Details

Time bar (total: 3.0m)

sample320.0ms

Algorithm
intervals
Results
132.0ms93×body1280valid
106.0ms29×body2560valid
32.0ms48×body640valid
14.0ms32×body320valid
10.0ms86×body80valid
7.0ms64×body80nan
4.0ms15×body160valid

simplify199.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
198.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 45.1b

localize24.0ms

Local error

Found 4 expressions with local error:

10.4b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
4.4b
(pow (+ 1 (/ i n)) n)
1.6b
(- (pow (+ 1 (/ i n)) n) 1)
0.1b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite523.0ms

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
210.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
180.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
112.0ms
(- (pow (+ 1 (/ i n)) n) 1)
9.0ms
(pow (+ 1 (/ i n)) n)

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
369.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
355.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
331.0ms
(- (pow (+ 1 (/ i n)) n) 1)
236.0ms
(pow (+ 1 (/ i n)) n)

simplify2.4m

Counts
653 → 508
Calls
653 calls:
Slowest
863.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) 1)
843.0ms
(/ (* (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (cbrt (- (pow (+ 1 (/ i n)) n) 1))) (sqrt (/ i n)))
674.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (sqrt (/ i n)))
668.0ms
(/ (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (/ i (cbrt n)))
662.0ms
(/ (* (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (cbrt (- (pow (+ 1 (/ i n)) n) 1))) i)

prune3.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.0b

localize20.0ms

Local error

Found 4 expressions with local error:

10.9b
(/ (expm1 (* n (log1p (/ i n)))) (/ i n))
10.9b
(* n (log1p (/ i n)))
3.9b
(log1p (/ i n))
0.1b
(* 100 (/ (expm1 (* n (log1p (/ i n)))) (/ i n)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
95×add-sqr-sqrt
84×*-un-lft-identity add-cube-cbrt
47×associate-*r*
20×add-cbrt-cube add-exp-log
13×associate-/r*
9×div-inv
8×pow1
6×cbrt-undiv div-exp associate-*l*
5×expm1-log1p-u
4×prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-/l*
2×pow-prod-down associate-/r/ *-commutative
1×log1p-udef clear-num frac-2neg div-sub log1p-expm1 associate-*r/ expm1-udef
Counts
4 → 176
Calls
4 calls:
Slowest
12.0ms
(* 100 (/ (expm1 (* n (log1p (/ i n)))) (/ i n)))
6.0ms
(/ (expm1 (* n (log1p (/ i n)))) (/ i n))
6.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))

series762.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
331.0ms
(* 100 (/ (expm1 (* n (log1p (/ i n)))) (/ i n)))
320.0ms
(/ (expm1 (* n (log1p (/ i n)))) (/ i n))
60.0ms
(* n (log1p (/ i n)))
50.0ms
(log1p (/ i n))

simplify5.5s

Counts
180 → 188
Calls
180 calls:
Slowest
311.0ms
(/ (* (cbrt (expm1 (* n (log1p (/ i n))))) (cbrt (expm1 (* n (log1p (/ i n)))))) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
263.0ms
(- (log (expm1 (* n (log1p (/ i n))))) (log (/ i n)))
243.0ms
(/ (* (* (expm1 (* n (log1p (/ i n)))) (expm1 (* n (log1p (/ i n))))) (expm1 (* n (log1p (/ i n))))) (* (* (/ i n) (/ i n)) (/ i n)))
192.0ms
(* (* (* n n) n) (* (* (log1p (/ i n)) (log1p (/ i n))) (log1p (/ i n))))
175.0ms
(* (* (* 100 100) 100) (/ (* (* (expm1 (* n (log1p (/ i n)))) (expm1 (* n (log1p (/ i n))))) (expm1 (* n (log1p (/ i n))))) (/ (* (* i i) i) (* (* n n) n))))

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

10.9b
(/ (expm1 (* n (log1p (/ i n)))) (/ i n))
10.9b
(* n (log1p (/ i n)))
3.9b
(log1p (/ i n))
0.2b
(* (sqrt 100) (* (sqrt 100) (/ (expm1 (* n (log1p (/ i n)))) (/ i n))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
52×add-sqr-sqrt
50×*-un-lft-identity add-cube-cbrt
25×add-cbrt-cube add-exp-log
13×associate-/r*
11×pow1
9×associate-*l*
8×prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×expm1-log1p-u div-inv
4×associate-*r* pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod associate-/l*
2×associate-*r/ *-commutative
1×log1p-udef clear-num frac-2neg div-sub log1p-expm1 associate-/r/ expm1-udef unswap-sqr
Counts
4 → 136
Calls
4 calls:
Slowest
27.0ms
(* (sqrt 100) (* (sqrt 100) (/ (expm1 (* n (log1p (/ i n)))) (/ i n))))
6.0ms
(/ (expm1 (* n (log1p (/ i n)))) (/ i n))
6.0ms
(* n (log1p (/ i n)))
1.0ms
(log1p (/ i n))

series742.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
323.0ms
(* (sqrt 100) (* (sqrt 100) (/ (expm1 (* n (log1p (/ i n)))) (/ i n))))
311.0ms
(/ (expm1 (* n (log1p (/ i n)))) (/ i n))
57.0ms
(* n (log1p (/ i n)))
51.0ms
(log1p (/ i n))

simplify5.9s

Counts
138 → 148
Calls
138 calls:
Slowest
311.0ms
(/ (* (cbrt (expm1 (* n (log1p (/ i n))))) (cbrt (expm1 (* n (log1p (/ i n)))))) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
291.0ms
(+ (log (sqrt 100)) (log (* (sqrt 100) (/ (expm1 (* n (log1p (/ i n)))) (/ i n)))))
290.0ms
(* (* (* (sqrt 100) (sqrt 100)) (sqrt 100)) (* (* (* (sqrt 100) (sqrt 100)) (sqrt 100)) (/ (* (* (expm1 (* n (log1p (/ i n)))) (expm1 (* n (log1p (/ i n))))) (expm1 (* n (log1p (/ i n))))) (/ (* (* i i) i) (* (* n n) n)))))
277.0ms
(+ (log (sqrt 100)) (+ (log (sqrt 100)) (- (log (expm1 (* n (log1p (/ i n))))) (log (/ i n)))))
255.0ms
(* (* (* (sqrt 100) (sqrt 100)) (sqrt 100)) (* (* (* (sqrt 100) (sqrt 100)) (sqrt 100)) (/ (* (* (expm1 (* n (log1p (/ i n)))) (expm1 (* n (log1p (/ i n))))) (expm1 (* n (log1p (/ i n))))) (* (* (/ i n) (/ i n)) (/ i n)))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

10.9b
(/ (expm1 (* n (expm1 (log1p (log1p (/ i n)))))) (/ i n))
10.9b
(* n (expm1 (log1p (log1p (/ i n)))))
3.9b
(log1p (/ i n))
0.3b
(expm1 (log1p (log1p (/ i n))))

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×expm1-log1p-u div-inv
4×insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-*r* associate-*l* associate-/l*
2×expm1-udef
1×log1p-udef expm1-log1p clear-num frac-2neg div-sub pow-prod-down prod-exp log1p-expm1 associate-/r/ *-commutative cbrt-unprod unswap-sqr
Counts
4 → 119
Calls
4 calls:
Slowest
6.0ms
(/ (expm1 (* n (expm1 (log1p (log1p (/ i n)))))) (/ i n))
6.0ms
(* n (expm1 (log1p (log1p (/ i n)))))
0.0ms
(log1p (/ i n))
0.0ms
(expm1 (log1p (log1p (/ i n))))

series548.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
347.0ms
(/ (expm1 (* n (expm1 (log1p (log1p (/ i n)))))) (/ i n))
78.0ms
(* n (expm1 (log1p (log1p (/ i n)))))
72.0ms
(expm1 (log1p (log1p (/ i n))))
51.0ms
(log1p (/ i n))

simplify3.6s

Counts
122 → 131
Calls
122 calls:
Slowest
307.0ms
(/ (* (cbrt (expm1 (* n (expm1 (log1p (log1p (/ i n))))))) (cbrt (expm1 (* n (expm1 (log1p (log1p (/ i n)))))))) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
238.0ms
(/ (* (* (expm1 (* n (expm1 (log1p (log1p (/ i n)))))) (expm1 (* n (expm1 (log1p (log1p (/ i n))))))) (expm1 (* n (expm1 (log1p (log1p (/ i n))))))) (* (* (/ i n) (/ i n)) (/ i n)))
221.0ms
(* (* (* n n) n) (* (* (expm1 (log1p (log1p (/ i n)))) (expm1 (log1p (log1p (/ i n))))) (expm1 (log1p (log1p (/ i n))))))
158.0ms
(/ (exp (* n (expm1 (log1p (log1p (/ i n)))))) (/ i n))
147.0ms
(/ (* (cbrt (expm1 (* n (expm1 (log1p (log1p (/ i n))))))) (cbrt (expm1 (* n (expm1 (log1p (log1p (/ i n)))))))) (/ 1 (* (cbrt n) (cbrt n))))

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes197.0ms

Accuracy

57.9% (8.6b remaining)

Error of 8.6b against oracle of 0.0b and baseline of 20.5b

bsearch8.0ms

end0.0ms

sample7.0s

Algorithm
intervals
Results
2.8s2564×body1280valid
2.1s999×body2560valid
802.0ms1607×body640valid
423.0ms2270×body80nan
285.0ms2999×body80valid
247.0ms800×body320valid
104.0ms465×body160valid
49.0ms8×body5120valid