Details

Time bar (total: 23.2s)

sample221.0ms

Algorithm
intervals
Results
81.0ms79×body1280valid
72.0ms29×body2560valid
27.0ms52×body640valid
10.0ms99×body80valid
7.0ms22×body320valid
6.0ms70×body80nan
4.0ms17×body160valid

simplify212.0ms

Calls
1 calls:
Slowest
212.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.6b

localize16.0ms

Local error

Found 3 expressions with local error:

9.4b
(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))
6.8b
(pow (+ 1 (/ i n)) n)
0.5b
(fma (pow (+ 1 (/ i n)) n) 100 -100)

rewrite7.0ms

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
4.0ms
(/ (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)

series936.0ms

Calls
3 calls:
Slowest
346.0ms
(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))
312.0ms
(fma (pow (+ 1 (/ i n)) n) 100 -100)
278.0ms
(pow (+ 1 (/ i n)) n)

simplify3.1s

Calls
46 calls:
Slowest
571.0ms
(/ (* (* (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)))
278.0ms
(/ (* (- (* 100 (exp (* n (- (log (/ -1 n)) (log (/ -1 i)))))) 100) n) i)
232.0ms
(- (* 100 (exp (* n (- (log (/ -1 n)) (log (/ -1 i)))))) 100)
218.0ms
(exp (* n (- (log (/ -1 n)) (log (/ -1 i)))))
210.0ms
(- (* 100 (exp (* (- (log (/ 1 n)) (log (/ 1 i))) n))) 100)

prune710.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.6b

localize14.0ms

Local error

Found 4 expressions with local error:

9.4b
(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))
9.4b
(* n (log1p (/ i n)))
6.6b
(log1p (/ i n))
2.8b
(fma (exp (* n (log1p (/ i n)))) 100 -100)

rewrite11.0ms

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
9.0ms
(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))
1.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))
0.0ms
(fma (exp (* n (log1p (/ i n)))) 100 -100)

series962.0ms

Calls
4 calls:
Slowest
479.0ms
(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))
348.0ms
(fma (exp (* n (log1p (/ i n)))) 100 -100)
80.0ms
(* n (log1p (/ i n)))
55.0ms
(log1p (/ i n))

simplify2.2s

Calls
48 calls:
Slowest
612.0ms
(/ (* (* (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)))
303.0ms
(- (+ (* 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)))))))))
83.0ms
(- (log (fma (exp (* n (log1p (/ i n)))) 100 -100)) (log (/ i n)))
77.0ms
(/ (* (- (* 100 (exp i)) 100) n) i)
74.0ms
(/ (* (- (* 100 (exp i)) 100) n) i)

prune842.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.3b

localize6.0ms

Local error

Found 4 expressions with local error:

9.4b
(* n (log1p (/ i n)))
8.5b
(/ (/ i n) (fma (exp (* n (log1p (/ i n)))) 100 -100))
6.6b
(log1p (/ i n))
2.8b
(fma (exp (* n (log1p (/ i n)))) 100 -100)

rewrite10.0ms

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 insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×associate-/r* associate-*r*
1×cbrt-undiv log1p-udef clear-num frac-2neg div-exp log1p-expm1 *-commutative fma-udef associate-/l/
Calls
4 calls:
Slowest
8.0ms
(/ (/ i n) (fma (exp (* n (log1p (/ i n)))) 100 -100))
2.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))
0.0ms
(fma (exp (* n (log1p (/ i n)))) 100 -100)

series1.5s

Calls
4 calls:
Slowest
1.2s
(/ (/ i n) (fma (exp (* n (log1p (/ i n)))) 100 -100))
244.0ms
(fma (exp (* n (log1p (/ i n)))) 100 -100)
65.0ms
(* n (log1p (/ i n)))
55.0ms
(log1p (/ i n))

simplify2.2s

Calls
47 calls:
Slowest
402.0ms
(/ (* (* (/ i n) (/ i n)) (/ i n)) (* (* (fma (exp (* n (log1p (/ i n)))) 100 -100) (fma (exp (* n (log1p (/ i n)))) 100 -100)) (fma (exp (* n (log1p (/ i n)))) 100 -100)))
250.0ms
(- (+ (* 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)))))))))
188.0ms
(/ i (* (- (* 100 (exp (* n (- (log (/ -1 n)) (log (/ -1 i)))))) 100) n))
187.0ms
(- (+ (* 1/200 (/ i (pow n 2))) (* 1/100 (/ 1 n))) (* 1/200 (/ i n)))
182.0ms
(/ i (* (- (* 100 (exp (* (- (log (/ 1 n)) (log (/ 1 i))) n))) 100) n))

prune727.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (fma (- (/ 1/200 n) 1/200) (/ i n) (/ 1/100 n)))
0.1b
(/ 1/200 n)
0.1b
(/ 1/100 n)
0.1b
(fma (- (/ 1/200 n) 1/200) (/ i n) (/ 1/100 n))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt pow1 *-un-lft-identity add-exp-log add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×clear-num associate-/r* frac-2neg div-inv
1×rec-exp fma-udef pow-flip inv-pow
Calls
4 calls:
Slowest
1.0ms
(/ 1 (fma (- (/ 1/200 n) 1/200) (/ i n) (/ 1/100 n)))
0.0ms
(/ 1/200 n)
0.0ms
(/ 1/100 n)
0.0ms
(fma (- (/ 1/200 n) 1/200) (/ i n) (/ 1/100 n))

series132.0ms

Calls
4 calls:
Slowest
67.0ms
(/ 1 (fma (- (/ 1/200 n) 1/200) (/ i n) (/ 1/100 n)))
32.0ms
(fma (- (/ 1/200 n) 1/200) (/ i n) (/ 1/100 n))
16.0ms
(/ 1/100 n)
16.0ms
(/ 1/200 n)

simplify1.2s

Calls
16 calls:
Slowest
190.0ms
(- (+ (* 200 (/ n i)) (+ (* 400 (/ n (pow i 2))) (* 200 (/ 1 i)))))
190.0ms
(- (+ (* 200 (/ n i)) (+ (* 400 (/ n (pow i 2))) (* 200 (/ 1 i)))))
190.0ms
(- (+ (* 1/200 (/ i (pow n 2))) (* 1/100 (/ 1 n))) (* 1/200 (/ i n)))
189.0ms
(- (+ (* 1/200 (/ i (pow n 2))) (* 1/100 (/ 1 n))) (* 1/200 (/ i n)))
189.0ms
(- (+ (* 1/200 (/ i (pow n 2))) (* 1/100 (/ 1 n))) (* 1/200 (/ i n)))

prune448.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.7b

regimes215.0ms

Accuracy

38.1% (10.6b remaining)

Error of 13.5b against oracle of 2.9b and baseline of 20.0b

bsearch406.0ms

end0.0ms

sample7.1s

Algorithm
intervals
Results
2.7s2493×body1280valid
2.2s1001×body2560valid
881.0ms1625×body640valid
371.0ms450×body160valid
285.0ms811×body320valid
280.0ms3019×body80valid
170.0ms2246×body80nan
23.0ms6×body5120valid