Details

sample229.0ms

Algorithm

intervals

Results

113.0ms	53×	body	2560	valid
68.0ms	87×	body	1280	valid
23.0ms	60×	body	640	valid
10.0ms	36×	body	320	valid
3.0ms	14×	body	160	valid
1.0ms	6×	body	80	valid

simplify24.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize16.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.2b	(- 1.0 (cos x))

rewrite79.0ms

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:

63.0ms	(/ (- 1.0 (cos x)) (sin x))
13.0ms	(- 1.0 (cos x))

series85.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- 1.0 (cos x)) (sin x))
38.0ms	(- 1.0 (cos x))

simplify917.0ms

Counts: 58 → 58

prune261.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (sqrt (- 1.0 (cos x))))
0.2b	(/ (sqrt (- 1.0 (cos x))) (/ (sin x) (sqrt (- 1.0 (cos x)))))
1.2b	(- 1.0 (cos x))
1.2b	(- 1.0 (cos x))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
346×	`add-sqr-sqrt` `*-un-lft-identity`
310×	`sqrt-prod`
218×	`add-cube-cbrt`
64×	`distribute-lft-out--` `difference-of-squares`
38×	`associate-/r*`
22×	`sqrt-div`
21×	`associate-/r/`
13×	`flip3--` `flip--`
11×	`add-exp-log` `add-cbrt-cube` `div-inv` `associate-/l*`
8×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `div-exp`
2×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 372

Calls

4 calls:

19.0ms	(/ (sin x) (sqrt (- 1.0 (cos x))))
71.0ms	(/ (sqrt (- 1.0 (cos x))) (/ (sin x) (sqrt (- 1.0 (cos x)))))
7.0ms	(- 1.0 (cos x))
7.0ms	(- 1.0 (cos x))

series246.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (sin x) (sqrt (- 1.0 (cos x))))
48.0ms	(/ (sqrt (- 1.0 (cos x))) (/ (sin x) (sqrt (- 1.0 (cos x)))))
22.0ms	(- 1.0 (cos x))
24.0ms	(- 1.0 (cos x))

simplify2.0s

Counts: 384 → 384

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.5b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.1b	(- (pow 1.0 3) (pow (cos x) 3))
1.2b	(- 1.0 (cos x))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
10×	`add-log-exp`
9×	`sqr-pow`
7×	`add-cube-cbrt`
6×	`distribute-lft-out--`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow-unpow`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`difference-cubes` `+-commutative` `cube-mult` `pow-to-exp` `sqr-cos` `associate-+l+` `distribute-rgt-out` `pow-pow` `flip3-+` `unpow3` `pow-exp` `sum-log` `flip-+` `rem-cube-cbrt`

Counts

4 → 84

Calls

4 calls:

4.0ms	(pow (cos x) 3)
14.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
46.0ms	(- (pow 1.0 3) (pow (cos x) 3))
12.0ms	(- 1.0 (cos x))

series240.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow (cos x) 3)
55.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
93.0ms	(- (pow 1.0 3) (pow (cos x) 3))
33.0ms	(- 1.0 (cos x))

simplify1.0s

Counts: 96 → 96

prune655.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.0b	(log (exp (pow (cos x) 3)))
1.1b	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))
1.2b	(- 1.0 (cos x))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `log-pow`
12×	`exp-prod`
9×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `log-prod`
5×	`difference-of-squares`
4×	`add-exp-log` `unpow-prod-down` `cube-prod` `add-cbrt-cube`
3×	`associate--r+` `distribute-lft-out--`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `sqr-pow`
1×	`+-commutative` `cube-mult` `sqr-cos` `associate-+l+` `distribute-rgt-out` `flip3-+` `unpow3` `rem-log-exp` `sum-log` `flip-+`

Counts

4 → 72

Calls

4 calls:

14.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
11.0ms	(log (exp (pow (cos x) 3)))
68.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))
7.0ms	(- 1.0 (cos x))

series188.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
30.0ms	(log (exp (pow (cos x) 3)))
68.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))
36.0ms	(- 1.0 (cos x))

simplify785.0ms

Counts: 84 → 84

prune558.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes296.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.0b

bsearch114.0ms

Steps

Iters	Range		Point
10	1.3099675947624547e-09	64828.07766974042	0.022130223242205784
9	-1.9338314318659307	-5.99435871131559e-06	-0.019455733193387614

simplify1.1s

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.5s	1627×	body	2560	valid
3.1s	2741×	body	1280	valid
1.3s	1866×	body	640	valid
398.0ms	937×	body	320	valid
97.0ms	350×	body	80	valid
96.0ms	476×	body	160	valid
18.0ms	3×	body	5120	valid