Details

sample36.0ms

Algorithm

intervals

Results

11.0ms	207×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	17×	body	1280	valid
2.0ms	13×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	6×	body	160	valid

simplify548.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	105	27
3	438	26
4	1620	26
done	5000	26

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))

0.0b

(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))

2.2b

(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
31×	`add-sqr-sqrt` `times-frac`
23×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`associate-/l*`
7×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`associate-/l/` `distribute-lft-out--` `difference-of-squares`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+` `div-inv`
1×	`flip3--` `div-sub` `flip--` `fma-udef`

Counts

3 → 92

Calls

3 calls:

12.0ms

(/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))

12.0ms

(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))

0.0ms

(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series390.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms

(/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))

74.0ms

(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))

242.0ms

(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify443.0ms

Counts

101 → 101

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	176	1908
1	395	1852
2	1275	1716
done	5001	1716

prune290.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
0.2b	(/ (/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.4b	(/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
6.3b	(fma (/ (/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

510×	`*-un-lft-identity`
505×	`times-frac`
288×	`sqrt-prod`
238×	`add-sqr-sqrt`
230×	`add-cube-cbrt`
136×	`distribute-lft-out`
43×	`associate-/l*`
20×	`sqrt-div` `associate-/r/`
17×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
11×	`flip3-+` `flip-+` `div-inv`
5×	`cbrt-undiv` `div-exp` `associate-/l/`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`frac-2neg` `clear-num`
1×	`flip3--` `div-sub` `flip--` `fma-udef`

Counts

4 → 405

Calls

4 calls:

9.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
30.0ms	(/ (/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
13.0ms	(/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.0ms	(fma (/ (/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series541.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
75.0ms	(/ (/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
141.0ms	(/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
247.0ms	(fma (/ (/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.2s

Counts

417 → 417

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	419	15923
1	958	14078
2	3076	12965
done	5000	12963

prune745.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))
0.4b	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.5b	(/ (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
8.0b	(fma (* (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite373.0ms

Algorithm

rewrite-expression-head

Rules

1198×	`times-frac`
1049×	`sqrt-prod`
799×	`*-un-lft-identity`
763×	`add-sqr-sqrt`
503×	`add-cube-cbrt`
276×	`associate-r`
136×	`distribute-lft-out`
64×	`unswap-sqr`
56×	`sqrt-div`
52×	`add-exp-log`
50×	`associate-/r/`
46×	`associate-l`
32×	`add-cbrt-cube`
30×	`associate-/l*`
25×	`flip3-+` `div-exp` `flip-+` `div-inv`
17×	`associate-/r*`
16×	`pow1`
13×	`cbrt-undiv`
11×	`sqrt-pow1`
10×	`prod-exp`
9×	`pow-flip`
8×	`pow-div`
7×	`pow1/2`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`inv-pow`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `associate-/l/`

Counts

4 → 815

Calls

4 calls:

268.0ms	(* (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))
7.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
25.0ms	(/ (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
0.0ms	(fma (* (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))
124.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
663.0ms	(/ (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
248.0ms	(fma (* (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify809.0ms

Counts

827 → 827

Iterations

Useful iterations: done (763.0ms)

Iter	Nodes	Cost
0	699	36225
1	2126	32289
done	5001	29466

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))
6.3b	(fma (/ (/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)
6.3b	(fma (/ (/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)
6.3b	(fma (/ (/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
28×	`times-frac`
22×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`sqrt-prod`
13×	`distribute-lft-out`
7×	`associate-/r*`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`fma-udef`
2×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 87

Calls

4 calls:

15.0ms	(/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))
0.0ms	(fma (/ (/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)
0.0ms	(fma (/ (/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)
0.0ms	(fma (/ (/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series894.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))
251.0ms	(fma (/ (/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)
246.0ms	(fma (/ (/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)
251.0ms	(fma (/ (/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.5s

Counts

99 → 99

Iterations

Useful iterations: 3 (360.0ms)

Iter	Nodes	Cost
0	147	2891
1	309	2366
2	932	2122
3	3804	2110
done	5000	2110

prune375.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.0b

regimes128.0ms

Accuracy

17.4% (5.5b remaining)

Error of 10.9b against oracle of 5.5b and baseline of 12.1b

bsearch60.0ms

Steps

Iters	Range		Point
7	1.4116812876132222e+209	2.791389625835243e+210	1.5371929371909745e+209

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	60
1	36	60
done	36	60

end0.0ms

sample802.0ms

Algorithm

intervals

Results

245.0ms	6387×	body	80	valid
129.0ms	8000×	pre	80	true
106.0ms	532×	body	1280	valid
82.0ms	529×	body	640	valid
40.0ms	341×	body	320	valid
17.0ms	211×	body	160	valid