Details

Time bar (total: 1.4m)

sample319.0ms

Algorithm
intervals
Results
113.0ms69×body1280valid
97.0ms28×body2560valid
33.0ms46×body640valid
26.0ms97×body80valid
13.0ms28×body320valid
9.0ms1×body5120valid
8.0ms68×body80nan
3.0ms10×body160valid

simplify197.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
197.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.6b

localize31.0ms

Local error

Found 4 expressions with local error:

9.7b
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
7.1b
(pow (+ 1 (/ i n)) n)
1.2b
(fma 100 (pow (+ 1 (/ i n)) n) -100)
0.0b
(+ 1 (/ i n))

rewrite27.0ms

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
Counts
4 → 123
Calls
4 calls:
Slowest
11.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
9.0ms
(pow (+ 1 (/ i n)) n)
6.0ms
(+ 1 (/ i n))
0.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
406.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
310.0ms
(pow (+ 1 (/ i n)) n)
305.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)
22.0ms
(+ 1 (/ i n))

simplify36.1s

Counts
121 → 135
Calls
121 calls:
Slowest
768.0ms
(/ (sqrt (fma 100 (pow (+ 1 (/ i n)) n) -100)) (* (cbrt (/ i n)) (cbrt (/ i n))))
749.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (cbrt i) (sqrt n)))
689.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (sqrt i) (cbrt n)))
684.0ms
(/ (* (cbrt (fma 100 (pow (+ 1 (/ i n)) n) -100)) (cbrt (fma 100 (pow (+ 1 (/ i n)) n) -100))) (/ (sqrt i) 1))
672.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (sqrt i) (sqrt n)))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

localize35.0ms

Local error

Found 4 expressions with local error:

9.7b
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
9.3b
(* n (log1p (/ i n)))
6.1b
(log1p (/ i n))
3.0b
(fma 100 (exp (* n (log1p (/ i n)))) -100)

rewrite19.0ms

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))
5.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))
0.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)

series879.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
467.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
277.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
77.0ms
(* n (log1p (/ i n)))
58.0ms
(log1p (/ i n))

simplify16.2s

Counts
120 → 129
Calls
120 calls:
Slowest
549.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (sqrt (/ i n)))
370.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ 1 (* (cbrt n) (cbrt n))))
335.0ms
(/ (* (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))))
301.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ (sqrt i) (* (cbrt n) (cbrt n))))
292.0ms
(* (* (* n n) n) (* (* (log1p (/ i n)) (log1p (/ i n))) (log1p (/ i n))))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.2b

localize19.0ms

Local error

Found 4 expressions with local error:

9.7b
(/ (+ (* 100 (exp (* n (log1p (/ i n))))) -100) (/ i n))
9.3b
(* n (log1p (/ i n)))
6.1b
(log1p (/ i n))
3.0b
(+ (* 100 (exp (* n (log1p (/ i n))))) -100)

rewrite44.0ms

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
24.0ms
(/ (+ (* 100 (exp (* n (log1p (/ i n))))) -100) (/ i n))
12.0ms
(+ (* 100 (exp (* n (log1p (/ i n))))) -100)
6.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))

series755.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
376.0ms
(/ (+ (* 100 (exp (* n (log1p (/ i n))))) -100) (/ i n))
259.0ms
(+ (* 100 (exp (* n (log1p (/ i n))))) -100)
65.0ms
(* n (log1p (/ i n)))
55.0ms
(log1p (/ i n))

simplify13.8s

Counts
123 → 135
Calls
123 calls:
Slowest
401.0ms
(/ (sqrt (+ (* 100 (exp (* n (log1p (/ i n))))) -100)) (/ (sqrt i) (sqrt n)))
370.0ms
(* (exp (* 100 (exp (* n (log1p (/ i n)))))) (exp -100))
298.0ms
(/ (* (cbrt (+ (* 100 (exp (* n (log1p (/ i n))))) -100)) (cbrt (+ (* 100 (exp (* n (log1p (/ i n))))) -100))) (/ 1 (* (cbrt n) (cbrt n))))
283.0ms
(/ (* (cbrt (+ (* 100 (exp (* n (log1p (/ i n))))) -100)) (cbrt (+ (* 100 (exp (* n (log1p (/ i n))))) -100))) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
282.0ms
(- (* (* 100 (exp (* n (log1p (/ i n))))) (* 100 (exp (* n (log1p (/ i n)))))) (* -100 -100))

prune948.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.2b

localize27.0ms

Local error

Found 4 expressions with local error:

15.8b
(cbrt (/ i n))
15.8b
(cbrt (/ i n))
15.8b
(cbrt (/ i n))
9.3b
(* n (log1p (/ i n)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
29×add-sqr-sqrt
27×*-un-lft-identity times-frac add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 associate-*r* associate-*l* div-inv
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 96
Calls
4 calls:
Slowest
5.0ms
(* n (log1p (/ i n)))
1.0ms
(cbrt (/ i n))
1.0ms
(cbrt (/ i n))
1.0ms
(cbrt (/ i n))

series241.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
64.0ms
(cbrt (/ i n))
60.0ms
(cbrt (/ i n))
59.0ms
(* n (log1p (/ i n)))
58.0ms
(cbrt (/ i n))

simplify2.0s

Counts
64 → 108
Calls
64 calls:
Slowest
215.0ms
(exp (* 1/3 (- (log (/ -1 n)) (log (/ -1 i)))))
215.0ms
(exp (* 1/3 (- (log (/ -1 n)) (log (/ -1 i)))))
215.0ms
(exp (* 1/3 (- (log (/ -1 n)) (log (/ -1 i)))))
205.0ms
(* (* (* n n) n) (* (* (log1p (/ i n)) (log1p (/ i n))) (log1p (/ i n))))
141.0ms
(exp (* 1/3 (- (log i) (log n))))

prune929.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.2b

regimes188.0ms

Accuracy

49.1% (13.0b remaining)

Error of 27.2b against oracle of 14.2b and baseline of 39.8b

bsearch835.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
3.0s2476×body1280valid
2.4s1043×body2560valid
897.0ms1592×body640valid
283.0ms2979×body80valid
259.0ms849×body320valid
170.0ms2230×body80nan
100.0ms403×body160valid
29.0ms8×body5120valid