Details

sample85.0ms

Algorithm

intervals

Results

49.0ms	256×	body	80	valid
14.0ms	256×	pre	80	true

simplify1.5s

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 54.5b

localize61.0ms

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))))
35.6b	(/ (/ (* (* 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))
48.3b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite739.0ms

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:

162.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
118.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
279.0ms	(/ (/ (* (* 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))
177.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.7s

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
167.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.2s	(/ (/ (* (* 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))
270.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify1.9s

Counts

224 → 224

Iterations

Iter	Nodes
done	5000
1	1342
0	368

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 32.4b

localize77.0ms

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))))
28.7b	(/ (* (/ (* (+ (+ 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)))
32.2b	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
33.4b	(/ (fma beta alpha (* (+ (+ alpha beta) i) i)) (- (+ alpha beta) (* 2 i)))

rewrite348.0ms

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:

163.0ms	(/ (/ (* (/ (* (+ (+ 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))))
118.0ms	(/ (* (/ (* (+ (+ 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)))
34.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
30.0ms	(/ (fma beta alpha (* (+ (+ alpha beta) i) i)) (- (+ alpha beta) (* 2 i)))

series1.6s

Counts

4 → 12

Calls

4 calls:

831.0ms	(/ (/ (* (/ (* (+ (+ 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))))
508.0ms	(/ (* (/ (* (+ (+ 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)))
113.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
161.0ms	(/ (fma beta alpha (* (+ (+ alpha beta) i) i)) (- (+ alpha beta) (* 2 i)))

simplify2.5s

Counts

178 → 178

Iterations

Iter	Nodes
done	5008
2	3425
1	841
0	294

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.3b

localize39.0ms

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)))

rewrite245.0ms

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:

17.0ms

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

117.0ms

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

108.0ms

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

series729.0ms

Counts

3 → 9

Calls

3 calls:

197.0ms

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

324.0ms

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

206.0ms

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

simplify1.9s

Counts

147 → 147

Iterations

Iter	Nodes
done	5000
2	2961
1	712
0	231

prune873.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.8b

localize73.0ms

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)))
21.6b	(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))))))

rewrite203.0ms

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:

23.0ms	(/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta))))
87.0ms	(* (/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta)))) (/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
89.0ms	(/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
1.0ms	(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))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta))))
454.0ms	(* (/ (* -1/8 i) (+ (sqrt 1.0) (fma 2 i (+ alpha beta)))) (/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
175.0ms	(/ (- (+ alpha beta) (* 2 i)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
436.0ms	(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))))))

simplify2.6s

Counts

161 → 161

Iterations

Iter	Nodes
done	5000
2	2981
1	723
0	242

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.7b

regimes409.0ms

Accuracy

62.6% (2.7b remaining)

Error of 10.5b against oracle of 7.9b and baseline of 15.0b

bsearch93.0ms

Steps

Iters	Range		Point
5	5.4039666828126895e+146	1.5043712263133658e+147	6.263709625600619e+146

simplify10.0ms

Iterations

Iter	Nodes
done	46
1	46
0	35

end0.0ms

sample2.7s

Algorithm

intervals

Results

2.1s	8000×	body	80	valid
371.0ms	8000×	pre	80	true