Details

sample57.0ms

Algorithm

intervals

Results

30.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	1808
2	295
1	60
0	17

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) i) i)
0.1b	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
36.0b	(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))
45.1b	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-cbrt-cube` `add-exp-log`
26×	`add-sqr-sqrt` `times-frac`
23×	`*-un-lft-identity`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
18×	`add-cube-cbrt`
11×	`pow1`
8×	`associate-l`
7×	`div-inv`
6×	`associate-l/` `associate-/l` `difference-of-squares`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+` `distribute-lft-out` `associate-/l/`
2×	`clear-num` `frac-2neg` `associate-/r/` `*-commutative`
1×	`flip3--` `flip--` `unswap-sqr`

Counts

4 → 137

Calls

4 calls:

61.0ms	(* (+ (+ alpha beta) i) i)
60.0ms	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
88.0ms	(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))
101.0ms	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))

series924.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (+ (+ alpha beta) i) i)
183.0ms	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
395.0ms	(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))
318.0ms	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))

simplify1.5s

Counts

149 → 149

Iterations

Iter	Nodes
done	5000
1	712
0	240

prune952.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 33.8b

localize78.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
0.1b	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
33.8b	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
34.7b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

266×	`times-frac`
193×	`*-un-lft-identity`
174×	`add-sqr-sqrt`
125×	`add-cube-cbrt`
70×	`add-cbrt-cube` `add-exp-log`
58×	`associate-l`
48×	`associate-r`
33×	`cbrt-undiv` `div-exp`
27×	`distribute-lft-out`
20×	`div-inv`
17×	`associate-/l*`
16×	`prod-exp` `cbrt-unprod`
14×	`difference-of-squares`
10×	`associate-/r*`
7×	`sqrt-prod` `distribute-lft-out--`
6×	`pow1` `associate-/r/` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `flip3-+` `associate-*l/` `flip-+` `associate-/l/`
1×	`frac-times` `flip3--` `pow-prod-down` `associate-r/` `-commutative` `flip--`

Counts

4 → 296

Calls

4 calls:

25.0ms	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
145.0ms	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
62.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
8.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

series1.5s

Counts

4 → 12

Calls

4 calls:

431.0ms	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
755.0ms	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
111.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
169.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

simplify2.2s

Counts

308 → 308

Iterations

Iter	Nodes
done	5000
1	1415
0	426

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.7b

localize78.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (* (/ (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))) 1) (/ (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))) (fma 2 i (+ alpha beta)))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
33.8b	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
34.7b	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
34.7b	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

193×	`add-exp-log`
145×	`add-cbrt-cube`
98×	`div-exp`
68×	`cbrt-undiv` `times-frac`
65×	`add-sqr-sqrt` `prod-exp`
48×	`associate-r`
47×	`cbrt-unprod`
46×	`*-un-lft-identity`
30×	`add-cube-cbrt`
14×	`difference-of-squares`
13×	`sqrt-prod`
10×	`associate-l`
9×	`div-inv`
8×	`pow1` `1-exp`
7×	`distribute-lft-out--`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l/`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `unswap-sqr` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `flip3--` `pow-prod-down` `associate-r/` `-commutative` `flip--` `distribute-lft-out` `associate-/l*`

Counts

4 → 189

Calls

4 calls:

125.0ms	(* (/ (* (/ (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))) 1) (/ (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))) (fma 2 i (+ alpha beta)))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
28.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
1.0ms	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
1.0ms	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))

series948.0ms

Counts

4 → 12

Calls

4 calls:

683.0ms	(* (/ (* (/ (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))) 1) (/ (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))) (fma 2 i (+ alpha beta)))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
109.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
64.0ms	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
91.0ms	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))

simplify1.4s

Counts

201 → 201

Iterations

Iter	Nodes
done	5000
1	1271
0	346

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 33.7b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))))
0.2b	(* (* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))) (/ 1 (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
33.8b	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
34.7b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

rewrite469.0ms

Algorithm

rewrite-expression-head

Rules

245×	`add-exp-log`
151×	`add-cbrt-cube`
124×	`times-frac`
101×	`prod-exp`
100×	`*-un-lft-identity`
98×	`div-exp`
89×	`add-sqr-sqrt`
68×	`add-cube-cbrt`
59×	`associate-l`
58×	`cbrt-undiv`
57×	`cbrt-unprod`
31×	`associate-r`
13×	`distribute-lft-out`
11×	`pow1`
10×	`rec-exp` `1-exp`
9×	`div-inv`
8×	`associate-*l/`
6×	`frac-times` `associate-/r*` `difference-of-squares`
4×	`expm1-log1p-u` `pow-prod-down` `associate-r/` `associate-/r/` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`sqrt-prod` `distribute-lft-out--` `unswap-sqr`
2×	`clear-num` `frac-2neg` `flip3-+` `*-commutative` `flip-+` `associate-/l/`
1×	`flip3--` `un-div-inv` `flip--`

Counts

4 → 263

Calls

4 calls:

76.0ms	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))))
328.0ms	(* (* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))) (/ 1 (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
51.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
4.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

series2.2s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))))
811.0ms	(* (* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))) (/ 1 (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
136.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
165.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

simplify1.7s

Counts

275 → 275

Iterations

Iter	Nodes
done	5000
1	1428
0	416

prune1.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 33.7b

regimes361.0ms

Accuracy

46.2% (1.5b remaining)

Error of 35.9b against oracle of 34.4b and baseline of 37.2b

bsearch102.0ms

Steps

Iters	Range		Point
7	1.5185210340582453e+216	6.531618038873483e+217	1.547494373636242e+216

simplify10.0ms

Iterations

Iter	Nodes
done	35
1	35
0	27

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
850.0ms	8000×	pre	80	true