Details

sample30.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	14	404
1	33	404
2	119	354
3	589	354
done	5000	354

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (fma 2.0 1.0 (+ alpha beta)))
0.0b	(/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))
0.1b	(/ (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (+ 1.0 (fma 2.0 1.0 (+ alpha beta))))
3.6b	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

736×	`times-frac`
551×	`*-un-lft-identity`
321×	`add-sqr-sqrt` `add-cube-cbrt`
115×	`distribute-lft-out`
72×	`associate-/l*`
27×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `associate-/l/`
3×	`clear-num` `fma-def` `frac-2neg` `flip3-+` `flip-+`
2×	`associate-/r/`
1×	`+-commutative` `associate-+r+` `sum-log` `fma-udef`

Counts

4 → 422

Calls

4 calls:

5.0ms	(+ 1.0 (fma 2.0 1.0 (+ alpha beta)))
25.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))
42.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (+ 1.0 (fma 2.0 1.0 (+ alpha beta))))
37.0ms	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ 1.0 (fma 2.0 1.0 (+ alpha beta)))
204.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))
240.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (+ 1.0 (fma 2.0 1.0 (+ alpha beta))))
122.0ms	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))

simplify1.9s

Counts

434 → 434

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	517	284613
1	1327	271623
done	5000	266103

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (sqrt (fma 2.0 1.0 (+ alpha beta)))) (/ (fma 2.0 1.0 (+ alpha beta)) (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (sqrt (fma 2.0 1.0 (+ alpha beta))))))
0.5b	(/ 1 (sqrt (fma 2.0 1.0 (+ alpha beta))))
1.8b	(/ (fma 2.0 1.0 (+ alpha beta)) (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (sqrt (fma 2.0 1.0 (+ alpha beta)))))
2.9b	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (sqrt (fma 2.0 1.0 (+ alpha beta))))

rewrite466.0ms

Algorithm

rewrite-expression-head

Rules

7388×	`times-frac`
3887×	`*-un-lft-identity`
2997×	`add-sqr-sqrt` `add-cube-cbrt`
1713×	`sqrt-prod`
445×	`distribute-lft-out`
190×	`div-inv`
129×	`associate-/r*`
54×	`add-exp-log`
36×	`div-exp`
34×	`add-cbrt-cube`
32×	`associate-/l*`
25×	`associate-/r/`
20×	`cbrt-undiv`
6×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `clear-num` `frac-2neg` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `associate-/l/`
1×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `inv-pow`

Counts

4 → 2330

Calls

4 calls:

93.0ms	(/ (/ 1 (sqrt (fma 2.0 1.0 (+ alpha beta)))) (/ (fma 2.0 1.0 (+ alpha beta)) (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (sqrt (fma 2.0 1.0 (+ alpha beta))))))
6.0ms	(/ 1 (sqrt (fma 2.0 1.0 (+ alpha beta))))
14.0ms	(/ (fma 2.0 1.0 (+ alpha beta)) (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (sqrt (fma 2.0 1.0 (+ alpha beta)))))
27.0ms	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (sqrt (fma 2.0 1.0 (+ alpha beta))))

series761.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ (/ 1 (sqrt (fma 2.0 1.0 (+ alpha beta)))) (/ (fma 2.0 1.0 (+ alpha beta)) (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (sqrt (fma 2.0 1.0 (+ alpha beta))))))
107.0ms	(/ 1 (sqrt (fma 2.0 1.0 (+ alpha beta))))
283.0ms	(/ (fma 2.0 1.0 (+ alpha beta)) (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (sqrt (fma 2.0 1.0 (+ alpha beta)))))
165.0ms	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (sqrt (fma 2.0 1.0 (+ alpha beta))))

simplify5.6s

Counts

2342 → 2342

Iterations

Useful iterations: done (4.6s)

Iter	Nodes	Cost
0	2235	2332746
done	5001	2241574

prune12.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))) (/ (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))) (+ 1.0 (fma 2.0 1.0 (+ alpha beta)))))
0.1b	(/ (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))) (+ 1.0 (fma 2.0 1.0 (+ alpha beta))))
3.6b	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))
3.6b	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))

rewrite541.0ms

Algorithm

rewrite-expression-head

Rules

1347×	`times-frac`
972×	`*-un-lft-identity`
637×	`add-sqr-sqrt`
554×	`add-cube-cbrt`
547×	`sqrt-prod`
226×	`associate-r`
209×	`distribute-lft-out`
63×	`associate-/l*`
55×	`associate-l`
44×	`div-inv`
20×	`unswap-sqr`
15×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r*`
6×	`pow1`
5×	`associate-/l/`
4×	`expm1-log1p-u` `cbrt-undiv` `flip3-+` `div-exp` `associate-/r/` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `sqrt-div`
2×	`prod-exp` `cbrt-unprod`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 685

Calls

4 calls:

373.0ms	(* (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))) (/ (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))) (+ 1.0 (fma 2.0 1.0 (+ alpha beta)))))
41.0ms	(/ (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))) (+ 1.0 (fma 2.0 1.0 (+ alpha beta))))
26.0ms	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))
27.0ms	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))

series682.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(* (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))) (/ (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))) (+ 1.0 (fma 2.0 1.0 (+ alpha beta)))))
204.0ms	(/ (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))) (+ 1.0 (fma 2.0 1.0 (+ alpha beta))))
112.0ms	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))
102.0ms	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))

simplify3.2s

Counts

697 → 697

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	781	494735
1	1758	470580
done	5001	459610

prune4.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (sqrt (fma 2.0 1.0 (+ alpha beta))))
1.4b	(/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (sqrt (fma 2.0 1.0 (+ alpha beta)))) (fma 2.0 1.0 (+ alpha beta)))
2.9b	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (sqrt (fma 2.0 1.0 (+ alpha beta))))
3.6b	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
204×	`*-un-lft-identity`
134×	`add-sqr-sqrt` `add-cube-cbrt`
75×	`sqrt-prod`
39×	`associate-/l*`
35×	`distribute-lft-out`
18×	`associate-/r*`
17×	`add-exp-log`
15×	`add-cbrt-cube`
8×	`div-inv`
7×	`div-exp`
6×	`pow1` `cbrt-undiv`
5×	`associate-/l/`
4×	`expm1-log1p-u` `clear-num` `frac-2neg` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip`
2×	`flip3-+` `flip-+`
1×	`rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `inv-pow`

Counts

4 → 264

Calls

4 calls:

9.0ms	(/ 1 (sqrt (fma 2.0 1.0 (+ alpha beta))))
34.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (sqrt (fma 2.0 1.0 (+ alpha beta)))) (fma 2.0 1.0 (+ alpha beta)))
28.0ms	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (sqrt (fma 2.0 1.0 (+ alpha beta))))
24.0ms	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))

series688.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ 1 (sqrt (fma 2.0 1.0 (+ alpha beta))))
299.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (sqrt (fma 2.0 1.0 (+ alpha beta)))) (fma 2.0 1.0 (+ alpha beta)))
137.0ms	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (sqrt (fma 2.0 1.0 (+ alpha beta))))
145.0ms	(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))

simplify1.5s

Counts

276 → 276

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	367	142110
1	930	131864
done	5000	129854

prune1.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.3b

regimes252.0ms

Accuracy

48.5% (1.2b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 3.6b

bsearch167.0ms

Steps

Iters	Range		Point
9	6.517508680297973e+213	6.266295390107009e+222	3.389187053396532e+214

simplify12.0ms

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	40	1413
1	50	1413
done	50	1413

end0.0ms

sample1.0s

Algorithm

intervals

Results

681.0ms	8000×	body	80	valid
162.0ms	8000×	pre	80	true