Details

Time bar (total: 38.6s)

sample40.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
6.0ms256×pre80true

simplify3.1s

Counts
1 → 1
Iterations
IterNodes
done5193
44059
3641
2119
136
015

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.6b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
4.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.1s

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-cbrt-cube add-exp-log
13×add-log-exp
10×cbrt-undiv associate-/r* div-exp
6×sum-log
4×pow1 insert-posit16 associate-/l/
3×clear-num frac-2neg
1×+-commutative associate-+l+
Counts
4 → 469
Calls
4 calls:
72.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
275.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
476.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
295.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series539.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
157.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
242.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
116.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.8s

Counts
481 → 481
Iterations
IterNodes
done5003
24498
11435
0606

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.8b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
0.3b
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
4.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
4.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
484×times-frac
370×*-un-lft-identity
302×sqrt-prod
284×add-sqr-sqrt
224×add-cube-cbrt
83×swap-sqr
64×distribute-lft-out
63×associate-*r* associate-*l*
38×associate-/r/
21×flip3-+ flip-+
19×pow1 div-inv
16×unswap-sqr
15×add-cbrt-cube add-exp-log
10×associate-/r*
9×associate-/l*
8×sqrt-pow1 pow1/2 sqrt-div
7×associate-/l/
5×pow-prod-up
4×cbrt-undiv div-exp insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down pow-sqr
2×frac-times associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×pow2 rem-square-sqrt pow-plus sqrt-unprod *-commutative
Counts
4 → 355
Calls
4 calls:
299.0ms
(/ (* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
681.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
274.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
226.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series740.0ms

Counts
4 → 12
Calls
4 calls:
262.0ms
(/ (* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
231.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
130.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
116.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify3.1s

Counts
367 → 367
Iterations
IterNodes
done5032
23936
11070
0553

prune2.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.8b

localize65.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))
0.8b
(/ (* (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))))
4.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
4.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
29×add-sqr-sqrt
25×times-frac add-cube-cbrt
22×add-cbrt-cube add-exp-log
16×flip3-+ sqrt-div flip-+
12×associate-/r/
9×frac-times distribute-lft-out associate-/l*
7×associate-/r* associate-/l/
6×pow1 cbrt-undiv div-exp associate-*r*
5×associate-*l/ prod-exp associate-*r/ cbrt-unprod
4×associate-*l* sqrt-prod insert-posit16 add-log-exp
3×clear-num frac-2neg div-inv
2×unswap-sqr
1×pow-prod-down *-commutative
Counts
4 → 137
Calls
4 calls:
338.0ms
(* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))
259.0ms
(/ (* (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))))
315.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
274.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series597.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))
232.0ms
(/ (* (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))))
123.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
137.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.6s

Counts
149 → 149
Iterations
IterNodes
done5041
22980
1681
0233

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.8b

localize71.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
0.6b
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ alpha beta) (* 2 1))))
4.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite849.0ms

Algorithm
rewrite-expression-head
Rules
3609×times-frac
2202×*-un-lft-identity
1980×sqrt-prod
1556×add-sqr-sqrt
1554×add-cube-cbrt
324×distribute-lft-out
183×associate-/l*
65×div-inv
34×associate-/r/
24×sqrt-div
21×add-exp-log
19×flip3-+ flip-+
18×add-cbrt-cube
13×associate-/r*
12×div-exp
9×cbrt-undiv
6×pow1
4×insert-posit16 add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
1×1-exp
Counts
4 → 1523
Calls
4 calls:
348.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
193.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ alpha beta) (* 2 1))))
89.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
112.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series709.0ms

Counts
4 → 12
Calls
4 calls:
258.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
265.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ alpha beta) (* 2 1))))
96.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
88.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify3.5s

Counts
1535 → 1535
Iterations
IterNodes
done5000
13105
01397

prune8.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.8b

regimes141.0ms

Accuracy

54.1% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.7b

bsearch111.0ms

Steps
ItersRangePoint
9
7.775450676221288e+157
3.9765790759248505e+164
1.1044946435875943e+164

simplify5.0ms

Iterations
IterNodes
done34
134
024

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.2s8000×body80valid
307.0ms8000×pre80true