Details

Time bar (total: 4.0m)

sample314.0ms

Algorithm
intervals
Results
114.0ms80×body1280valid
109.0ms32×body2560valid
39.0ms56×body640valid
13.0ms30×body320valid
11.0ms92×body80valid
9.0ms72×body80nan
4.0ms15×body160valid

simplify571.0ms

Calls
1 calls:
Slowest
571.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.7b

localize37.0ms

Local error

Found 4 expressions with local error:

10.2b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
6.8b
(pow (+ 1 (/ i n)) n)
1.1b
(- (pow (+ 1 (/ i n)) n) 1)
0.0b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite820.0ms

Algorithm
rewrite-expression-head
Rules
593×times-frac
522×add-sqr-sqrt
410×*-un-lft-identity
252×add-cube-cbrt
182×associate-*r*
174×difference-of-squares
107×unpow-prod-down
92×sqr-pow
87×difference-of-sqr-1
34×associate-/l*
32×associate-/r*
31×associate-*r/
30×div-inv distribute-lft-out--
24×prod-diff
21×add-exp-log
18×add-cbrt-cube associate-/r/
8×fma-neg
7×pow1
6×cbrt-undiv div-exp add-log-exp
5×clear-num distribute-lft-out
4×expm1-log1p-u frac-2neg insert-posit16 log1p-expm1-u associate-/l/
3×pow-unpow expm1-def flip3-- associate-*l* prod-exp un-div-inv cbrt-unprod flip-- unswap-sqr
2×pow-to-exp pow-exp
1×sub-neg pow-pow diff-log div-sub pow-prod-down *-commutative
Calls
4 calls:
Slowest
399.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
256.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
142.0ms
(- (pow (+ 1 (/ i n)) n) 1)
10.0ms
(pow (+ 1 (/ i n)) n)

series1.5s

Calls
4 calls:
Slowest
489.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
414.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
322.0ms
(- (pow (+ 1 (/ i n)) n) 1)
271.0ms
(pow (+ 1 (/ i n)) n)

simplify3.2m

Calls
700 calls:
Slowest
962.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ i (cbrt n)))
803.0ms
(/ (- (pow (+ 1 (/ i n)) (/ n 2)) 1) (/ (cbrt i) (sqrt n)))
751.0ms
(/ (* (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (cbrt (- (pow (+ 1 (/ i n)) n) 1))) (* (cbrt (/ i n)) (cbrt (/ i n))))
699.0ms
(fma (pow (* (cbrt (+ 1 (/ i n))) (cbrt (+ 1 (/ i n)))) n) (pow (cbrt (+ 1 (/ i n))) n) (- (* (sqrt 1) (sqrt 1))))
670.0ms
(- (pow (pow (+ 1 (/ i n)) n) 3) (pow 1 3))

prune4.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.7b

localize18.0ms

Local error

Found 4 expressions with local error:

10.3b
(/ (expm1 (* n (log1p (/ i n)))) (/ i n))
10.2b
(* n (log1p (/ i n)))
5.8b
(log1p (/ i n))
0.1b
(* 100 (/ (expm1 (* n (log1p (/ i n)))) (/ i n)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
153×times-frac
107×add-sqr-sqrt
97×*-un-lft-identity
96×add-cube-cbrt
55×associate-*r*
32×associate-/r*
20×add-cbrt-cube add-exp-log
19×associate-*r/
18×associate-/r/
13×associate-/l*
10×div-inv
8×pow1
6×cbrt-undiv div-exp associate-*l*
5×expm1-log1p-u clear-num
4×frac-2neg prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down un-div-inv *-commutative
1×log1p-udef div-sub log1p-expm1 expm1-udef
Calls
4 calls:
Slowest
20.0ms
(* 100 (/ (expm1 (* n (log1p (/ i n)))) (/ i n)))
7.0ms
(/ (expm1 (* n (log1p (/ i n)))) (/ i n))
6.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))

series827.0ms

Calls
4 calls:
Slowest
356.0ms
(* 100 (/ (expm1 (* n (log1p (/ i n)))) (/ i n)))
346.0ms
(/ (expm1 (* n (log1p (/ i n)))) (/ i n))
66.0ms
(* n (log1p (/ i n)))
59.0ms
(log1p (/ i n))

simplify6.5s

Calls
214 calls:
Slowest
356.0ms
(/ (* (cbrt (expm1 (* n (log1p (/ i n))))) (cbrt (expm1 (* n (log1p (/ i n)))))) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
276.0ms
(/ (* (* (expm1 (* n (log1p (/ i n)))) (expm1 (* n (log1p (/ i n))))) (expm1 (* n (log1p (/ i n))))) (* (* (/ i n) (/ i n)) (/ i n)))
224.0ms
(* (* (* n n) n) (* (* (log1p (/ i n)) (log1p (/ i n))) (log1p (/ i n))))
199.0ms
(* (* (* 100 100) 100) (/ (* (* (expm1 (* n (log1p (/ i n)))) (expm1 (* n (log1p (/ i n))))) (expm1 (* n (log1p (/ i n))))) (/ (* (* i i) i) (* (* n n) n))))
192.0ms
(+ (log 100) (- (log (expm1 (* n (log1p (/ i n))))) (- (log i) (log n))))

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

10.3b
(/ (expm1 (* n (log1p (/ i n)))) (/ i n))
10.2b
(* n (log1p (/ i n)))
5.8b
(log1p (/ i n))
0.1b
(* (/ (expm1 (* n (log1p (/ i n)))) (/ i n)) 100)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
153×times-frac
107×add-sqr-sqrt
96×*-un-lft-identity add-cube-cbrt
55×associate-*l*
32×associate-/r*
20×add-cbrt-cube add-exp-log
19×associate-*l/
18×associate-/r/
12×associate-/l*
10×div-inv
8×pow1
6×cbrt-undiv div-exp associate-*r*
5×expm1-log1p-u
4×clear-num frac-2neg prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down *-commutative
1×log1p-udef div-sub log1p-expm1 expm1-udef
Calls
4 calls:
Slowest
20.0ms
(* (/ (expm1 (* n (log1p (/ i n)))) (/ i n)) 100)
8.0ms
(/ (expm1 (* n (log1p (/ i n)))) (/ i n))
6.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))

series832.0ms

Calls
4 calls:
Slowest
360.0ms
(* (/ (expm1 (* n (log1p (/ i n)))) (/ i n)) 100)
352.0ms
(/ (expm1 (* n (log1p (/ i n)))) (/ i n))
60.0ms
(* n (log1p (/ i n)))
60.0ms
(log1p (/ i n))

simplify9.1s

Calls
213 calls:
Slowest
354.0ms
(/ (* (cbrt (expm1 (* n (log1p (/ i n))))) (cbrt (expm1 (* n (log1p (/ i n)))))) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
352.0ms
(/ (* (cbrt (expm1 (* n (log1p (/ i n))))) (cbrt (expm1 (* n (log1p (/ i n)))))) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
311.0ms
(* (/ (expm1 (* n (log1p (/ i n)))) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n)))) 100)
276.0ms
(/ (* (* (expm1 (* n (log1p (/ i n)))) (expm1 (* n (log1p (/ i n))))) (expm1 (* n (log1p (/ i n))))) (* (* (/ i n) (/ i n)) (/ i n)))
221.0ms
(* (* (* n n) n) (* (* (log1p (/ i n)) (log1p (/ i n))) (log1p (/ i n))))

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

10.3b
(/ (expm1 (* n (log1p (/ i n)))) (/ i n))
10.2b
(* n (log1p (/ i n)))
5.8b
(log1p (/ i n))
0.1b
(* 100 (/ (expm1 (* n (log1p (/ i n)))) (/ i n)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
153×times-frac
107×add-sqr-sqrt
97×*-un-lft-identity
96×add-cube-cbrt
55×associate-*r*
32×associate-/r*
20×add-cbrt-cube add-exp-log
19×associate-*r/
18×associate-/r/
13×associate-/l*
10×div-inv
8×pow1
6×cbrt-undiv div-exp associate-*l*
5×expm1-log1p-u clear-num
4×frac-2neg prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down un-div-inv *-commutative
1×log1p-udef div-sub log1p-expm1 expm1-udef
Calls
4 calls:
Slowest
19.0ms
(* 100 (/ (expm1 (* n (log1p (/ i n)))) (/ i n)))
7.0ms
(/ (expm1 (* n (log1p (/ i n)))) (/ i n))
6.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))

series803.0ms

Calls
4 calls:
Slowest
348.0ms
(* 100 (/ (expm1 (* n (log1p (/ i n)))) (/ i n)))
336.0ms
(/ (expm1 (* n (log1p (/ i n)))) (/ i n))
62.0ms
(* n (log1p (/ i n)))
57.0ms
(log1p (/ i n))

simplify6.4s

Calls
214 calls:
Slowest
352.0ms
(/ (* (cbrt (expm1 (* n (log1p (/ i n))))) (cbrt (expm1 (* n (log1p (/ i n)))))) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
274.0ms
(/ (* (* (expm1 (* n (log1p (/ i n)))) (expm1 (* n (log1p (/ i n))))) (expm1 (* n (log1p (/ i n))))) (* (* (/ i n) (/ i n)) (/ i n)))
212.0ms
(* (* (* n n) n) (* (* (log1p (/ i n)) (log1p (/ i n))) (log1p (/ i n))))
198.0ms
(* (* (* 100 100) 100) (/ (* (* (expm1 (* n (log1p (/ i n)))) (expm1 (* n (log1p (/ i n))))) (expm1 (* n (log1p (/ i n))))) (/ (* (* i i) i) (* (* n n) n))))
189.0ms
(+ (log 100) (- (log (expm1 (* n (log1p (/ i n))))) (- (log i) (log n))))

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes172.0ms

Accuracy

57.3% (8.6b remaining)

Error of 8.6b against oracle of 0.0b and baseline of 20.1b

bsearch526.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
3.0s2483×body1280valid
2.3s981×body2560valid
998.0ms1591×body640valid
329.0ms3050×body80valid
304.0ms881×body320valid
222.0ms2251×body80nan
91.0ms451×body160valid
29.0ms7×body5120valid