Details

Time bar (total: 1.4m)

sample319.0ms

Algorithm
intervals
Results
103.0ms80×body1280valid
95.0ms30×body2560valid
38.0ms53×body640valid
14.0ms28×body320valid
12.0ms91×body80valid
10.0ms83×body80nan
5.0ms1×body5120valid
4.0ms16×body160valid

simplify141.0ms

Calls
1 calls:
Slowest
141.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.3b

localize21.0ms

Local error

Found 4 expressions with local error:

10.7b
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
7.3b
(pow (+ 1 (/ i n)) n)
1.8b
(fma 100 (pow (+ 1 (/ i n)) n) -100)
0.0b
(+ 1 (/ i n))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
53×*-un-lft-identity
49×add-sqr-sqrt add-cube-cbrt
13×associate-/r*
10×add-exp-log
9×add-cbrt-cube
6×add-log-exp
5×pow1 div-inv
4×expm1-log1p-u unpow-prod-down insert-posit16 log1p-expm1-u
3×cbrt-undiv pow-unpow fma-def div-exp associate-/l*
2×distribute-lft-out
1×pow-to-exp +-commutative clear-num sum-log pow-pow frac-2neg flip3-+ pow-exp associate-/r/ flip-+ fma-udef sqr-pow
Calls
4 calls:
Slowest
15.0ms
(pow (+ 1 (/ i n)) n)
12.0ms
(+ 1 (/ i n))
6.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
0.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)

series1.0s

Calls
4 calls:
Slowest
430.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
321.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)
269.0ms
(pow (+ 1 (/ i n)) n)
13.0ms
(+ 1 (/ i n))

simplify37.5s

Calls
121 calls:
Slowest
996.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (sqrt i) n))
859.0ms
(/ (cbrt (fma 100 (pow (+ 1 (/ i n)) n) -100)) (/ (cbrt i) (sqrt n)))
791.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (sqrt i) (cbrt n)))
704.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (sqrt i) (sqrt n)))
700.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (cbrt i) (sqrt n)))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.7b

localize35.0ms

Local error

Found 4 expressions with local error:

10.7b
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
10.3b
(* n (log1p (/ i n)))
5.8b
(log1p (/ i n))
3.9b
(fma 100 (exp (* n (log1p (/ i n)))) -100)

rewrite32.0ms

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
Calls
4 calls:
Slowest
17.0ms
(/ (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)

series993.0ms

Calls
4 calls:
Slowest
498.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
327.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
99.0ms
(* n (log1p (/ i n)))
70.0ms
(log1p (/ i n))

simplify17.1s

Calls
120 calls:
Slowest
383.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ 1 (* (cbrt n) (cbrt n))))
332.0ms
(/ (sqrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
328.0ms
(/ (* (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))))
291.0ms
(/ (sqrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (/ (cbrt i) (cbrt n)))
290.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ (* (cbrt i) (cbrt i)) (sqrt n)))

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.8b

localize28.0ms

Local error

Found 4 expressions with local error:

10.3b
(* n (log1p (/ i n)))
5.8b
(log1p (/ i n))
3.9b
(fma 100 (exp (* n (log1p (/ i n)))) -100)
0.1b
(* (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i) n)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
16×associate-*l*
14×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×times-frac
8×pow1
6×associate-*r*
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×prod-exp cbrt-unprod unswap-sqr
2×pow-prod-down *-commutative
1×cbrt-undiv log1p-udef div-exp associate-*l/ log1p-expm1 fma-udef div-inv
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)

series849.0ms

Calls
4 calls:
Slowest
406.0ms
(* (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i) n)
290.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
87.0ms
(* n (log1p (/ i n)))
65.0ms
(log1p (/ i n))

simplify5.3s

Calls
47 calls:
Slowest
870.0ms
(* (* (* (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i) (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i)) (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i)) (* (* n n) n))
281.0ms
(* (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i) n)
270.0ms
(* (* (* n n) n) (* (* (log1p (/ i n)) (log1p (/ i n))) (log1p (/ i n))))
265.0ms
(* (fma 100 (exp (* n (log1p (/ i n)))) -100) n)
242.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (* (cbrt i) (cbrt i)))

prune865.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.8b

localize33.0ms

Local error

Found 4 expressions with local error:

10.3b
(* n (log1p (/ i n)))
5.8b
(log1p (/ i n))
3.9b
(fma (exp (* n (log1p (/ i n)))) 100 -100)
0.1b
(* (/ 1 i) (* (fma (exp (* n (log1p (/ i n)))) 100 -100) n))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
18×add-cbrt-cube
16×associate-*l*
15×add-sqr-sqrt
13×*-un-lft-identity prod-exp add-cube-cbrt
11×pow1
9×times-frac
7×cbrt-unprod
5×expm1-log1p-u
4×div-exp associate-*r* pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv rec-exp 1-exp *-commutative
1×log1p-udef associate-*l/ log1p-expm1 fma-udef div-inv unswap-sqr
Calls
4 calls:
Slowest
20.0ms
(* (/ 1 i) (* (fma (exp (* n (log1p (/ i n)))) 100 -100) n))
5.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))
0.0ms
(fma (exp (* n (log1p (/ i n)))) 100 -100)

series802.0ms

Calls
4 calls:
Slowest
363.0ms
(* (/ 1 i) (* (fma (exp (* n (log1p (/ i n)))) 100 -100) n))
286.0ms
(fma (exp (* n (log1p (/ i n)))) 100 -100)
86.0ms
(* n (log1p (/ i n)))
66.0ms
(log1p (/ i n))

simplify5.3s

Calls
49 calls:
Slowest
420.0ms
(* (/ (* (* 1 1) 1) (* (* i i) i)) (* (* (* (fma (exp (* n (log1p (/ i n)))) 100 -100) n) (* (fma (exp (* n (log1p (/ i n)))) 100 -100) n)) (* (fma (exp (* n (log1p (/ i n)))) 100 -100) n)))
364.0ms
(+ (log (/ 1 i)) (log (* (fma (exp (* n (log1p (/ i n)))) 100 -100) n)))
348.0ms
(* (* (* (/ 1 i) (/ 1 i)) (/ 1 i)) (* (* (* (fma (exp (* n (log1p (/ i n)))) 100 -100) n) (* (fma (exp (* n (log1p (/ i n)))) 100 -100) n)) (* (fma (exp (* n (log1p (/ i n)))) 100 -100) n)))
338.0ms
(+ (- 0 (log i)) (+ (log (fma (exp (* n (log1p (/ i n)))) 100 -100)) (log n)))
320.0ms
(* 1 (* (fma (exp (* n (log1p (/ i n)))) 100 -100) n))

prune757.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.8b

regimes211.0ms

Accuracy

50.4% (12.0b remaining)

Error of 25.5b against oracle of 13.5b and baseline of 37.8b

bsearch323.0ms

end0.0ms

sample7.1s

Algorithm
intervals
Results
2.6s2443×body1280valid
2.2s948×body2560valid
1.1s1666×body640valid
420.0ms3079×body80valid
337.0ms879×body320valid
202.0ms2337×body80nan
111.0ms445×body160valid
20.0ms6×body5120valid