Details

sample50.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	17	53
1	60	52
2	295	48
3	1651	48
done	5002	48

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 51.7b

localize38.0ms

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))))
35.2b	(/ (/ (* (* 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))
44.3b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite970.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-cbrt-cube`
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` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative`
1×	`flip3--` `flip--` `unswap-sqr`

Counts

4 → 197

Calls

4 calls:

123.0ms	(* i (+ (+ alpha beta) i))
154.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
392.0ms	(/ (/ (* (* 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))
277.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.7s

Counts

4 → 12

Calls

4 calls:

32.0ms	(* i (+ (+ alpha beta) i))
140.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.3s	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
263.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify799.0ms

Counts

209 → 209

Iterations

Useful iterations: done (790.0ms)

Iter	Nodes	Cost
0	353	11780
1	1190	10755
done	5000	9194

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 35.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta)))
4.1b	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))))
32.7b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
38.3b	(/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite396.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log` `add-cbrt-cube`
43×	`times-frac`
40×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity`
22×	`cbrt-undiv` `div-exp`
16×	`associate-l`
14×	`associate-/l*`
12×	`prod-exp` `cbrt-unprod`
7×	`associate-/r*` `associate-/r/` `difference-of-squares`
6×	`pow1` `div-inv`
5×	`associate-/l/`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num`
2×	`associate-r/` `associate-l/` `fma-udef` `unswap-sqr`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `div-sub` `pow-prod-down` `*-commutative` `flip--`

Counts

4 → 153

Calls

4 calls:

46.0ms	(* (/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta)))
171.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))))
114.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
55.0ms	(/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.9s

Counts

4 → 12

Calls

4 calls:

336.0ms	(* (/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta)))
1.2s	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))))
136.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
268.0ms	(/ (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify2.3s

Counts

165 → 165

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	289	7425
1	837	7228
2	4034	5617
done	5000	5613

prune801.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (fma 2.0 i (+ alpha beta)))
4.1b	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (fma 2.0 i (+ alpha beta))))
32.7b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.9b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

rewrite388.0ms

Algorithm

rewrite-expression-head

Rules

207×	`times-frac`
167×	`*-un-lft-identity`
160×	`add-sqr-sqrt`
101×	`associate-l`
87×	`add-cube-cbrt`
74×	`add-exp-log` `add-cbrt-cube`
35×	`cbrt-undiv` `div-exp`
32×	`difference-of-squares`
24×	`distribute-lft-out`
18×	`associate-/r/`
17×	`prod-exp` `cbrt-unprod`
16×	`sqrt-prod` `distribute-lft-out--`
13×	`associate-/l*`
10×	`associate-/r*` `div-inv`
6×	`pow1`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `associate-/l/` `unswap-sqr`
2×	`associate-r/` `associate-l/` `fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative`

Counts

4 → 254

Calls

4 calls:

114.0ms	(* (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (fma 2.0 i (+ alpha beta)))
167.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (fma 2.0 i (+ alpha beta))))
74.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
15.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

series4.9s

Counts

4 → 12

Calls

4 calls:

611.0ms	(* (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (fma 2.0 i (+ alpha beta)))
3.6s	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (fma 2.0 i (+ alpha beta))))
162.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
518.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

simplify835.0ms

Counts

266 → 266

Iterations

Useful iterations: done (814.0ms)

Iter	Nodes	Cost
0	418	12069
1	1142	11504
done	5001	9518

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 33.2b

localize49.0ms

Local error

Found 4 expressions with local error:

4.1b	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (sqrt (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))) (* (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (sqrt (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))) (fma 2.0 i (+ alpha beta)))))
32.7b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.9b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
32.9b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

rewrite415.0ms

Algorithm

rewrite-expression-head

Rules

121×	`add-exp-log` `add-cbrt-cube`
64×	`add-sqr-sqrt`
54×	`cbrt-undiv` `times-frac` `div-exp`
48×	`*-un-lft-identity`
38×	`prod-exp` `cbrt-unprod`
32×	`add-cube-cbrt`
16×	`associate-/r` `associate-/l` `difference-of-squares`
13×	`associate-/r/`
8×	`sqrt-prod` `distribute-lft-out--`
6×	`div-inv`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `flip3-+` `clear-num` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `associate-l/` `associate-/l/`
2×	`flip3--` `flip--`
1×	`frac-times`

Counts

4 → 190

Calls

4 calls:

298.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (sqrt (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))) (* (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (sqrt (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))) (fma 2.0 i (+ alpha beta)))))
78.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
15.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
15.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

series5.0s

Counts

4 → 12

Calls

4 calls:

3.8s	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (sqrt (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))) (* (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (sqrt (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))) (fma 2.0 i (+ alpha beta)))))
144.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
454.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
549.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

simplify2.6s

Counts

202 → 202

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	309	14413
1	877	13197
2	4147	7697
done	5000	7684

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 32.2b

regimes214.0ms

Accuracy

35.4% (2.4b remaining)

Error of 36.7b against oracle of 34.3b and baseline of 38.1b

bsearch92.0ms

Steps

Iters	Range		Point
8	1.4228466486321157e+203	4.845497225576045e+206	1.4407489768135957e+203

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	128
1	42	128
done	42	128

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
335.0ms	8000×	pre	80	true