Details

Time bar (total: 1.9m)

sample393.0ms

Algorithm
intervals
Results
151.0ms31×body2560valid
129.0ms80×body1280valid
46.0ms53×body640valid
15.0ms104×body80valid
15.0ms26×body320valid
11.0ms72×body80nan
7.0ms20×body160valid

simplify153.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
153.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.7b

localize29.0ms

Local error

Found 3 expressions with local error:

10.2b
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
6.1b
(pow (+ 1 (/ i n)) n)
0.8b
(fma 100 (pow (+ 1 (/ i n)) n) -100)

rewrite34.0ms

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
18.0ms
(pow (+ 1 (/ i n)) n)
12.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
0.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)

series1.0s

Counts
3 → 9
Calls
3 calls:
Slowest
451.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
301.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)
283.0ms
(pow (+ 1 (/ i n)) n)

simplify55.7s

Counts
159 → 114
Calls
159 calls:
Slowest
907.0ms
(* (cbrt (/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))) (cbrt (/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))))
773.0ms
(log (/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n)))
750.0ms
(log1p (fma 100 (pow (+ 1 (/ i n)) n) -100))
741.0ms
(/ (sqrt (fma 100 (pow (+ 1 (/ i n)) n) -100)) (/ 1 1))
730.0ms
(exp (/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n)))

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.1b

localize21.0ms

Local error

Found 4 expressions with local error:

10.2b
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
10.0b
(* n (log1p (/ i n)))
5.8b
(log1p (/ i n))
2.4b
(fma 100 (exp (* n (log1p (/ i n)))) -100)

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

series894.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
461.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
275.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
87.0ms
(* n (log1p (/ i n)))
71.0ms
(log1p (/ i n))

simplify23.0s

Counts
168 → 129
Calls
168 calls:
Slowest
544.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ 1 (* (cbrt n) (cbrt n))))
362.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ 1 (* (cbrt n) (cbrt n))))
349.0ms
(/ (* (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)) (sqrt n)))
307.0ms
(/ (* (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100)) (cbrt (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ (* (cbrt i) (cbrt i)) 1))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.2b

localize21.0ms

Local error

Found 4 expressions with local error:

11.2b
(* (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ n i))
10.0b
(* n (log1p (/ i n)))
5.8b
(log1p (/ i n))
2.4b
(fma 100 (exp (* n (log1p (/ i n)))) -100)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
16×associate-*r*
14×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×times-frac
8×pow1
6×associate-*l*
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 log1p-expm1 associate-*r/ fma-udef div-inv
Counts
4 → 79
Calls
4 calls:
Slowest
9.0ms
(* (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ n i))
6.0ms
(* n (log1p (/ i n)))
0.0ms
(log1p (/ i n))
0.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)

series717.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
359.0ms
(* (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ n i))
242.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
61.0ms
(* n (log1p (/ i n)))
56.0ms
(log1p (/ i n))

simplify9.1s

Counts
91 → 91
Calls
91 calls:
Slowest
395.0ms
(* (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ 1 (sqrt i)))
391.0ms
(* (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ (sqrt n) 1))
268.0ms
(* (fma 100 (exp (* n (log1p (/ i n)))) -100) (sqrt (/ n i)))
261.0ms
(* (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ (* (cbrt n) (cbrt n)) 1))
259.0ms
(* (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ 1 (* (cbrt i) (cbrt i))))

prune777.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.2b

localize37.0ms

Local error

Found 4 expressions with local error:

11.2b
(* (cbrt (* (* (fma 100 (exp (* n (log1p (/ i n)))) -100) (fma 100 (exp (* n (log1p (/ i n)))) -100)) (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ n i))
10.0b
(* n (log1p (/ i n)))
10.0b
(* n (log1p (/ i n)))
10.0b
(* n (log1p (/ i n)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×associate-*r*
18×*-un-lft-identity add-cube-cbrt
15×add-exp-log
13×add-cbrt-cube associate-*l*
12×pow1
10×times-frac
5×prod-exp cbrt-unprod unswap-sqr
4×expm1-log1p-u pow-prod-down *-commutative insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-prod cbrt-undiv div-exp associate-*r/ div-inv
Counts
4 → 99
Calls
4 calls:
Slowest
19.0ms
(* (cbrt (* (* (fma 100 (exp (* n (log1p (/ i n)))) -100) (fma 100 (exp (* n (log1p (/ i n)))) -100)) (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ n i))
6.0ms
(* n (log1p (/ i n)))
6.0ms
(* n (log1p (/ i n)))
6.0ms
(* n (log1p (/ i n)))

series561.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
370.0ms
(* (cbrt (* (* (fma 100 (exp (* n (log1p (/ i n)))) -100) (fma 100 (exp (* n (log1p (/ i n)))) -100)) (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ n i))
65.0ms
(* n (log1p (/ i n)))
64.0ms
(* n (log1p (/ i n)))
61.0ms
(* n (log1p (/ i n)))

simplify8.4s

Counts
112 → 111
Calls
112 calls:
Slowest
474.0ms
(* (* (* (cbrt (* (* (fma 100 (exp (* n (log1p (/ i n)))) -100) (fma 100 (exp (* n (log1p (/ i n)))) -100)) (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ n i)) (* (cbrt (* (* (fma 100 (exp (* n (log1p (/ i n)))) -100) (fma 100 (exp (* n (log1p (/ i n)))) -100)) (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ n i))) (* (cbrt (* (* (fma 100 (exp (* n (log1p (/ i n)))) -100) (fma 100 (exp (* n (log1p (/ i n)))) -100)) (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ n i)))
431.0ms
(* (cbrt (* (* (fma 100 (exp (* n (log1p (/ i n)))) -100) (fma 100 (exp (* n (log1p (/ i n)))) -100)) (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ 1 (sqrt i)))
256.0ms
(* (* (* n n) n) (* (* (log1p (/ i n)) (log1p (/ i n))) (log1p (/ i n))))
254.0ms
(* (* (* n n) n) (* (* (log1p (/ i n)) (log1p (/ i n))) (log1p (/ i n))))
239.0ms
(* (* (* n n) n) (* (* (log1p (/ i n)) (log1p (/ i n))) (log1p (/ i n))))

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.2b

regimes200.0ms

Accuracy

45.7% (14.0b remaining)

Error of 27.4b against oracle of 13.4b and baseline of 39.2b

bsearch883.0ms

end0.0ms

sample6.9s

Algorithm
intervals
Results
2.4s2450×body1280valid
2.2s964×body2560valid
1.1s1623×body640valid
334.0ms3139×body80valid
303.0ms869×body320valid
209.0ms2268×body80nan
150.0ms468×body160valid
22.0ms6×body5120valid