Details

Time bar (total: 32.2s)

sample243.0ms

Algorithm
intervals
Results
99.0ms35×body2560valid
79.0ms76×body1280valid
28.0ms58×body640valid
9.0ms97×body80valid
6.0ms73×body80nan
6.0ms16×body320valid
4.0ms19×body160valid

simplify4.7s

Counts
1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.4b

localize24.0ms

Local error

Found 4 expressions with local error:

11.4b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
8.1b
(pow (+ 1 (/ i n)) n)
2.4b
(- (pow (+ 1 (/ i n)) n) 1)
0.0b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite601.0ms

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
260.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
179.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
141.0ms
(- (pow (+ 1 (/ i n)) n) 1)
9.0ms
(pow (+ 1 (/ i n)) n)

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
369.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
363.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
294.0ms
(- (pow (+ 1 (/ i n)) n) 1)
263.0ms
(pow (+ 1 (/ i n)) n)

simplify883.0ms

Counts
508 → 508

prune5.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.3b

localize27.0ms

Local error

Found 4 expressions with local error:

11.4b
(/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n))
10.1b
(log (+ 1 (/ i n)))
0.1b
(* (log (+ 1 (/ i n))) n)
0.1b
(* 100 (/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
96×add-sqr-sqrt
87×*-un-lft-identity
85×add-cube-cbrt
47×associate-*r*
21×add-exp-log
20×add-cbrt-cube
13×associate-/r*
10×pow1
9×div-inv
7×associate-*l*
6×cbrt-undiv div-exp
4×expm1-log1p-u log-prod prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-/l*
2×log-div pow-prod-down associate-/r/ log-pow *-commutative
1×clear-num frac-2neg log1p-def flip3-+ div-sub rem-log-exp associate-*r/ flip-+ distribute-lft-out expm1-udef
Counts
4 → 184
Calls
4 calls:
Slowest
23.0ms
(* 100 (/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n)))
9.0ms
(* (log (+ 1 (/ i n))) n)
6.0ms
(/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n))
5.0ms
(log (+ 1 (/ i n)))

series941.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
387.0ms
(* 100 (/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n)))
370.0ms
(/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n))
111.0ms
(* (log (+ 1 (/ i n))) n)
73.0ms
(log (+ 1 (/ i n)))

simplify987.0ms

Counts
196 → 196

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.8b

localize22.0ms

Local error

Found 4 expressions with local error:

11.0b
(/ (* (expm1 (* n (log1p (/ i n)))) 100) (/ i n))
11.0b
(* n (log1p (/ i n)))
7.3b
(log1p (/ i n))
0.1b
(* (expm1 (* n (log1p (/ i n)))) 100)

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
26×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
20×add-cbrt-cube add-exp-log
13×associate-/r*
8×pow1
6×cbrt-undiv div-exp associate-*r* associate-*l*
5×expm1-log1p-u
4×prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×pow-prod-down *-commutative unswap-sqr
1×log1p-udef clear-num frac-2neg log1p-expm1 associate-/r/ associate-/l*
Counts
4 → 103
Calls
4 calls:
Slowest
16.0ms
(* (expm1 (* n (log1p (/ i n)))) 100)
11.0ms
(/ (* (expm1 (* n (log1p (/ i n)))) 100) (/ i n))
6.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))

series828.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
446.0ms
(/ (* (expm1 (* n (log1p (/ i n)))) 100) (/ i n))
258.0ms
(* (expm1 (* n (log1p (/ i n)))) 100)
67.0ms
(* n (log1p (/ i n)))
56.0ms
(log1p (/ i n))

simplify736.0ms

Counts
115 → 115

prune952.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.8b

localize25.0ms

Local error

Found 4 expressions with local error:

11.1b
(/ (expm1 (* n (log1p (/ i n)))) (/ (/ i n) 100))
11.0b
(* n (log1p (/ i n)))
7.3b
(log1p (/ i n))
0.2b
(/ (/ i n) 100)

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
468×times-frac
234×add-sqr-sqrt
232×*-un-lft-identity add-cube-cbrt
46×associate-/r*
22×div-inv
20×add-cbrt-cube add-exp-log
16×associate-/l*
9×cbrt-undiv div-exp
6×pow1
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×clear-num frac-2neg
1×log1p-udef div-sub pow-prod-down prod-exp log1p-expm1 associate-/r/ *-commutative cbrt-unprod expm1-udef unswap-sqr associate-/l/
Counts
4 → 302
Calls
4 calls:
Slowest
8.0ms
(/ (expm1 (* n (log1p (/ i n)))) (/ (/ i n) 100))
7.0ms
(/ (/ i n) 100)
6.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))

series504.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
360.0ms
(/ (expm1 (* n (log1p (/ i n)))) (/ (/ i n) 100))
65.0ms
(* n (log1p (/ i n)))
60.0ms
(log1p (/ i n))
19.0ms
(/ (/ i n) 100)

simplify461.0ms

Counts
314 → 314

prune2.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.8b

regimes169.0ms

Accuracy

12.5% (9.2b remaining)

Error of 19.0b against oracle of 9.7b and baseline of 20.3b

bsearch741.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
3.0s2486×body1280valid
2.4s1014×body2560valid
959.0ms1594×body640valid
320.0ms835×body320valid
316.0ms2992×body80valid
197.0ms2215×body80nan
97.0ms463×body160valid
36.0ms9×body5120valid