

regimes57.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.0b

bsearch91.0ms

Steps

Iters	Range		Point
11	4.2024004726508306e-08	6.674133934408259e+24	0.029977379511048872
11	-2447455033457.8765	-6.073684978905436e-17	-0.026466559055398395

simplify629.0ms

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	1591×	body	2560	valid
362.0ms	1247×	body	1280	valid
357.0ms	1534×	body	640	valid
109.0ms	932×	body	320	valid
79.0ms	2212×	body	80	valid
39.0ms	484×	body	160	valid