Details

sample173.0ms

Algorithm

intervals

Results

67.0ms	49×	body	2560	valid
49.0ms	81×	body	1280	valid
20.0ms	69×	body	640	valid
15.0ms	2×	body	5120	valid
7.0ms	31×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	11×	body	80	valid

simplify18.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.3b	(- 1.0 (cos x))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

66.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series110.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(/ (- 1.0 (cos x)) (sin x))
39.0ms	(- 1.0 (cos x))

simplify924.0ms

Counts: 58 → 58

prune232.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
0.9b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.3b	(- 1.0 (cos x))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

22.0ms	(/ (- 1.0 (cos x)) (sin x))
32.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
34.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
13.0ms	(- 1.0 (cos x))

series187.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (- 1.0 (cos x)) (sin x))
59.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
45.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
31.0ms	(- 1.0 (cos x))

simplify971.0ms

Counts: 124 → 124

prune527.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
1.3b	(- 1.0 (cos x))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
105×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 159

Calls

3 calls:

43.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
33.0ms	(/ (sin x) (- 1.0 (cos x)))
12.0ms	(- 1.0 (cos x))

series166.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
65.0ms	(/ (sin x) (- 1.0 (cos x)))
36.0ms	(- 1.0 (cos x))

simplify1.0s

Counts: 168 → 168

prune468.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
0.4b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
1.1b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
48×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
15×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
3×	`difference-cubes` `pow-unpow`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-*l/` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 139

Calls

4 calls:

125.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
4.0ms	(pow (cos x) 3)
17.0ms	(+ (cos x) 1.0)
37.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series344.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
37.0ms	(pow (cos x) 3)
15.0ms	(+ (cos x) 1.0)
59.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.3s

Counts: 151 → 151

prune576.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.1b

regimes281.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.2b

bsearch151.0ms

Steps

Iters	Range		Point
9	0.0024368900564104884	555.6593536559827	0.021340329488372885
10	-248837311.7084542	-0.0006576197608759923	-0.01783437632320246

simplify1.1s

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.7s	1631×	body	2560	valid
2.5s	2781×	body	1280	valid
1.0s	1785×	body	640	valid
712.0ms	947×	body	320	valid
176.0ms	466×	body	160	valid
90.0ms	382×	body	80	valid
50.0ms	8×	body	5120	valid