Details

Time bar (total: 4.1m)

sample328.0ms

Algorithm
intervals
Results
116.0ms31×body2560valid
110.0ms67×body1280valid
51.0ms63×body640valid
12.0ms83×body80valid
10.0ms22×body320valid
6.0ms47×body80nan
6.0ms17×body160valid

simplify197.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize35.0ms

Local error

Found 4 expressions with local error:

9.7b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
6.0b
(pow (+ 1 (/ i n)) n)
1.2b
(- (pow (+ 1 (/ i n)) n) 1)
0.0b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite692.0ms

Algorithm
rewrite-expression-head
Rules
584×times-frac
485×add-sqr-sqrt
366×*-un-lft-identity
224×add-cube-cbrt
174×associate-*r*
168×difference-of-squares
88×unpow-prod-down
85×sqr-pow
84×difference-of-sqr-1
29×div-inv
28×distribute-lft-out--
19×add-exp-log
18×add-cbrt-cube
13×associate-/r* associate-/l*
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×insert-posit16
3×pow-unpow associate-*l* prod-exp cbrt-unprod unswap-sqr
2×flip3-- associate-/r/ flip-- associate-/l/
1×pow-to-exp clear-num sub-neg pow-pow frac-2neg diff-log div-sub pow-prod-down pow-exp associate-*r/ *-commutative distribute-lft-out
Counts
4 → 453
Calls
4 calls:
Slowest
293.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
233.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
137.0ms
(- (pow (+ 1 (/ i n)) n) 1)
10.0ms
(pow (+ 1 (/ i n)) n)

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
441.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
400.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
301.0ms
(pow (+ 1 (/ i n)) n)
276.0ms
(- (pow (+ 1 (/ i n)) n) 1)

simplify2.5m

Counts
595 → 465
Calls
595 calls:
Slowest
845.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ 1 (sqrt n)))
642.0ms
(/ (- (pow (+ 1 (/ i n)) (/ n 2)) 1) (/ i (sqrt n)))
637.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (sqrt i) (cbrt n)))
630.0ms
(/ (* (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (cbrt (- (pow (+ 1 (/ i n)) n) 1))) (/ (sqrt i) 1))
622.0ms
(/ (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (cbrt i) (sqrt n)))

prune3.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.7b

localize18.0ms

Local error

Found 4 expressions with local error:

4.4b
(pow (/ 1 (/ n i)) n)
2.3b
(- (pow (/ 1 (/ n i)) n) 1)
0.8b
(/ 1 (/ n i))
0.1b
(* (* (/ n i) (- (pow (/ 1 (/ n i)) n) 1)) 100)

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
159×times-frac
120×add-sqr-sqrt
98×*-un-lft-identity
83×add-cube-cbrt
59×unpow-prod-down
36×add-exp-log
18×add-cbrt-cube
15×div-exp
14×difference-of-squares
13×associate-/r*
12×pow1
9×div-inv
7×difference-of-sqr-1 pow-exp
6×associate-*l/ add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv rec-exp 1-exp insert-posit16 sqr-pow
3×pow-unpow pow-pow flip3-- associate-*r* pow-prod-down flip-- associate-/l*
2×frac-times associate-*r/ associate-/r/ pow-flip inv-pow
1×pow-to-exp clear-num sub-neg frac-2neg diff-log associate-*l* *-commutative distribute-lft-out--
Counts
4 → 205
Calls
4 calls:
Slowest
94.0ms
(* (* (/ n i) (- (pow (/ 1 (/ n i)) n) 1)) 100)
35.0ms
(- (pow (/ 1 (/ n i)) n) 1)
7.0ms
(pow (/ 1 (/ n i)) n)
6.0ms
(/ 1 (/ n i))

series248.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(* (* (/ n i) (- (pow (/ 1 (/ n i)) n) 1)) 100)
63.0ms
(- (pow (/ 1 (/ n i)) n) 1)
37.0ms
(pow (/ 1 (/ n i)) n)
10.0ms
(/ 1 (/ n i))

simplify22.0s

Counts
221 → 217
Calls
221 calls:
Slowest
375.0ms
(- (pow (sqrt (/ 1 (/ n i))) n) (sqrt 1))
363.0ms
(- (pow (/ 1 (/ n i)) (/ n 2)) (sqrt 1))
361.0ms
(- (pow (/ 1 (/ (sqrt n) (sqrt i))) n) (sqrt 1))
360.0ms
(- (pow (/ (sqrt 1) (sqrt (/ n i))) n) (sqrt 1))
353.0ms
(- (pow (/ 1 (/ (sqrt n) (sqrt i))) n) 1)

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.4b

localize17.0ms

Local error

Found 4 expressions with local error:

4.4b
(pow (/ i n) n)
2.3b
(- (* 100 (pow (/ i n) n)) 100)
0.1b
(/ (- (* 100 (pow (/ i n) n)) 100) (/ i n))
0.0b
(* 100 (pow (/ i n) n))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
94×times-frac
71×add-sqr-sqrt
63×*-un-lft-identity add-cube-cbrt
28×unpow-prod-down
20×add-exp-log
17×associate-*r*
13×associate-/r*
11×add-cbrt-cube
7×div-inv
6×add-log-exp
5×pow1 div-exp
4×pow-exp prod-exp insert-posit16 unswap-sqr
3×cbrt-undiv pow-unpow associate-*l* associate-/l* sqr-pow
2×pow-to-exp flip3-- flip-- associate-/l/
1×clear-num sub-neg pow-pow frac-2neg diff-log div-sub associate-/r/ *-commutative cbrt-unprod
Counts
4 → 154
Calls
4 calls:
Slowest
24.0ms
(/ (- (* 100 (pow (/ i n) n)) 100) (/ i n))
13.0ms
(* 100 (pow (/ i n) n))
9.0ms
(- (* 100 (pow (/ i n) n)) 100)
4.0ms
(pow (/ i n) n)

series340.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
156.0ms
(/ (- (* 100 (pow (/ i n) n)) 100) (/ i n))
82.0ms
(- (* 100 (pow (/ i n) n)) 100)
54.0ms
(* 100 (pow (/ i n) n))
48.0ms
(pow (/ i n) n)

simplify30.7s

Counts
163 → 166
Calls
163 calls:
Slowest
634.0ms
(/ (sqrt (- (* 100 (pow (/ i n) n)) 100)) (sqrt (/ i n)))
512.0ms
(- (+ (* 100/3 (/ (* (pow n 4) (* (pow (log n) 2) (log i))) i)) (+ (* 50/3 (/ (* (pow n 4) (* (log i) (pow (log n) 2))) i)) (+ (* 50/3 (/ (* (pow n 4) (pow (log i) 3)) i)) (+ (* 100 (/ (* (pow n 2) (log i)) i)) (+ (* 50 (/ (* (pow n 3) (pow (log i) 2)) i)) (* 50 (/ (* (pow n 3) (pow (log n) 2)) i))))))) (+ (* 50/3 (/ (* (pow n 4) (pow (log n) 3)) i)) (+ (* 50/3 (/ (* (pow n 4) (* (log n) (pow (log i) 2))) i)) (+ (* 50 (/ (* (pow n 3) (* (log n) (log i))) i)) (+ (* 100/3 (/ (* (pow n 4) (* (pow (log i) 2) (log n))) i)) (+ (* 100 (/ (* (pow n 2) (log n)) i)) (* 50 (/ (* (pow n 3) (* (log i) (log n))) i))))))))
457.0ms
(/ (sqrt (- (* 100 (pow (/ i n) n)) 100)) (/ (sqrt i) (* (cbrt n) (cbrt n))))
435.0ms
(/ (* (cbrt (- (* 100 (pow (/ i n) n)) 100)) (cbrt (- (* 100 (pow (/ i n) n)) 100))) (/ (sqrt i) 1))
428.0ms
(/ (sqrt (- (* 100 (pow (/ i n) n)) 100)) (/ 1 (sqrt n)))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.4b

localize29.0ms

Local error

Found 4 expressions with local error:

4.4b
(pow (/ 1 (/ n i)) n)
4.4b
(pow (/ 1 (/ n i)) n)
4.4b
(pow (/ 1 (/ n i)) n)
2.2b
(- (* (pow (/ 1 (/ n i)) n) (pow (/ 1 (/ n i)) n)) (* 1 1))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
198×times-frac
132×unpow-prod-down
112×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
40×add-exp-log
21×div-exp pow-exp
12×div-inv
10×pow1
9×pow-unpow pow-pow
6×rec-exp 1-exp add-log-exp
4×add-cbrt-cube insert-posit16
3×pow-to-exp associate-/r/ pow-flip inv-pow sqr-pow
1×sub-neg flip3-- diff-log flip-- difference-of-squares
Counts
4 → 215
Calls
4 calls:
Slowest
15.0ms
(- (* (pow (/ 1 (/ n i)) n) (pow (/ 1 (/ n i)) n)) (* 1 1))
12.0ms
(pow (/ 1 (/ n i)) n)
7.0ms
(pow (/ 1 (/ n i)) n)
7.0ms
(pow (/ 1 (/ n i)) n)

series186.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
77.0ms
(- (* (pow (/ 1 (/ n i)) n) (pow (/ 1 (/ n i)) n)) (* 1 1))
38.0ms
(pow (/ 1 (/ n i)) n)
36.0ms
(pow (/ 1 (/ n i)) n)
35.0ms
(pow (/ 1 (/ n i)) n)

simplify21.9s

Counts
183 → 227
Calls
183 calls:
Slowest
414.0ms
(pow (/ 1 (/ 1 (sqrt i))) n)
316.0ms
(- (pow (/ 1 (/ n i)) n) 1)
283.0ms
(/ (exp (* (pow (/ 1 (/ n i)) n) (pow (/ 1 (/ n i)) n))) (exp (* 1 1)))
269.0ms
(- (pow (exp (* (- (log (/ 1 n)) (log (/ 1 i))) n)) 2) 1)
249.0ms
(pow (/ 1 (/ (* (cbrt n) (cbrt n)) (* (cbrt i) (cbrt i)))) n)

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.4b

regimes226.0ms

Accuracy

49.1% (13.9b remaining)

Error of 30.4b against oracle of 16.6b and baseline of 43.8b

bsearch815.0ms

end0.0ms

sample7.2s

Algorithm
intervals
Results
2.6s2480×body1280valid
2.3s957×body2560valid
939.0ms1626×body640valid
596.0ms2960×body80valid
281.0ms846×body320valid
209.0ms2174×body80nan
94.0ms483×body160valid
27.0ms6×body5120valid