Details

sample41.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify3.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	119	31
3	586	31
4	4387	31
done	5000	31

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
0.0b	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
0.1b	(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
3.4b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite163.0ms

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-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`fma-def` `frac-2neg` `flip3-+` `clear-num` `flip-+`
2×	`associate-/r/`
1×	`+-commutative` `associate-+l+` `sum-log` `fma-udef`

Counts

4 → 422

Calls

4 calls:

6.0ms	(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
31.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
62.0ms	(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
31.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series613.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
200.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
245.0ms	(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
135.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify2.4s

Counts

434 → 434

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	516	20618
1	1175	20002
2	3277	19166
done	5000	18557

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 2.0) (+ (+ alpha beta) 1.0))
0.0b	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
0.1b	(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (* 1.0 2.0) (+ (+ alpha beta) 1.0)))
3.4b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite516.0ms

Algorithm

rewrite-expression-head

Rules

600×	`times-frac`
383×	`*-un-lft-identity`
279×	`add-sqr-sqrt` `add-cube-cbrt`
72×	`associate-/l*`
52×	`distribute-lft-out`
23×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
9×	`associate-/r*`
6×	`sum-log`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
2×	`associate-/r/`
1×	`+-commutative` `associate-+r+` `fma-def`

Counts

4 → 368

Calls

4 calls:

131.0ms	(+ (* 1.0 2.0) (+ (+ alpha beta) 1.0))
46.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
255.0ms	(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (* 1.0 2.0) (+ (+ alpha beta) 1.0)))
36.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series553.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (* 1.0 2.0) (+ (+ alpha beta) 1.0))
195.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
228.0ms	(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (* 1.0 2.0) (+ (+ alpha beta) 1.0)))
115.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify2.1s

Counts

380 → 380

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	529	18010
1	1230	17218
2	3843	16397
done	5000	15894

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ (+ alpha beta) 1.0))))
0.1b	(/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ (+ alpha beta) 1.0)))
3.4b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
3.4b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite493.0ms

Algorithm

rewrite-expression-head

Rules

1069×	`times-frac`
630×	`*-un-lft-identity`
553×	`add-sqr-sqrt`
470×	`add-cube-cbrt`
443×	`sqrt-prod`
169×	`associate-r`
80×	`distribute-lft-out`
63×	`associate-/l*`
55×	`associate-l`
36×	`div-inv`
20×	`unswap-sqr`
15×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*`
6×	`pow1`
5×	`associate-/l/`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `sqrt-div` `clear-num`
2×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 570

Calls

4 calls:

307.0ms	(* (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ (+ alpha beta) 1.0))))
47.0ms	(/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ (+ alpha beta) 1.0)))
34.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
19.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series676.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(* (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ (+ alpha beta) 1.0))))
175.0ms	(/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ (+ alpha beta) 1.0)))
119.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
131.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify3.2s

Counts

582 → 582

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	773	32756
1	1460	31246
2	3951	29412
done	5000	28524

prune3.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.3b

localize57.0ms

Local error

Found 4 expressions with local error:

3.4b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
3.4b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
3.4b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
3.4b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
48×	`times-frac`
40×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`distribute-lft-out` `associate-/l*`
12×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
8×	`associate-/l/`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

4 → 140

Calls

4 calls:

33.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
38.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
39.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
39.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series508.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
116.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
137.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
139.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.4s

Counts

152 → 152

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	79	3528
1	174	3440
2	503	3172
3	2037	3172
done	5001	3160

prune1.2s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.3b

regimes73.0ms

Accuracy

51.5% (1.2b remaining)

Error of 2.5b against oracle of 1.3b and baseline of 3.8b

bsearch90.0ms

Steps

Iters	Range		Point
7	3.1361112362224422e+175	3.7249396222924635e+177	5.056793302986321e+175

simplify7.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	26	64
1	34	64
done	34	64

end0.0ms

sample1.3s

Algorithm

intervals

Results

772.0ms	8000×	body	80	valid
248.0ms	8000×	pre	80	true