Details

sample132.0ms

Algorithm

intervals

Results

43.0ms	47×	body	2560	valid
34.0ms	46×	body	640	valid
22.0ms	46×	body	1280	valid
9.0ms	37×	body	320	valid
4.0ms	64×	body	80	valid
3.0ms	16×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	28	8
done	28	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize20.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1.0 (cos x))
14.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite53.0ms

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:

8.0ms	(- 1.0 (cos x))
42.0ms	(/ (- 1.0 (cos x)) (* x x))

series99.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(- 1.0 (cos x))
67.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.3s

Counts

48 → 48

Iterations

Useful iterations: 2 (209.0ms)

Iter	Nodes	Cost
0	88	507
1	232	489
2	1094	441
done	5001	441

prune189.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite71.0ms

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:

25.0ms	(/ (/ (- 1.0 (cos x)) x) x)
30.0ms	(/ (- 1.0 (cos x)) x)
8.0ms	(- 1.0 (cos x))

series155.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ (/ (- 1.0 (cos x)) x) x)
64.0ms	(/ (- 1.0 (cos x)) x)
33.0ms	(- 1.0 (cos x))

simplify1.3s

Counts

156 → 156

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	229	2262
1	549	2156
2	2484	2048
done	5000	2028

prune645.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

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:

28.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
7.0ms	(exp (log (- 1.0 (cos x))))
5.0ms	(log (- 1.0 (cos x)))
12.0ms	(- 1.0 (cos x))

series234.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
20.0ms	(exp (log (- 1.0 (cos x))))
118.0ms	(log (- 1.0 (cos x)))
26.0ms	(- 1.0 (cos x))

simplify516.0ms

Counts

110 → 110

Iterations

Useful iterations: done (511.0ms)

Iter	Nodes	Cost
0	169	1343
1	309	1102
2	930	1032
done	5001	1031

prune437.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow E (log (- 1.0 (cos x)))) x)
0.3b	(pow E (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.5b	(- 1.0 (cos x))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`times-frac`
33×	`add-cube-cbrt`
30×	`log-prod`
25×	`unpow-prod-up`
15×	`unpow-prod-down`
12×	`add-exp-log` `associate-/l*`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`log-div` `add-cbrt-cube` `add-log-exp`
5×	`sqr-pow`
4×	`pow-unpow` `flip3--` `div-exp` `pow-exp` `flip--` `pow-sub`
3×	`associate-/r*`
2×	`pow-to-exp` `e-exp-1` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 124

Calls

4 calls:

27.0ms	(/ (pow E (log (- 1.0 (cos x)))) x)
19.0ms	(pow E (log (- 1.0 (cos x))))
7.0ms	(log (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series799.0ms

Counts

4 → 12

Calls

4 calls:

427.0ms	(/ (pow E (log (- 1.0 (cos x)))) x)
271.0ms	(pow E (log (- 1.0 (cos x))))
80.0ms	(log (- 1.0 (cos x)))
20.0ms	(- 1.0 (cos x))

simplify1.1s

Counts

136 → 136

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	215	1940
1	464	1826
2	1856	1535
done	5001	1527

prune480.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

regimes178.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.7b

bsearch98.0ms

Steps

Iters	Range		Point
11	9.093534403752284e-26	13730598.322931442	0.028184310562944685
8	-24.398001816905442	-0.001242952878385433	-0.034013493959747065

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	41
1	31	32
done	31	32

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.4s	1584×	body	2560	valid
888.0ms	1258×	body	1280	valid
397.0ms	1519×	body	640	valid
177.0ms	953×	body	320	valid
118.0ms	2228×	body	80	valid
55.0ms	458×	body	160	valid