Details

Time bar (total: 16.1s)

sample27.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
3.0ms256×pre80true

simplify878.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01435
13335
211035
348035
4239835
done500135

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.1b

localize18.0ms

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))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite694.0ms

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:
57.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
180.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
269.0ms
(/ (/ (/ (+ (+ (+ 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))
152.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series572.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
133.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
147.0ms
(/ (/ (/ (+ (+ (+ 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))
277.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify558.0ms

Counts
477 → 477
Iterations

Useful iterations: done (527.0ms)

IterNodesCost
060325954
1149125182
done500125025

prune994.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
0.1b
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite583.0ms

Algorithm
rewrite-expression-head
Rules
64×add-exp-log
58×*-un-lft-identity
55×add-sqr-sqrt
53×times-frac
38×add-cube-cbrt add-cbrt-cube
28×div-exp
18×associate-*l*
16×prod-exp
15×cbrt-undiv associate-*r*
10×associate-/r* associate-/r/
9×distribute-lft-out
8×cbrt-unprod associate-/l*
7×pow1
6×flip3-+ flip-+ associate-/l/ unswap-sqr
5×rec-exp 1-exp div-inv
4×add-log-exp
3×frac-2neg clear-num
2×frac-times associate-*r/ associate-*l/ un-div-inv
1×pow-flip pow-prod-down *-commutative inv-pow
Counts
4 → 171
Calls
4 calls:
19.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
245.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
158.0ms
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
155.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
135.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
149.0ms
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
75.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.1s

Counts
183 → 183
Iterations

Useful iterations: 2 (384.0ms)

IterNodesCost
02485651
17605215
230684499
done50014499

prune390.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (* (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (/ (/ (+ (+ (+ 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) (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite855.0ms

Algorithm
rewrite-expression-head
Rules
1517×times-frac
931×*-un-lft-identity
511×add-sqr-sqrt add-cube-cbrt
480×cbrt-prod
266×associate-/r*
210×distribute-lft-out
73×associate-/r/
38×flip3-+ flip-+ div-inv
22×add-exp-log
16×add-cbrt-cube
13×associate-/l*
9×cbrt-undiv div-exp associate-/l/
6×cbrt-div
4×pow1 frac-2neg clear-num add-log-exp
2×prod-exp cbrt-unprod
1×frac-times associate-*r/ associate-*l/
Counts
4 → 642
Calls
4 calls:
327.0ms
(/ (* (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (/ (/ (+ (+ (+ 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) (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
152.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
151.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
153.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(/ (* (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (/ (/ (+ (+ (+ 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) (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
78.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
73.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.7s

Counts
654 → 654
Iterations

Useful iterations: 1 (1.2s)

IterNodesCost
0110262064
1241560729
done500060729

prune1.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.7b

localize37.0ms

Local error

Found 4 expressions with local error:

2.1b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (cbrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
4.6b
(cbrt (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0))))))

rewrite545.0ms

Algorithm
rewrite-expression-head
Rules
414×times-frac
303×*-un-lft-identity
203×add-sqr-sqrt add-cube-cbrt
120×cbrt-prod
102×sqrt-prod
50×distribute-lft-out
38×associate-/l*
30×associate-/r/
27×cbrt-div
19×flip3-+ flip-+
13×add-exp-log
12×associate-/r* add-cbrt-cube div-inv
5×cbrt-undiv div-exp associate-/l/
4×pow1 frac-times sqrt-div add-log-exp
3×frac-2neg clear-num
2×associate-*r/ associate-*l/
1×pow1/3
Counts
4 → 348
Calls
4 calls:
187.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (cbrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
149.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
150.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
35.0ms
(cbrt (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0))))))

series643.0ms

Counts
4 → 12
Calls
4 calls:
224.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (cbrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
78.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
261.0ms
(cbrt (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0))))))

simplify1.4s

Counts
360 → 360
Iterations

Useful iterations: 2 (691.0ms)

IterNodesCost
058416357
1129415609
2382715218
done500015218

prune1.8s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.7b

regimes78.0ms

Accuracy

54.8% (1.2b remaining)

Error of 2.2b against oracle of 1.1b and baseline of 3.6b

bsearch34.0ms

Steps
ItersRangePoint
5
1.2761513080479214e+167
3.467445464211409e+167
3.2116744201778903e+167

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02152
13052
done3052

end0.0ms

sample538.0ms

Algorithm
intervals
Results
296.0ms8000×body80valid
97.0ms8000×pre80true