Details

Time bar (total: 24.2s)

sample30.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
4.0ms256×pre80true

simplify1.2s

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize14.0ms

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))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
804×times-frac
586×*-un-lft-identity
340×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 associate-/l/
3×frac-2neg clear-num
1×+-commutative associate-+l+
Counts
4 → 465
Calls
4 calls:
193.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
506.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
773.0ms
(/ (/ (/ (+ (+ (+ 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))
417.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series543.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
181.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
211.0ms
(/ (/ (/ (+ (+ (+ 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))
136.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.1s

Counts
477 → 477

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.4b
(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite969.0ms

Algorithm
rewrite-expression-head
Rules
354×times-frac
259×*-un-lft-identity
240×sqrt-prod
195×add-sqr-sqrt
193×add-cube-cbrt
54×associate-/r*
33×distribute-lft-out
16×sqrt-div
11×add-exp-log associate-/r/ add-cbrt-cube
10×associate-/l*
9×flip3-+ flip-+
6×pow1 div-inv
4×cbrt-undiv div-exp associate-/l/ add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×sqrt-undiv
Counts
4 → 316
Calls
4 calls:
288.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
307.0ms
(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
143.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
191.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series910.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
596.0ms
(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
83.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
92.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify2.2s

Counts
328 → 328

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.4b
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite960.0ms

Algorithm
rewrite-expression-head
Rules
339×times-frac
246×*-un-lft-identity
222×sqrt-prod
188×add-sqr-sqrt
186×add-cube-cbrt
32×associate-/l*
30×distribute-lft-out
13×add-exp-log
12×associate-/r*
11×add-cbrt-cube
10×sqrt-div
9×div-inv
6×pow1 div-exp
5×flip3-+ flip-+
4×cbrt-undiv associate-/r/ add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×sqrt-undiv 1-exp
Counts
4 → 303
Calls
4 calls:
339.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
306.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
156.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
127.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series416.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
141.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
56.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
66.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.2s

Counts
315 → 315

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
0.7b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
1740×sqrt-prod
1314×times-frac
864×*-un-lft-identity
662×add-sqr-sqrt
660×add-cube-cbrt
102×distribute-lft-out
76×associate-/l*
54×sqrt-div
24×associate-/r/
18×associate-/r*
15×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×sqrt-undiv associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 845
Calls
4 calls:
465.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
356.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
177.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
163.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series546.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
196.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
94.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
93.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.7s

Counts
857 → 857

prune2.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.0b

regimes88.0ms

Accuracy

-33.9% (3.7b remaining)

Error of 4.9b against oracle of 1.2b and baseline of 4.0b

bsearch0.0ms

simplify903.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s8000×body80valid
229.0ms8000×pre80true