Details

Time bar (total: 1.7m)

sample346.0ms

Algorithm
intervals
Results
158.0ms89×body1280valid
94.0ms26×body2560valid
38.0ms46×body640valid
16.0ms104×body80valid
11.0ms20×body320valid
8.0ms58×body80nan
2.0ms8×body160valid

simplify137.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
137.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.4b

localize26.0ms

Local error

Found 3 expressions with local error:

10.4b
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
5.1b
(pow (+ 1 (/ i n)) n)
0.6b
(fma 100 (pow (+ 1 (/ i n)) n) -100)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
49×*-un-lft-identity
47×add-sqr-sqrt add-cube-cbrt
13×associate-/r*
9×add-exp-log
8×add-cbrt-cube
5×div-inv
4×pow1 unpow-prod-down
3×expm1-log1p-u cbrt-undiv pow-unpow div-exp insert-posit16 log1p-expm1-u associate-/l* add-log-exp
1×pow-to-exp clear-num pow-pow frac-2neg pow-exp associate-/r/ fma-udef distribute-lft-out sqr-pow
Counts
3 → 105
Calls
3 calls:
Slowest
9.0ms
(pow (+ 1 (/ i n)) n)
6.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
0.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)

series1.1s

Counts
3 → 9
Calls
3 calls:
Slowest
386.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
339.0ms
(pow (+ 1 (/ i n)) n)
327.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)

simplify37.9s

Counts
114 → 114
Calls
114 calls:
Slowest
1.0s
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i (sqrt n)))
865.0ms
(/ (cbrt (fma 100 (pow (+ 1 (/ i n)) n) -100)) (/ (sqrt i) (cbrt n)))
731.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (cbrt i) (cbrt n)))
721.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (cbrt i) (sqrt n)))
702.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (sqrt i) (cbrt n)))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.3b

localize24.0ms

Local error

Found 4 expressions with local error:

10.8b
(* n (log1p (/ i n)))
10.5b
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
4.6b
(log1p (/ i n))
3.0b
(fma 100 (exp (* n (log1p (/ i n)))) -100)

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
50×add-sqr-sqrt
48×*-un-lft-identity add-cube-cbrt
13×associate-/r*
11×add-cbrt-cube add-exp-log
6×pow1
5×expm1-log1p-u div-inv
4×insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-*r* associate-*l* associate-/l*
1×log1p-udef clear-num frac-2neg pow-prod-down prod-exp log1p-expm1 associate-/r/ *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 117
Calls
4 calls:
Slowest
9.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
6.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))
0.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)

series942.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
459.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
329.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
87.0ms
(* n (log1p (/ i n)))
67.0ms
(log1p (/ i n))

simplify17.2s

Counts
120 → 129
Calls
120 calls:
Slowest
427.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ (sqrt i) (* (cbrt n) (cbrt n))))
404.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
390.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ (* (cbrt i) (cbrt i)) (sqrt n)))
354.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ (* (cbrt i) (cbrt i)) 1))
337.0ms
(/ (sqrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.8b

localize19.0ms

Local error

Found 4 expressions with local error:

10.8b
(* n (log1p (/ i n)))
10.5b
(/ (+ (* 100 (exp (* n (log1p (/ i n))))) -100) (/ i n))
4.6b
(log1p (/ i n))
3.0b
(+ (* 100 (exp (* n (log1p (/ i n))))) -100)

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
50×add-sqr-sqrt
48×*-un-lft-identity add-cube-cbrt
13×associate-/r*
11×add-cbrt-cube add-exp-log
6×pow1 add-log-exp
5×expm1-log1p-u div-inv
4×insert-posit16 log1p-expm1-u
3×cbrt-undiv div-exp associate-*r* associate-*l* associate-/l*
2×flip3-+ flip-+ associate-/l/
1×+-commutative log1p-udef clear-num sum-log fma-def frac-2neg pow-prod-down prod-exp log1p-expm1 associate-/r/ *-commutative cbrt-unprod unswap-sqr
Counts
4 → 123
Calls
4 calls:
Slowest
36.0ms
(/ (+ (* 100 (exp (* n (log1p (/ i n))))) -100) (/ i n))
9.0ms
(+ (* 100 (exp (* n (log1p (/ i n))))) -100)
6.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))

series828.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
426.0ms
(/ (+ (* 100 (exp (* n (log1p (/ i n))))) -100) (/ i n))
282.0ms
(+ (* 100 (exp (* n (log1p (/ i n))))) -100)
63.0ms
(* n (log1p (/ i n)))
58.0ms
(log1p (/ i n))

simplify13.7s

Counts
123 → 135
Calls
123 calls:
Slowest
540.0ms
(/ (* (cbrt (+ (* 100 (exp (* n (log1p (/ i n))))) -100)) (cbrt (+ (* 100 (exp (* n (log1p (/ i n))))) -100))) (/ 1 (* (cbrt n) (cbrt n))))
361.0ms
(* (exp (* 100 (exp (* n (log1p (/ i n)))))) (exp -100))
282.0ms
(/ (* (cbrt (+ (* 100 (exp (* n (log1p (/ i n))))) -100)) (cbrt (+ (* 100 (exp (* n (log1p (/ i n))))) -100))) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
273.0ms
(- (* (* 100 (exp (* n (log1p (/ i n))))) (* 100 (exp (* n (log1p (/ i n)))))) (* -100 -100))
259.0ms
(* (* (* n n) n) (* (* (log1p (/ i n)) (log1p (/ i n))) (log1p (/ i n))))

prune951.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.8b

localize35.0ms

Local error

Found 4 expressions with local error:

44.3b
(posit16->real (real->posit16 (log1p (/ i n))))
10.8b
(* n (posit16->real (real->posit16 (log1p (/ i n)))))
10.5b
(/ (+ (* 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n))))))) -100) (/ i n))
4.6b
(log1p (/ i n))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
50×add-sqr-sqrt
48×*-un-lft-identity add-cube-cbrt
13×associate-/r*
11×add-cbrt-cube add-exp-log
6×pow1
5×expm1-log1p-u div-inv
4×insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-*r* associate-*l* associate-/l*
2×associate-/l/
1×log1p-udef clear-num frac-2neg flip3-+ pow-prod-down prod-exp log1p-expm1 associate-/r/ *-commutative cbrt-unprod flip-+ remove-posit16 unswap-sqr
Counts
4 → 119
Calls
4 calls:
Slowest
27.0ms
(/ (+ (* 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n))))))) -100) (/ i n))
5.0ms
(* n (posit16->real (real->posit16 (log1p (/ i n)))))
0.0ms
(log1p (/ i n))
0.0ms
(posit16->real (real->posit16 (log1p (/ i n))))

series518.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
349.0ms
(/ (+ (* 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n))))))) -100) (/ i n))
61.0ms
(* n (posit16->real (real->posit16 (log1p (/ i n)))))
54.0ms
(log1p (/ i n))
53.0ms
(posit16->real (real->posit16 (log1p (/ i n))))

simplify14.1s

Counts
123 → 131
Calls
123 calls:
Slowest
336.0ms
(/ 1 (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
296.0ms
(- (* (* 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n))))))) (* 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))))) (* -100 -100))
284.0ms
(/ (* (cbrt (+ (* 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n))))))) -100)) (cbrt (+ (* 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n))))))) -100))) (/ 1 (* (cbrt n) (cbrt n))))
271.0ms
(/ (* (cbrt (+ (* 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n))))))) -100)) (cbrt (+ (* 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n))))))) -100))) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
270.0ms
(/ (* (cbrt (+ (* 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n))))))) -100)) (cbrt (+ (* 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n))))))) -100))) (/ (* (cbrt i) (cbrt i)) (sqrt n)))

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.8b

regimes190.0ms

Accuracy

38.5% (14.9b remaining)

Error of 28.3b against oracle of 13.4b and baseline of 37.6b

bsearch305.0ms

end0.0ms

sample6.9s

Algorithm
intervals
Results
2.5s2557×body1280valid
2.0s951×body2560valid
930.0ms1670×body640valid
511.0ms2965×body80valid
307.0ms846×body320valid
221.0ms2219×body80nan
96.0ms415×body160valid
34.0ms8×body5120valid