Details

sample133.0ms

Algorithm

intervals

Results

65.0ms	53×	body	2560	valid
37.0ms	82×	body	1280	valid
15.0ms	62×	body	640	valid
5.0ms	30×	body	320	valid
3.0ms	26×	body	160	valid
0.0ms	3×	body	80	valid

simplify16.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.6b	(- 1.0 (cos x))

rewrite45.0ms

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:

38.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series56.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
21.0ms	(- 1.0 (cos x))

simplify773.0ms

Counts: 58 → 58

prune236.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

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:

34.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
10.0ms	(exp (log (- 1.0 (cos x))))
7.0ms	(log (- 1.0 (cos x)))
9.0ms	(- 1.0 (cos x))

series536.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
26.0ms	(exp (log (- 1.0 (cos x))))
431.0ms	(log (- 1.0 (cos x)))
26.0ms	(- 1.0 (cos x))

simplify765.0ms

Counts: 110 → 110

prune219.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.2b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.6b	(- 1.0 (cos x))

rewrite66.0ms

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:

18.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
21.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
6.0ms	(- 1.0 (cos x))

series133.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
45.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
35.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify761.0ms

Counts: 124 → 124

prune288.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- 1.0 (cos x)))
0.3b	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
1.2b	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
1.6b	(- 1.0 (cos x))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

231×	`times-frac`
159×	`add-sqr-sqrt` `*-un-lft-identity`
136×	`exp-prod`
113×	`add-cube-cbrt`
69×	`log-pow`
23×	`distribute-lft-out--` `difference-of-squares`
16×	`associate-/r/`
9×	`div-inv`
8×	`flip3--` `flip--`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*`
3×	`log-prod` `associate-/l*`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 207

Calls

4 calls:

14.0ms	(/ (sin x) (- 1.0 (cos x)))
33.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
34.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
9.0ms	(- 1.0 (cos x))

series137.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (sin x) (- 1.0 (cos x)))
42.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
35.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
22.0ms	(- 1.0 (cos x))

simplify567.0ms

Counts: 219 → 219

prune512.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.1b

regimes175.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.6b

bsearch103.0ms

Steps

Iters	Range		Point
11	4.2024004726508306e-08	6.674133934408259e+24	0.018551741562738398
11	-2447455033457.8765	-6.073684978905436e-17	-0.021392005747781384

simplify853.0ms

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.7s	1586×	body	2560	valid
1.4s	2726×	body	1280	valid
680.0ms	1907×	body	640	valid
190.0ms	930×	body	320	valid
123.0ms	480×	body	160	valid
25.0ms	366×	body	80	valid
13.0ms	5×	body	5120	valid