Details

sample64.0ms

Algorithm

intervals

Results

31.0ms	256×	body	80	valid
14.0ms	256×	pre	80	true

simplify789.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
3	1615
2	280
1	60
0	17

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.0b

localize54.0ms

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))
38.8b	(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
48.4b	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 136

Calls

4 calls:

6.0ms	(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))
51.0ms	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
99.0ms	(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
108.0ms	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))
181.0ms	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
349.0ms	(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
814.0ms	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))

simplify665.0ms

Counts

148 → 148

Iterations

Iter	Nodes
done	2001
1	727
0	253

prune815.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 34.8b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
0.1b	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))) (/ (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))))
35.0b	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
35.4b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac`
188×	`*-un-lft-identity`
169×	`add-sqr-sqrt`
128×	`add-cube-cbrt`
70×	`add-cbrt-cube` `add-exp-log`
58×	`associate-l`
40×	`associate-r`
33×	`cbrt-undiv` `div-exp`
25×	`distribute-lft-out`
24×	`associate-/r/`
22×	`associate-/l*`
16×	`prod-exp` `cbrt-unprod`
15×	`div-inv`
13×	`associate-/r*`
10×	`difference-of-squares`
9×	`flip3-+` `flip-+`
6×	`pow1` `unswap-sqr`
5×	`sqrt-prod` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*l/` `associate-/l/`
1×	`frac-times` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 306

Calls

4 calls:

22.0ms	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
104.0ms	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))) (/ (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))))
48.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
20.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

series1.7s

Counts

4 → 12

Calls

4 calls:

355.0ms	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
685.0ms	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))) (/ (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))))
265.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
402.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

simplify1.2s

Counts

318 → 318

Iterations

Iter	Nodes
done	2001
1	1513
0	462

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 34.7b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
0.1b	(/ (+ (+ alpha beta) i) (/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) i))
0.1b	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))) (/ (/ (+ (+ alpha beta) i) (/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) i)) (fma 2 i (+ alpha beta))))
35.4b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

rewrite304.0ms

Algorithm

rewrite-expression-head

Rules

1397×	`times-frac`
1146×	`*-un-lft-identity`
831×	`add-sqr-sqrt`
525×	`add-cube-cbrt`
349×	`associate-r`
292×	`distribute-lft-out`
126×	`difference-of-squares`
70×	`add-cbrt-cube` `add-exp-log`
63×	`sqrt-prod` `distribute-lft-out--`
58×	`associate-l`
37×	`cbrt-undiv` `div-exp`
36×	`div-inv`
29×	`associate-/r*`
26×	`associate-/l*`
20×	`associate-/r/`
12×	`prod-exp` `cbrt-unprod` `unswap-sqr`
9×	`flip3-+` `flip-+`
6×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/l/`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 744

Calls

4 calls:

30.0ms	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
79.0ms	(/ (+ (+ alpha beta) i) (/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) i))
147.0ms	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))) (/ (/ (+ (+ alpha beta) i) (/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) i)) (fma 2 i (+ alpha beta))))
9.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

series2.1s

Counts

4 → 12

Calls

4 calls:

453.0ms	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
252.0ms	(/ (+ (+ alpha beta) i) (/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) i))
661.0ms	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))) (/ (/ (+ (+ alpha beta) i) (/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) i)) (fma 2 i (+ alpha beta))))
727.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

simplify1.2s

Counts

756 → 756

Iterations

Iter	Nodes
done	2001
0	843

prune3.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 28.6b

localize75.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (+ alpha beta) i) (/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) i))
0.1b	(* (* (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ 1 (fma 2 i (+ alpha beta)))) (/ (/ (+ (+ alpha beta) i) (/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) i)) (fma 2 i (+ alpha beta))))
0.2b	(* (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ 1 (fma 2 i (+ alpha beta))))
35.4b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

1203×	`times-frac`
1033×	`*-un-lft-identity`
715×	`add-sqr-sqrt`
446×	`add-cube-cbrt`
362×	`associate-r`
274×	`distribute-lft-out`
215×	`add-exp-log`
126×	`difference-of-squares`
125×	`add-cbrt-cube`
98×	`div-exp`
76×	`prod-exp`
63×	`sqrt-prod` `distribute-lft-out--`
54×	`cbrt-undiv`
40×	`cbrt-unprod`
29×	`div-inv`
26×	`associate-/r*`
19×	`associate-l`
11×	`pow1`
10×	`rec-exp` `1-exp`
8×	`associate-/r/` `associate-/l*`
7×	`frac-times` `associate-*l/`
6×	`unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `un-div-inv` `flip-+`
2×	`clear-num` `frac-2neg` `*-commutative` `associate-/l/`

Counts

4 → 686

Calls

4 calls:

60.0ms	(/ (+ (+ alpha beta) i) (/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) i))
139.0ms	(* (* (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ 1 (fma 2 i (+ alpha beta)))) (/ (/ (+ (+ alpha beta) i) (/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) i)) (fma 2 i (+ alpha beta))))
38.0ms	(* (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ 1 (fma 2 i (+ alpha beta))))
14.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

series1.7s

Counts

4 → 12

Calls

4 calls:

211.0ms	(/ (+ (+ alpha beta) i) (/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) i))
782.0ms	(* (* (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ 1 (fma 2 i (+ alpha beta)))) (/ (/ (+ (+ alpha beta) i) (/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) i)) (fma 2 i (+ alpha beta))))
377.0ms	(* (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ 1 (fma 2 i (+ alpha beta))))
349.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

simplify1.3s

Counts

698 → 698

Iterations

Iter	Nodes
done	2001
0	795

prune3.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 28.6b

regimes321.0ms

Accuracy

60.9% (3.2b remaining)

Error of 31.9b against oracle of 28.7b and baseline of 36.9b

bsearch88.0ms

Steps

Iters	Range		Point
6	1.7966209333831277e+128	7.687170426383009e+128	1.8246756895617496e+128

simplify7.0ms

Iterations

Iter	Nodes
done	45
1	45
0	33

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
441.0ms	8000×	pre	80	true