Details

Time bar (total: 11.6s)

sample267.0ms

Algorithm
intervals
Results
95.0ms76×body1280valid
87.0ms33×body2560valid
26.0ms44×body640valid
14.0ms35×body320valid
11.0ms99×body80valid
9.0ms2×body5120valid
8.0ms81×body80nan
3.0ms15×body160valid

simplify293.0ms

Calls
1 calls:
Slowest
293.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.8b

localize28.0ms

Local error

Found 3 expressions with local error:

11.4b
(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))
7.3b
(pow (+ 1 (/ i n)) n)
1.7b
(fma (pow (+ 1 (/ i n)) n) 100 -100)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×times-frac
6×add-exp-log
5×add-cbrt-cube div-inv
4×pow1 associate-/r*
3×expm1-log1p-u unpow-prod-down insert-posit16 log1p-expm1-u associate-/l* add-log-exp
1×pow-to-exp cbrt-undiv clear-num pow-pow frac-2neg div-exp pow-exp associate-/r/ fma-udef
Calls
3 calls:
Slowest
6.0ms
(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))
2.0ms
(pow (+ 1 (/ i n)) n)
0.0ms
(fma (pow (+ 1 (/ i n)) n) 100 -100)

series972.0ms

Calls
3 calls:
Slowest
433.0ms
(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))
287.0ms
(pow (+ 1 (/ i n)) n)
252.0ms
(fma (pow (+ 1 (/ i n)) n) 100 -100)

simplify3.4s

Calls
46 calls:
Slowest
530.0ms
(/ (* (* (fma (pow (+ 1 (/ i n)) n) 100 -100) (fma (pow (+ 1 (/ i n)) n) 100 -100)) (fma (pow (+ 1 (/ i n)) n) 100 -100)) (* (* (/ i n) (/ i n)) (/ i n)))
289.0ms
(- (* 100 (exp (* (- (log (/ 1 n)) (log (/ 1 i))) n))) 100)
284.0ms
(+ (* 100 i) (+ (* 50 (pow i 2)) (* 50/3 (pow i 3))))
271.0ms
(/ (* (- (* 100 (exp (* n (- (log (/ -1 n)) (log (/ -1 i)))))) 100) n) i)
215.0ms
(- (* 100 (exp (* n (- (log (/ -1 n)) (log (/ -1 i)))))) 100)

prune625.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.3b

localize14.0ms

Local error

Found 4 expressions with local error:

11.6b
(* n (log1p (/ i n)))
11.4b
(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))
6.6b
(log1p (/ i n))
3.7b
(fma (exp (* n (log1p (/ i n)))) 100 -100)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×times-frac
6×add-cbrt-cube add-exp-log
5×expm1-log1p-u div-inv
4×pow1 associate-/r* insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-/l*
1×cbrt-undiv log1p-udef clear-num frac-2neg div-exp log1p-expm1 associate-/r/ *-commutative fma-udef
Calls
4 calls:
Slowest
4.0ms
(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))
2.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))
0.0ms
(fma (exp (* n (log1p (/ i n)))) 100 -100)

series879.0ms

Calls
4 calls:
Slowest
385.0ms
(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))
364.0ms
(fma (exp (* n (log1p (/ i n)))) 100 -100)
68.0ms
(* n (log1p (/ i n)))
61.0ms
(log1p (/ i n))

simplify2.4s

Calls
48 calls:
Slowest
597.0ms
(/ (* (* (fma (exp (* n (log1p (/ i n)))) 100 -100) (fma (exp (* n (log1p (/ i n)))) 100 -100)) (fma (exp (* n (log1p (/ i n)))) 100 -100)) (* (* (/ i n) (/ i n)) (/ i n)))
296.0ms
(- (+ (* 50 (* (pow n 2) (pow (log n) 2))) (+ (* 50/3 (* (pow n 3) (pow (log i) 3))) (+ (* 100 (* n (log i))) (+ (* 100/3 (* (pow n 3) (* (pow (log n) 2) (log i)))) (+ (* 50/3 (* (pow n 3) (* (log i) (pow (log n) 2)))) (* 50 (* (pow n 2) (pow (log i) 2)))))))) (+ (* 100/3 (* (pow n 3) (* (pow (log i) 2) (log n)))) (+ (* 50 (* (pow n 2) (* (log n) (log i)))) (+ (* 50 (* (pow n 2) (* (log i) (log n)))) (+ (* 50/3 (* (pow n 3) (pow (log n) 3))) (+ (* 50/3 (* (pow n 3) (* (log n) (pow (log i) 2)))) (* 100 (* n (log n)))))))))
106.0ms
(/ (* (- (* 100 (exp i)) 100) n) i)
95.0ms
(- (log (fma (exp (* n (log1p (/ i n)))) 100 -100)) (log (/ i n)))
91.0ms
(/ (sqrt (fma (exp (* n (log1p (/ i n)))) 100 -100)) (/ 1 n))

prune662.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.4b

localize6.0ms

Local error

Found 4 expressions with local error:

11.6b
(* n (log1p (/ i n)))
6.6b
(log1p (/ i n))
3.7b
(fma (exp (* n (log1p (/ i n)))) 100 -100)
0.0b
(* (/ (fma (exp (* n (log1p (/ i n)))) 100 -100) i) n)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×expm1-log1p-u
4×pow1 add-cbrt-cube associate-*l* add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r*
2×*-commutative
1×log1p-udef associate-*l/ log1p-expm1 fma-udef div-inv
Calls
4 calls:
Slowest
4.0ms
(* (/ (fma (exp (* n (log1p (/ i n)))) 100 -100) i) n)
2.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))
0.0ms
(fma (exp (* n (log1p (/ i n)))) 100 -100)

series794.0ms

Calls
4 calls:
Slowest
391.0ms
(* (/ (fma (exp (* n (log1p (/ i n)))) 100 -100) i) n)
275.0ms
(fma (exp (* n (log1p (/ i n)))) 100 -100)
70.0ms
(* n (log1p (/ i n)))
58.0ms
(log1p (/ i n))

simplify697.0ms

Calls
20 calls:
Slowest
264.0ms
(- (+ (* 50 (* (pow n 2) (pow (log n) 2))) (+ (* 50/3 (* (pow n 3) (pow (log i) 3))) (+ (* 100 (* n (log i))) (+ (* 100/3 (* (pow n 3) (* (pow (log n) 2) (log i)))) (+ (* 50/3 (* (pow n 3) (* (log i) (pow (log n) 2)))) (* 50 (* (pow n 2) (pow (log i) 2)))))))) (+ (* 100/3 (* (pow n 3) (* (pow (log i) 2) (log n)))) (+ (* 50 (* (pow n 2) (* (log n) (log i)))) (+ (* 50 (* (pow n 2) (* (log i) (log n)))) (+ (* 50/3 (* (pow n 3) (pow (log n) 3))) (+ (* 50/3 (* (pow n 3) (* (log n) (pow (log i) 2)))) (* 100 (* n (log n)))))))))
78.0ms
(/ (* (- (* 100 (exp i)) 100) n) i)
76.0ms
(/ (* (- (* 100 (exp i)) 100) n) i)
64.0ms
(- (log (/ -1 n)) (log (/ -1 i)))
39.0ms
(* (fma (exp (* n (log1p (/ i n)))) 100 -100) n)

prune539.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.4b