Details

sample245.0ms

Algorithm

intervals

Results

111.0ms	47×	body	2560	valid
74.0ms	87×	body	1280	valid
27.0ms	58×	body	640	valid
11.0ms	37×	body	320	valid
3.0ms	16×	body	160	valid
1.0ms	11×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize22.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.5b	(- 1.0 (cos x))

rewrite75.0ms

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:

58.0ms	(/ (- 1.0 (cos x)) (sin x))
14.0ms	(- 1.0 (cos x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
23.0ms	(- 1.0 (cos x))

simplify3.3s

Counts

58 → 58

Iterations

Useful iterations: 3 (972.0ms)

Iter	Nodes	Cost
0	106	665
1	240	645
2	805	611
3	4711	609
done	5002	609

prune277.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.5b	(- 1.0 (cos x))

rewrite73.0ms

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:

31.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
15.0ms	(exp (log (- 1.0 (cos x))))
10.0ms	(log (- 1.0 (cos x)))
13.0ms	(- 1.0 (cos x))

series207.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
28.0ms	(exp (log (- 1.0 (cos x))))
108.0ms	(log (- 1.0 (cos x)))
29.0ms	(- 1.0 (cos x))

simplify2.7s

Counts

110 → 110

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	168	1421
1	302	1183
2	837	1107
3	4191	1107
done	5000	1089

prune521.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.5b	(- 1.0 (cos x))

rewrite43.0ms

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:

33.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series74.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(- 1.0 (cos x))

simplify3.2s

Counts

58 → 58

Iterations

Useful iterations: 3 (910.0ms)

Iter	Nodes	Cost
0	106	665
1	240	645
2	805	611
3	4711	609
done	5002	609

prune243.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))
0.3b	(+ 1.0 (cos x))
0.3b	(pow (cos x) 3)
1.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite198.0ms

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-+` `associate-*r/` `div-exp` `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:

121.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))
7.0ms	(+ 1.0 (cos x))
4.0ms	(pow (cos x) 3)
54.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series408.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))
19.0ms	(+ 1.0 (cos x))
40.0ms	(pow (cos x) 3)
80.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.2s

Counts

151 → 151

Iterations

Useful iterations: 2 (882.0ms)

Iter	Nodes	Cost
0	219	3074
1	641	2891
2	3365	2723
done	5001	2723

prune526.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.1b

regimes132.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.2b

bsearch111.0ms

Steps

Iters	Range		Point
11	9.093534403752284e-26	13730598.322931442	0.020030176231735596
8	-24.398001816905442	-0.001242952878385433	-0.020453446252013504

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	41
1	34	33
done	34	33

end0.0ms

sample8.4s

Algorithm

intervals

Results

3.9s	1581×	body	2560	valid
2.9s	2726×	body	1280	valid
865.0ms	1918×	body	640	valid
277.0ms	955×	body	320	valid
87.0ms	454×	body	160	valid
74.0ms	4×	body	5120	valid
40.0ms	362×	body	80	valid