Details

Time bar (total: 45.9s)

sample42.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
7.0ms256×pre80true

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
done2006
42006
3680
2123
136
015

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.5b

localize29.0ms

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))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
804×times-frac
587×*-un-lft-identity
341×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×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l/
3×clear-num fma-def frac-2neg
1×+-commutative associate-+l+
Counts
4 → 480
Calls
4 calls:
150.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
285.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
355.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
209.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
145.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
160.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
109.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.3s

Counts
492 → 492
Iterations
IterNodes
done2008
22008
11452
0614

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.8b

localize37.0ms

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))))
0.1b
(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
819×times-frac
601×*-un-lft-identity
360×sqrt-prod
355×add-sqr-sqrt
349×add-cube-cbrt
126×distribute-lft-out
69×associate-/r*
53×associate-/r/
29×flip3-+ flip-+
27×div-inv
12×associate-/l*
10×add-cbrt-cube add-exp-log
6×associate-/l/
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv rem-sqrt-square clear-num frac-2neg div-exp
2×sqrt-div
1×sqrt-pow1 pow1/2
Counts
4 → 489
Calls
4 calls:
139.0ms
(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))
358.0ms
(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
228.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
266.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series735.0ms

Counts
4 → 12
Calls
4 calls:
218.0ms
(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))
305.0ms
(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
104.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
107.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.6s

Counts
501 → 501
Iterations
IterNodes
done2004
22004
11257
0707

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1)))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
12.0b
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2 1)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1)))))

rewrite868.0ms

Algorithm
rewrite-expression-head
Rules
7742×times-frac
4062×*-un-lft-identity
3066×add-sqr-sqrt
3060×add-cube-cbrt
2004×sqrt-prod
501×distribute-lft-out
193×div-inv
185×associate-/r/
89×associate-/r*
82×flip3-+ flip-+
36×add-exp-log
32×associate-/l*
27×add-cbrt-cube
25×div-exp
16×cbrt-undiv
6×pow1 sqrt-div
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×1-exp associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 hypot-def
Counts
4 → 2381
Calls
4 calls:
169.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1)))
108.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
90.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
341.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2 1)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1)))))

series568.0ms

Counts
4 → 12
Calls
4 calls:
247.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1)))
67.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
68.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
185.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2 1)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1)))))

simplify4.4s

Counts
2393 → 2393
Iterations
IterNodes
done2518
02518

prune13.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.8b

localize70.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ (/ (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))))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite831.0ms

Algorithm
rewrite-expression-head
Rules
3609×times-frac
2202×*-un-lft-identity
1980×sqrt-prod
1560×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×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 hypot-def associate-/l/
1×1-exp
Counts
4 → 1533
Calls
4 calls:
320.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
213.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ alpha beta) (* 2 1))))
111.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
98.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series563.0ms

Counts
4 → 12
Calls
4 calls:
216.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
223.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ alpha beta) (* 2 1))))
63.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
60.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify2.8s

Counts
1545 → 1545
Iterations
IterNodes
done2000
12000
01403

prune8.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.8b

regimes159.0ms

Accuracy

51.4% (1.2b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 3.7b

bsearch118.0ms

Steps
ItersRangePoint
7
7.759695545517782e+161
7.872712566567013e+163
7.876427020943232e+161

simplify11.0ms

Iterations
IterNodes
done39
139
029

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.3s8000×body80valid
307.0ms8000×pre80true