Details

sample62.0ms

Algorithm

intervals

Results

16.0ms	203×	body	80	valid
7.0ms	18×	body	1280	valid
7.0ms	256×	pre	80	true
4.0ms	16×	body	320	valid
4.0ms	13×	body	640	valid
1.0ms	6×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	106	27
3	478	26
4	2747	26
done	5000	26

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.0b

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

1.6b

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

rewrite57.0ms

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×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`distribute-lft-out--` `difference-of-squares` `associate-/l/`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `associate-/r/` `flip-+` `div-inv`
1×	`flip3--` `div-sub` `fma-udef` `flip--`

Counts

3 → 92

Calls

3 calls:

38.0ms

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

14.0ms

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

0.0ms

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

series589.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms

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

141.0ms

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

348.0ms

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

simplify1.0s

Counts

101 → 101

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	176	1908
1	406	1851
2	1713	1721
done	5000	1717

prune592.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
0.6b	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
0.6b	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
8.6b	(fma (/ (/ (+ alpha beta) (* (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

4.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
9.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
3.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
0.0ms	(fma (/ (/ (+ alpha beta) (* (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series1.7s

Counts

4 → 12

Calls

4 calls:

462.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
409.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
459.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
380.0ms	(fma (/ (/ (+ alpha beta) (* (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.9s

Counts

70 → 70

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	111	1746
1	256	1689
2	770	1322
3	3506	1195
done	5000	1144

prune568.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))))
0.4b	(/ 1 (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))
0.4b	(/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))
6.4b	(fma (* (/ 1 (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

136×	`*-un-lft-identity`
120×	`times-frac`
114×	`add-sqr-sqrt`
75×	`sqrt-prod`
68×	`add-cube-cbrt`
34×	`associate-r`
32×	`add-exp-log`
31×	`distribute-lft-out`
27×	`associate-l`
20×	`add-cbrt-cube`
15×	`unswap-sqr`
14×	`associate-/r*`
11×	`div-exp`
8×	`pow1` `sqrt-div` `prod-exp` `associate-/r/`
7×	`associate-/l*`
6×	`cbrt-undiv`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp` `pow-flip`
2×	`clear-num` `frac-2neg` `associate-/l/`
1×	`frac-times` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 222

Calls

4 calls:

133.0ms	(* (/ 1 (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))))
12.0ms	(/ 1 (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))
50.0ms	(/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))
1.0ms	(fma (* (/ 1 (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series750.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(* (/ 1 (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))))
192.0ms	(/ 1 (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))
187.0ms	(/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))
129.0ms	(fma (* (/ 1 (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (/ (+ alpha beta) (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify503.0ms

Counts

234 → 234

Iterations

Useful iterations: done (491.0ms)

Iter	Nodes	Cost
0	276	6218
1	779	5737
done	5001	5183

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))
0.6b	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
0.6b	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
6.9b	(fma (* (/ (/ 1 (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (fabs (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (+ alpha beta) (sqrt (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

19.0ms	(/ 1 (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))
6.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
13.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
0.0ms	(fma (* (/ (/ 1 (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (fabs (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (+ alpha beta) (sqrt (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series3.1s

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ 1 (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))
386.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
428.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
2.1s	(fma (* (/ (/ 1 (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (fabs (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (+ alpha beta) (sqrt (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify643.0ms

Counts

107 → 107

Iterations

Useful iterations: done (639.0ms)

Iter	Nodes	Cost
0	193	2422
1	404	2220
2	1312	2014
done	5001	1927

prune737.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.6b

regimes299.0ms

Accuracy

20.3% (5.4b remaining)

Error of 11.3b against oracle of 6.0b and baseline of 12.7b

bsearch117.0ms

Steps

Iters	Range		Point
8	1.538992510133342e+149	5.820374342875008e+152	1.2663211663858966e+151

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	72
1	41	72
done	41	72

end0.0ms

sample2.5s

Algorithm

intervals

Results

982.0ms	6318×	body	80	valid
396.0ms	8000×	pre	80	true
294.0ms	512×	body	1280	valid
266.0ms	598×	body	640	valid
93.0ms	363×	body	320	valid
86.0ms	209×	body	160	valid