Details

Time bar (total: 3.0m)

sample420.0ms

Algorithm
intervals
Results
167.0ms105×body1280valid
59.0ms63×body640valid
41.0ms33×body10240exit
29.0ms163×body80valid
25.0ms182×body80nan
22.0ms17×body1280nan
21.0ms21×body640nan
15.0ms26×body320valid
6.0ms14×body160valid
5.0ms7×body320nan
3.0ms8×body160nan

simplify277.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
277.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize23.0ms

Local error

Found 3 expressions with local error:

1.7b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.0b
(pow (+ x 1) (/ 1 n))
0.3b
(pow x (/ 1 n))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
73×unpow-prod-down
63×add-sqr-sqrt
56×prod-diff
51×add-cube-cbrt
26×pow-unpow
24×sqr-pow
18×times-frac
10×distribute-lft-out
9×difference-of-squares
8×fma-neg
5×pow1 add-exp-log add-log-exp
3×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u distribute-lft-out--
2×pow-to-exp pow-pow pow-exp div-inv
1×sub-neg flip3-- diff-log flip--
Counts
3 → 152
Calls
3 calls:
Slowest
62.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
7.0ms
(pow (+ x 1) (/ 1 n))
3.0ms
(pow x (/ 1 n))

series437.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
257.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
109.0ms
(pow (+ x 1) (/ 1 n))
71.0ms
(pow x (/ 1 n))

simplify39.7s

Counts
188 → 161
Calls
188 calls:
Slowest
594.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))
558.0ms
(+ (sqrt (pow (+ x 1) (/ 1 n))) (pow (sqrt x) (/ 1 n)))
549.0ms
(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))
546.0ms
(fma (pow 1 (/ 1 n)) (pow (+ x 1) (/ 1 n)) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
510.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.7b

localize45.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.0b
(pow (+ x 1) (/ 1 n))
0.3b
(pow x (/ 1 n))
0.1b
(exp (log (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
86×*-un-lft-identity
83×unpow-prod-down
78×add-sqr-sqrt
56×prod-diff
54×add-cube-cbrt
30×sqr-pow
26×pow-unpow
18×times-frac difference-of-squares
15×log-prod exp-sum
11×distribute-lft-out
8×fma-neg
7×pow1
6×add-exp-log distribute-lft-out-- add-log-exp
4×expm1-log1p-u exp-prod add-cbrt-cube insert-posit16 log1p-expm1-u
2×pow-to-exp log-div pow-pow flip3-- exp-diff pow-exp div-inv flip--
1×sub-neg diff-log log-pow rem-exp-log
Counts
4 → 184
Calls
4 calls:
Slowest
116.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
51.0ms
(exp (log (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
14.0ms
(pow (+ x 1) (/ 1 n))
5.0ms
(pow x (/ 1 n))

series680.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
235.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
229.0ms
(exp (log (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
116.0ms
(pow (+ x 1) (/ 1 n))
101.0ms
(pow x (/ 1 n))

simplify45.3s

Counts
213 → 196
Calls
213 calls:
Slowest
780.0ms
(fma (- (sqrt (pow x (/ 1 n)))) (sqrt (pow x (/ 1 n))) (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n)))))
556.0ms
(+ (sqrt (pow (+ x 1) (/ 1 n))) (pow (sqrt x) (/ 1 n)))
542.0ms
(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
539.0ms
(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))
516.0ms
(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.7b

localize43.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.0b
(pow (+ x 1) (/ 1 n))
0.3b
(pow x (/ 1 n))
0.1b
(pow E (log (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
87×*-un-lft-identity
86×unpow-prod-down
79×add-sqr-sqrt
56×prod-diff
55×add-cube-cbrt
31×sqr-pow
30×pow-unpow
18×times-frac difference-of-squares
15×unpow-prod-up log-prod
11×distribute-lft-out
8×pow1 fma-neg
7×add-exp-log
6×distribute-lft-out-- add-log-exp
4×expm1-log1p-u add-cbrt-cube pow-exp insert-posit16 log1p-expm1-u
3×pow-to-exp pow-pow
2×log-div flip3-- div-inv flip-- pow-sub
1×e-exp-1 sub-neg diff-log log-pow
Counts
4 → 191
Calls
4 calls:
Slowest
73.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
34.0ms
(pow E (log (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
13.0ms
(pow (+ x 1) (/ 1 n))
5.0ms
(pow x (/ 1 n))

series767.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
307.0ms
(pow E (log (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
246.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
123.0ms
(pow (+ x 1) (/ 1 n))
91.0ms
(pow x (/ 1 n))

simplify49.4s

Counts
217 → 203
Calls
217 calls:
Slowest
755.0ms
(fma (- (sqrt (pow x (/ 1 n)))) (sqrt (pow x (/ 1 n))) (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n)))))
576.0ms
(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
562.0ms
(pow E (log (- (pow (sqrt (+ x 1)) (/ 1 n)) (pow x (/ (/ 1 n) 2)))))
543.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))
539.0ms
(+ (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))

prune2.6s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 18.5b

localize34.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (exp (/ (log1p x) n)) (pow x (/ 1 n)))
0.9b
(log (- (exp (/ (log1p x) n)) (pow x (/ 1 n))))
0.3b
(pow x (/ 1 n))
0.1b
(/ (log1p x) n)

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
39×*-un-lft-identity
35×add-cube-cbrt
21×prod-diff
18×times-frac
14×unpow-prod-down
13×pow-unpow
8×add-exp-log
7×log-prod
6×pow1 add-cbrt-cube add-log-exp difference-of-squares sqr-pow
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg associate-/l*
2×log-div flip3-- div-inv flip-- distribute-lft-out--
1×pow-to-exp cbrt-undiv clear-num sub-neg pow-pow frac-2neg diff-log div-exp rem-log-exp pow-exp log-pow
Counts
4 → 124
Calls
4 calls:
Slowest
27.0ms
(log (- (exp (/ (log1p x) n)) (pow x (/ 1 n))))
26.0ms
(- (exp (/ (log1p x) n)) (pow x (/ 1 n)))
8.0ms
(/ (log1p x) n)
5.0ms
(pow x (/ 1 n))

series649.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
251.0ms
(log (- (exp (/ (log1p x) n)) (pow x (/ 1 n))))
222.0ms
(- (exp (/ (log1p x) n)) (pow x (/ 1 n)))
94.0ms
(pow x (/ 1 n))
82.0ms
(/ (log1p x) n)

simplify22.9s

Counts
115 → 136
Calls
115 calls:
Slowest
739.0ms
(- (+ (/ (log -1) n) (+ (log (/ -1 x)) (log (/ -1 n)))) (+ (/ (log (/ -1 x)) n) (* 1/2 (/ 1 x))))
668.0ms
(log (sqrt (- (exp (/ (log1p x) n)) (pow x (/ 1 n)))))
661.0ms
(fma (* (cbrt (exp (/ (log1p x) n))) (cbrt (exp (/ (log1p x) n)))) (cbrt (exp (/ (log1p x) n))) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))
626.0ms
(fma (sqrt (exp (/ (log1p x) n))) (sqrt (exp (/ (log1p x) n))) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))
620.0ms
(- (exp (/ (log1p x) n)) (pow x (/ 1 n)))

prune2.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 18.3b

regimes550.0ms

Accuracy

87.4% (1.6b remaining)

Error of 19.3b against oracle of 17.7b and baseline of 30.2b

bsearch1.0s

end0.0ms

sample10.5s

Algorithm
intervals
Results
4.2s3187×body1280valid
1.3s1598×body640valid
1.2s1094×body10240exit
748.0ms628×body1280nan
730.0ms4699×body80valid
591.0ms4945×body80nan
499.0ms638×body640nan
459.0ms876×body320valid
163.0ms348×body320nan
131.0ms439×body160valid
56.0ms204×body160nan