Details

sample218.0ms

Algorithm

intervals

Results

87.0ms	49×	body	2560	valid
83.0ms	81×	body	1280	valid
24.0ms	64×	body	640	valid
9.0ms	34×	body	320	valid
3.0ms	15×	body	160	valid
1.0ms	13×	body	80	valid

simplify7.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.6b	(- 1.0 (cos x))

rewrite45.0ms

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:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series87.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (- 1.0 (cos x)) (sin x))
35.0ms	(- 1.0 (cos x))

simplify3.0s

Counts

58 → 58

Iterations

Useful iterations: 3 (992.0ms)

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

prune249.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

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)))
2.6b	(- 1.0 (cos x))

rewrite85.0ms

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:

28.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
34.0ms	(/ (sin x) (- 1.0 (cos x)))
14.0ms	(- 1.0 (cos x))

series143.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
52.0ms	(/ (sin x) (- 1.0 (cos x)))
35.0ms	(- 1.0 (cos x))

simplify1.8s

Counts

168 → 168

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	239	2702
1	583	2361
2	2654	2196
done	5001	2092

prune373.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

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)))
2.0b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.6b	(- 1.0 (cos x))

rewrite114.0ms

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

Counts

4 → 112

Calls

4 calls:

19.0ms	(/ (- 1.0 (cos x)) (sin x))
50.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
32.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
7.0ms	(- 1.0 (cos x))

series210.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (- 1.0 (cos x)) (sin x))
61.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
56.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
38.0ms	(- 1.0 (cos x))

simplify621.0ms

Counts

124 → 124

Iterations

Useful iterations: done (617.0ms)

Iter	Nodes	Cost
0	163	1406
1	318	1293
2	952	1222
done	5000	1218

prune424.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

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))
0.4b	(pow (cos x) 3)
2.5b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite185.0ms

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:

120.0ms	(/ (- (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)
49.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series373.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(/ (- (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))
42.0ms	(pow (cos x) 3)
59.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.7s

Counts

151 → 151

Iterations

Useful iterations: 2 (662.0ms)

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

prune514.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes85.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.4b

bsearch118.0ms

Steps

Iters	Range		Point
8	0.01136632641909174	309.51167567074003	0.01746364724227396
10	-1950712569354.648	-0.00015980627971116164	-0.020806865409918218

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	74
1	46	74
done	46	74

end0.0ms

sample8.8s

Algorithm

intervals

Results

4.3s	1560×	body	2560	valid
2.6s	2767×	body	1280	valid
929.0ms	1892×	body	640	valid
446.0ms	952×	body	320	valid
101.0ms	479×	body	160	valid
41.0ms	346×	body	80	valid
16.0ms	4×	body	5120	valid