Details

Time bar (total: 4.1m)

sample250.0ms

Algorithm
intervals
Results
96.0ms87×body1280valid
65.0ms26×body2560valid
45.0ms63×body640valid
9.0ms84×body80valid
8.0ms81×body80nan
8.0ms20×body320valid
4.0ms1×body5120valid
4.0ms16×body160valid

simplify145.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
145.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.3b

localize28.0ms

Local error

Found 4 expressions with local error:

8.7b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
5.5b
(pow (+ 1 (/ i n)) n)
2.1b
(- (pow (+ 1 (/ i n)) n) 1)
0.0b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite526.0ms

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
198.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
190.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
104.0ms
(- (pow (+ 1 (/ i n)) n) 1)
18.0ms
(pow (+ 1 (/ i n)) n)

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
447.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
414.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
313.0ms
(pow (+ 1 (/ i n)) n)
296.0ms
(- (pow (+ 1 (/ i n)) n) 1)

simplify2.4m

Counts
595 → 465
Calls
595 calls:
Slowest
860.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ i n))
815.0ms
(/ (* (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (cbrt (- (pow (+ 1 (/ i n)) n) 1))) (* (cbrt (/ i n)) (cbrt (/ i n))))
677.0ms
(/ (* (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (cbrt (- (pow (+ 1 (/ i n)) n) 1))) (/ (sqrt i) 1))
637.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ i (sqrt n)))
632.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (sqrt i) n))

prune3.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 19.0b

localize21.0ms

Local error

Found 4 expressions with local error:

15.0b
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
0.4b
(* 1/6 i)
0.0b
(* (* i i) (+ (* 1/6 i) 1/2))
0.0b
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))

rewrite85.0ms

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
33.0ms
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
27.0ms
(* (* 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)

series228.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
72.0ms
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))
71.0ms
(* (* i i) (+ (* 1/6 i) 1/2))
69.0ms
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
15.0ms
(* 1/6 i)

simplify23.6s

Counts
194 → 195
Calls
194 calls:
Slowest
503.0ms
(* (* (* 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))))
464.0ms
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ (cbrt i) n))
430.0ms
(* (* (* 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))))
302.0ms
(/ (* (* (+ 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)))
263.0ms
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))

prune1.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.1b

localize24.0ms

Local error

Found 4 expressions with local error:

11.5b
(* (* 100 (/ 1 i)) (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))
1.0b
(* n (+ i (* i (* (+ (* i 1/6) 1/2) i))))
0.4b
(* i 1/6)
0.3b
(* 100 (/ 1 i))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log
34×add-cbrt-cube
29×prod-exp
27×add-sqr-sqrt
22×pow1
20×associate-*r*
17×*-un-lft-identity cbrt-unprod
16×add-cube-cbrt
14×associate-*r/
11×times-frac pow-prod-down
10×associate-*l*
6×div-exp
5×distribute-rgt-in distribute-lft-in unswap-sqr
4×frac-times flip3-+ un-div-inv *-commutative flip-+ insert-posit16 add-log-exp
3×cbrt-undiv rec-exp 1-exp
2×associate-*l/
1×div-inv
Counts
4 → 122
Calls
4 calls:
Slowest
38.0ms
(* (* 100 (/ 1 i)) (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))
11.0ms
(* n (+ i (* i (* (+ (* i 1/6) 1/2) i))))
8.0ms
(* 100 (/ 1 i))
5.0ms
(* i 1/6)

series171.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
70.0ms
(* (* 100 (/ 1 i)) (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))
68.0ms
(* n (+ i (* i (* (+ (* i 1/6) 1/2) i))))
18.0ms
(* 100 (/ 1 i))
15.0ms
(* i 1/6)

simplify13.0s

Counts
100 → 134
Calls
100 calls:
Slowest
625.0ms
(* (* (* (* 100 100) 100) (/ (* (* 1 1) 1) (* (* i i) i))) (* (* (* n n) n) (* (* (+ i (* i (* (+ (* i 1/6) 1/2) i))) (+ i (* i (* (+ (* i 1/6) 1/2) i)))) (+ i (* i (* (+ (* i 1/6) 1/2) i))))))
579.0ms
(* (* (* (* 100 100) 100) (/ (* (* 1 1) 1) (* (* i i) i))) (* (* (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))) (* n (+ i (* i (* (+ (* i 1/6) 1/2) i))))) (* n (+ i (* i (* (+ (* i 1/6) 1/2) i))))))
550.0ms
(* (* (* (* 100 100) 100) (* (* (/ 1 i) (/ 1 i)) (/ 1 i))) (* (* (* n n) n) (* (* (+ i (* i (* (+ (* i 1/6) 1/2) i))) (+ i (* i (* (+ (* i 1/6) 1/2) i)))) (+ i (* i (* (+ (* i 1/6) 1/2) i))))))
517.0ms
(* (* 100 (/ 1 i)) (* n (* i (* (+ (* i 1/6) 1/2) i))))
516.0ms
(+ (* i i) (- (* (* i (* (+ (* i 1/6) 1/2) i)) (* i (* (+ (* i 1/6) 1/2) i))) (* i (* i (* (+ (* i 1/6) 1/2) i)))))

prune936.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 10.1b

localize38.0ms

Local error

Found 4 expressions with local error:

19.8b
(cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))
19.8b
(cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))
19.8b
(cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))
11.4b
(* (* 100 (/ 1 i)) (* (* (cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i))))) (cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))) (cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
245×associate-*r/
168×cbrt-div
136×frac-times
84×flip3-+ flip-+
64×add-exp-log
44×associate-*l/
42×prod-exp
28×add-cbrt-cube
27×un-div-inv
25×pow1
24×cbrt-unprod
15×pow-prod-down
6×div-exp
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt insert-posit16 add-log-exp
3×cbrt-prod cbrt-undiv rec-exp pow1/3 1-exp
1×associate-*r* associate-*l* *-commutative
Counts
4 → 157
Calls
4 calls:
Slowest
140.0ms
(* (* 100 (/ 1 i)) (* (* (cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i))))) (cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))) (cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))))
4.0ms
(cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))
4.0ms
(cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))
4.0ms
(cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))

series499.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))
133.0ms
(cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))
133.0ms
(cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))
98.0ms
(* (* 100 (/ 1 i)) (* (* (cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i))))) (cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))) (cbrt (* n (+ i (* i (* (+ (* i 1/6) 1/2) i)))))))

simplify49.9s

Counts
184 → 169
Calls
184 calls:
Slowest
839.0ms
(* i (* (cbrt (+ (* i i) (- (* (* i (* (+ (* i 1/6) 1/2) i)) (* i (* (+ (* i 1/6) 1/2) i))) (* i (* i (* (+ (* i 1/6) 1/2) i)))))) (cbrt (- i (* i (* (+ (* i 1/6) 1/2) i))))))
749.0ms
(* i (* (cbrt (+ (* i i) (- (* (* i (* (+ (* i 1/6) 1/2) i)) (* i (* (+ (* i 1/6) 1/2) i))) (* i (* i (* (+ (* i 1/6) 1/2) i)))))) (cbrt (+ (* i i) (- (* (* i (* (+ (* i 1/6) 1/2) i)) (* i (* (+ (* i 1/6) 1/2) i))) (* i (* i (* (+ (* i 1/6) 1/2) i))))))))
740.0ms
(cbrt (+ (* i i) (- (* (* i (* (+ (* i 1/6) 1/2) i)) (* i (* (+ (* i 1/6) 1/2) i))) (* i (* i (* (+ (* i 1/6) 1/2) i))))))
591.0ms
(* i (* (cbrt (+ (* i i) (- (* (* i (* (+ (* i 1/6) 1/2) i)) (* i (* (+ (* i 1/6) 1/2) i))) (* i (* i (* (+ (* i 1/6) 1/2) i)))))) (cbrt (- i (* i (* (+ (* i 1/6) 1/2) i))))))
589.0ms
(* i (* (cbrt (+ (* i i) (- (* (* i (* (+ (* i 1/6) 1/2) i)) (* i (* (+ (* i 1/6) 1/2) i))) (* i (* i (* (+ (* i 1/6) 1/2) i)))))) (cbrt (- i (* i (* (+ (* i 1/6) 1/2) i))))))

prune1.7s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 10.1b

regimes398.0ms

Accuracy

58.6% (10.0b remaining)

Error of 18.4b against oracle of 8.4b and baseline of 32.6b

bsearch227.0ms

end0.0ms

sample6.8s

Algorithm
intervals
Results
2.4s2447×body1280valid
2.1s954×body2560valid
824.0ms1616×body640valid
557.0ms3004×body80valid
342.0ms963×body320valid
204.0ms2243×body80nan
83.0ms447×body160valid
44.0ms12×body5120valid