Details

Time bar (total: 22.0s)

sample31.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
4.0ms256×pre80true

simplify774.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01435
13335
211135
355735
done500135

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 3 expressions with local error:

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))
5.0b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
804×times-frac
583×*-un-lft-identity
339×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
28×flip3-+ flip-+
27×div-inv
19×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
4×associate-/l/
3×pow1 frac-2neg clear-num add-log-exp
Counts
3 → 450
Calls
3 calls:
483.0ms
(/ (/ (+ (+ (+ 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))
431.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series423.0ms

Counts
3 → 9
Calls
3 calls:
150.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
187.0ms
(/ (/ (/ (+ (+ (+ 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))
86.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify793.0ms

Counts
459 → 459
Iterations

Useful iterations: done (759.0ms)

IterNodesCost
058025719
1155824955
done500024070

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.9b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (* 1 (/ (/ (+ (+ (+ 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))
5.0b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
118×times-frac
101×*-un-lft-identity
65×add-sqr-sqrt add-cube-cbrt
33×add-exp-log
24×add-cbrt-cube
23×associate-/l*
18×distribute-lft-out
17×div-exp
14×associate-/r/
11×cbrt-undiv
10×associate-/r*
8×flip3-+ flip-+
7×div-inv
6×prod-exp
4×associate-/l/
3×pow1 frac-2neg 1-exp clear-num cbrt-unprod add-log-exp
1×associate-*r/
Counts
3 → 160
Calls
3 calls:
542.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
305.0ms
(/ (* 1 (/ (/ (+ (+ (+ 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))
300.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series489.0ms

Counts
3 → 9
Calls
3 calls:
187.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
185.0ms
(/ (* 1 (/ (/ (+ (+ (+ 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))
118.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.5s

Counts
169 → 169
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02776726
17836440
246095807
done50025653

prune586.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
0.4b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
5.0b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.0b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite895.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
76×sqrt-prod
63×times-frac
54×add-sqr-sqrt
52×add-cube-cbrt
14×associate-/l*
13×distribute-lft-out
10×sqrt-div
9×associate-/r*
8×add-exp-log add-cbrt-cube
6×pow1 flip3-+ flip-+
4×associate-/r/ associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
1×sqrt-undiv
Counts
4 → 151
Calls
4 calls:
248.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
282.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
176.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
183.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series497.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
147.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
64.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
57.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.2s

Counts
163 → 163
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02214616
14884253
219564105
done50014101

prune770.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.9b

localize34.0ms

Local error

Found 4 expressions with local error:

5.0b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
5.0b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
17.0b
(sqrt (/ (/ (/ (+ (+ (+ 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)))
17.0b
(sqrt (/ (/ (/ (+ (+ (+ 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)))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
1236×times-frac
888×*-un-lft-identity
508×add-sqr-sqrt
492×sqrt-prod
488×add-cube-cbrt
200×distribute-lft-out
72×associate-/r/
38×flip3-+ flip-+
36×div-inv
8×add-exp-log rem-sqrt-square add-cbrt-cube associate-/l*
6×pow1 associate-/r*
4×associate-/l/ add-log-exp
2×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
4 → 590
Calls
4 calls:
410.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
403.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
492.0ms
(sqrt (/ (/ (/ (+ (+ (+ 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)))
433.0ms
(sqrt (/ (/ (/ (+ (+ (+ 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)))

series1.2s

Counts
4 → 12
Calls
4 calls:
121.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
130.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
470.0ms
(sqrt (/ (/ (/ (+ (+ (+ 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)))
462.0ms
(sqrt (/ (/ (/ (+ (+ (+ 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)))

simplify893.0ms

Counts
602 → 602
Iterations

Useful iterations: done (846.0ms)

IterNodesCost
081739574
1168138248
done500136810

prune2.9s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.9b

regimes192.0ms

Accuracy

70% (0.8b remaining)

Error of 1.9b against oracle of 1.2b and baseline of 3.7b

bsearch4.0ms

simplify15.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
029106
141102
243102
done43102

end0.0ms

sample1.7s

Algorithm
intervals
Results
769.0ms8000×body80valid
633.0ms8000×pre80true