Details

sample53.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
3	1746
2	295
1	60
0	17

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.5b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))
0.1b	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
39.2b	(/ (/ (* (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))
46.7b	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-cbrt-cube` `add-exp-log`
28×	`add-sqr-sqrt`
26×	`times-frac`
22×	`prod-exp` `cbrt-unprod`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`cbrt-undiv` `div-exp`
16×	`pow1`
7×	`div-inv`
6×	`associate-l` `associate-/l*` `difference-of-squares`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `associate-l/` `associate-r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `associate-/r/` `*-commutative` `flip-+` `fma-udef`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `flip3--` `pow-sqr` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 142

Calls

4 calls:

9.0ms	(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))
67.0ms	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
71.0ms	(/ (/ (* (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))
102.0ms	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))

series1.1s

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))
209.0ms	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
425.0ms	(/ (/ (* (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))
359.0ms	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))

simplify2.5s

Counts

154 → 154

Iterations

Iter	Nodes
done	5000
2	3647
1	736
0	253

prune972.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 36.6b

localize62.0ms

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))))
37.0b	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
38.2b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

rewrite234.0ms

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:

27.0ms	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
136.0ms	(* (/ (/ (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))))
55.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
5.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

series1.5s

Counts

4 → 12

Calls

4 calls:

393.0ms	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
842.0ms	(* (/ (/ (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))))
106.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
168.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

simplify2.3s

Counts

308 → 308

Iterations

Iter	Nodes
done	5001
1	1361
0	426

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 36.5b

localize59.0ms

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	(* (/ (+ (+ alpha beta) i) 1) (/ i (fma 2 i (+ alpha beta))))
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) 1) (/ i (fma 2 i (+ alpha beta)))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
38.2b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
194×	`*-un-lft-identity`
154×	`add-exp-log`
151×	`add-sqr-sqrt`
121×	`add-cube-cbrt`
116×	`add-cbrt-cube`
77×	`div-exp` `associate-l`
53×	`cbrt-undiv`
48×	`prod-exp`
36×	`distribute-lft-out`
34×	`cbrt-unprod`
25×	`associate-r`
16×	`associate-/l*`
15×	`div-inv`
9×	`unswap-sqr`
8×	`pow1` `1-exp`
7×	`associate-/r*`
6×	`associate-/r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `clear-num` `frac-2neg` `flip3-+` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip-+` `difference-of-squares`
1×	`flip3--` `sqrt-prod` `flip--` `distribute-lft-out--` `associate-/l/`

Counts

4 → 312

Calls

4 calls:

15.0ms	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
82.0ms	(* (/ (+ (+ alpha beta) i) 1) (/ i (fma 2 i (+ alpha beta))))
95.0ms	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (* (/ (+ (+ alpha beta) i) 1) (/ i (fma 2 i (+ alpha beta)))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
8.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

series1.4s

Counts

4 → 12

Calls

4 calls:

374.0ms	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
108.0ms	(* (/ (+ (+ alpha beta) i) 1) (/ i (fma 2 i (+ alpha beta))))
776.0ms	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (* (/ (+ (+ alpha beta) i) 1) (/ i (fma 2 i (+ alpha beta)))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
126.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

simplify2.8s

Counts

324 → 324

Iterations

Iter	Nodes
done	5000
2	4814
1	1378
0	457

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.5b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma 1/4 (+ beta alpha) (* 1/2 i)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
0.0b	(/ i (fma 2 i (+ alpha beta)))
0.0b	(/ (* (/ (+ (+ alpha beta) i) 1) (/ i (fma 2 i (+ alpha beta)))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
0.1b	(* (/ (+ (+ alpha beta) i) 1) (/ i (fma 2 i (+ alpha beta))))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 172

Calls

4 calls:

18.0ms	(/ (fma 1/4 (+ beta alpha) (* 1/2 i)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
8.0ms	(/ i (fma 2 i (+ alpha beta)))
72.0ms	(/ (* (/ (+ (+ alpha beta) i) 1) (/ i (fma 2 i (+ alpha beta)))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
77.0ms	(* (/ (+ (+ alpha beta) i) 1) (/ i (fma 2 i (+ alpha beta))))

series825.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (fma 1/4 (+ beta alpha) (* 1/2 i)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
113.0ms	(/ i (fma 2 i (+ alpha beta)))
421.0ms	(/ (* (/ (+ (+ alpha beta) i) 1) (/ i (fma 2 i (+ alpha beta)))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
103.0ms	(* (/ (+ (+ alpha beta) i) 1) (/ i (fma 2 i (+ alpha beta))))

simplify1.6s

Counts

184 → 184

Iterations

Iter	Nodes
done	5000
2	2573
1	702
0	282

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.4b

regimes294.0ms

Accuracy

43.9% (9.3b remaining)

Error of 11.2b against oracle of 1.9b and baseline of 18.5b

bsearch116.0ms

Steps

Iters	Range		Point
7	4.180155208905662e+119	1.7530375893929083e+121	2.495505368754722e+120

simplify7.0ms

Iterations

Iter	Nodes
done	42
1	42
0	33

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.1s	8000×	body	80	valid
387.0ms	8000×	pre	80	true