Details

Time bar (total: 51.7s)

sample45.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
6.0ms256×pre80true

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01435
13335
211135
355035
4408735
done500035

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize24.0ms

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))
2.2b
(/ (+ (+ (+ 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:
129.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
495.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
726.0ms
(/ (/ (/ (+ (+ (+ 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))
465.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series551.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
207.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
210.0ms
(/ (/ (/ (+ (+ (+ 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))
111.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.4s

Counts
477 → 477
Iterations

Useful iterations: done (2.3s)

IterNodesCost
060325954
1144325182
2475424241
done500123501

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

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))
2.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite3.0s

Algorithm
rewrite-expression-head
Rules
5500×times-frac
3741×*-un-lft-identity
2185×add-sqr-sqrt add-cube-cbrt
1821×distribute-lft-neg-in distribute-rgt-neg-in
778×distribute-lft-out
450×associate-/l*
302×neg-mul-1
260×associate-/r/
132×flip3-+ flip-+
130×div-inv
17×associate-/r*
13×add-exp-log add-cbrt-cube distribute-neg-frac add-log-exp
6×sum-log
5×cbrt-undiv div-exp
4×pow1 associate-/l/
3×frac-2neg div-sub distribute-frac-neg clear-num
2×neg-sub0
1×+-commutative associate-+l+
Counts
4 → 2570
Calls
4 calls:
144.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
864.0ms
(/ (- (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0))))
1.1s
(/ (/ (- (/ (+ (+ (+ 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))
430.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series767.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
313.0ms
(/ (- (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0))))
306.0ms
(/ (/ (- (/ (+ (+ (+ 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))
133.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.3s

Counts
2582 → 2582
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02641161985
done5000158076

prune9.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 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) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
0.1b
(/ (/ 1 1) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
2.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite3.1s

Algorithm
rewrite-expression-head
Rules
14603×times-frac
8256×*-un-lft-identity
5324×add-sqr-sqrt add-cube-cbrt
1466×distribute-lft-out
516×associate-/r/
512×div-inv
311×associate-/r*
252×flip3-+ flip-+
114×add-exp-log
96×div-exp
52×add-cbrt-cube
39×associate-/l*
34×cbrt-undiv
20×1-exp
8×rec-exp
6×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
Counts
4 → 3941
Calls
4 calls:
562.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
641.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
558.0ms
(/ (/ 1 1) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
440.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series823.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
289.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
231.0ms
(/ (/ 1 1) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
138.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify4.2s

Counts
3953 → 3953
Iterations

Useful iterations: done (3.7s)

IterNodesCost
04155306477
done5000284875

prune9.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
0.1b
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))
0.1b
(/ (/ 1 1) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))))
15.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
356×times-frac
205×add-exp-log
194×*-un-lft-identity
156×add-sqr-sqrt
144×add-cube-cbrt
143×div-exp
92×add-cbrt-cube
52×associate-/r/
50×cbrt-undiv
36×prod-exp
31×div-inv
30×1-exp
25×distribute-lft-out
22×associate-*l*
21×associate-/l*
16×frac-times associate-*r/ associate-*l/ associate-/r* cbrt-unprod
15×associate-*r*
12×rec-exp
9×difference-of-squares
6×pow1
5×associate-/l/
4×add-log-exp unswap-sqr
3×frac-2neg flip3-+ clear-num flip-+
2×flip3-- flip--
1×pow-prod-down *-commutative
Counts
4 → 368
Calls
4 calls:
890.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
638.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))
396.0ms
(/ (/ 1 1) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))))
447.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

series1.3s

Counts
4 → 12
Calls
4 calls:
365.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
468.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))
322.0ms
(/ (/ 1 1) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))))
167.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

simplify3.4s

Counts
380 → 380
Iterations

Useful iterations: 2 (1.6s)

IterNodesCost
059025064
1158123321
2489520417
done500020417

prune876.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

regimes110.0ms

Accuracy

59.8% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.8b

bsearch105.0ms

Steps
ItersRangePoint
10
1.46236334807091e+179
8.784028271748913e+188
1.1358904398290614e+184

simplify17.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02042
13442
25042
35342
45742
done5742

end0.0ms

sample932.0ms

Algorithm
intervals
Results
483.0ms8000×body80valid
136.0ms8000×pre80true