Details

sample60.0ms

Algorithm

intervals

Results

16.0ms	553×	body	80	nan
13.0ms	253×	body	160	nan
8.0ms	256×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	11	9
2	12	9
done	12	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ x (sqrt (- (* x x) 1.0))))
0.0b	(- (* x x) 1.0)
0.0b	(+ x (sqrt (- (* x x) 1.0)))
30.1b	(sqrt (- (* x x) 1.0))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log-prod` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `prod-diff`
2×	`log-div` `flip3--` `flip3-+` `sqrt-div` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `rem-log-exp` `sum-log` `log-pow`

Counts

4 → 71

Calls

4 calls:

16.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
11.0ms	(- (* x x) 1.0)
17.0ms	(+ x (sqrt (- (* x x) 1.0)))
13.0ms	(sqrt (- (* x x) 1.0))

series337.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
41.0ms	(- (* x x) 1.0)
65.0ms	(+ x (sqrt (- (* x x) 1.0)))
48.0ms	(sqrt (- (* x x) 1.0))

simplify1.8s

Counts

83 → 83

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	172	1045
1	380	921
2	1040	833
3	4247	754
done	5000	753

prune199.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(log (- (- (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))
0.5b	(/ 0.125 (pow x 3))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
40×	`times-frac`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt`
13×	`unpow-prod-down` `cube-prod`
12×	`associate-/r*`
9×	`log-prod`
8×	`add-exp-log`
5×	`difference-of-squares` `sqr-pow`
4×	`cube-mult` `log-div` `unpow3` `add-cbrt-cube`
3×	`pow1` `div-exp` `associate-/l*`
2×	`expm1-log1p-u` `flip3--` `frac-sub` `flip--` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `div-inv` `distribute-lft-out--`

Counts

2 → 91

Calls

2 calls:

75.0ms	(log (- (- (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))
8.0ms	(/ 0.125 (pow x 3))

series196.0ms

Counts

2 → 6

Calls

2 calls:

158.0ms	(log (- (- (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))
38.0ms	(/ 0.125 (pow x 3))

simplify728.0ms

Counts

97 → 97

Iterations

Useful iterations: done (724.0ms)

Iter	Nodes	Cost
0	208	1501
1	443	1307
2	1340	1248
done	5001	1237

prune198.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- (- (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))
0.5b	(cbrt (- (- (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))
0.5b	(/ 0.125 (pow x 3))
0.5b	(/ 0.125 (pow x 3))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
80×	`times-frac`
60×	`*-un-lft-identity`
56×	`add-cube-cbrt`
26×	`unpow-prod-down` `cube-prod`
24×	`associate-/r*`
18×	`cbrt-prod`
14×	`add-exp-log`
10×	`difference-of-squares` `sqr-pow`
8×	`cube-mult` `cbrt-div` `unpow3` `add-cbrt-cube`
6×	`div-exp` `associate-/l*`
4×	`pow1` `expm1-log1p-u` `flip3--` `frac-sub` `flip--` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow1/3` `pow-exp` `clear-num` `div-inv` `distribute-lft-out--`

Counts

4 → 180

Calls

4 calls:

52.0ms	(cbrt (- (- (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))
53.0ms	(cbrt (- (- (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))
8.0ms	(/ 0.125 (pow x 3))
9.0ms	(/ 0.125 (pow x 3))

series561.0ms

Counts

4 → 12

Calls

4 calls:

238.0ms	(cbrt (- (- (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))
243.0ms	(cbrt (- (- (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))
38.0ms	(/ 0.125 (pow x 3))
42.0ms	(/ 0.125 (pow x 3))

simplify724.0ms

Counts

192 → 192

Iterations

Useful iterations: done (718.0ms)

Iter	Nodes	Cost
0	219	3136
1	466	2752
2	1417	2666
done	5000	2564

prune598.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes11.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	13	14
done	13	14

end0.0ms

sample1.4s

Algorithm

intervals

Results

352.0ms	7853×	body	160	nan
332.0ms	16650×	body	80	nan
227.0ms	8000×	body	80	valid