Details

Time bar (total: 1.2m)

sample288.0ms

Algorithm
intervals
Results
106.0ms33×body2560valid
98.0ms76×body1280valid
26.0ms44×body640valid
15.0ms35×body320valid
11.0ms99×body80valid
9.0ms81×body80nan
7.0ms2×body5120valid
4.0ms15×body160valid

simplify162.0ms

Calls
1 calls:
Slowest
162.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.8b

localize31.0ms

Local error

Found 3 expressions with local error:

11.4b
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
7.3b
(pow (+ 1 (/ i n)) n)
1.7b
(fma 100 (pow (+ 1 (/ i n)) n) -100)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
49×*-un-lft-identity
47×add-sqr-sqrt add-cube-cbrt
13×associate-/r*
9×add-exp-log
8×add-cbrt-cube
5×div-inv
4×pow1 unpow-prod-down
3×expm1-log1p-u cbrt-undiv pow-unpow div-exp insert-posit16 log1p-expm1-u associate-/l* add-log-exp
1×pow-to-exp clear-num pow-pow frac-2neg pow-exp associate-/r/ fma-udef distribute-lft-out sqr-pow
Calls
3 calls:
Slowest
14.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
8.0ms
(pow (+ 1 (/ i n)) n)
0.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)

series1.0s

Calls
3 calls:
Slowest
425.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
350.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)
255.0ms
(pow (+ 1 (/ i n)) n)

simplify37.0s

Calls
114 calls:
Slowest
934.0ms
(- (log (fma 100 (pow (+ 1 (/ i n)) n) -100)) (log (/ i n)))
850.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (cbrt (/ i n)))
733.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (sqrt i) (sqrt n)))
720.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (sqrt i) (cbrt n)))
694.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (cbrt i) (cbrt n)))

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.3b

localize31.0ms

Local error

Found 4 expressions with local error:

11.6b
(* n (log1p (/ i n)))
11.4b
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
6.6b
(log1p (/ i n))
3.7b
(fma 100 (exp (* n (log1p (/ i n)))) -100)

rewrite27.0ms

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*
1×log1p-udef clear-num frac-2neg pow-prod-down prod-exp log1p-expm1 associate-/r/ *-commutative cbrt-unprod fma-udef unswap-sqr
Calls
4 calls:
Slowest
12.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
11.0ms
(* n (log1p (/ i n)))
1.0ms
(log1p (/ i n))
0.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)

series1.0s

Calls
4 calls:
Slowest
550.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
307.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
110.0ms
(* n (log1p (/ i n)))
61.0ms
(log1p (/ i n))

simplify15.2s

Calls
120 calls:
Slowest
383.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ 1 (* (cbrt n) (cbrt n))))
356.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
313.0ms
(/ 1 (/ (sqrt i) (* (cbrt n) (cbrt n))))
296.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ (sqrt i) (* (cbrt n) (cbrt n))))
290.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ (* (cbrt i) (cbrt i)) (sqrt n)))

prune974.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.4b

localize24.0ms

Local error

Found 4 expressions with local error:

11.6b
(* n (log1p (/ i n)))
6.6b
(log1p (/ i n))
3.7b
(fma 100 (exp (* n (log1p (/ i n)))) -100)
0.0b
(* (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i) n)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
16×associate-*l*
14×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×times-frac
8×pow1
6×associate-*r*
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×prod-exp cbrt-unprod unswap-sqr
2×pow-prod-down *-commutative
1×cbrt-undiv log1p-udef div-exp associate-*l/ log1p-expm1 fma-udef div-inv
Calls
4 calls:
Slowest
9.0ms
(* (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i) n)
5.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))
0.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)

series736.0ms

Calls
4 calls:
Slowest
364.0ms
(* (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i) n)
250.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
66.0ms
(* n (log1p (/ i n)))
55.0ms
(log1p (/ i n))

simplify4.0s

Calls
47 calls:
Slowest
417.0ms
(* (* (* (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i) (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i)) (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i)) (* (* n n) n))
245.0ms
(* (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i) n)
219.0ms
(* (fma 100 (exp (* n (log1p (/ i n)))) -100) n)
218.0ms
(* (* (* n n) n) (* (* (log1p (/ i n)) (log1p (/ i n))) (log1p (/ i n))))
200.0ms
(- (+ (* 50 (* (pow n 2) (pow (log n) 2))) (+ (* 50/3 (* (pow n 3) (pow (log i) 3))) (+ (* 100 (* n (log i))) (+ (* 100/3 (* (pow n 3) (* (pow (log n) 2) (log i)))) (+ (* 50/3 (* (pow n 3) (* (log i) (pow (log n) 2)))) (* 50 (* (pow n 2) (pow (log i) 2)))))))) (+ (* 100/3 (* (pow n 3) (* (pow (log i) 2) (log n)))) (+ (* 50 (* (pow n 2) (* (log n) (log i)))) (+ (* 50 (* (pow n 2) (* (log i) (log n)))) (+ (* 50/3 (* (pow n 3) (pow (log n) 3))) (+ (* 50/3 (* (pow n 3) (* (log n) (pow (log i) 2)))) (* 100 (* n (log n)))))))))

prune715.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.4b

localize44.0ms

Local error

Found 4 expressions with local error:

42.3b
(posit16->real (real->posit16 (log1p (/ i n))))
11.6b
(* n (posit16->real (real->posit16 (log1p (/ i n)))))
6.6b
(log1p (/ i n))
3.7b
(fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×log1p-udef pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod fma-udef remove-posit16 unswap-sqr
Calls
4 calls:
Slowest
5.0ms
(* n (posit16->real (real->posit16 (log1p (/ i n)))))
0.0ms
(log1p (/ i n))
0.0ms
(posit16->real (real->posit16 (log1p (/ i n))))
0.0ms
(fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100)

series437.0ms

Calls
4 calls:
Slowest
252.0ms
(fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100)
66.0ms
(* n (posit16->real (real->posit16 (log1p (/ i n)))))
63.0ms
(posit16->real (real->posit16 (log1p (/ i n))))
55.0ms
(log1p (/ i n))

simplify777.0ms

Calls
24 calls:
Slowest
281.0ms
(* (* (* n n) n) (* (* (posit16->real (real->posit16 (log1p (/ i n)))) (posit16->real (real->posit16 (log1p (/ i n))))) (posit16->real (real->posit16 (log1p (/ i n))))))
204.0ms
(- (+ (* 50 (* (pow n 2) (pow (log n) 2))) (+ (* 50/3 (* (pow n 3) (pow (log i) 3))) (+ (* 100 (* n (log i))) (+ (* 100/3 (* (pow n 3) (* (pow (log n) 2) (log i)))) (+ (* 50/3 (* (pow n 3) (* (log i) (pow (log n) 2)))) (* 50 (* (pow n 2) (pow (log i) 2)))))))) (+ (* 100/3 (* (pow n 3) (* (pow (log i) 2) (log n)))) (+ (* 50 (* (pow n 2) (* (log n) (log i)))) (+ (* 50 (* (pow n 2) (* (log i) (log n)))) (+ (* 50/3 (* (pow n 3) (pow (log n) 3))) (+ (* 50/3 (* (pow n 3) (* (log n) (pow (log i) 2)))) (* 100 (* n (log n)))))))))
65.0ms
(- (log (/ -1 n)) (log (/ -1 i)))
63.0ms
(- (log (/ -1 n)) (log (/ -1 i)))
38.0ms
(- (log (/ 1 n)) (log (/ 1 i)))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 15.4b

regimes153.0ms

Accuracy

50.6% (12.0b remaining)

Error of 25.6b against oracle of 13.6b and baseline of 37.9b

bsearch661.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
2.6s2502×body1280valid
2.3s1004×body2560valid
1.1s1603×body640valid
536.0ms3000×body80valid
379.0ms924×body320valid
206.0ms2210×body80nan
80.0ms428×body160valid
41.0ms11×body5120valid