Details

sample76.0ms

Algorithm

intervals

Results

38.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
4	2000
3	1615
2	280
1	60
0	17

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.0b

localize32.0ms

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))
37.2b	(/ (/ (* (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))))
46.6b	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))

rewrite247.0ms

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:

10.0ms	(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))
64.0ms	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
76.0ms	(/ (/ (* (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))))
92.0ms	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))
150.0ms	(* (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))) 1.0)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
858.0ms	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))

simplify1.0s

Counts

148 → 148

Iterations

Iter	Nodes
done	2003
2	2003
1	727
0	253

prune681.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 33.7b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (* (+ (+ alpha beta) i) i) (- (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))))
33.8b	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
34.5b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

231×	`times-frac`
155×	`add-sqr-sqrt`
142×	`*-un-lft-identity`
98×	`add-cube-cbrt`
74×	`add-cbrt-cube` `add-exp-log`
58×	`associate-l`
40×	`associate-r`
35×	`cbrt-undiv` `div-exp`
24×	`associate-/r/`
18×	`difference-of-squares`
17×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
15×	`div-inv`
13×	`associate-/r*` `distribute-lft-out`
9×	`sqrt-prod` `distribute-lft-out--`
8×	`flip3--` `flip--`
6×	`pow1` `unswap-sqr`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*l/` `associate-/l/`
1×	`frac-times` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 284

Calls

4 calls:

44.0ms	(/ (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
107.0ms	(* (/ (/ (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))))
47.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
13.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

series1.7s

Counts

4 → 12

Calls

4 calls:

312.0ms	(/ (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
666.0ms	(* (/ (/ (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)))
429.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

simplify1.5s

Counts

296 → 296

Iterations

Iter	Nodes
done	2003
2	2003
1	1437
0	445

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 33.7b

localize74.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (fma 2 i (+ alpha beta)) (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))))
0.1b	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))) (/ 1 (/ (fma 2 i (+ alpha beta)) (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))))
33.8b	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
34.5b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

765×	`times-frac`
424×	`add-sqr-sqrt`
353×	`*-un-lft-identity`
275×	`add-cube-cbrt`
228×	`add-exp-log`
134×	`div-exp`
128×	`associate-r`
100×	`add-cbrt-cube`
61×	`associate-/r/`
58×	`associate-l`
54×	`cbrt-undiv`
52×	`prod-exp`
51×	`associate-/r*`
46×	`difference-of-squares`
36×	`div-inv`
23×	`sqrt-prod` `distribute-lft-out--`
22×	`flip3--` `flip--`
20×	`cbrt-unprod`
16×	`rec-exp` `1-exp`
15×	`unswap-sqr`
13×	`distribute-lft-out`
7×	`pow1` `associate-/l*`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*l/`
2×	`associate-/l/`
1×	`frac-times` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 540

Calls

4 calls:

39.0ms	(/ 1 (/ (fma 2 i (+ alpha beta)) (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))))
132.0ms	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))) (/ 1 (/ (fma 2 i (+ alpha beta)) (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))))
65.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
18.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

series1.8s

Counts

4 → 12

Calls

4 calls:

300.0ms	(/ 1 (/ (fma 2 i (+ alpha beta)) (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))))
838.0ms	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))) (/ 1 (/ (fma 2 i (+ alpha beta)) (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))))
224.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
428.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

simplify1.4s

Counts

552 → 552

Iterations

Iter	Nodes
done	2000
1	2000
0	778

prune3.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 33.7b

localize74.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (/ (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))) (/ (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)) (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))))) (fma 2 i (+ alpha beta))) (/ 1 (/ (fma 2 i (+ alpha beta)) (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))))
33.8b	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
34.4b	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
34.4b	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

1879×	`times-frac`
976×	`*-un-lft-identity`
965×	`add-sqr-sqrt`
722×	`add-cube-cbrt`
523×	`associate-l`
510×	`sqrt-prod`
279×	`add-exp-log`
172×	`div-exp`
128×	`associate-r`
119×	`add-cbrt-cube`
108×	`distribute-lft-out`
68×	`cbrt-undiv`
65×	`prod-exp`
40×	`unswap-sqr`
36×	`div-inv`
27×	`associate-/r/`
25×	`cbrt-unprod`
22×	`difference-of-squares`
16×	`rec-exp` `1-exp`
11×	`distribute-lft-out--`
10×	`flip3--` `flip--`
8×	`pow1`
6×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-*l/`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `flip3-+` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `flip-+` `associate-/l*`

Counts

4 → 845

Calls

4 calls:

216.0ms	(* (/ (/ (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))) (/ (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)) (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))))) (fma 2 i (+ alpha beta))) (/ 1 (/ (fma 2 i (+ alpha beta)) (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))))
53.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
1.0ms	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
1.0ms	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))

series1.1s

Counts

4 → 12

Calls

4 calls:

737.0ms	(* (/ (/ (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))) (/ (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)) (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))))) (fma 2 i (+ alpha beta))) (/ 1 (/ (fma 2 i (+ alpha beta)) (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))))
236.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
66.0ms	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
72.0ms	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))

simplify1.6s

Counts

857 → 857

Iterations

Iter	Nodes
done	2000
1	2000
0	1030

prune5.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.7b

regimes343.0ms

Accuracy

43.7% (1.6b remaining)

Error of 35.6b against oracle of 34.0b and baseline of 36.8b

bsearch79.0ms

Steps

Iters	Range		Point
7	4.1289973515507565e+197	1.0803440393261062e+199	4.18445548900063e+197

simplify7.0ms

Iterations

Iter	Nodes
done	33
1	33
0	27

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
821.0ms	8000×	pre	80	true