Details

Time bar (total: 1.8m)

sample341.0ms

Algorithm
intervals
Results
170.0ms95×body1280valid
90.0ms29×body2560valid
30.0ms43×body640valid
10.0ms91×body80valid
10.0ms25×body320valid
7.0ms66×body80nan
6.0ms21×body160valid

simplify188.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
187.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.3b

localize23.0ms

Local error

Found 3 expressions with local error:

11.2b
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
6.1b
(pow (+ 1 (/ i n)) n)
2.3b
(fma 100 (pow (+ 1 (/ i n)) n) -100)

rewrite33.0ms

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
17.0ms
(pow (+ 1 (/ i n)) n)
12.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
1.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)

series1.0s

Counts
3 → 9
Calls
3 calls:
Slowest
427.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
322.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)
286.0ms
(pow (+ 1 (/ i n)) n)

simplify36.9s

Counts
114 → 114
Calls
114 calls:
Slowest
930.0ms
(- (log (fma 100 (pow (+ 1 (/ i n)) n) -100)) (log (/ i n)))
892.0ms
(/ (sqrt (fma 100 (pow (+ 1 (/ i n)) n) -100)) (/ 1 n))
742.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (cbrt i) (cbrt n)))
727.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (sqrt i) (cbrt n)))
691.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (cbrt i) (sqrt n)))

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.1b

localize17.0ms

Local error

Found 4 expressions with local error:

11.2b
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
11.1b
(* n (log1p (/ i n)))
5.1b
(log1p (/ i n))
3.8b
(fma 100 (exp (* n (log1p (/ i n)))) -100)

rewrite21.0ms

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
13.0ms
(* n (log1p (/ i n)))
6.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
0.0ms
(log1p (/ i n))
0.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)

series871.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
461.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
283.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
70.0ms
(* n (log1p (/ i n)))
57.0ms
(log1p (/ i n))

simplify16.0s

Counts
120 → 129
Calls
120 calls:
Slowest
475.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ 1 n))
365.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ 1 (* (cbrt n) (cbrt n))))
345.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ (sqrt i) (* (cbrt n) (cbrt n))))
336.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ (* (cbrt i) (cbrt i)) (sqrt n)))
332.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ (* (cbrt i) (cbrt i)) 1))

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.4b

localize22.0ms

Local error

Found 4 expressions with local error:

11.2b
(/ (log (exp (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ i n))
11.1b
(* n (log1p (/ i n)))
5.1b
(log1p (/ i n))
3.8b
(fma 100 (exp (* n (log1p (/ i n)))) -100)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
163×times-frac
92×add-sqr-sqrt
90×*-un-lft-identity add-cube-cbrt
56×log-pow
42×exp-prod
20×pow1
13×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv
7×associate-/l*
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-*r* 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 → 173
Calls
4 calls:
Slowest
13.0ms
(/ (log (exp (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)

series738.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
369.0ms
(/ (log (exp (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ i n))
251.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
60.0ms
(* n (log1p (/ i n)))
58.0ms
(log1p (/ i n))

simplify34.6s

Counts
227 → 185
Calls
227 calls:
Slowest
355.0ms
(/ (log (exp (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))))) (/ (cbrt i) (cbrt n)))
352.0ms
(/ (log (exp (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))))) (/ (cbrt i) (sqrt n)))
350.0ms
(/ (log (exp (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))))) (/ (sqrt i) (sqrt n)))
348.0ms
(/ (log (exp (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))))) (/ (sqrt i) (cbrt n)))
333.0ms
(/ (log (exp (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))))) (/ 1 n))

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 13.4b

localize30.0ms

Local error

Found 4 expressions with local error:

11.1b
(* n (log1p (/ i n)))
5.1b
(log1p (/ i n))
3.8b
(fma 100 (exp (* n (log1p (/ i n)))) -100)
3.5b
(log (exp (fma 100 (exp (* n (log1p (/ i n)))) -100)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×pow1
6×add-cbrt-cube add-exp-log
5×expm1-log1p-u
4×log-prod log-pow insert-posit16 log1p-expm1-u add-log-exp
3×exp-prod associate-*r* associate-*l*
2×fma-udef
1×log1p-udef rem-log-exp exp-sum pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod unswap-sqr
Counts
4 → 63
Calls
4 calls:
Slowest
6.0ms
(* n (log1p (/ i n)))
2.0ms
(log (exp (fma 100 (exp (* n (log1p (/ i n)))) -100)))
0.0ms
(log1p (/ i n))
0.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)

series813.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
294.0ms
(log1p (/ i n))
230.0ms
(log (exp (fma 100 (exp (* n (log1p (/ i n)))) -100)))
229.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
59.0ms
(* n (log1p (/ i n)))

simplify1.8s

Counts
30 → 75
Calls
30 calls:
Slowest
362.0ms
(log (exp (* 100 (exp (* n (log1p (/ i n)))))))
202.0ms
(* (* (* n n) n) (* (* (log1p (/ i n)) (log1p (/ i n))) (log1p (/ i n))))
191.0ms
(log (sqrt (exp (fma 100 (exp (* n (log1p (/ i n)))) -100))))
184.0ms
(- (+ (* 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)))))))))
184.0ms
(- (+ (* 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)))))))))

prune618.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.4b

regimes151.0ms

Accuracy

56.1% (11.5b remaining)

Error of 25.2b against oracle of 13.7b and baseline of 39.9b

bsearch353.0ms

end0.0ms

sample7.0s

Algorithm
intervals
Results
2.6s2508×body1280valid
2.5s980×body2560valid
817.0ms1577×body640valid
286.0ms901×body320valid
282.0ms3015×body80valid
186.0ms2198×body80nan
85.0ms440×body160valid
22.0ms6×body5120valid