Details

sample273.0ms

Algorithm

intervals

Results

128.0ms	85×	body	1280	valid
69.0ms	28×	body	2560	valid
32.0ms	52×	body	640	valid
11.0ms	97×	body	80	valid
9.0ms	26×	body	320	valid
7.0ms	69×	body	80	nan
4.0ms	16×	body	160	valid

simplify3.2s

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.9b

localize16.0ms

Local error

Found 4 expressions with local error:

8.7b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
6.7b	(pow (+ 1 (/ i n)) n)
2.0b	(- (pow (+ 1 (/ i n)) n) 1)
0.1b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite462.0ms

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

188.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
175.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
73.0ms	(- (pow (+ 1 (/ i n)) n) 1)
15.0ms	(pow (+ 1 (/ i n)) n)

series1.4s

Counts

4 → 12

Calls

4 calls:

Slowest

440.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
356.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
312.0ms	(- (pow (+ 1 (/ i n)) n) 1)
269.0ms	(pow (+ 1 (/ i n)) n)

simplify767.0ms

Counts: 465 → 465

prune4.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.7b

localize28.0ms

Local error

Found 4 expressions with local error:

16.3b	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ i n))
9.5b	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
0.1b	(* 1/6 (* i (* i i)))
0.1b	(* i (* i i))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

97×	`times-frac`
83×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
55×	`add-cube-cbrt`
27×	`pow1`
23×	`add-cbrt-cube` `add-exp-log`
14×	`distribute-lft-out`
13×	`associate-/r*`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-l` `div-inv` `add-log-exp`
5×	`pow-prod-up`
4×	`insert-posit16` `associate-/l*`
3×	`cbrt-undiv` `div-exp`
2×	`flip3-+` `associate-r` `*-commutative` `flip-+` `associate-/l/`
1×	`pow2` `+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-plus` `cube-unmult` `associate-/r/` `pow-sqr` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

Slowest

168.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ i n))
38.0ms	(* 1/6 (* i (* i i)))
20.0ms	(* i (* i i))
19.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))

series320.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

122.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
91.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ i n))
55.0ms	(* 1/6 (* i (* i i)))
52.0ms	(* i (* i i))

simplify802.0ms

Counts: 158 → 158

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.9b

localize32.0ms

Local error

Found 4 expressions with local error:

9.5b	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
5.4b	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i)
2.1b	(* (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i) n)
0.1b	(* 1/6 (* i (* i i)))

rewrite472.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
23×	`add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
19×	`associate-l`
15×	`pow1`
8×	`prod-exp` `cbrt-unprod`
7×	`pow-prod-down` `distribute-lft-out`
6×	`add-log-exp`
4×	`associate-r` `insert-posit16` `associate-/l*`
3×	`associate-/r*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `*-commutative` `flip-+` `div-inv` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `associate-*l/`

Counts

4 → 104

Calls

4 calls:

Slowest

204.0ms	(* (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i) n)
198.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i)
38.0ms	(* 1/6 (* i (* i i)))
31.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

131.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
85.0ms	(* (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i) n)
64.0ms	(* 1/6 (* i (* i i)))
48.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i)

simplify2.5s

Counts: 116 → 116

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.9b

localize17.0ms

Local error

Found 4 expressions with local error:

2.1b	(* n (* i (+ 1/2 (* 1/6 i))))
0.3b	(* 1/6 i)
0.1b	(* i (+ 1/2 (* 1/6 i)))
0.0b	(* 100 (+ n (* n (* i (+ 1/2 (* 1/6 i))))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`associate-l`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-r`
8×	`associate-*r/`
6×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`*-commutative` `insert-posit16` `add-log-exp`
3×	`flip3-+` `flip-+` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

Slowest

25.0ms	(* n (* i (+ 1/2 (* 1/6 i))))
20.0ms	(* i (+ 1/2 (* 1/6 i)))
18.0ms	(* 100 (+ n (* n (* i (+ 1/2 (* 1/6 i))))))
5.0ms	(* 1/6 i)

series283.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

87.0ms	(* n (* i (+ 1/2 (* 1/6 i))))
87.0ms	(* 100 (+ n (* n (* i (+ 1/2 (* 1/6 i))))))
86.0ms	(* i (+ 1/2 (* 1/6 i)))
22.0ms	(* 1/6 i)

simplify2.8s

Counts: 102 → 102

prune834.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.9b

regimes292.0ms

Accuracy

55.1% (10.2b remaining)

Error of 21.3b against oracle of 11.1b and baseline of 33.8b

bsearch529.0ms

end0.0ms

sample8.3s

Algorithm

intervals

Results

3.1s	2511×	body	1280	valid
2.5s	974×	body	2560	valid
1.3s	1598×	body	640	valid
456.0ms	3047×	body	80	valid
340.0ms	892×	body	320	valid
256.0ms	2316×	body	80	nan
102.0ms	430×	body	160	valid
23.0ms	5×	body	5120	valid