Details

Time bar (total: 3.5m)

sample313.0ms

Algorithm
intervals
Results
141.0ms95×body1280valid
93.0ms29×body2560valid
28.0ms43×body640valid
12.0ms25×body320valid
11.0ms91×body80valid
7.0ms66×body80nan
6.0ms21×body160valid

simplify175.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
175.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.3b

localize27.0ms

Local error

Found 4 expressions with local error:

11.1b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
6.1b
(pow (+ 1 (/ i n)) n)
2.3b
(- (pow (+ 1 (/ i n)) n) 1)
0.1b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite531.0ms

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
213.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
210.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
78.0ms
(- (pow (+ 1 (/ i n)) n) 1)
15.0ms
(pow (+ 1 (/ i n)) n)

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
380.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
377.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
307.0ms
(- (pow (+ 1 (/ i n)) n) 1)
283.0ms
(pow (+ 1 (/ i n)) n)

simplify2.3m

Counts
595 → 465
Calls
595 calls:
Slowest
858.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (sqrt (/ i n)))
676.0ms
(/ (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (/ i (cbrt n)))
667.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (cbrt i) (cbrt n)))
603.0ms
(/ (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (sqrt (/ i n)))
600.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ i (cbrt n)))

prune3.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.9b

localize24.0ms

Local error

Found 4 expressions with local error:

17.3b
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
0.3b
(* 1/6 i)
0.1b
(* (* i i) (+ (* 1/6 i) 1/2))
0.0b
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
97×add-sqr-sqrt
85×*-un-lft-identity add-cube-cbrt
50×associate-*r*
25×add-cbrt-cube add-exp-log
13×pow1 associate-/r*
9×div-inv
7×associate-*l* prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow-prod-down unswap-sqr
4×insert-posit16 add-log-exp
3×associate-*r/ *-commutative associate-/l*
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in
Counts
4 → 183
Calls
4 calls:
Slowest
30.0ms
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
29.0ms
(* (* i i) (+ (* 1/6 i) 1/2))
17.0ms
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))
5.0ms
(* 1/6 i)

series237.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
75.0ms
(* (* i i) (+ (* 1/6 i) 1/2))
75.0ms
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))
72.0ms
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
15.0ms
(* 1/6 i)

simplify22.7s

Counts
194 → 195
Calls
194 calls:
Slowest
500.0ms
(* (* (* 100 100) 100) (/ (* (* (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (/ (* (* i i) i) (* (* n n) n))))
471.0ms
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ (sqrt i) (sqrt n)))
425.0ms
(* (* (* 100 100) 100) (/ (* (* (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (* (* (/ i n) (/ i n)) (/ i n))))
294.0ms
(/ (* (* (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (/ (* (* i i) i) (* (* n n) n)))
253.0ms
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))

prune1.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.8b

localize41.0ms

Local error

Found 4 expressions with local error:

15.5b
(cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))
15.5b
(cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))
15.5b
(cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))
12.4b
(/ (* (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))) i)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
9×cbrt-prod add-sqr-sqrt *-un-lft-identity flip3-+ add-exp-log add-cube-cbrt flip-+
8×associate-/l/
7×add-cbrt-cube
4×frac-times pow1 insert-posit16 add-log-exp
3×associate-/r* times-frac pow1/3
2×cbrt-undiv div-exp associate-*l/ associate-*r/
1×clear-num frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 72
Calls
4 calls:
Slowest
13.0ms
(/ (* (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))) i)
2.0ms
(cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))
2.0ms
(cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))
2.0ms
(cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))

series292.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
104.0ms
(/ (* (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))) i)
65.0ms
(cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))
64.0ms
(cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))
60.0ms
(cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))

simplify6.5s

Counts
48 → 84
Calls
48 calls:
Slowest
455.0ms
(+ (exp (* 1/3 (- (log -1/6) (* 3 (log (/ -1 i)))))) (+ (/ (exp (* 1/3 (- (log -1/6) (* 3 (log (/ -1 i)))))) i) (/ (exp (* 1/3 (- (log -1/6) (* 3 (log (/ -1 i)))))) (pow i 2))))
272.0ms
(* (cbrt (- (* i i) (* (* (* i i) (+ (* 1/6 i) 1/2)) (* (* i i) (+ (* 1/6 i) 1/2))))) (cbrt (+ (pow i 3) (pow (* (* i i) (+ (* 1/6 i) 1/2)) 3))))
271.0ms
(* (cbrt (+ (pow i 3) (pow (* (* i i) (+ (* 1/6 i) 1/2)) 3))) (cbrt (- (* i i) (* (* (* i i) (+ (* 1/6 i) 1/2)) (* (* i i) (+ (* 1/6 i) 1/2))))))
249.0ms
(+ (/ (exp (* 1/3 (- (log 1/36) (* 6 (log (/ -1 i)))))) i) (+ (* 2 (/ (exp (* 1/3 (- (log 1/36) (* 6 (log (/ -1 i)))))) (pow i 2))) (* 3 (/ (exp (* 1/3 (- (log 1/36) (* 6 (log (/ -1 i)))))) (pow i 3)))))
238.0ms
(+ (/ (exp (* 1/3 (- (log 1/36) (* 6 (log (/ 1 i)))))) i) (+ (* 2 (/ (exp (* 1/3 (- (log 1/36) (* 6 (log (/ 1 i)))))) (pow i 2))) (* 3 (/ (exp (* 1/3 (- (log 1/36) (* 6 (log (/ 1 i)))))) (pow i 3)))))

prune836.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 7.7b

localize57.0ms

Local error

Found 4 expressions with local error:

35.5b
(cbrt (* i i))
21.7b
(cbrt (pow i 5))
15.5b
(cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))
2.3b
(* (+ (* (cbrt (* i i)) 1/3) (+ (* 1/12 (cbrt (pow i 5))) (cbrt (/ 1 i)))) (/ (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (/ 1 n)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
142×times-frac
99×add-sqr-sqrt
83×associate-*r*
79×*-un-lft-identity
77×add-cube-cbrt
53×cbrt-prod
19×add-exp-log
11×add-cbrt-cube
7×div-inv unswap-sqr
6×pow1 div-exp
5×prod-exp
4×insert-posit16 add-log-exp
3×cbrt-undiv unpow-prod-down flip3-+ pow1/3 associate-*l* cbrt-unprod flip-+
2×frac-times cbrt-div associate-*l/
1×rec-exp 1-exp pow-prod-down associate-*r/ associate-/r/ *-commutative sqr-pow
Counts
4 → 156
Calls
4 calls:
Slowest
103.0ms
(* (+ (* (cbrt (* i i)) 1/3) (+ (* 1/12 (cbrt (pow i 5))) (cbrt (/ 1 i)))) (/ (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (/ 1 n)))
3.0ms
(cbrt (* i i))
2.0ms
(cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))
1.0ms
(cbrt (pow i 5))

series903.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
409.0ms
(* (+ (* (cbrt (* i i)) 1/3) (+ (* 1/12 (cbrt (pow i 5))) (cbrt (/ 1 i)))) (/ (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (/ 1 n)))
237.0ms
(cbrt (pow i 5))
198.0ms
(cbrt (* i i))
60.0ms
(cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))

simplify20.0s

Counts
139 → 168
Calls
139 calls:
Slowest
695.0ms
(* (* (* (+ (* (cbrt (* i i)) 1/3) (+ (* 1/12 (cbrt (pow i 5))) (cbrt (/ 1 i)))) (+ (* (cbrt (* i i)) 1/3) (+ (* 1/12 (cbrt (pow i 5))) (cbrt (/ 1 i))))) (+ (* (cbrt (* i i)) 1/3) (+ (* 1/12 (cbrt (pow i 5))) (cbrt (/ 1 i))))) (* (* (/ (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (/ 1 n)) (/ (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (/ 1 n))) (/ (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (/ 1 n))))
458.0ms
(* (* (* (+ (* (cbrt (* i i)) 1/3) (+ (* 1/12 (cbrt (pow i 5))) (cbrt (/ 1 i)))) (+ (* (cbrt (* i i)) 1/3) (+ (* 1/12 (cbrt (pow i 5))) (cbrt (/ 1 i))))) (+ (* (cbrt (* i i)) 1/3) (+ (* 1/12 (cbrt (pow i 5))) (cbrt (/ 1 i))))) (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ (* (* 1 1) 1) (* (* n n) n))))
446.0ms
(* (* (* (+ (* (cbrt (* i i)) 1/3) (+ (* 1/12 (cbrt (pow i 5))) (cbrt (/ 1 i)))) (+ (* (cbrt (* i i)) 1/3) (+ (* 1/12 (cbrt (pow i 5))) (cbrt (/ 1 i))))) (+ (* (cbrt (* i i)) 1/3) (+ (* 1/12 (cbrt (pow i 5))) (cbrt (/ 1 i))))) (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (* (* (/ 1 n) (/ 1 n)) (/ 1 n))))
383.0ms
(/ (sqrt (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))) (/ (sqrt 1) n))
301.0ms
(+ (* 1/6 (* (pow i 2) n)) (+ (* 5/216 (* (pow i 3) n)) (+ (* 1/432 (* (pow i 4) n)) (+ (* 1/2 (* i n)) n))))

prune2.3s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 7.7b

regimes457.0ms

Accuracy

57.6% (10.5b remaining)

Error of 18.8b against oracle of 8.2b and baseline of 33.1b

bsearch459.0ms

end0.0ms

sample6.9s

Algorithm
intervals
Results
2.8s2508×body1280valid
2.2s980×body2560valid
793.0ms1577×body640valid
321.0ms901×body320valid
289.0ms3015×body80valid
199.0ms2198×body80nan
141.0ms440×body160valid
22.0ms6×body5120valid