Details

sample244.0ms

Algorithm

intervals

Results

118.0ms	53×	body	2560	valid
76.0ms	96×	body	1280	valid
21.0ms	50×	body	640	valid
10.0ms	34×	body	320	valid
3.0ms	13×	body	160	valid
2.0ms	10×	body	80	valid

simplify3.0ms

Counts: 1 → 1

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.9b	(- 1.0 (cos x))

rewrite49.0ms

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:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(- 1.0 (cos x))

series121.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(/ (- 1.0 (cos x)) (sin x))
38.0ms	(- 1.0 (cos x))

simplify124.0ms

Counts: 58 → 58

prune249.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/240 (pow x 5)) (* 1/2 x))
0.0b	(* 1/240 (pow x 5))
0.2b	(* 1/24 (pow x 3))

rewrite76.0ms

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`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`add-log-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `flip3-+` `unpow3` `sum-log` `flip-+`

Counts

3 → 67

Calls

3 calls:

20.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
23.0ms	(* 1/240 (pow x 5))
29.0ms	(* 1/24 (pow x 3))

series398.0ms

Counts

3 → 9

Calls

3 calls:

246.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
86.0ms	(* 1/240 (pow x 5))
66.0ms	(* 1/24 (pow x 3))

simplify175.0ms

Counts: 76 → 76

prune267.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.1b	(/ (sin x) (- 1.0 (cos x)))
1.9b	(- 1.0 (cos x))

rewrite86.0ms

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:

44.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
18.0ms	(/ (sin x) (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series163.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
73.0ms	(/ (sin x) (- 1.0 (cos x)))
37.0ms	(- 1.0 (cos x))

simplify84.0ms

Counts: 168 → 168

prune653.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 2 x) (* 1/6 x))
0.1b	(* 1/360 (pow x 3))
0.4b	(/ 1 (- (- (/ 2 x) (* 1/6 x)) (* 1/360 (pow x 3))))
0.4b	(* 1/6 x)

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
15×	`add-exp-log` `associate-r`
10×	`add-cbrt-cube`
9×	`times-frac`
7×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `cube-prod` `prod-exp`
3×	`associate-/r` `associate-/l`
2×	`flip3--` `div-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `sqr-pow`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `sub-neg` `rec-exp` `pow-flip` `frac-2neg` `diff-log` `1-exp` `unpow3` `pow-prod-down` `pow-exp` `clear-num` `div-inv` `inv-pow`

Counts

4 → 94

Calls

4 calls:

30.0ms	(- (/ 2 x) (* 1/6 x))
18.0ms	(* 1/360 (pow x 3))
170.0ms	(/ 1 (- (- (/ 2 x) (* 1/6 x)) (* 1/360 (pow x 3))))
16.0ms	(* 1/6 x)

series281.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (/ 2 x) (* 1/6 x))
50.0ms	(* 1/360 (pow x 3))
92.0ms	(/ 1 (- (- (/ 2 x) (* 1/6 x)) (* 1/360 (pow x 3))))
16.0ms	(* 1/6 x)

simplify45.0ms

Counts: 106 → 106

prune386.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes206.0ms

Accuracy

97.7% (0.7b remaining)

Error of 0.9b against oracle of 0.2b and baseline of 31.3b

bsearch2.0ms

simplify113.0ms

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.6s	1605×	body	2560	valid
2.9s	2707×	body	1280	valid
792.0ms	1887×	body	640	valid
735.0ms	900×	body	320	valid
131.0ms	496×	body	160	valid
52.0ms	400×	body	80	valid
19.0ms	5×	body	5120	valid