Details

sample68.0ms

Algorithm

intervals

Results

29.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	1807
2	295
1	60
0	17

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.0b	(/ (/ (* (* 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))
45.8b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite609.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-cbrt-cube` `add-exp-log`
58×	`times-frac`
50×	`associate-/r/`
49×	`flip3-+` `flip-+`
38×	`add-sqr-sqrt`
32×	`frac-times`
28×	`associate-*r/`
24×	`*-un-lft-identity` `add-cube-cbrt`
21×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
16×	`associate-*l/`
14×	`associate-/l*` `difference-of-squares`
9×	`pow1` `associate-/l/`
7×	`div-inv`
6×	`add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `pow-prod-down`
2×	`distribute-rgt-in` `associate-+r+` `clear-num` `frac-2neg` `distribute-lft-in`
1×	`+-commutative` `sum-log` `fma-def` `flip3--` `associate-l` `*-commutative` `flip--`

Counts

4 → 187

Calls

4 calls:

29.0ms	(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
115.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
284.0ms	(/ (/ (* (* 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))
165.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.8s

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
163.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.2s	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
308.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify1.7s

Counts

199 → 199

Iterations

Iter	Nodes
done	5000
1	1262
0	347

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.3b

localize38.0ms

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))))
35.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.6s

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` `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 → 372

Calls

4 calls:

317.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
972.0ms	(* (/ (/ (* 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))))
83.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
165.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.0s

Counts

4 → 12

Calls

4 calls:

462.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
3.3s	(* (/ (/ (* 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))))
117.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
166.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify2.2s

Counts

384 → 384

Iterations

Iter	Nodes
done	5001
1	1811
0	509

prune2.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.3b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

1852×	`times-frac`
1455×	`*-un-lft-identity`
892×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
380×	`distribute-lft-out`
278×	`associate-l`
99×	`associate-/r/`
96×	`associate-r`
86×	`associate-/l*`
74×	`add-cbrt-cube` `add-exp-log`
62×	`difference-of-squares`
54×	`div-inv`
44×	`flip3-+` `flip-+`
40×	`cbrt-undiv` `div-exp`
31×	`sqrt-prod` `distribute-lft-out--`
13×	`associate-/r*`
12×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`clear-num` `frac-2neg`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 952

Calls

4 calls:

318.0ms	(/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
340.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
1.3s	(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) 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))))
161.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.3s

Counts

4 → 12

Calls

4 calls:

372.0ms	(/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
452.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
3.3s	(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) 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))))
169.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify3.0s

Counts

964 → 964

Iterations

Iter	Nodes
done	5000
1	3584
0	1040

prune6.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (fma 0.25 (+ alpha beta) (* 0.5 i)) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
0.0b	(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))
0.0b	(/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i)))
0.0b	(/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

1688×	`times-frac`
1426×	`*-un-lft-identity`
705×	`add-sqr-sqrt`
661×	`add-cube-cbrt`
428×	`distribute-lft-out`
278×	`associate-l`
80×	`associate-/r/`
74×	`associate-/l*`
52×	`add-cbrt-cube` `add-exp-log`
45×	`div-inv`
35×	`flip3-+` `flip-+`
30×	`associate-/r*`
26×	`cbrt-undiv` `div-exp`
24×	`associate-r`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`pow1` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `sqrt-prod` `distribute-lft-out--` `associate-/l/`
1×	`frac-times` `flip3--` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 850

Calls

4 calls:

1.0s	(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (fma 0.25 (+ alpha beta) (* 0.5 i)) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
153.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))
78.0ms	(/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i)))
338.0ms	(/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

670.0ms	(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (fma 0.25 (+ alpha beta) (* 0.5 i)) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
103.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))
120.0ms	(/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i)))
431.0ms	(/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))

simplify2.6s

Counts

862 → 862

Iterations

Iter	Nodes
done	5001
1	2703
0	824

prune5.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.2b

regimes424.0ms

Accuracy

38.3% (9.4b remaining)

Error of 11.4b against oracle of 1.9b and baseline of 17.2b

bsearch105.0ms

Steps

Iters	Range		Point
6	3.710562679513184e+121	1.5715503341522111e+122	7.435536344855911e+121

simplify10.0ms

Iterations

Iter	Nodes
done	51
1	51
0	37

end0.0ms

sample1.8s

Algorithm

intervals

Results

931.0ms	8000×	body	80	valid
592.0ms	8000×	pre	80	true