Details

Time bar (total: 50.2s)

sample59.0ms

Algorithm
intervals
Results
26.0ms256×body80valid
10.0ms256×pre80true

simplify2.9s

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.8b

localize51.0ms

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))
4.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.8s

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:
184.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
460.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
765.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
370.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series615.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
230.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
234.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
134.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.8s

Counts
481 → 481
Iterations
IterNodes
done5003
24498
11435
0606

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.6b

localize37.0ms

Local error

Found 3 expressions with local error:

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)))
4.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
954×times-frac
827×*-un-lft-identity
382×add-sqr-sqrt add-cube-cbrt
253×distribute-lft-out
82×associate-/l*
66×associate-/r/
36×flip3-+ flip-+
31×div-inv
19×add-cbrt-cube add-exp-log
11×associate-/r*
10×cbrt-undiv div-exp
4×frac-add associate-/l/
3×pow1 clear-num frac-2neg insert-posit16 add-log-exp
Counts
3 → 518
Calls
3 calls:
528.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
661.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (+ (* 2 1) 1.0)))
390.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series482.0ms

Counts
3 → 9
Calls
3 calls:
182.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
188.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (+ (* 2 1) 1.0)))
112.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify3.1s

Counts
527 → 527
Iterations
IterNodes
done5000
24961
11511
0616

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2 1)))) (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))))
0.6b
(/ 1 (sqrt (+ (+ alpha beta) (* 2 1))))
2.6b
(/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))))
3.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
8286×times-frac
4237×*-un-lft-identity
3275×add-sqr-sqrt add-cube-cbrt
1839×sqrt-prod
481×distribute-lft-out
381×associate-/r/
354×sqrt-div
204×div-inv
179×flip3-+ flip-+
137×associate-/r*
54×add-exp-log
36×div-exp
34×add-cbrt-cube associate-/l*
20×cbrt-undiv
6×pow1
5×associate-/l/
4×rec-exp clear-num frac-2neg 1-exp insert-posit16 add-log-exp
3×pow-flip
1×sqrt-pow1 pow1/2 inv-pow
Counts
4 → 2670
Calls
4 calls:
345.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2 1)))) (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))))
39.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2 1))))
308.0ms
(/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))))
370.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))

series955.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2 1)))) (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))))
79.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2 1))))
570.0ms
(/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))))
119.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))

simplify5.6s

Counts
2682 → 2682
Iterations
IterNodes
done5000
02710

prune14.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
0.2b
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
4.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
4.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
444×times-frac
384×sqrt-prod
336×*-un-lft-identity
236×add-sqr-sqrt add-cube-cbrt
50×distribute-lft-out associate-/l*
36×associate-/r/
20×flip3-+ flip-+
18×associate-/r* div-inv
12×add-cbrt-cube add-exp-log
6×sqrt-div associate-/l/
4×pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 add-log-exp
2×sqrt-undiv
Counts
4 → 412
Calls
4 calls:
344.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
380.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
402.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
450.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series813.0ms

Counts
4 → 12
Calls
4 calls:
320.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
248.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
122.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
123.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.9s

Counts
424 → 424
Iterations
IterNodes
done5000
21602
1630
0333

prune2.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.6b

regimes114.0ms

Accuracy

50.3% (1.2b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 3.6b

bsearch137.0ms

Steps
ItersRangePoint
7
8.965404690253628e+207
1.0216326951022218e+210
1.00414566459986e+210

simplify23.0ms

Iterations
IterNodes
done61
161
042

end0.0ms

sample1.8s

Algorithm
intervals
Results
950.0ms8000×body80valid
690.0ms8000×pre80true