Details

Time bar (total: 1.5m)

sample284.0ms

Algorithm
intervals
Results
101.0ms32×body2560valid
79.0ms57×body1280valid
51.0ms58×body640valid
14.0ms116×body80valid
10.0ms24×body320valid
9.0ms79×body80nan
4.0ms16×body160valid

simplify197.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
197.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.8b

localize16.0ms

Local error

Found 3 expressions with local error:

9.4b
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
9.1b
(pow (+ 1 (/ i n)) n)
0.9b
(fma 100 (pow (+ 1 (/ i n)) n) -100)

rewrite18.0ms

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
Counts
3 → 105
Calls
3 calls:
Slowest
10.0ms
(pow (+ 1 (/ i n)) n)
6.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
0.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)

series995.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
406.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
312.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)
277.0ms
(pow (+ 1 (/ i n)) n)

simplify38.5s

Counts
114 → 114
Calls
114 calls:
Slowest
873.0ms
(/ (sqrt (fma 100 (pow (+ 1 (/ i n)) n) -100)) (/ (sqrt i) (sqrt n)))
831.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (cbrt i) (cbrt n)))
766.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (sqrt i) (cbrt n)))
714.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (cbrt i) (sqrt n)))
676.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ (sqrt i) (sqrt n)))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.6b

localize18.0ms

Local error

Found 4 expressions with local error:

9.5b
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
9.2b
(* n (log1p (/ i n)))
7.1b
(log1p (/ i n))
3.0b
(fma 100 (exp (* n (log1p (/ i n)))) -100)

rewrite22.0ms

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
Counts
4 → 117
Calls
4 calls:
Slowest
11.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
8.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))
0.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)

series925.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
466.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
307.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
82.0ms
(* n (log1p (/ i n)))
69.0ms
(log1p (/ i n))

simplify17.0s

Counts
120 → 129
Calls
120 calls:
Slowest
502.0ms
(/ (sqrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (/ (sqrt i) (sqrt n)))
458.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ 1 (* (cbrt n) (cbrt n))))
421.0ms
(/ (* (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))))
316.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ (* (cbrt i) (cbrt i)) 1))
314.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ (sqrt i) (* (cbrt n) (cbrt n))))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.0b

localize41.0ms

Local error

Found 4 expressions with local error:

43.8b
(posit16->real (real->posit16 (log1p (/ i n))))
9.5b
(/ (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100) (/ i n))
9.2b
(* n (posit16->real (real->posit16 (log1p (/ i n)))))
7.1b
(log1p (/ i n))

rewrite14.0ms

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 remove-posit16 unswap-sqr
Counts
4 → 117
Calls
4 calls:
Slowest
6.0ms
(/ (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100) (/ i n))
6.0ms
(* n (posit16->real (real->posit16 (log1p (/ i n)))))
0.0ms
(log1p (/ i n))
0.0ms
(posit16->real (real->posit16 (log1p (/ i n))))

series658.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
443.0ms
(/ (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100) (/ i n))
79.0ms
(* n (posit16->real (real->posit16 (log1p (/ i n)))))
69.0ms
(posit16->real (real->posit16 (log1p (/ i n))))
66.0ms
(log1p (/ i n))

simplify17.3s

Counts
121 → 129
Calls
121 calls:
Slowest
550.0ms
(* (* (* n n) n) (* (* (posit16->real (real->posit16 (log1p (/ i n)))) (posit16->real (real->posit16 (log1p (/ i n))))) (posit16->real (real->posit16 (log1p (/ i n))))))
393.0ms
(/ (* (cbrt (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100)) (cbrt (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100))) (/ 1 (* (cbrt n) (cbrt n))))
365.0ms
(/ (* (cbrt (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100)) (cbrt (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100))) (/ (* (cbrt i) (cbrt i)) 1))
346.0ms
(/ (* (cbrt (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100)) (cbrt (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100))) (/ (* (cbrt i) (cbrt i)) (sqrt n)))
334.0ms
(/ (* (cbrt (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100)) (cbrt (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100))) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.0b

localize41.0ms

Local error

Found 4 expressions with local error:

43.8b
(posit16->real (real->posit16 (log1p (/ i n))))
9.2b
(* n (posit16->real (real->posit16 (log1p (/ i n)))))
7.1b
(log1p (/ i n))
3.0b
(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
Counts
4 → 55
Calls
4 calls:
Slowest
6.0ms
(* 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)

series430.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
251.0ms
(fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100)
65.0ms
(* n (posit16->real (real->posit16 (log1p (/ i n)))))
59.0ms
(log1p (/ i n))
55.0ms
(posit16->real (real->posit16 (log1p (/ i n))))

simplify790.0ms

Counts
24 → 67
Calls
24 calls:
Slowest
291.0ms
(* (* (* n n) n) (* (* (posit16->real (real->posit16 (log1p (/ i n)))) (posit16->real (real->posit16 (log1p (/ i n))))) (posit16->real (real->posit16 (log1p (/ i n))))))
199.0ms
(- (+ (* 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)))))))))
67.0ms
(- (log (/ -1 n)) (log (/ -1 i)))
66.0ms
(- (log (/ -1 n)) (log (/ -1 i)))
37.0ms
(- (log (/ 1 n)) (log (/ 1 i)))

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.0b

regimes203.0ms

Accuracy

52.3% (11.5b remaining)

Error of 25.0b against oracle of 13.5b and baseline of 37.7b

bsearch349.0ms

end0.0ms

sample7.1s

Algorithm
intervals
Results
2.5s2491×body1280valid
2.3s1010×body2560valid
1.1s1585×body640valid
378.0ms3031×body80valid
250.0ms835×body320valid
220.0ms2382×body80nan
85.0ms453×body160valid
27.0ms7×body5120valid