Details

sample70.0ms

Algorithm

intervals

Results

31.0ms	49×	body	2560	valid
10.0ms	38×	body	1280	valid
10.0ms	50×	body	640	valid
4.0ms	32×	body	320	valid
4.0ms	76×	body	80	valid
1.0ms	11×	body	160	valid

simplify26.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize8.0ms

Local error

Found 2 expressions with local error:

1.1b	(- 1.0 (cos x))
13.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

6.0ms	(- 1.0 (cos x))
21.0ms	(/ (- 1.0 (cos x)) (* x x))

series101.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(- 1.0 (cos x))
79.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify887.0ms

Counts: 48 → 48

prune191.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
1.1b	(- 1.0 (cos x))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 114

Calls

3 calls:

73.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
20.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series167.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
60.0ms	(/ (- 1.0 (cos x)) x)
31.0ms	(- 1.0 (cos x))

simplify984.0ms

Counts: 123 → 123

prune418.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.1b	(- 1.0 (cos x))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
103×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 147

Calls

3 calls:

48.0ms	(/ (/ (- 1.0 (cos x)) x) x)
33.0ms	(/ (- 1.0 (cos x)) x)
12.0ms	(- 1.0 (cos x))

series184.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ (/ (- 1.0 (cos x)) x) x)
78.0ms	(/ (- 1.0 (cos x)) x)
34.0ms	(- 1.0 (cos x))

simplify723.0ms

Counts: 156 → 156

prune471.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) x))
0.3b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
0.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
48×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
15×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
3×	`difference-cubes` `pow-unpow`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-*l/` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 139

Calls

4 calls:

131.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) x))
3.0ms	(pow (cos x) 3)
7.0ms	(+ (cos x) 1.0)
43.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series393.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) x))
47.0ms	(pow (cos x) 3)
17.0ms	(+ (cos x) 1.0)
61.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.3s

Counts: 151 → 151

prune574.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes105.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 30.7b

bsearch154.0ms

Steps

Iters	Range		Point
8	0.00022617661863457038	0.0815671925612537	0.0307485140243717
11	-31.62993370098301	-4.221128360075206e-33	-0.03288362802178943

simplify735.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.3s	1580×	body	2560	valid
956.0ms	1249×	body	1280	valid
463.0ms	1461×	body	640	valid
211.0ms	935×	body	320	valid
153.0ms	2308×	body	80	valid
59.0ms	467×	body	160	valid