Details

Time bar (total: 1.7m)

sample420.0ms

Algorithm
intervals
Results
157.0ms86×body1280valid
156.0ms39×body2560valid
40.0ms42×body640valid
17.0ms102×body80valid
15.0ms24×body320valid
11.0ms72×body80nan
5.0ms15×body160valid

simplify192.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
192.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.1b

localize34.0ms

Local error

Found 3 expressions with local error:

12.2b
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
5.3b
(pow (+ 1 (/ i n)) n)
2.0b
(fma 100 (pow (+ 1 (/ i n)) n) -100)

rewrite18.0ms

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
10.0ms
(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
488.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
322.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)
318.0ms
(pow (+ 1 (/ i n)) n)

simplify37.8s

Counts
114 → 114
Calls
114 calls:
Slowest
868.0ms
(/ (sqrt (fma 100 (pow (+ 1 (/ i n)) n) -100)) (/ (cbrt i) (sqrt n)))
816.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (cbrt i) (cbrt n)))
713.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (cbrt i) (sqrt n)))
686.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (sqrt i) (cbrt n)))
675.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (sqrt i) (sqrt n)))

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.4b

localize23.0ms

Local error

Found 4 expressions with local error:

12.3b
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
12.1b
(* n (log1p (/ i n)))
4.1b
(log1p (/ i n))
3.7b
(fma 100 (exp (* n (log1p (/ i n)))) -100)

rewrite20.0ms

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
(* n (log1p (/ i n)))
6.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
1.0ms
(log1p (/ i n))
1.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)

series945.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
472.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
327.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
79.0ms
(* n (log1p (/ i n)))
66.0ms
(log1p (/ i n))

simplify18.8s

Counts
120 → 129
Calls
120 calls:
Slowest
950.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ 1 (* (cbrt n) (cbrt n))))
365.0ms
(/ (* (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
(/ (sqrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
339.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ (sqrt i) (cbrt n)))
334.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ (cbrt i) n))

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.7b

localize51.0ms

Local error

Found 4 expressions with local error:

12.1b
(* n (log1p (/ i n)))
11.1b
(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
4.1b
(log1p (/ i n))
3.7b
(fma 100 (exp (* n (log1p (/ i n)))) -100)

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
50×add-sqr-sqrt
48×*-un-lft-identity add-cube-cbrt
13×associate-/l*
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 associate-/r* div-exp associate-*r* associate-*l*
1×log1p-udef clear-num frac-2neg pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod fma-udef unswap-sqr associate-/l/
Counts
4 → 117
Calls
4 calls:
Slowest
14.0ms
(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
11.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))
0.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)

series1.8s

Counts
4 → 12
Calls
4 calls:
Slowest
1.2s
(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
416.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
93.0ms
(log1p (/ i n))
78.0ms
(* n (log1p (/ i n)))

simplify19.4s

Counts
119 → 129
Calls
119 calls:
Slowest
598.0ms
(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
418.0ms
(/ (/ (cbrt i) (sqrt n)) (fma 100 (exp (* n (log1p (/ i n)))) -100))
404.0ms
(/ (/ (cbrt i) n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
404.0ms
(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
401.0ms
(/ (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))) (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (fma (/ i n) (- (/ 1/200 n) 1/200) (/ 1/100 n)))
0.2b
(/ 1/100 n)
0.2b
(/ 1/200 n)
0.1b
(fma (/ i n) (- (/ 1/200 n) 1/200) (/ 1/100 n))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×times-frac
12×add-exp-log
10×add-cbrt-cube
9×associate-/r* associate-/l*
5×pow1
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv clear-num frac-2neg div-inv
1×rec-exp 1-exp fma-udef pow-flip inv-pow
Counts
4 → 105
Calls
4 calls:
Slowest
7.0ms
(/ 1/200 n)
5.0ms
(/ 1/100 n)
5.0ms
(/ 1 (fma (/ i n) (- (/ 1/200 n) 1/200) (/ 1/100 n)))
0.0ms
(fma (/ i n) (- (/ 1/200 n) 1/200) (/ 1/100 n))

series151.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
66.0ms
(/ 1 (fma (/ i n) (- (/ 1/200 n) 1/200) (/ 1/100 n)))
42.0ms
(fma (/ i n) (- (/ 1/200 n) 1/200) (/ 1/100 n))
25.0ms
(/ 1/200 n)
18.0ms
(/ 1/100 n)

simplify5.0s

Counts
87 → 117
Calls
87 calls:
Slowest
289.0ms
(- (+ (* 1/200 (/ i (pow n 2))) (* 1/100 (/ 1 n))) (* 1/200 (/ i n)))
287.0ms
(- (+ (* 1/200 (/ i (pow n 2))) (* 1/100 (/ 1 n))) (* 1/200 (/ i n)))
286.0ms
(/ (* (* 1 1) 1) (* (* (fma (/ i n) (- (/ 1/200 n) 1/200) (/ 1/100 n)) (fma (/ i n) (- (/ 1/200 n) 1/200) (/ 1/100 n))) (fma (/ i n) (- (/ 1/200 n) 1/200) (/ 1/100 n))))
268.0ms
(/ (* (* 1/200 1/200) 1/200) (* (* n n) n))
265.0ms
(/ (* (* 1/100 1/100) 1/100) (* (* n n) n))

prune1.1s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 2.3b

regimes336.0ms

Accuracy

47.5% (9.1b remaining)

Error of 12.1b against oracle of 3.0b and baseline of 20.3b

bsearch517.0ms

end0.0ms

sample9.1s

Algorithm
intervals
Results
3.7s2487×body1280valid
2.8s999×body2560valid
1.0s1561×body640valid
401.0ms3104×body80valid
378.0ms849×body320valid
266.0ms2298×body80nan
175.0ms449×body160valid
24.0ms4×body5120valid