Details

sample185.0ms

Algorithm

intervals

Results

64.0ms	109×	body	1280	valid
23.0ms	35×	body	10240	exit
21.0ms	47×	body	640	valid
16.0ms	24×	body	1280	nan
9.0ms	129×	body	80	valid
8.0ms	162×	body	80	nan
7.0ms	17×	body	640	nan
6.0ms	19×	body	320	valid
3.0ms	11×	body	320	nan
3.0ms	14×	body	160	valid
1.0ms	8×	body	160	nan

simplify196.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize21.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite201.0ms

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:

4.0ms	(pow x (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
184.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series775.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(pow x (/ 1.0 n))
232.0ms	(pow (+ x 1.0) (/ 1.0 n))
434.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify46.0ms

Counts: 88 → 88

prune372.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(* (cbrt x) (cbrt x))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`cbrt-prod`
13×	`pow-unpow`
12×	`pow1`
9×	`times-frac`
7×	`add-exp-log` `pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `pow-plus` `diff-log` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

1.0ms	(cbrt x)
11.0ms	(* (cbrt x) (cbrt x))
14.0ms	(pow (+ x 1.0) (/ 1.0 n))
114.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

series1.7s

Counts

4 → 12

Calls

4 calls:

301.0ms	(cbrt x)
388.0ms	(* (cbrt x) (cbrt x))
240.0ms	(pow (+ x 1.0) (/ 1.0 n))
723.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

simplify60.0ms

Counts: 103 → 103

prune858.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
0.8b	(pow (cbrt (cbrt x)) 4)
1.0b	(pow (+ x 1.0) (/ 1.0 n))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (pow (cbrt (cbrt x)) 4) (* (cbrt (cbrt x)) (cbrt (cbrt x)))) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

1.0ms	(cbrt (cbrt x))
4.0ms	(pow (cbrt (cbrt x)) 4)
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
106.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (pow (cbrt (cbrt x)) 4) (* (cbrt (cbrt x)) (cbrt (cbrt x)))) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

series1.5s

Counts

4 → 12

Calls

4 calls:

370.0ms	(cbrt (cbrt x))
347.0ms	(pow (cbrt (cbrt x)) 4)
173.0ms	(pow (+ x 1.0) (/ 1.0 n))
610.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (pow (cbrt (cbrt x)) 4) (* (cbrt (cbrt x)) (cbrt (cbrt x)))) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

simplify54.0ms

Counts: 90 → 90

prune618.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
0.8b	(pow (cbrt (cbrt x)) 4)
1.0b	(pow (+ x 1.0) (/ 1.0 n))
5.0b	(log (exp (pow (cbrt (cbrt x)) 4)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
25×	`*-un-lft-identity`
23×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`unpow-prod-down`
16×	`pow-unpow`
14×	`log-pow`
13×	`exp-prod`
9×	`times-frac`
7×	`pow1`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`log-prod` `pow-pow` `sqr-pow`
2×	`pow-to-exp` `pow1/3` `pow-exp`
1×	`rem-log-exp` `div-inv` `distribute-lft-out`

Counts

4 → 91

Calls

4 calls:

1.0ms	(cbrt (cbrt x))
4.0ms	(pow (cbrt (cbrt x)) 4)
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
23.0ms	(log (exp (pow (cbrt (cbrt x)) 4)))

series1.6s

Counts

4 → 12

Calls

4 calls:

373.0ms	(cbrt (cbrt x))
505.0ms	(pow (cbrt (cbrt x)) 4)
212.0ms	(pow (+ x 1.0) (/ 1.0 n))
523.0ms	(log (exp (pow (cbrt (cbrt x)) 4)))

simplify75.0ms

Counts: 103 → 103

prune669.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.2b

regimes291.0ms

Accuracy

90.4% (1.8b remaining)

Error of 22.5b against oracle of 20.7b and baseline of 39.7b

bsearch388.0ms

Steps

Iters	Range		Point
8	5.803242851779569e-05	0.9435061171835805	0.9298484945110257
11	-3592450.023809973	-9.7230406766574e-18	-1.854090949258976

simplify46.0ms

end0.0ms

sample8.2s

Algorithm

intervals

Results

2.7s	3122×	body	1280	valid
1.3s	1180×	body	10240	exit
958.0ms	1620×	body	640	valid
629.0ms	4668×	body	80	valid
549.0ms	702×	body	1280	nan
440.0ms	5103×	body	80	nan
343.0ms	834×	body	320	valid
332.0ms	661×	body	640	nan
110.0ms	357×	body	320	nan
96.0ms	465×	body	160	valid
32.0ms	179×	body	160	nan