Details

sample231.0ms

Algorithm

intervals

Results

62.0ms	89×	body	1280	valid
33.0ms	63×	body	640	valid
29.0ms	34×	body	10240	exit
24.0ms	21×	body	1280	nan
13.0ms	154×	body	80	valid
12.0ms	22×	body	640	nan
11.0ms	33×	body	320	valid
10.0ms	163×	body	80	nan
3.0ms	11×	body	320	nan
2.0ms	7×	body	160	valid
1.0ms	7×	body	160	nan

simplify2.6s

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize21.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow (+ x 1.0) (/ 1.0 n))
0.8b	(pow x (/ 1.0 n))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

24.0ms	(pow (+ x 1.0) (/ 1.0 n))
9.0ms	(pow x (/ 1.0 n))
128.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series696.0ms

Counts

3 → 9

Calls

3 calls:

210.0ms	(pow (+ x 1.0) (/ 1.0 n))
85.0ms	(pow x (/ 1.0 n))
400.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify641.0ms

Counts: 88 → 88

prune375.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.8b	(pow (cbrt x) (/ 1.0 n))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`pow-unpow`
9×	`cbrt-prod` `times-frac`
6×	`unpow-prod-down` `add-log-exp`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube`
3×	`pow1/3`
2×	`pow-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `flip--` `div-inv` `sqr-pow`

Counts

4 → 65

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
6.0ms	(pow (cbrt x) (/ 1.0 n))
137.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

series1.4s

Counts

4 → 12

Calls

4 calls:

332.0ms	(cbrt x)
294.0ms	(cbrt x)
133.0ms	(pow (cbrt x) (/ 1.0 n))
665.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

simplify865.0ms

Counts: 77 → 77

prune608.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.3b	(pow (cbrt x) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (pow (cbrt x) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n)))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `add-log-exp`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube`
3×	`pow1/3`
2×	`pow-pow`
1×	`pow-to-exp` `sub-neg` `pow-unpow` `flip3--` `diff-log` `pow-exp` `flip--` `sqr-pow`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt x)
2.0ms	(cbrt x)
7.0ms	(pow (cbrt x) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
112.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (pow (cbrt x) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n)))))

series2.1s

Counts

4 → 12

Calls

4 calls:

264.0ms	(cbrt x)
293.0ms	(cbrt x)
434.0ms	(pow (cbrt x) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
1.1s	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (pow (cbrt x) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n)))))

simplify815.0ms

Counts: 65 → 65

prune556.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ x 1.0) (/ 1.0 n))
0.8b	(pow x (/ 1.0 n))
1.6b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite471.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
27×	`unpow-prod-down`
26×	`pow-unpow`
22×	`add-cube-cbrt`
18×	`times-frac` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
14×	`sqr-pow`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
5×	`log-prod`
4×	`add-cbrt-cube`
3×	`distribute-lft-out`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 109

Calls

4 calls:

12.0ms	(pow (+ x 1.0) (/ 1.0 n))
5.0ms	(pow x (/ 1.0 n))
290.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
156.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.2s

Counts

4 → 12

Calls

4 calls:

250.0ms	(pow (+ x 1.0) (/ 1.0 n))
80.0ms	(pow x (/ 1.0 n))
383.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
465.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify706.0ms

Counts: 121 → 121

prune558.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.4b

regimes475.0ms

Accuracy

78.8% (1.9b remaining)

Error of 22.1b against oracle of 20.3b and baseline of 29.0b

bsearch273.0ms

Steps

Iters	Range		Point
10	396137.46865418117	4.3576843107348035e+18	254252678.20771694
8	-2.5110737868734752e+35	-5.657379002236054e+31	-5.75337696177514e+31

simplify753.0ms

end0.0ms

sample8.3s

Algorithm

intervals

Results

2.5s	3072×	body	1280	valid
1.5s	1641×	body	640	valid
1.1s	1089×	body	10240	exit
604.0ms	4774×	body	80	valid
543.0ms	617×	body	1280	nan
380.0ms	643×	body	640	nan
321.0ms	887×	body	320	valid
318.0ms	4964×	body	80	nan
179.0ms	319×	body	320	nan
85.0ms	393×	body	160	valid
33.0ms	175×	body	160	nan