Details

sample221.0ms

Algorithm

intervals

Results

106.0ms	42×	body	2560	valid
62.0ms	86×	body	1280	valid
27.0ms	68×	body	640	valid
9.0ms	34×	body	320	valid
3.0ms	18×	body	160	valid
1.0ms	8×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

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:

14.0ms	(/ (- 1.0 (cos x)) (sin x))
5.0ms	(- 1.0 (cos x))

series111.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(/ (- 1.0 (cos x)) (sin x))
46.0ms	(- 1.0 (cos x))

simplify819.0ms

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
2	805
1	240
0	106

prune372.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

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))

rewrite38.0ms

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:

14.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
12.0ms	(/ (sin x) (- 1.0 (cos x)))
5.0ms	(- 1.0 (cos x))

series135.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
60.0ms	(/ (sin x) (- 1.0 (cos x)))
29.0ms	(- 1.0 (cos x))

simplify2.0s

Counts

168 → 168

Iterations

Iter	Nodes
done	5004
2	2765
1	583
0	239

prune731.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize49.0ms

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))

rewrite48.0ms

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:

18.0ms	(/ (* (+ 1.0 (cos x)) (- 1.0 (cos x))) (sin x))
5.0ms	(+ 1.0 (cos x))
10.0ms	(+ 1.0 (cos x))
10.0ms	(- 1.0 (cos x))

series212.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (* (+ 1.0 (cos x)) (- 1.0 (cos x))) (sin x))
18.0ms	(+ 1.0 (cos x))
21.0ms	(+ 1.0 (cos x))
31.0ms	(- 1.0 (cos x))

simplify1.7s

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	1620
1	344
0	123

prune500.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
0.8b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.2b	(- 1.0 (cos x))

rewrite108.0ms

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

Counts

4 → 112

Calls

4 calls:

20.0ms	(/ (- 1.0 (cos x)) (sin x))
37.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
11.0ms	(- 1.0 (cos x))

series182.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (- 1.0 (cos x)) (sin x))
67.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
38.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
21.0ms	(- 1.0 (cos x))

simplify796.0ms

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	962
1	318
0	163

prune656.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.2b

regimes372.0ms

Accuracy

98.8% (0.4b remaining)

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

bsearch138.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	0.024496002194949438
10	-17239113253358.373	-4.96108325192681e-05	-0.0196273269902602

simplify11.0ms

Iterations

Iter	Nodes
done	43
1	43
0	32

end0.0ms

sample7.9s

Algorithm

intervals

Results

4.2s	1660×	body	2560	valid
2.1s	2710×	body	1280	valid
1.0s	1881×	body	640	valid
324.0ms	940×	body	320	valid
88.0ms	474×	body	160	valid
77.0ms	332×	body	80	valid
14.0ms	3×	body	5120	valid