Details

Time bar (total: 14.4s)

sample138.0ms

Algorithm
intervals
Results
52.0ms113×body1280valid
17.0ms31×body10240exit
16.0ms45×body640valid
10.0ms24×body1280nan
8.0ms151×body80valid
5.0ms25×body320valid
5.0ms21×body640nan
5.0ms134×body80nan
2.0ms11×body320nan
2.0ms14×body160valid
1.0ms11×body160nan

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0813
11713
23413
38113
420913
565613
6324413
done500013

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.5b
(pow x (/ 1.0 n))
1.2b
(pow (+ x 1.0) (/ 1.0 n))
2.3b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite49.0ms

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:
2.0ms
(pow x (/ 1.0 n))
5.0ms
(pow (+ x 1.0) (/ 1.0 n))
39.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series470.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(pow x (/ 1.0 n))
139.0ms
(pow (+ x 1.0) (/ 1.0 n))
273.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify552.0ms

Counts
88 → 88
Iterations

Useful iterations: 2 (158.0ms)

IterNodesCost
01901337
14781246
213911206
done50001206

prune239.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow x (/ 1.0 n))
0.5b
(pow x (/ 1.0 n))
1.2b
(pow (+ x 1.0) (/ 1.0 n))
4.2b
(- (pow (+ x 1.0) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
39×pow-unpow
30×add-sqr-sqrt *-un-lft-identity
28×add-cube-cbrt
27×times-frac
11×unpow-prod-down
7×pow1 add-exp-log
6×add-log-exp
4×add-cbrt-cube sqr-pow
3×pow-to-exp pow-pow pow-exp div-inv difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out
Counts
4 → 97
Calls
4 calls:
2.0ms
(pow x (/ 1.0 n))
2.0ms
(pow x (/ 1.0 n))
7.0ms
(pow (+ x 1.0) (/ 1.0 n))
36.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

series523.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(pow x (/ 1.0 n))
56.0ms
(pow x (/ 1.0 n))
141.0ms
(pow (+ x 1.0) (/ 1.0 n))
266.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

simplify585.0ms

Counts
109 → 109
Iterations

Useful iterations: 2 (164.0ms)

IterNodesCost
01811579
14671298
214121256
done50001256

prune347.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 19.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow x (/ 1.0 n))
1.2b
(pow (+ x 1.0) (/ 1.0 n))
2.3b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b
(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite140.0ms

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:
2.0ms
(pow x (/ 1.0 n))
5.0ms
(pow (+ x 1.0) (/ 1.0 n))
40.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
89.0ms
(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series757.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(pow x (/ 1.0 n))
148.0ms
(pow (+ x 1.0) (/ 1.0 n))
279.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
274.0ms
(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify608.0ms

Counts
121 → 121
Iterations

Useful iterations: 2 (189.0ms)

IterNodesCost
02351971
15431802
215031714
done50001714

prune372.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 18.8b

localize18.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b
(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.3b
(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
22×*-un-lft-identity
20×unpow-prod-down
18×difference-of-squares
16×log-prod
12×sqr-pow
10×cbrt-prod
8×add-cube-cbrt add-log-exp
6×pow1 add-exp-log distribute-lft-out--
4×sub-neg exp-sum log-pow add-cbrt-cube
2×log-div cbrt-div flip3-- exp-diff pow1/3 diff-log rem-log-exp flip-- distribute-lft-out
Counts
4 → 86
Calls
4 calls:
39.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
39.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
36.0ms
(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
33.0ms
(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
281.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
276.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
438.0ms
(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
443.0ms
(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify1.2s

Counts
98 → 98
Iterations

Useful iterations: 3 (288.0ms)

IterNodesCost
01412446
13012374
27732196
329342148
done50002148

prune426.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.7b

regimes274.0ms

Accuracy

76.7% (2.0b remaining)

Error of 22.4b against oracle of 20.3b and baseline of 29.0b

bsearch2.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03689
14589
24989
35289
done5289

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.5s3210×body1280valid
541.0ms1581×body640valid
449.0ms1119×body10240exit
325.0ms660×body1280nan
247.0ms4726×body80valid
215.0ms676×body640nan
187.0ms4956×body80nan
187.0ms848×body320valid
66.0ms341×body320nan
61.0ms438×body160valid
21.0ms191×body160nan