Details

sample53.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5007
3	1614
2	280
1	60
0	17

prune56.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.7b

localize87.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (+ (+ alpha beta) i))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.4b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
45.6b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

61×	`add-cbrt-cube` `add-exp-log`
58×	`times-frac`
50×	`associate-/r/`
49×	`flip3-+` `flip-+`
42×	`add-sqr-sqrt`
32×	`frac-times`
31×	`*-un-lft-identity`
30×	`associate-*r/`
26×	`add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
16×	`associate-*l/`
14×	`associate-/l*` `difference-of-squares`
11×	`pow1`
9×	`associate-/l/`
8×	`associate-r`
7×	`div-inv`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `*-commutative`
1×	`flip3--` `flip--` `unswap-sqr`

Counts

4 → 201

Calls

4 calls:

198.0ms	(* i (+ (+ alpha beta) i))
241.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
503.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
285.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series3.3s

Counts

4 → 12

Calls

4 calls:

42.0ms	(* i (+ (+ alpha beta) i))
231.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
2.6s	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
450.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify3.2s

Counts

213 → 213

Iterations

Iter	Nodes
done	5000
1	1289
0	360

prune2.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 35.5b

localize147.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
35.4b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite2.7s

Algorithm

rewrite-expression-head

Rules

366×	`times-frac`
300×	`add-sqr-sqrt`
235×	`*-un-lft-identity`
155×	`add-cube-cbrt`
96×	`associate-r`
70×	`add-cbrt-cube` `add-exp-log`
62×	`difference-of-squares`
44×	`associate-/r/`
42×	`associate-l`
33×	`cbrt-undiv` `div-exp`
31×	`sqrt-prod` `distribute-lft-out--`
22×	`flip3-+` `flip-+` `div-inv`
19×	`associate-/l*`
16×	`prod-exp` `cbrt-unprod`
12×	`associate-/r*`
9×	`distribute-lft-out`
6×	`pow1` `unswap-sqr`
5×	`associate-/l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 376

Calls

4 calls:

576.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
1.7s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
149.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
279.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series6.1s

Counts

4 → 12

Calls

4 calls:

610.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
5.0s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
172.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
274.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify4.1s

Counts

388 → 388

Iterations

Iter	Nodes
done	5002
1	1746
0	513

prune5.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 35.5b

localize134.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
35.4b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite3.0s

Algorithm

rewrite-expression-head

Rules

1669×	`times-frac`
1103×	`add-sqr-sqrt`
864×	`*-un-lft-identity`
630×	`add-cube-cbrt`
290×	`associate-r`
220×	`add-exp-log`
210×	`difference-of-squares`
128×	`div-exp`
107×	`associate-/r/`
105×	`sqrt-prod` `distribute-lft-out--`
101×	`associate-/r*`
100×	`add-cbrt-cube`
58×	`div-inv`
53×	`cbrt-undiv`
51×	`flip3-+` `prod-exp` `flip-+`
42×	`associate-l`
21×	`cbrt-unprod`
15×	`rec-exp` `1-exp`
14×	`unswap-sqr`
9×	`distribute-lft-out`
7×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`clear-num` `frac-2neg` `associate-*r/`
1×	`frac-times` `pow-prod-down` `associate-l/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 891

Calls

4 calls:

322.0ms	(/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))
2.0s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
171.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
276.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series5.9s

Counts

4 → 12

Calls

4 calls:

578.0ms	(/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))
5.0s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
171.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
220.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify7.1s

Counts

903 → 903

Iterations

Iter	Nodes
done	5000
1	3816
0	1056

prune11.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.5b

localize125.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (sqrt (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))) (sqrt (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
35.4b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
36.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite23.9s

Algorithm

rewrite-expression-head

Rules

144397×	`times-frac`
80866×	`add-sqr-sqrt`
65670×	`sqrt-prod`
62956×	`*-un-lft-identity`
45046×	`add-cube-cbrt`
17910×	`difference-of-squares`
8955×	`distribute-lft-out--`
7867×	`associate-/r/`
4282×	`div-inv`
3588×	`flip3-+` `flip-+`
306×	`associate-/l*`
107×	`associate-/r*`
100×	`sqrt-div`
22×	`add-exp-log`
18×	`add-cbrt-cube`
11×	`pow1`
10×	`div-exp`
7×	`cbrt-undiv` `associate-/l/`
6×	`pow-div`
5×	`pow-flip`
4×	`expm1-log1p-u` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-*r/`
1×	`rec-exp` `1-exp` `prod-exp` `cbrt-unprod` `inv-pow`

Counts

4 → 29822

Calls

4 calls:

1.9s	(/ (/ 1 (sqrt (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))) (sqrt (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
164.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
242.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
313.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series1.3s

Counts

4 → 12

Calls

4 calls:

636.0ms	(/ (/ 1 (sqrt (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))) (sqrt (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
154.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
215.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
247.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify1.4m

Counts

29834 → 29834

Iterations

Iter	Nodes
done	25993
0	25993

prune5.2m

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 35.5b

regimes529.0ms

Accuracy

22.4% (2.9b remaining)

Error of 36.9b against oracle of 34.0b and baseline of 37.8b

bsearch80.0ms

Steps

Iters	Range		Point
8	5.908223814084248e+165	4.564177572510244e+168	1.1221989962196496e+166

simplify25.0ms

Iterations

Iter	Nodes
done	38
1	38
0	28

end0.0ms

sample1.1s

Algorithm

intervals

Results

647.0ms	8000×	body	80	valid
195.0ms	8000×	pre	80	true