Details

sample235.0ms

Algorithm

intervals

Results

99.0ms	51×	body	2560	valid
70.0ms	94×	body	1280	valid
32.0ms	33×	body	320	valid
19.0ms	54×	body	640	valid
2.0ms	12×	body	160	valid
2.0ms	12×	body	80	valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.7b	(- 1.0 (cos x))

rewrite26.0ms

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:

18.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series75.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(- 1.0 (cos x))

simplify95.0ms

Counts: 58 → 58

prune209.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
0.1b	(* 1/24 (pow x 3))
0.3b	(* 1/240 (pow x 5))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `flip-+`

Counts

3 → 69

Calls

3 calls:

32.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
13.0ms	(* 1/24 (pow x 3))
16.0ms	(* 1/240 (pow x 5))

series191.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
46.0ms	(* 1/24 (pow x 3))
70.0ms	(* 1/240 (pow x 5))

simplify31.0ms

Counts: 78 → 78

prune214.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

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)))
1.2b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.7b	(- 1.0 (cos x))

rewrite123.0ms

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:

37.0ms	(/ (- 1.0 (cos x)) (sin x))
23.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
37.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
13.0ms	(- 1.0 (cos x))

series258.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (- 1.0 (cos x)) (sin x))
89.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
67.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
36.0ms	(- 1.0 (cos x))

simplify71.0ms

Counts: 124 → 124

prune457.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

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)))
1.7b	(- 1.0 (cos x))

rewrite80.0ms

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:

40.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
13.0ms	(exp (log (- 1.0 (cos x))))
9.0ms	(log (- 1.0 (cos x)))
13.0ms	(- 1.0 (cos x))

series222.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
20.0ms	(exp (log (- 1.0 (cos x))))
137.0ms	(log (- 1.0 (cos x)))
25.0ms	(- 1.0 (cos x))

simplify59.0ms

Counts: 110 → 110

prune354.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes269.0ms

Accuracy

98.1% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 31.6b

bsearch2.0ms

simplify93.0ms

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.5s	1634×	body	2560	valid
2.4s	2721×	body	1280	valid
2.0s	1865×	body	640	valid
394.0ms	947×	body	320	valid
103.0ms	351×	body	80	valid
94.0ms	477×	body	160	valid
23.0ms	5×	body	5120	valid