Details

Time bar (total: 20.3s)

sample29.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
4.0ms256×pre80true

simplify5.6s

Counts
1 → 1
Iterations

Useful iterations: 4 (3.6s)

IterNodesCost
01025
13225
216823
389419
4335315
done500015

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ 1.0 (* i i))
0.5b
(/ 1 (* (- (* 2.0 2.0) (/ 1.0 (* i i))) (* 2.0 2.0)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
16×add-cbrt-cube
10×prod-exp
8×pow1 div-exp
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac associate-/l*
5×cbrt-undiv
4×cbrt-unprod
3×rec-exp pow-flip 1-exp pow-prod-down
2×expm1-log1p-u frac-2neg associate-*l/ clear-num associate-/r* associate-/r/ log1p-expm1-u div-inv add-log-exp
1×flip3-- flip-- inv-pow
Counts
2 → 60
Calls
2 calls:
15.0ms
(/ 1.0 (* i i))
82.0ms
(/ 1 (* (- (* 2.0 2.0) (/ 1.0 (* i i))) (* 2.0 2.0)))

series109.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(/ 1.0 (* i i))
72.0ms
(/ 1 (* (- (* 2.0 2.0) (/ 1.0 (* i i))) (* 2.0 2.0)))

simplify3.1s

Counts
66 → 66
Iterations

Useful iterations: 3 (1.7s)

IterNodesCost
0136944
1322853
2943732
33845730
done5001730

prune166.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- (pow 2.0 4) (/ (* 1.0 1.0) (pow i 4))))
0.1b
(/ 1.0 (* i i))
0.3b
(/ (* 1.0 1.0) (pow i 4))
20.7b
(* (/ (/ 1 (- (pow 2.0 4) (/ (* 1.0 1.0) (pow i 4)))) (* 2.0 2.0)) (+ (* 2.0 2.0) (/ 1.0 (* i i))))

rewrite393.0ms

Algorithm
rewrite-expression-head
Rules
228×times-frac
181×add-sqr-sqrt
84×difference-of-squares
68×*-un-lft-identity
58×add-exp-log associate-*l*
55×unpow-prod-down
53×add-cube-cbrt
51×sqr-pow
34×add-cbrt-cube
24×associate-/r*
22×div-exp
17×prod-exp
11×cbrt-undiv
9×cbrt-unprod
7×pow1 associate-/l* distribute-lft-out--
5×div-inv
4×expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp unswap-sqr
3×rec-exp frac-2neg 1-exp associate-*r* clear-num
2×frac-times pow-to-exp flip3-- flip3-+ associate-*r/ pow-exp flip-- flip-+
1×distribute-rgt-in pow-flip distribute-lft-in pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 242
Calls
4 calls:
59.0ms
(/ 1 (- (pow 2.0 4) (/ (* 1.0 1.0) (pow i 4))))
17.0ms
(/ 1.0 (* i i))
25.0ms
(/ (* 1.0 1.0) (pow i 4))
277.0ms
(* (/ (/ 1 (- (pow 2.0 4) (/ (* 1.0 1.0) (pow i 4)))) (* 2.0 2.0)) (+ (* 2.0 2.0) (/ 1.0 (* i i))))

series395.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ 1 (- (pow 2.0 4) (/ (* 1.0 1.0) (pow i 4))))
51.0ms
(/ 1.0 (* i i))
62.0ms
(/ (* 1.0 1.0) (pow i 4))
135.0ms
(* (/ (/ 1 (- (pow 2.0 4) (/ (* 1.0 1.0) (pow i 4)))) (* 2.0 2.0)) (+ (* 2.0 2.0) (/ 1.0 (* i i))))

simplify2.9s

Counts
254 → 254
Iterations

Useful iterations: done (2.9s)

IterNodesCost
04875901
115025309
243444743
done50004729

prune996.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (* i i))
0.1b
(/ 1.0 (* i i))
0.5b
(/ (* (cbrt 1) (cbrt 1)) (+ (sqrt (pow 2.0 4)) (/ 1.0 (pow i (/ 4 2)))))
15.0b
(/ (fma 2.0 2.0 (/ 1.0 (* i i))) (- (sqrt (pow 2.0 4)) (/ 1.0 (* i i))))

rewrite227.0ms

Algorithm
rewrite-expression-head
Rules
83×add-sqr-sqrt
62×times-frac
39×*-un-lft-identity
32×difference-of-squares
27×add-cube-cbrt
24×sqrt-prod
21×add-exp-log
19×add-cbrt-cube
18×associate-/r*
10×associate-/l*
8×unpow-prod-down sqr-pow
7×cbrt-undiv div-exp
4×pow1 expm1-log1p-u frac-2neg clear-num associate-/r/ log1p-expm1-u div-inv distribute-lft-out-- add-log-exp
3×prod-exp cbrt-unprod
2×distribute-lft-out
1×flip3-- flip3-+ flip-- flip-+
Counts
4 → 140
Calls
4 calls:
17.0ms
(/ 1.0 (* i i))
17.0ms
(/ 1.0 (* i i))
111.0ms
(/ (* (cbrt 1) (cbrt 1)) (+ (sqrt (pow 2.0 4)) (/ 1.0 (pow i (/ 4 2)))))
74.0ms
(/ (fma 2.0 2.0 (/ 1.0 (* i i))) (- (sqrt (pow 2.0 4)) (/ 1.0 (* i i))))

series264.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ 1.0 (* i i))
55.0ms
(/ 1.0 (* i i))
66.0ms
(/ (* (cbrt 1) (cbrt 1)) (+ (sqrt (pow 2.0 4)) (/ 1.0 (pow i (/ 4 2)))))
115.0ms
(/ (fma 2.0 2.0 (/ 1.0 (* i i))) (- (sqrt (pow 2.0 4)) (/ 1.0 (* i i))))

simplify2.5s

Counts
152 → 152
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02503384
15263075
212442858
332302816
done50002807

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 1.0 (pow i 4) (* 4.0 (pow i 6)))
0.0b
(fma 0.25 (pow i 2) (fma 1.0 (pow i 4) (* 4.0 (pow i 6))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
0.0ms
(fma 1.0 (pow i 4) (* 4.0 (pow i 6)))
0.0ms
(fma 0.25 (pow i 2) (fma 1.0 (pow i 4) (* 4.0 (pow i 6))))

series259.0ms

Counts
2 → 6
Calls
2 calls:
170.0ms
(fma 1.0 (pow i 4) (* 4.0 (pow i 6)))
90.0ms
(fma 0.25 (pow i 2) (fma 1.0 (pow i 4) (* 4.0 (pow i 6))))

simplify1.0s

Counts
26 → 26
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
035418
156409
2155359
3764359
done5000359

prune95.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
11315
done1315

end0.0ms

sample873.0ms

Algorithm
intervals
Results
591.0ms8000×body80valid
123.0ms8000×pre80true