Details

sample224.0ms

Algorithm

intervals

Results

100.0ms	51×	body	2560	valid
71.0ms	92×	body	1280	valid
24.0ms	60×	body	640	valid
10.0ms	33×	body	320	valid
3.0ms	11×	body	160	valid
1.0ms	9×	body	80	valid

simplify26.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.3b	(- 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:

65.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series77.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(- 1.0 (cos x))

simplify955.0ms

Counts: 58 → 58

prune257.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin x) (- 1.0 (cos x)))
0.2b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
2.3b	(- 1.0 (cos x))

rewrite55.0ms

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:

22.0ms	(/ (sin x) (- 1.0 (cos x)))
19.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
6.0ms	(- 1.0 (cos x))

series141.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (sin x) (- 1.0 (cos x)))
68.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
21.0ms	(- 1.0 (cos x))

simplify900.0ms

Counts: 168 → 168

prune477.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.3b	(- 1.0 (cos x))

rewrite38.0ms

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:

23.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(- 1.0 (cos x))

series76.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- 1.0 (cos x)) (sin x))
29.0ms	(- 1.0 (cos x))

simplify848.0ms

Counts: 58 → 58

prune154.0ms

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))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.6b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.3b	(- 1.0 (cos x))

rewrite112.0ms

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:

24.0ms	(/ (- 1.0 (cos x)) (sin x))
22.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
49.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
12.0ms	(- 1.0 (cos x))

series200.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (- 1.0 (cos x)) (sin x))
57.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
43.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
28.0ms	(- 1.0 (cos x))

simplify1.0s

Counts: 124 → 124

prune423.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

regimes193.0ms

Accuracy

97.9% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 30.3b

bsearch3.0ms

simplify1.2s

end0.0ms

sample8.6s

Algorithm

intervals

Results

4.2s	1631×	body	2560	valid
2.6s	2764×	body	1280	valid
901.0ms	1850×	body	640	valid
364.0ms	936×	body	320	valid
266.0ms	468×	body	160	valid
38.0ms	347×	body	80	valid
27.0ms	4×	body	5120	valid