Details

sample226.0ms

Algorithm

intervals

Results

100.0ms	42×	body	2560	valid
67.0ms	86×	body	1280	valid
29.0ms	68×	body	640	valid
10.0ms	34×	body	320	valid
4.0ms	18×	body	160	valid
1.0ms	8×	body	80	valid

simplify14.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize19.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.2b	(- 1.0 (cos x))

rewrite55.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 52

Calls

2 calls:

23.0ms	(/ (- 1.0 (cos x)) (sin x))
8.0ms	(- 1.0 (cos x))

series84.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- 1.0 (cos x)) (sin x))
40.0ms	(- 1.0 (cos x))

simplify1.3s

Counts

58 → 58

Iterations

Iter	Nodes
done	5002
3	1941
2	596
1	240
0	106

prune376.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
1.2b	(- 1.0 (cos x))

rewrite59.0ms

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--` `div-inv` `flip--` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `diff-log` `pow-flip` `inv-pow`

Counts

3 → 159

Calls

3 calls:

35.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
12.0ms	(/ (sin x) (- 1.0 (cos x)))
5.0ms	(- 1.0 (cos x))

series127.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
55.0ms	(/ (sin x) (- 1.0 (cos x)))
21.0ms	(- 1.0 (cos x))

simplify2.1s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
2	1774
1	575
0	239

prune556.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (+ 1.0 (cos x)) (- 1.0 (cos x))) (sin x))
0.4b	(+ 1.0 (cos x))
0.4b	(+ 1.0 (cos x))
1.2b	(- 1.0 (cos x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

26.0ms	(/ (* (+ 1.0 (cos x)) (- 1.0 (cos x))) (sin x))
10.0ms	(+ 1.0 (cos x))
10.0ms	(+ 1.0 (cos x))
8.0ms	(- 1.0 (cos x))

series164.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (* (+ 1.0 (cos x)) (- 1.0 (cos x))) (sin x))
13.0ms	(+ 1.0 (cos x))
18.0ms	(+ 1.0 (cos x))
24.0ms	(- 1.0 (cos x))

simplify1.4s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
2	1197
1	344
0	123

prune531.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (+ 1.0 (cos x)) (- 1.0 (cos x))) (sin x))
0.4b	(+ 1.0 (cos x))
0.4b	(+ 1.0 (cos x))
1.2b	(- 1.0 (cos x))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

35.0ms	(/ (* (+ 1.0 (cos x)) (- 1.0 (cos x))) (sin x))
5.0ms	(+ 1.0 (cos x))
5.0ms	(+ 1.0 (cos x))
5.0ms	(- 1.0 (cos x))

series204.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (* (+ 1.0 (cos x)) (- 1.0 (cos x))) (sin x))
11.0ms	(+ 1.0 (cos x))
17.0ms	(+ 1.0 (cos x))
38.0ms	(- 1.0 (cos x))

simplify1.6s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
2	1197
1	344
0	123

prune452.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

regimes326.0ms

Accuracy

98.8% (0.3b remaining)

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

bsearch158.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	0.027845000675864373
10	-17239113253358.373	-4.96108325192681e-05	-0.027638311984739105

simplify8.0ms

Iterations

Iter	Nodes
done	41
1	41
0	31

end0.0ms

sample8.3s

Algorithm

intervals

Results

4.0s	1660×	body	2560	valid
2.7s	2710×	body	1280	valid
953.0ms	1881×	body	640	valid
333.0ms	940×	body	320	valid
89.0ms	474×	body	160	valid
36.0ms	332×	body	80	valid
20.0ms	3×	body	5120	valid