Details

sample48.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	1615
2	280
1	60
0	17

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 54.5b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
38.7b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
47.8b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

61×	`add-cbrt-cube` `add-exp-log`
58×	`times-frac`
54×	`flip3-+` `flip-+`
50×	`associate-/r/`
44×	`add-sqr-sqrt`
36×	`frac-times`
30×	`associate-*r/`
28×	`*-un-lft-identity` `add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
18×	`associate-*l/`
16×	`pow1`
14×	`associate-/l*` `difference-of-squares`
9×	`associate-/l/`
7×	`div-inv`
6×	`associate-r`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `*-commutative`
1×	`pow2` `pow-plus` `flip3--` `pow-sqr` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 212

Calls

4 calls:

213.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
160.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
370.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
246.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.8s

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
161.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.3s	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
296.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify2.0s

Counts

224 → 224

Iterations

Iter	Nodes
done	5000
1	1342
0	368

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 34.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (* (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (/ (fma beta alpha (* (+ (+ alpha beta) i) i)) (- (+ alpha beta) (* 2 i)))) (fma 2 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2 i (+ alpha beta))))
31.7b	(/ (* (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (/ (fma beta alpha (* (+ (+ alpha beta) i) i)) (- (+ alpha beta) (* 2 i)))) (fma 2 i (+ alpha beta)))
34.8b	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
35.5b	(/ (fma beta alpha (* (+ (+ alpha beta) i) i)) (- (+ alpha beta) (* 2 i)))

rewrite508.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-cbrt-cube` `add-exp-log`
58×	`times-frac`
50×	`*-un-lft-identity`
39×	`cbrt-undiv` `div-exp`
34×	`add-sqr-sqrt` `add-cube-cbrt`
17×	`prod-exp` `cbrt-unprod`
13×	`associate-/r*`
12×	`associate-/l*`
9×	`div-inv`
8×	`distribute-lft-out`
6×	`associate-/l/`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-*l/`
2×	`flip3-+` `flip-+`
1×	`frac-times` `flip3--` `associate-*r/` `flip--`

Counts

4 → 166

Calls

4 calls:

173.0ms	(/ (/ (* (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (/ (fma beta alpha (* (+ (+ alpha beta) i) i)) (- (+ alpha beta) (* 2 i)))) (fma 2 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2 i (+ alpha beta))))
208.0ms	(/ (* (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (/ (fma beta alpha (* (+ (+ alpha beta) i) i)) (- (+ alpha beta) (* 2 i)))) (fma 2 i (+ alpha beta)))
78.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
43.0ms	(/ (fma beta alpha (* (+ (+ alpha beta) i) i)) (- (+ alpha beta) (* 2 i)))

series1.6s

Counts

4 → 12

Calls

4 calls:

771.0ms	(/ (/ (* (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (/ (fma beta alpha (* (+ (+ alpha beta) i) i)) (- (+ alpha beta) (* 2 i)))) (fma 2 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2 i (+ alpha beta))))
565.0ms	(/ (* (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (/ (fma beta alpha (* (+ (+ alpha beta) i) i)) (- (+ alpha beta) (* 2 i)))) (fma 2 i (+ alpha beta)))
138.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
153.0ms	(/ (fma beta alpha (* (+ (+ alpha beta) i) i)) (- (+ alpha beta) (* 2 i)))

simplify2.8s

Counts

178 → 178

Iterations

Iter	Nodes
done	5008
2	3425
1	841
0	294

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.8b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta))))

0.0b

(* (/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta)))) (/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))

0.0b

(/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))

rewrite382.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
45×	`times-frac`
31×	`add-cbrt-cube` `add-exp-log`
28×	`add-cube-cbrt`
24×	`associate-r`
14×	`difference-of-squares`
10×	`cbrt-undiv` `associate-/r` `div-exp` `associate-l*`
9×	`prod-exp` `cbrt-unprod`
8×	`associate-/r/`
7×	`sqrt-prod` `distribute-lft-out--`
5×	`pow1`
4×	`div-inv` `associate-/l*`
3×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out` `add-log-exp`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+` `unswap-sqr` `associate-/l/`
1×	`frac-times` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 138

Calls

3 calls:

32.0ms

(/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta))))

200.0ms

(* (/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta)))) (/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))

143.0ms

(/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))

series735.0ms

Counts

3 → 9

Calls

3 calls:

181.0ms

(/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta))))

347.0ms

(* (/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta)))) (/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))

207.0ms

(/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))

simplify2.7s

Counts

147 → 147

Iterations

Iter	Nodes
done	5000
2	2961
1	712
0	231

prune858.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.6b

localize86.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta))))
0.0b	(* (/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta)))) (/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
0.0b	(/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
19.6b	(posit16->real (real->posit16 (* (/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta)))) (/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))))

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
45×	`times-frac`
32×	`add-cbrt-cube` `add-exp-log`
29×	`add-cube-cbrt`
24×	`associate-r`
14×	`difference-of-squares`
10×	`cbrt-undiv` `associate-/r` `div-exp` `associate-l*`
9×	`prod-exp` `cbrt-unprod`
8×	`associate-/r/`
7×	`sqrt-prod` `distribute-lft-out--`
6×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`flip3--` `flip--` `distribute-lft-out`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+` `unswap-sqr` `associate-/l/`
1×	`frac-times` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `remove-posit16`

Counts

4 → 149

Calls

4 calls:

21.0ms	(/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta))))
164.0ms	(* (/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta)))) (/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
134.0ms	(/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
0.0ms	(posit16->real (real->posit16 (* (/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta)))) (/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta))))
373.0ms	(* (/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta)))) (/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
188.0ms	(/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
371.0ms	(posit16->real (real->posit16 (* (/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta)))) (/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))))

simplify2.2s

Counts

161 → 161

Iterations

Iter	Nodes
done	5000
2	2981
1	723
0	242

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.5b

regimes366.0ms

Accuracy

61.9% (2.6b remaining)

Error of 10.8b against oracle of 8.2b and baseline of 15.0b

bsearch96.0ms

Steps

Iters	Range		Point
6	8.496678904995568e+122	1.0626311280640883e+124	3.7191341897452675e+123

simplify20.0ms

Iterations

Iter	Nodes
done	42
1	42
0	33

end0.0ms

sample1.5s

Algorithm

intervals

Results

932.0ms	8000×	body	80	valid
354.0ms	8000×	pre	80	true