Details

Time bar (total: 4.1m)

sample322.0ms

Algorithm
intervals
Results
138.0ms92×body1280valid
87.0ms26×body2560valid
37.0ms50×body640valid
14.0ms30×body320valid
11.0ms66×body80nan
11.0ms82×body80valid
5.0ms17×body160valid

simplify208.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
208.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.5b

localize34.0ms

Local error

Found 4 expressions with local error:

10.2b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
5.9b
(pow (+ 1 (/ i n)) n)
1.4b
(- (pow (+ 1 (/ i n)) n) 1)
0.0b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite614.0ms

Algorithm
rewrite-expression-head
Rules
584×times-frac
501×add-sqr-sqrt
390×*-un-lft-identity
240×add-cube-cbrt
174×associate-*r*
168×difference-of-squares
104×unpow-prod-down
89×sqr-pow
84×difference-of-sqr-1
29×div-inv
28×distribute-lft-out--
24×prod-diff
21×add-exp-log
18×add-cbrt-cube
13×associate-/r* associate-/l*
8×fma-neg
7×pow1
6×cbrt-undiv div-exp add-log-exp
5×distribute-lft-out
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×pow-unpow expm1-def associate-*l* prod-exp cbrt-unprod unswap-sqr
2×pow-to-exp flip3-- pow-exp associate-/r/ flip-- associate-/l/
1×clear-num sub-neg pow-pow frac-2neg diff-log div-sub pow-prod-down associate-*r/ *-commutative
Counts
4 → 496
Calls
4 calls:
Slowest
261.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
204.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
113.0ms
(- (pow (+ 1 (/ i n)) n) 1)
9.0ms
(pow (+ 1 (/ i n)) n)

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
441.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
416.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
321.0ms
(pow (+ 1 (/ i n)) n)
278.0ms
(- (pow (+ 1 (/ i n)) n) 1)

simplify3.2m

Counts
718 → 508
Calls
718 calls:
Slowest
1.1s
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (cbrt i) (cbrt n)))
774.0ms
(/ (- (pow (+ 1 (/ i n)) (/ n 2)) (sqrt 1)) (/ (cbrt i) n))
763.0ms
(/ (* (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (cbrt (- (pow (+ 1 (/ i n)) n) 1))) i)
754.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ i (sqrt n)))
749.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (sqrt (/ i n)))

prune3.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.3b

localize19.0ms

Local error

Found 4 expressions with local error:

17.2b
(/ (fma (* i (fma i 1/6 1/2)) i i) (/ i n))
0.1b
(fma i 1/6 1/2)
0.1b
(* i (fma i 1/6 1/2))
0.1b
(fma (* i (fma i 1/6 1/2)) i i)

rewrite13.0ms

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×div-inv
4×expm1-log1p-u fma-udef insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-*r* associate-*l* associate-/l*
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod unswap-sqr
Counts
4 → 118
Calls
4 calls:
Slowest
6.0ms
(/ (fma (* i (fma i 1/6 1/2)) i i) (/ i n))
5.0ms
(* i (fma i 1/6 1/2))
0.0ms
(fma (* i (fma i 1/6 1/2)) i i)
0.0ms
(fma i 1/6 1/2)

series216.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
80.0ms
(/ (fma (* i (fma i 1/6 1/2)) i i) (/ i n))
59.0ms
(* i (fma i 1/6 1/2))
38.0ms
(fma i 1/6 1/2)
38.0ms
(fma (* i (fma i 1/6 1/2)) i i)

simplify19.3s

Counts
172 → 130
Calls
172 calls:
Slowest
537.0ms
(* (* (* i (fma i 1/6 1/2)) (* i (fma i 1/6 1/2))) (* i (fma i 1/6 1/2)))
460.0ms
(* (* (* i i) i) (* (* (fma i 1/6 1/2) (fma i 1/6 1/2)) (fma i 1/6 1/2)))
369.0ms
(/ (sqrt (fma (* i (fma i 1/6 1/2)) i i)) (/ 1 (sqrt n)))
338.0ms
(* (* (fma i 1/6 1/2) (fma i 1/6 1/2)) (fma i 1/6 1/2))
278.0ms
(- (fma (* i (fma i 1/6 1/2)) i i))

prune889.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (fma (fma 1/6 i 1/2) i 1) n)
0.1b
(fma 1/6 i 1/2)
0.1b
(fma (fma 1/6 i 1/2) i 1)
0.1b
(* 100 (* (fma (fma 1/6 i 1/2) i 1) n))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×*-commutative fma-udef
1×unswap-sqr
Counts
4 → 64
Calls
4 calls:
Slowest
13.0ms
(* 100 (* (fma (fma 1/6 i 1/2) i 1) n))
5.0ms
(* (fma (fma 1/6 i 1/2) i 1) n)
0.0ms
(fma 1/6 i 1/2)
0.0ms
(fma (fma 1/6 i 1/2) i 1)

series137.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
41.0ms
(* 100 (* (fma (fma 1/6 i 1/2) i 1) n))
38.0ms
(* (fma (fma 1/6 i 1/2) i 1) n)
33.0ms
(fma 1/6 i 1/2)
24.0ms
(fma (fma 1/6 i 1/2) i 1)

simplify7.6s

Counts
75 → 76
Calls
75 calls:
Slowest
561.0ms
(* (* (fma (fma 1/6 i 1/2) i 1) (fma (fma 1/6 i 1/2) i 1)) (fma (fma 1/6 i 1/2) i 1))
459.0ms
(* (* (* (fma (fma 1/6 i 1/2) i 1) n) (* (fma (fma 1/6 i 1/2) i 1) n)) (* (fma (fma 1/6 i 1/2) i 1) n))
344.0ms
(* (* (fma 1/6 i 1/2) (fma 1/6 i 1/2)) (fma 1/6 i 1/2))
272.0ms
(exp (* 100 (* (fma (fma 1/6 i 1/2) i 1) n)))
263.0ms
(* (cbrt 100) (* (fma (fma 1/6 i 1/2) i 1) n))

prune468.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (fma (+ (* 5/3 i) 5) i 10) n)
0.3b
(* 5/3 i)
0.2b
(* (sqrt 100) (* (fma (+ (* 5/3 i) 5) i 10) n))
0.1b
(fma (+ (* 5/3 i) 5) i 10)

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×pow1 add-cbrt-cube add-exp-log
12×associate-*l*
10×*-un-lft-identity add-cube-cbrt
7×associate-*r*
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative sqrt-prod
2×unswap-sqr
1×fma-udef
Counts
4 → 77
Calls
4 calls:
Slowest
16.0ms
(* (sqrt 100) (* (fma (+ (* 5/3 i) 5) i 10) n))
6.0ms
(* (fma (+ (* 5/3 i) 5) i 10) n)
5.0ms
(* 5/3 i)
0.0ms
(fma (+ (* 5/3 i) 5) i 10)

series127.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
44.0ms
(* (fma (+ (* 5/3 i) 5) i 10) n)
42.0ms
(* (sqrt 100) (* (fma (+ (* 5/3 i) 5) i 10) n))
25.0ms
(fma (+ (* 5/3 i) 5) i 10)
16.0ms
(* 5/3 i)

simplify9.3s

Counts
88 → 89
Calls
88 calls:
Slowest
525.0ms
(* (* (* (fma (+ (* 5/3 i) 5) i 10) (fma (+ (* 5/3 i) 5) i 10)) (fma (+ (* 5/3 i) 5) i 10)) (* (* n n) n))
244.0ms
(log (* (sqrt 100) (* (fma (+ (* 5/3 i) 5) i 10) n)))
241.0ms
(sqrt (* (sqrt 100) (* (fma (+ (* 5/3 i) 5) i 10) n)))
238.0ms
(cbrt (* (sqrt 100) (* (fma (+ (* 5/3 i) 5) i 10) n)))
238.0ms
(sqrt (* (sqrt 100) (* (fma (+ (* 5/3 i) 5) i 10) n)))

prune548.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.3b

regimes178.0ms

Accuracy

54.5% (15.4b remaining)

Error of 15.7b against oracle of 0.4b and baseline of 34.1b

bsearch932.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
2.6s2518×body1280valid
2.1s929×body2560valid
996.0ms1540×body640valid
393.0ms504×body160valid
378.0ms888×body320valid
277.0ms3030×body80valid
240.0ms2276×body80nan
43.0ms11×body5120valid