Details

sample420.0ms

Algorithm

intervals

Results

170.0ms	45×	body	2560	valid
142.0ms	77×	body	1280	valid
45.0ms	46×	body	640	valid
16.0ms	98×	body	80	valid
15.0ms	25×	body	320	valid
10.0ms	77×	body	80	nan
4.0ms	13×	body	160	valid

simplify175.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

174.0ms

(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.2b

localize28.0ms

Local error

Found 4 expressions with local error:

13.6b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
6.1b	(pow (+ 1 (/ i n)) n)
1.4b	(- (pow (+ 1 (/ i n)) n) 1)
0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite517.0ms

Algorithm

rewrite-expression-head

Rules

584×	`times-frac`
485×	`add-sqr-sqrt`
366×	`*-un-lft-identity`
224×	`add-cube-cbrt`
174×	`associate-r`
168×	`difference-of-squares`
88×	`unpow-prod-down`
85×	`sqr-pow`
84×	`difference-of-sqr-1`
29×	`div-inv`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`associate-/r` `associate-/l`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`insert-posit16`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `pow-exp` `associate-r/` `-commutative` `distribute-lft-out`

Counts

4 → 453

Calls

4 calls:

Slowest

214.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
181.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
100.0ms	(- (pow (+ 1 (/ i n)) n) 1)
10.0ms	(pow (+ 1 (/ i n)) n)

series1.5s

Counts

4 → 12

Calls

4 calls:

Slowest

429.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
420.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
345.0ms	(- (pow (+ 1 (/ i n)) n) 1)
310.0ms	(pow (+ 1 (/ i n)) n)

simplify2.3m

Counts

595 → 465

Calls

595 calls:

Slowest

889.0ms	(/ (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (/ i (sqrt n)))
638.0ms	(/ (* (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (cbrt (- (pow (+ 1 (/ i n)) n) 1))) (/ (sqrt i) 1))
627.0ms	(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (sqrt i) n))
625.0ms	(/ (- (pow (sqrt (+ 1 (/ i n))) n) (sqrt 1)) (/ (sqrt i) (sqrt n)))
607.0ms	(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (sqrt i) 1))

prune3.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.8b

localize21.0ms

Local error

Found 4 expressions with local error:

19.3b	(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
0.3b	(* 1/6 i)
0.0b	(* (* i i) (+ (* 1/6 i) 1/2))
0.0b	(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
97×	`add-sqr-sqrt`
85×	`*-un-lft-identity` `add-cube-cbrt`
50×	`associate-r`
25×	`add-cbrt-cube` `add-exp-log`
13×	`pow1` `associate-/r*`
9×	`div-inv`
7×	`associate-l` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow-prod-down` `unswap-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`associate-r/` `-commutative` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in`

Counts

4 → 183

Calls

4 calls:

Slowest

33.0ms	(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
25.0ms	(* (* i i) (+ (* 1/6 i) 1/2))
17.0ms	(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))
5.0ms	(* 1/6 i)

series236.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

75.0ms	(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))
71.0ms	(* (* i i) (+ (* 1/6 i) 1/2))
69.0ms	(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
20.0ms	(* 1/6 i)

simplify22.9s

Counts

194 → 195

Calls

194 calls:

Slowest

498.0ms	(* (* (* 100 100) 100) (/ (* (* (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (/ (* (* i i) i) (* (* n n) n))))
424.0ms	(* (* (* 100 100) 100) (/ (* (* (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (* (* (/ i n) (/ i n)) (/ i n))))
381.0ms	(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (cbrt (/ i n)))
291.0ms	(/ (* (* (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (/ (* (* i i) i) (* (* n n) n)))
253.0ms	(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.6b

localize14.0ms

Local error

Found 4 expressions with local error:

2.4b	(* n (+ 100 (* i (+ (* 50/3 i) 50))))
0.4b	(* 50/3 i)
0.1b	(* i (+ (* 50/3 i) 50))
0.0b	(+ 100 (* i (+ (* 50/3 i) 50)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
4×	`associate-*r/` `insert-posit16`
3×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`associate-+r+`
1×	`+-commutative` `sum-log`

Counts

4 → 79

Calls

4 calls:

Slowest

18.0ms	(* i (+ (* 50/3 i) 50))
14.0ms	(* n (+ 100 (* i (+ (* 50/3 i) 50))))
5.0ms	(+ 100 (* i (+ (* 50/3 i) 50)))
5.0ms	(* 50/3 i)

series155.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

65.0ms	(* i (+ (* 50/3 i) 50))
52.0ms	(* n (+ 100 (* i (+ (* 50/3 i) 50))))
22.0ms	(+ 100 (* i (+ (* 50/3 i) 50)))
16.0ms	(* 50/3 i)

simplify2.2s

Counts

52 → 91

Calls

52 calls:

Slowest

216.0ms	(* (* (* n n) n) (* (* (+ 100 (* i (+ (* 50/3 i) 50))) (+ 100 (* i (+ (* 50/3 i) 50)))) (+ 100 (* i (+ (* 50/3 i) 50)))))
168.0ms	(+ (* (* 50/3 i) (* 50/3 i)) (- (* 50 50) (* (* 50/3 i) 50)))
146.0ms	(+ (* 50/3 (* (pow i 2) n)) (+ (* 100 n) (* 50 (* i n))))
146.0ms	(+ (* 50/3 (* (pow i 2) n)) (+ (* 100 n) (* 50 (* i n))))
144.0ms	(+ (* 50/3 (* (pow i 2) n)) (+ (* 100 n) (* 50 (* i n))))

prune556.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.6b

localize35.0ms

Local error

Found 4 expressions with local error:

10.8b	(posit16->real (real->posit16 (+ 100 (* i (+ (* 50/3 i) 50)))))
2.4b	(* n (posit16->real (real->posit16 (+ 100 (* i (+ (* 50/3 i) 50))))))
0.4b	(* 50/3 i)
0.1b	(* i (+ (* 50/3 i) 50))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+` `remove-posit16`

Counts

4 → 70

Calls

4 calls:

Slowest

17.0ms	(* i (+ (* 50/3 i) 50))
5.0ms	(* n (posit16->real (real->posit16 (+ 100 (* i (+ (* 50/3 i) 50))))))
5.0ms	(* 50/3 i)
0.0ms	(posit16->real (real->posit16 (+ 100 (* i (+ (* 50/3 i) 50)))))

series159.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

65.0ms	(* i (+ (* 50/3 i) 50))
50.0ms	(* n (posit16->real (real->posit16 (+ 100 (* i (+ (* 50/3 i) 50))))))
28.0ms	(posit16->real (real->posit16 (+ 100 (* i (+ (* 50/3 i) 50)))))
15.0ms	(* 50/3 i)

simplify1.6s

Counts

45 → 82

Calls

45 calls:

Slowest

167.0ms	(+ (* (* 50/3 i) (* 50/3 i)) (- (* 50 50) (* (* 50/3 i) 50)))
147.0ms	(+ (* 50/3 (* (pow i 2) n)) (+ (* 100 n) (* 50 (* i n))))
144.0ms	(+ (* 50/3 (* (pow i 2) n)) (+ (* 100 n) (* 50 (* i n))))
143.0ms	(+ (* 50/3 (* (pow i 2) n)) (+ (* 100 n) (* 50 (* i n))))
141.0ms	(* (* (* i i) i) (* (* (+ (* 50/3 i) 50) (+ (* 50/3 i) 50)) (+ (* 50/3 i) 50)))

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.6b

regimes255.0ms

Accuracy

54.7% (11.3b remaining)

Error of 19.5b against oracle of 8.2b and baseline of 33.2b

bsearch266.0ms

end0.0ms

sample7.3s

Algorithm

intervals

Results

2.5s	2480×	body	1280	valid
2.5s	1015×	body	2560	valid
1.1s	1566×	body	640	valid
344.0ms	3014×	body	80	valid
334.0ms	893×	body	320	valid
233.0ms	2318×	body	80	nan
104.0ms	429×	body	160	valid
31.0ms	9×	body	5120	valid