Details

sample161.0ms

Algorithm

intervals

Results

81.0ms	61×	body	2560	valid
45.0ms	82×	body	1280	valid
16.0ms	59×	body	640	valid
5.0ms	27×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	14×	body	80	valid

simplify2.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite47.0ms

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:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
24.0ms	(- 1.0 (cos x))

simplify77.0ms

Counts: 58 → 58

prune173.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.7b	(- 1.0 (cos x))

rewrite48.0ms

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:

26.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
7.0ms	(exp (log (- 1.0 (cos x))))
5.0ms	(log (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series164.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
22.0ms	(exp (log (- 1.0 (cos x))))
82.0ms	(log (- 1.0 (cos x)))
21.0ms	(- 1.0 (cos x))

simplify80.0ms

Counts: 110 → 110

prune259.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
0.3b	(log (- 1.0 (cos x)))
0.3b	(pow E (log (- 1.0 (cos x))))
1.7b	(- 1.0 (cos x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`times-frac`
33×	`add-cube-cbrt`
30×	`log-prod`
25×	`unpow-prod-up`
15×	`unpow-prod-down`
12×	`add-exp-log` `associate-/l*`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`log-div` `add-cbrt-cube` `add-log-exp`
5×	`sqr-pow`
4×	`pow-unpow` `flip3--` `div-exp` `pow-exp` `flip--` `pow-sub`
3×	`associate-/r*`
2×	`pow-to-exp` `e-exp-1` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 124

Calls

4 calls:

21.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
5.0ms	(log (- 1.0 (cos x)))
7.0ms	(pow E (log (- 1.0 (cos x))))
12.0ms	(- 1.0 (cos x))

series857.0ms

Counts

4 → 12

Calls

4 calls:

515.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
85.0ms	(log (- 1.0 (cos x)))
237.0ms	(pow E (log (- 1.0 (cos x))))
21.0ms	(- 1.0 (cos x))

simplify44.0ms

Counts: 136 → 136

prune500.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
0.6b	(log (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x)))))
0.8b	(log (- (pow 1.0 3) (pow (cos x) 3)))
1.5b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite79.0ms

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:

13.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
19.0ms	(log (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x)))))
19.0ms	(log (- (pow 1.0 3) (pow (cos x) 3)))
23.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series363.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
140.0ms	(log (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x)))))
118.0ms	(log (- (pow 1.0 3) (pow (cos x) 3)))
57.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify48.0ms

Counts: 109 → 109

prune404.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

regimes156.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.4b

bsearch84.0ms

Steps

Iters	Range		Point
8	0.00035048323440066366	1.494961173861339	0.019582639523059296
7	-0.023229637516429813	-0.00044970739729878565	-0.02150701321781053

simplify1.0ms

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.3s	2764×	body	1280	valid
2.3s	1604×	body	2560	valid
659.0ms	1873×	body	640	valid
335.0ms	906×	body	320	valid
111.0ms	511×	body	160	valid
28.0ms	339×	body	80	valid
14.0ms	3×	body	5120	valid