Details

Time bar (total: 3.0m)

sample281.0ms

Algorithm
intervals
Results
98.0ms75×body1280valid
90.0ms31×body2560valid
40.0ms60×body640valid
12.0ms98×body80valid
11.0ms30×body320valid
8.0ms70×body80nan
5.0ms17×body160valid

simplify218.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
218.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.4b

localize34.0ms

Local error

Found 3 expressions with local error:

9.4b
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
4.6b
(pow (+ 1 (/ i n)) n)
1.6b
(fma 100 (pow (+ 1 (/ i n)) n) -100)

rewrite16.0ms

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
470.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
305.0ms
(pow (+ 1 (/ i n)) n)
291.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)

simplify38.1s

Counts
114 → 114
Calls
114 calls:
Slowest
924.0ms
(/ (sqrt (fma 100 (pow (+ 1 (/ i n)) n) -100)) (/ 1 (* (cbrt n) (cbrt n))))
730.0ms
(/ (* (cbrt (fma 100 (pow (+ 1 (/ i n)) n) -100)) (cbrt (fma 100 (pow (+ 1 (/ i n)) n) -100))) (* (cbrt (/ i n)) (cbrt (/ i n))))
679.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i (sqrt n)))
636.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (sqrt i) (cbrt n)))
627.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.7b

localize38.0ms

Local error

Found 4 expressions with local error:

9.6b
(* n (log1p (/ i n)))
9.4b
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
4.7b
(fma 100 (exp (* n (log1p (/ i n)))) -100)
4.1b
(log1p (/ i n))

rewrite25.0ms

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
11.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
11.0ms
(* n (log1p (/ i n)))
1.0ms
(log1p (/ i n))
0.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
580.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
334.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
88.0ms
(* n (log1p (/ i n)))
72.0ms
(log1p (/ i n))

simplify16.5s

Counts
120 → 129
Calls
120 calls:
Slowest
511.0ms
(/ (sqrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (/ (* (cbrt i) (cbrt i)) 1))
379.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ 1 (* (cbrt n) (cbrt n))))
352.0ms
(/ (sqrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
346.0ms
(/ (* (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))))
343.0ms
(* (* (* n n) n) (* (* (log1p (/ i n)) (log1p (/ i n))) (log1p (/ i n))))

prune970.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.2b

localize20.0ms

Local error

Found 4 expressions with local error:

10.9b
(* (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ 1 (/ i n)))
9.6b
(* n (log1p (/ i n)))
4.7b
(fma 100 (exp (* n (log1p (/ i n)))) -100)
4.1b
(log1p (/ i n))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
58×add-sqr-sqrt
47×associate-*r*
44×*-un-lft-identity
42×add-cube-cbrt
25×add-exp-log
15×add-cbrt-cube
8×pow1 prod-exp
7×div-exp
6×associate-*l* unswap-sqr
5×expm1-log1p-u
4×cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
3×cbrt-undiv
2×rec-exp 1-exp pow-prod-down *-commutative
1×log1p-udef log1p-expm1 associate-*r/ associate-/r/ un-div-inv fma-udef
Counts
4 → 120
Calls
4 calls:
Slowest
13.0ms
(* (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ 1 (/ i n)))
9.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))
0.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)

series707.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
352.0ms
(* (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ 1 (/ i n)))
237.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
63.0ms
(* n (log1p (/ i n)))
56.0ms
(log1p (/ i n))

simplify5.9s

Counts
91 → 132
Calls
91 calls:
Slowest
305.0ms
(+ (log (fma 100 (exp (* n (log1p (/ i n)))) -100)) (- 0 (log (/ i n))))
297.0ms
(+ (log (fma 100 (exp (* n (log1p (/ i n)))) -100)) (- 0 (- (log i) (log n))))
294.0ms
(* (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ 1 (/ i n)))
247.0ms
(* (* (* n n) n) (* (* (log1p (/ i n)) (log1p (/ i n))) (log1p (/ i n))))
228.0ms
(+ (log (fma 100 (exp (* n (log1p (/ i n)))) -100)) (- (log 1) (- (log i) (log n))))

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.2b

localize20.0ms

Local error

Found 4 expressions with local error:

4.6b
(pow (+ 1 (/ i n)) n)
1.6b
(fma 100 (pow (+ 1 (/ i n)) n) -100)
0.0b
(/ (/ (fma 100 (pow (+ 1 (/ i n)) n) -100) i) (/ 1 n))
0.0b
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) i)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
430×times-frac
212×*-un-lft-identity
210×add-sqr-sqrt add-cube-cbrt
30×div-inv
29×add-exp-log
18×add-cbrt-cube
17×div-exp
16×associate-/r* associate-/l*
9×cbrt-undiv
5×pow1
4×expm1-log1p-u unpow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow
2×rec-exp clear-num frac-2neg 1-exp
1×pow-to-exp pow-pow pow-exp associate-/r/ fma-udef distribute-lft-out sqr-pow associate-/l/
Counts
4 → 284
Calls
4 calls:
Slowest
9.0ms
(/ (/ (fma 100 (pow (+ 1 (/ i n)) n) -100) i) (/ 1 n))
9.0ms
(pow (+ 1 (/ i n)) n)
8.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) i)
0.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)

series880.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
302.0ms
(/ (/ (fma 100 (pow (+ 1 (/ i n)) n) -100) i) (/ 1 n))
231.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)
211.0ms
(pow (+ 1 (/ i n)) n)
136.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) i)

simplify1.8m

Counts
420 → 296
Calls
420 calls:
Slowest
664.0ms
(/ (/ (sqrt (fma 100 (pow (+ 1 (/ i n)) n) -100)) (sqrt i)) (/ (* (cbrt 1) (cbrt 1)) (sqrt n)))
605.0ms
(/ (cbrt (/ (fma 100 (pow (+ 1 (/ i n)) n) -100) i)) (/ (cbrt 1) n))
602.0ms
(/ (/ (cbrt (fma 100 (pow (+ 1 (/ i n)) n) -100)) i) (/ (cbrt 1) n))
589.0ms
(/ (/ (fma 100 (pow (+ 1 (/ i n)) n) -100) i) (/ (cbrt 1) (sqrt n)))
536.0ms
(/ (/ (* (cbrt (fma 100 (pow (+ 1 (/ i n)) n) -100)) (cbrt (fma 100 (pow (+ 1 (/ i n)) n) -100))) (* (cbrt i) (cbrt i))) (/ (* (cbrt 1) (cbrt 1)) (sqrt n)))

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.8b

regimes158.0ms

Accuracy

61.6% (11.6b remaining)

Error of 15.1b against oracle of 3.5b and baseline of 33.7b

bsearch506.0ms

end0.0ms

sample6.7s

Algorithm
intervals
Results
2.8s2519×body1280valid
2.1s982×body2560valid
734.0ms1597×body640valid
285.0ms886×body320valid
281.0ms3005×body80valid
202.0ms2263×body80nan
120.0ms474×body160valid
17.0ms4×body5120valid