Details

Time bar (total: 23.4s)

sample57.0ms

Algorithm
intervals
Results
26.0ms256×body80valid
7.0ms256×pre80true

simplify1.5s

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize47.0ms

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))
5.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.8s

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:
145.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
468.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
738.0ms
(/ (/ (/ (+ (+ (+ 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))
409.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series544.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
204.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
208.0ms
(/ (/ (/ (+ (+ (+ 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))
115.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.0s

Counts
477 → 477

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
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 3.0)))
5.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
954×times-frac
828×*-un-lft-identity
383×add-sqr-sqrt add-cube-cbrt
253×distribute-lft-out
82×associate-/l*
62×associate-/r/
33×flip3-+ flip-+
31×div-inv
20×add-exp-log add-cbrt-cube
11×associate-/r*
10×cbrt-undiv div-exp
9×add-log-exp
4×pow1 associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 524
Calls
4 calls:
32.0ms
(+ (+ alpha beta) (* beta alpha))
483.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
550.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
466.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series563.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(+ (+ alpha beta) (* beta alpha))
195.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
240.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
109.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.1s

Counts
536 → 536

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ alpha (+ beta 3.0)))
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))) (/ 1 (+ alpha (+ beta 3.0))))
5.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
249×times-frac
214×*-un-lft-identity
156×add-sqr-sqrt
126×add-cube-cbrt
60×associate-*l*
54×add-exp-log
46×distribute-lft-out
34×add-cbrt-cube
25×associate-/l*
24×div-exp associate-/r/
21×associate-*r*
14×cbrt-undiv
13×flip3-+ flip-+
12×prod-exp div-inv
11×associate-/r*
9×unswap-sqr
7×pow1
6×cbrt-unprod
4×rec-exp 1-exp add-log-exp
3×frac-2neg clear-num associate-/l/
1×frac-times pow-flip associate-*r/ pow-prod-down associate-*l/ un-div-inv *-commutative inv-pow
Counts
4 → 289
Calls
4 calls:
42.0ms
(/ 1 (+ alpha (+ beta 3.0)))
449.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
818.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ alpha (+ beta 3.0))))
411.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series594.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(/ 1 (+ alpha (+ beta 3.0)))
210.0ms
(/ (/ (+ (+ (+ 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))) (/ 1 (+ alpha (+ beta 3.0))))
115.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify780.0ms

Counts
301 → 301

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
5.7b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.7b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
10.7b
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
175×times-frac
126×*-un-lft-identity
122×add-sqr-sqrt
94×add-cube-cbrt
87×associate-*r*
70×sqrt-prod
16×distribute-lft-out
15×add-exp-log add-cbrt-cube
10×flip3-+ sqrt-div associate-/r/ flip-+
8×pow1 unswap-sqr
7×associate-*l* associate-/l*
5×div-inv
4×cbrt-undiv div-exp add-log-exp
3×prod-exp associate-/r* cbrt-unprod
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ associate-/l/
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 201
Calls
4 calls:
386.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
240.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
239.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
1.1s
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

series654.0ms

Counts
4 → 12
Calls
4 calls:
300.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
73.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
74.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
207.0ms
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

simplify1.8s

Counts
213 → 213

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.0b

regimes111.0ms

Accuracy

53% (1.3b remaining)

Error of 2.5b against oracle of 1.2b and baseline of 3.9b

bsearch122.0ms

Steps
ItersRangePoint
9
7.994693915907928e+128
2.997223888954887e+134
1.3404619349916037e+134

simplify541.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.1s8000×body80valid
279.0ms8000×pre80true