Details

sample23.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify81.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	33	17
1	122	15
2	598	13
3	4475	13
4	5001	13
done	5001	13

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.9b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
587×	`*-un-lft-identity`
341×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sum-log`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`fma-def` `frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 476

Calls

4 calls:

119.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
340.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
481.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
284.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
139.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
154.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
82.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify123.0ms

Counts

488 → 488

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1513	12983
1	5002	12137
done	5002	12137

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))))
0.1b	(/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.6b	(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

rewrite606.0ms

Algorithm

rewrite-expression-head

Rules

4254×	`times-frac`
2985×	`*-un-lft-identity`
1628×	`add-sqr-sqrt` `add-cube-cbrt`
772×	`distribute-lft-out`
284×	`associate-/l*`
158×	`associate-/r/`
89×	`div-inv`
69×	`flip3-+` `flip-+`
64×	`add-exp-log`
44×	`div-exp`
34×	`add-cbrt-cube`
33×	`associate-/r*`
20×	`cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`pow1`
4×	`expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 1530

Calls

4 calls:

95.0ms	(/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))) (+ (+ alpha beta) (* 2.0 1.0)))
34.0ms	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))))
278.0ms	(/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
28.0ms	(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

series541.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))) (+ (+ alpha beta) (* 2.0 1.0)))
90.0ms	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))))
183.0ms	(/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
105.0ms	(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

simplify407.0ms

Counts

1542 → 1542

Iterations

Useful iterations: 1 (61.0ms)

Iter	Nodes	Cost
0	3890	43268
1	5001	40901
done	5001	40901

prune3.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ beta (+ alpha (fma alpha beta 1.0)))))
3.6b	(sqrt (+ beta (+ alpha (fma alpha beta 1.0))))
3.6b	(sqrt (+ beta (+ alpha (fma alpha beta 1.0))))
10.4b	(* (* (* (cbrt 1) (cbrt 1)) (sqrt (+ beta (+ alpha (fma alpha beta 1.0))))) (/ (/ (cbrt 1) (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ beta (+ alpha (fma alpha beta 1.0)))))) (+ (+ alpha beta) (* 2.0 1.0))))

rewrite533.0ms

Algorithm

rewrite-expression-head

Rules

1551×	`times-frac`
962×	`*-un-lft-identity`
668×	`add-sqr-sqrt`
662×	`add-cube-cbrt`
561×	`associate-r`
300×	`sqrt-prod`
270×	`cbrt-prod`
180×	`distribute-lft-out`
60×	`add-exp-log`
46×	`sqrt-div` `add-cbrt-cube`
43×	`associate-/r/`
24×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
23×	`div-inv`
19×	`cbrt-undiv` `div-exp`
15×	`pow1`
8×	`associate-/r*`
6×	`pow-prod-down`
5×	`associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/` `hypot-def`
1×	`frac-2neg` `associate-l` `clear-num` `*-commutative`

Counts

4 → 695

Calls

4 calls:

29.0ms	(/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ beta (+ alpha (fma alpha beta 1.0)))))
29.0ms	(sqrt (+ beta (+ alpha (fma alpha beta 1.0))))
26.0ms	(sqrt (+ beta (+ alpha (fma alpha beta 1.0))))
376.0ms	(* (* (* (cbrt 1) (cbrt 1)) (sqrt (+ beta (+ alpha (fma alpha beta 1.0))))) (/ (/ (cbrt 1) (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ beta (+ alpha (fma alpha beta 1.0)))))) (+ (+ alpha beta) (* 2.0 1.0))))

series553.0ms

Counts

4 → 12

Calls

4 calls:

271.0ms	(/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ beta (+ alpha (fma alpha beta 1.0)))))
52.0ms	(sqrt (+ beta (+ alpha (fma alpha beta 1.0))))
62.0ms	(sqrt (+ beta (+ alpha (fma alpha beta 1.0))))
168.0ms	(* (* (* (cbrt 1) (cbrt 1)) (sqrt (+ beta (+ alpha (fma alpha beta 1.0))))) (/ (/ (cbrt 1) (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ beta (+ alpha (fma alpha beta 1.0)))))) (+ (+ alpha beta) (* 2.0 1.0))))

simplify206.0ms

Counts

707 → 707

Iterations

Useful iterations: 1 (77.0ms)

Iter	Nodes	Cost
0	4186	16403
1	5002	15393
done	5002	15393

prune2.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

1.6b	(/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (* (cbrt (+ beta (+ alpha (fma alpha beta 1.0)))) (cbrt (+ beta (+ alpha (fma alpha beta 1.0))))))
3.8b	(cbrt (+ beta (+ alpha (fma alpha beta 1.0))))
3.8b	(cbrt (+ beta (+ alpha (fma alpha beta 1.0))))
3.8b	(cbrt (+ beta (+ alpha (fma alpha beta 1.0))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`add-exp-log` `flip3-+` `flip-+` `distribute-lft-out`
8×	`associate-/r/`
7×	`add-cbrt-cube`
6×	`times-frac` `sqrt-prod` `associate-/l*`
4×	`pow1` `expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/`
1×	`frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 88

Calls

4 calls:

39.0ms	(/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (* (cbrt (+ beta (+ alpha (fma alpha beta 1.0)))) (cbrt (+ beta (+ alpha (fma alpha beta 1.0))))))
13.0ms	(cbrt (+ beta (+ alpha (fma alpha beta 1.0))))
12.0ms	(cbrt (+ beta (+ alpha (fma alpha beta 1.0))))
12.0ms	(cbrt (+ beta (+ alpha (fma alpha beta 1.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

1.0s	(/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (* (cbrt (+ beta (+ alpha (fma alpha beta 1.0)))) (cbrt (+ beta (+ alpha (fma alpha beta 1.0))))))
73.0ms	(cbrt (+ beta (+ alpha (fma alpha beta 1.0))))
66.0ms	(cbrt (+ beta (+ alpha (fma alpha beta 1.0))))
73.0ms	(cbrt (+ beta (+ alpha (fma alpha beta 1.0))))

simplify49.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	498	1287
1	1450	1191
2	5001	1156
done	5001	1156

prune590.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes88.0ms

Accuracy

74.4% (1.0b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 4.0b

bsearch76.0ms

Steps

Iters	Range		Point
10	5.8905493550764755e+156	4.41290631616548e+167	1.6091078706466608e+158

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	32
1	39	32
done	39	32

end0.0ms

sample564.0ms

Algorithm

intervals

Results

287.0ms	8000×	body	80	valid
91.0ms	8000×	pre	80	true