Details

Time bar (total: 23.9s)

sample251.0ms

Algorithm
intervals
Results
97.0ms37×body2560valid
82.0ms74×body1280valid
23.0ms44×body640valid
20.0ms98×body80valid
9.0ms24×body320valid
7.0ms83×body80nan
2.0ms7×body160valid

simplify242.0ms

Calls
1 calls:
Slowest
242.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.9b

localize21.0ms

Local error

Found 3 expressions with local error:

12.1b
(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))
5.8b
(pow (+ 1 (/ i n)) n)
1.5b
(fma (pow (+ 1 (/ i n)) n) 100 -100)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×times-frac
6×add-exp-log
5×add-cbrt-cube div-inv
4×pow1 associate-/r*
3×expm1-log1p-u unpow-prod-down insert-posit16 log1p-expm1-u associate-/l* add-log-exp
1×pow-to-exp cbrt-undiv clear-num pow-pow frac-2neg div-exp pow-exp associate-/r/ fma-udef
Calls
3 calls:
Slowest
6.0ms
(pow (+ 1 (/ i n)) n)
6.0ms
(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))
0.0ms
(fma (pow (+ 1 (/ i n)) n) 100 -100)

series417.0ms

Calls
3 calls:
Slowest
175.0ms
(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))
144.0ms
(fma (pow (+ 1 (/ i n)) n) 100 -100)
98.0ms
(pow (+ 1 (/ i n)) n)

simplify3.0s

Calls
46 calls:
Slowest
548.0ms
(/ (* (* (fma (pow (+ 1 (/ i n)) n) 100 -100) (fma (pow (+ 1 (/ i n)) n) 100 -100)) (fma (pow (+ 1 (/ i n)) n) 100 -100)) (* (* (/ i n) (/ i n)) (/ i n)))
301.0ms
(/ (* (- (* 100 (exp (* n (- (log (/ -1 n)) (log (/ -1 i)))))) 100) n) i)
222.0ms
(- (* 100 (exp (* (- (log (/ 1 n)) (log (/ 1 i))) n))) 100)
213.0ms
(- (* 100 (exp (* n (- (log (/ -1 n)) (log (/ -1 i)))))) 100)
194.0ms
(exp (* (- (log (/ 1 n)) (log (/ 1 i))) n))

prune628.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.6b

localize19.0ms

Local error

Found 4 expressions with local error:

12.2b
(* n (log1p (/ i n)))
12.2b
(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))
5.8b
(log1p (/ i n))
3.3b
(fma (exp (* n (log1p (/ i n)))) 100 -100)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×times-frac
6×add-cbrt-cube add-exp-log
5×expm1-log1p-u div-inv
4×pow1 associate-/r* insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-/l*
1×cbrt-undiv log1p-udef clear-num frac-2neg div-exp log1p-expm1 associate-/r/ *-commutative fma-udef
Calls
4 calls:
Slowest
6.0ms
(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))
2.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))
0.0ms
(fma (exp (* n (log1p (/ i n)))) 100 -100)

series489.0ms

Calls
4 calls:
Slowest
240.0ms
(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))
150.0ms
(fma (exp (* n (log1p (/ i n)))) 100 -100)
51.0ms
(* n (log1p (/ i n)))
48.0ms
(log1p (/ i n))

simplify2.2s

Calls
48 calls:
Slowest
539.0ms
(/ (* (* (fma (exp (* n (log1p (/ i n)))) 100 -100) (fma (exp (* n (log1p (/ i n)))) 100 -100)) (fma (exp (* n (log1p (/ i n)))) 100 -100)) (* (* (/ i n) (/ i n)) (/ i n)))
329.0ms
(- (+ (* 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)))))))))
93.0ms
(/ (* (- (* 100 (exp i)) 100) n) i)
90.0ms
(/ (* (- (* 100 (exp i)) 100) n) i)
79.0ms
(- (log (fma (exp (* n (log1p (/ i n)))) 100 -100)) (log (/ i n)))

prune877.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.4b

localize6.0ms

Local error

Found 4 expressions with local error:

13.4b
(* (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ 1 (/ i n)))
12.2b
(* n (log1p (/ i n)))
5.8b
(log1p (/ i n))
3.3b
(fma (exp (* n (log1p (/ i n)))) 100 -100)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-*r* add-exp-log
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×prod-exp *-commutative
1×rec-exp log1p-udef pow-prod-down log1p-expm1 associate-*r/ associate-/r/ un-div-inv cbrt-unprod fma-udef div-inv
Calls
4 calls:
Slowest
5.0ms
(* (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ 1 (/ i n)))
1.0ms
(* n (log1p (/ i n)))
1.0ms
(log1p (/ i n))
0.0ms
(fma (exp (* n (log1p (/ i n)))) 100 -100)

series479.0ms

Calls
4 calls:
Slowest
254.0ms
(* (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ 1 (/ i n)))
138.0ms
(fma (exp (* n (log1p (/ i n)))) 100 -100)
44.0ms
(log1p (/ i n))
43.0ms
(* n (log1p (/ i n)))

simplify1.3s

Calls
28 calls:
Slowest
273.0ms
(* (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ 1 (/ i n)))
252.0ms
(- (+ (* 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)))))))))
128.0ms
(* (* (* (fma (exp (* n (log1p (/ i n)))) 100 -100) (fma (exp (* n (log1p (/ i n)))) 100 -100)) (fma (exp (* n (log1p (/ i n)))) 100 -100)) (* (* (/ 1 (/ i n)) (/ 1 (/ i n))) (/ 1 (/ i n))))
127.0ms
(+ (log (fma (exp (* n (log1p (/ i n)))) 100 -100)) (log (/ 1 (/ i n))))
95.0ms
(/ (* (- (* 100 (exp i)) 100) n) i)

prune802.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.4b

localize47.0ms

Local error

Found 4 expressions with local error:

42.3b
(posit16->real (real->posit16 (log1p (/ i n))))
13.4b
(* (fma (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) 100 -100) (/ 1 (/ i n)))
12.2b
(* n (posit16->real (real->posit16 (log1p (/ i n)))))
5.8b
(log1p (/ i n))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-*r* add-exp-log
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×prod-exp *-commutative
1×rec-exp log1p-udef pow-prod-down log1p-expm1 associate-*r/ associate-/r/ un-div-inv cbrt-unprod div-inv remove-posit16
Calls
4 calls:
Slowest
7.0ms
(* (fma (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) 100 -100) (/ 1 (/ i n)))
2.0ms
(* n (posit16->real (real->posit16 (log1p (/ i n)))))
0.0ms
(log1p (/ i n))
0.0ms
(posit16->real (real->posit16 (log1p (/ i n))))

series426.0ms

Calls
4 calls:
Slowest
290.0ms
(* (fma (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) 100 -100) (/ 1 (/ i n)))
47.0ms
(log1p (/ i n))
47.0ms
(* n (posit16->real (real->posit16 (log1p (/ i n)))))
42.0ms
(posit16->real (real->posit16 (log1p (/ i n))))

simplify1.2s

Calls
29 calls:
Slowest
283.0ms
(* (fma (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) 100 -100) (/ 1 (/ i n)))
159.0ms
(* (* (* (fma (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) 100 -100) (fma (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) 100 -100)) (fma (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) 100 -100)) (* (* (/ 1 (/ i n)) (/ 1 (/ i n))) (/ 1 (/ i n))))
131.0ms
(+ (log (fma (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) 100 -100)) (log (/ 1 (/ i n))))
85.0ms
(+ (log (fma (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) 100 -100)) (- (log (/ i n))))
84.0ms
(/ (* (- (* 100 (exp i)) 100) n) i)

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.4b

regimes248.0ms

Accuracy

48.6% (12.1b remaining)

Error of 25.8b against oracle of 13.7b and baseline of 37.2b

bsearch678.0ms

end0.0ms

sample9.0s

Algorithm
intervals
Results
3.4s967×body2560valid
3.1s2474×body1280valid
1.1s1650×body640valid
400.0ms3049×body80valid
361.0ms812×body320valid
303.0ms2185×body80nan
106.0ms436×body160valid
51.0ms11×body5120valid