Details

Time bar (total: 3.4m)

sample363.0ms

Algorithm
intervals
Results
118.0ms109×body1280valid
72.0ms61×body640valid
41.0ms31×body10240exit
23.0ms133×body80valid
20.0ms23×body640nan
20.0ms19×body1280nan
20.0ms161×body80nan
13.0ms25×body320valid
8.0ms15×body320nan
6.0ms16×body160valid
0.0ms1×body160nan

simplify308.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
307.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize29.0ms

Local error

Found 3 expressions with local error:

2.1b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.0b
(pow (+ x 1) (/ 1 n))
0.3b
(pow x (/ 1 n))

rewrite102.0ms

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
88.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
7.0ms
(pow (+ x 1) (/ 1 n))
3.0ms
(pow x (/ 1 n))

series410.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
253.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
87.0ms
(pow (+ x 1) (/ 1 n))
70.0ms
(pow x (/ 1 n))

simplify41.4s

Counts
188 → 161
Calls
188 calls:
Slowest
592.0ms
(+ (sqrt (pow (+ x 1) (/ 1 n))) (pow (sqrt x) (/ 1 n)))
590.0ms
(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))
571.0ms
(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
552.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))
549.0ms
(- (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.6b

localize34.0ms

Local error

Found 4 expressions with local error:

5.3b
(log (pow x (/ 1 n)))
2.1b
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))
1.0b
(pow (+ x 1) (/ 1 n))
0.3b
(pow x (/ 1 n))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
94×*-un-lft-identity
85×add-sqr-sqrt unpow-prod-down
80×prod-diff
72×log-prod
68×add-cube-cbrt
65×exp-sum
29×sqr-pow
26×pow-unpow
18×times-frac
12×distribute-lft-out difference-of-squares
8×fma-neg add-exp-log
6×pow1 add-log-exp
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
3×pow-to-exp rem-log-exp pow-exp
2×pow-pow div-inv
1×sub-neg flip3-- diff-log log-pow flip-- distribute-lft-out--
Counts
4 → 198
Calls
4 calls:
Slowest
122.0ms
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))
14.0ms
(pow (+ x 1) (/ 1 n))
6.0ms
(log (pow x (/ 1 n)))
5.0ms
(pow x (/ 1 n))

series583.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
300.0ms
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))
108.0ms
(log (pow x (/ 1 n)))
100.0ms
(pow (+ x 1) (/ 1 n))
76.0ms
(pow x (/ 1 n))

simplify1.1m

Counts
252 → 210
Calls
252 calls:
Slowest
812.0ms
(fma (- (exp (log (sqrt (pow x (/ 1 n)))))) (exp (log (sqrt (pow x (/ 1 n))))) (* (exp (log (sqrt (pow x (/ 1 n))))) (exp (log (sqrt (pow x (/ 1 n)))))))
744.0ms
(+ (pow (+ x 1) (/ (/ 1 n) 2)) (sqrt (exp (log (pow x (/ 1 n))))))
720.0ms
(fma (- (exp (log (sqrt (pow x (/ 1 n)))))) (exp (log (sqrt (pow x (/ 1 n))))) (* (exp (log (sqrt (pow x (/ 1 n))))) (exp (log (sqrt (pow x (/ 1 n)))))))
635.0ms
(- (pow (+ x 1) (/ (/ 1 n) 2)) (exp (log (pow (sqrt x) (/ 1 n)))))
634.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (exp (log (pow x (/ (/ 1 n) 2)))))

prune2.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.6b

localize50.0ms

Local error

Found 4 expressions with local error:

5.1b
(log (pow x (/ (/ 1 n) 2)))
5.1b
(log (pow x (/ (/ 1 n) 2)))
2.1b
(- (pow (+ x 1) (/ (/ 1 n) 2)) (exp (log (pow x (/ (/ 1 n) 2)))))
1.0b
(pow (+ x 1) (/ (/ 1 n) 2))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
116×*-un-lft-identity
107×add-sqr-sqrt
90×add-cube-cbrt
85×unpow-prod-down
80×prod-diff
79×log-prod
66×times-frac
65×exp-sum
43×pow-unpow
29×sqr-pow
12×distribute-lft-out difference-of-squares
9×add-exp-log
8×fma-neg
6×rem-log-exp add-log-exp
5×pow1
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u div-inv
3×pow-to-exp pow-exp
2×log-pow
1×sub-neg pow-pow flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 219
Calls
4 calls:
Slowest
93.0ms
(- (pow (+ x 1) (/ (/ 1 n) 2)) (exp (log (pow x (/ (/ 1 n) 2)))))
8.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
8.0ms
(log (pow x (/ (/ 1 n) 2)))
7.0ms
(log (pow x (/ (/ 1 n) 2)))

series538.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
242.0ms
(- (pow (+ x 1) (/ (/ 1 n) 2)) (exp (log (pow x (/ (/ 1 n) 2)))))
107.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
96.0ms
(log (pow x (/ (/ 1 n) 2)))
93.0ms
(log (pow x (/ (/ 1 n) 2)))

simplify59.2s

Counts
276 → 231
Calls
276 calls:
Slowest
654.0ms
(fma (- (exp (log (pow x (/ (/ (/ 1 n) 2) 2))))) (exp (log (pow x (/ (/ (/ 1 n) 2) 2)))) (* (exp (log (pow x (/ (/ (/ 1 n) 2) 2)))) (exp (log (pow x (/ (/ (/ 1 n) 2) 2))))))
632.0ms
(* -1 (/ (- (* 1/2 (log (/ -1 x))) (* 1/2 (log -1))) n))
613.0ms
(fma (- (exp (log (pow x (/ (/ (/ 1 n) 2) 2))))) (exp (log (pow x (/ (/ (/ 1 n) 2) 2)))) (* (exp (log (pow x (/ (/ (/ 1 n) 2) 2)))) (exp (log (pow x (/ (/ (/ 1 n) 2) 2))))))
603.0ms
(pow (+ x 1) (/ (/ (/ 1 n) 2) 2))
575.0ms
(* -1 (/ (- (* 1/2 (log (/ -1 x))) (* 1/2 (log -1))) n))

prune3.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.6b

localize74.0ms

Local error

Found 4 expressions with local error:

5.1b
(log (pow x (/ (/ 1 n) 2)))
5.1b
(log (pow x (/ (/ 1 n) 2)))
5.1b
(log (pow x (/ (/ 1 n) 2)))
5.1b
(log (pow x (/ (/ 1 n) 2)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
28×log-prod
12×add-sqr-sqrt unpow-prod-down *-un-lft-identity rem-log-exp add-exp-log add-cube-cbrt
4×expm1-log1p-u pow-to-exp pow1 add-cbrt-cube pow-exp log-pow insert-posit16 log1p-expm1-u add-log-exp sqr-pow
Counts
4 → 84
Calls
4 calls:
Slowest
4.0ms
(log (pow x (/ (/ 1 n) 2)))
4.0ms
(log (pow x (/ (/ 1 n) 2)))
4.0ms
(log (pow x (/ (/ 1 n) 2)))
4.0ms
(log (pow x (/ (/ 1 n) 2)))

series470.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(log (pow x (/ (/ 1 n) 2)))
136.0ms
(log (pow x (/ (/ 1 n) 2)))
96.0ms
(log (pow x (/ (/ 1 n) 2)))
95.0ms
(log (pow x (/ (/ 1 n) 2)))

simplify12.2s

Counts
56 → 96
Calls
56 calls:
Slowest
889.0ms
(log (pow (* (cbrt x) (cbrt x)) (/ (/ 1 n) 2)))
677.0ms
(* -1 (/ (- (* 1/2 (log (/ -1 x))) (* 1/2 (log -1))) n))
597.0ms
(* -1 (/ (- (* 1/2 (log (/ -1 x))) (* 1/2 (log -1))) n))
571.0ms
(* -1 (/ (- (* 1/2 (log (/ -1 x))) (* 1/2 (log -1))) n))
549.0ms
(* -1 (/ (- (* 1/2 (log (/ -1 x))) (* 1/2 (log -1))) n))

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.6b

regimes296.0ms

Accuracy

89.2% (1.3b remaining)

Error of 18.9b against oracle of 17.7b and baseline of 29.4b

bsearch823.0ms

end0.0ms

sample10.9s

Algorithm
intervals
Results
3.4s3188×body1280valid
1.8s1611×body640valid
1.4s1054×body10240exit
741.0ms656×body1280nan
721.0ms4697×body80valid
672.0ms5043×body80nan
588.0ms634×body640nan
469.0ms821×body320valid
405.0ms178×body160nan
241.0ms366×body320nan
146.0ms458×body160valid