Details

Time bar (total: 34.9s)

sample54.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
6.0ms256×pre80true

simplify624.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
3554
2111
133
014

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.1b

localize28.0ms

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) (* 2.0 1.0)) 1.0))
4.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
804×times-frac
584×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-cbrt-cube add-exp-log
10×cbrt-undiv associate-/r* div-exp
9×add-log-exp
4×pow1 associate-/l/
3×clear-num sum-log frac-2neg
1×+-commutative associate-+l+
Counts
4 → 463
Calls
4 calls:
26.0ms
(+ (+ alpha beta) (* beta alpha))
374.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
558.0ms
(/ (/ (/ (+ (+ (+ 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))
307.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series568.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (+ alpha beta) (* beta alpha))
226.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
202.0ms
(/ (/ (/ (+ (+ (+ 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))
123.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify835.0ms

Counts
475 → 475
Iterations
IterNodes
done5001
11628
0604

prune2.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize22.0ms

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
(/ (pow (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) 1) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
4.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
820×times-frac
601×*-un-lft-identity
349×add-sqr-sqrt add-cube-cbrt
300×unpow-prod-down
126×distribute-lft-out
86×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
23×add-exp-log
13×add-cbrt-cube
12×div-exp
10×associate-/r*
9×add-log-exp
5×cbrt-undiv sqr-pow
4×pow1
3×clear-num sum-log frac-2neg pow-exp associate-/l/
1×pow-to-exp +-commutative associate-+l+
Counts
4 → 482
Calls
4 calls:
28.0ms
(+ (+ alpha beta) (* beta alpha))
373.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
949.0ms
(/ (pow (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) 1) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
358.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series597.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (+ alpha beta) (* beta alpha))
210.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
246.0ms
(/ (pow (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) 1) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
114.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.1s

Counts
494 → 494
Iterations
IterNodes
done5000
11796
0734

prune2.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (+ beta (+ alpha (+ (* alpha beta) 1.0)))) (+ (+ (* 2.0 1.0) alpha) beta))
0.1b
(/ (sqrt (+ beta (+ alpha (+ (* alpha beta) 1.0)))) (+ (+ (* 2.0 1.0) alpha) beta))
4.7b
(sqrt (+ beta (+ alpha (+ (* alpha beta) 1.0))))
4.7b
(sqrt (+ beta (+ alpha (+ (* alpha beta) 1.0))))

rewrite624.0ms

Algorithm
rewrite-expression-head
Rules
140×*-un-lft-identity
64×times-frac
60×sqrt-prod
54×distribute-lft-out
46×add-sqr-sqrt
44×add-cube-cbrt
16×associate-/l*
8×associate-/r* add-cbrt-cube sqrt-div add-exp-log
6×pow1 flip3-+ flip-+
4×associate-/r/ add-log-exp associate-/l/
2×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 154
Calls
4 calls:
232.0ms
(/ (sqrt (+ beta (+ alpha (+ (* alpha beta) 1.0)))) (+ (+ (* 2.0 1.0) alpha) beta))
193.0ms
(/ (sqrt (+ beta (+ alpha (+ (* alpha beta) 1.0)))) (+ (+ (* 2.0 1.0) alpha) beta))
113.0ms
(sqrt (+ beta (+ alpha (+ (* alpha beta) 1.0))))
78.0ms
(sqrt (+ beta (+ alpha (+ (* alpha beta) 1.0))))

series749.0ms

Counts
4 → 12
Calls
4 calls:
297.0ms
(/ (sqrt (+ beta (+ alpha (+ (* alpha beta) 1.0)))) (+ (+ (* 2.0 1.0) alpha) beta))
293.0ms
(/ (sqrt (+ beta (+ alpha (+ (* alpha beta) 1.0)))) (+ (+ (* 2.0 1.0) alpha) beta))
76.0ms
(sqrt (+ beta (+ alpha (+ (* alpha beta) 1.0))))
81.0ms
(sqrt (+ beta (+ alpha (+ (* alpha beta) 1.0))))

simplify680.0ms

Counts
166 → 166
Iterations
IterNodes
done5002
21324
1336
0141

prune955.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ 1 (+ alpha (+ beta (* 2.0 1.0)))) (sqrt (+ alpha (+ beta (* 2.0 1.0)))))
1.3b
(* (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ alpha (+ beta (* 2.0 1.0))))) (sqrt (+ (+ alpha (+ beta (* 2.0 1.0))) 1.0))) (/ (/ (/ 1 (+ alpha (+ beta (* 2.0 1.0)))) (sqrt (+ alpha (+ beta (* 2.0 1.0))))) (sqrt (+ (+ alpha (+ beta (* 2.0 1.0))) 1.0))))
2.6b
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ alpha (+ beta (* 2.0 1.0))))) (sqrt (+ (+ alpha (+ beta (* 2.0 1.0))) 1.0)))
3.2b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ alpha (+ beta (* 2.0 1.0)))))

rewrite6.0s

Algorithm
rewrite-expression-head
Rules
4394×times-frac
3687×*-un-lft-identity
2115×sqrt-prod
2114×add-sqr-sqrt
1544×add-cube-cbrt
1158×distribute-lft-out
1062×associate-*r*
278×associate-*l*
188×associate-/r/
105×unswap-sqr
104×add-exp-log
95×flip3-+ flip-+
94×div-inv
70×add-cbrt-cube
61×div-exp
60×sqrt-div
56×associate-/l*
37×cbrt-undiv
22×associate-/r*
18×prod-exp
12×cbrt-unprod
10×pow1
4×rec-exp 1-exp add-log-exp pow-div associate-/l/
3×clear-num frac-2neg
2×sqrt-pow1 pow1/2 pow-flip inv-pow
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 2047
Calls
4 calls:
64.0ms
(/ (/ 1 (+ alpha (+ beta (* 2.0 1.0)))) (sqrt (+ alpha (+ beta (* 2.0 1.0)))))
5.1s
(* (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ alpha (+ beta (* 2.0 1.0))))) (sqrt (+ (+ alpha (+ beta (* 2.0 1.0))) 1.0))) (/ (/ (/ 1 (+ alpha (+ beta (* 2.0 1.0)))) (sqrt (+ alpha (+ beta (* 2.0 1.0))))) (sqrt (+ (+ alpha (+ beta (* 2.0 1.0))) 1.0))))
330.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ alpha (+ beta (* 2.0 1.0))))) (sqrt (+ (+ alpha (+ beta (* 2.0 1.0))) 1.0)))
215.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ alpha (+ beta (* 2.0 1.0)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ (/ 1 (+ alpha (+ beta (* 2.0 1.0)))) (sqrt (+ alpha (+ beta (* 2.0 1.0)))))
247.0ms
(* (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ alpha (+ beta (* 2.0 1.0))))) (sqrt (+ (+ alpha (+ beta (* 2.0 1.0))) 1.0))) (/ (/ (/ 1 (+ alpha (+ beta (* 2.0 1.0)))) (sqrt (+ alpha (+ beta (* 2.0 1.0))))) (sqrt (+ (+ alpha (+ beta (* 2.0 1.0))) 1.0))))
250.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ alpha (+ beta (* 2.0 1.0))))) (sqrt (+ (+ alpha (+ beta (* 2.0 1.0))) 1.0)))
596.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ alpha (+ beta (* 2.0 1.0)))))

simplify1.2s

Counts
2059 → 2059
Iterations
IterNodes
done5000
01463

prune9.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.0b

regimes213.0ms

Accuracy

35.2% (1.7b remaining)

Error of 2.9b against oracle of 1.2b and baseline of 3.9b

bsearch191.0ms

Steps
ItersRangePoint
11
1.0703537743171578e+130
8.192764061108593e+151
8.099889163284841e+151

simplify13.0ms

Iterations
IterNodes
done66
166
045

end0.0ms

sample1.3s

Algorithm
intervals
Results
783.0ms8000×body80valid
233.0ms8000×pre80true