Details

Time bar (total: 59.7s)

sample84.0ms

Algorithm
intervals
Results
48.0ms256×body80valid
13.0ms256×pre80true

simplify849.0ms

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.5b

localize55.0ms

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))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.4s

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:
133.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
378.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
557.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
265.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series534.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
173.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
208.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
125.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.6s

Counts
492 → 492
Iterations
IterNodes
done2008
22008
11452
0614

prune5.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.1b

localize50.0ms

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 1))) (+ (+ alpha beta) (* 2 1)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.1s

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
10×cbrt-undiv associate-/r* div-exp
9×add-log-exp
4×expm1-log1p-u pow1 fma-def insert-posit16 log1p-expm1-u associate-/l/
3×clear-num sum-log frac-2neg
1×+-commutative associate-+l+
Counts
4 → 479
Calls
4 calls:
40.0ms
(+ (+ alpha beta) (* beta alpha))
301.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
532.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
242.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series580.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (+ alpha beta) (* beta alpha))
225.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
210.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
116.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.6s

Counts
491 → 491
Iterations
IterNodes
done2007
22007
11475
0616

prune5.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.1b

localize82.0ms

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)))) 1) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1)))))
0.1b
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
1930×times-frac
1248×*-un-lft-identity
945×add-sqr-sqrt
777×sqrt-prod
742×add-cube-cbrt
258×associate-*r*
243×distribute-lft-out
193×associate-*l*
104×associate-/r/
71×associate-/l*
54×flip3-+ flip-+
53×div-inv
45×unswap-sqr
27×add-exp-log
22×add-cbrt-cube
10×associate-/r* div-exp
7×cbrt-undiv
6×pow1 prod-exp
5×associate-/l/
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×1-exp
1×frac-times sqrt-div pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 934
Calls
4 calls:
850.0ms
(* (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) 1) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1)))))
360.0ms
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
305.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
280.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series1.0s

Counts
4 → 12
Calls
4 calls:
251.0ms
(* (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) 1) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1)))))
172.0ms
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
499.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
110.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.2s

Counts
946 → 946
Iterations
IterNodes
done2000
12000
01189

prune16.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize85.0ms

Local error

Found 4 expressions with local error:

3.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
4.2b
(* (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1)))))
8.9b
(sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
1127×times-frac
744×*-un-lft-identity
664×sqrt-prod
540×add-sqr-sqrt
462×add-cube-cbrt
366×associate-*r*
141×distribute-lft-out
44×associate-/r/
26×flip3-+ flip-+
22×div-inv
18×unswap-sqr
11×add-cbrt-cube sqrt-div add-exp-log
10×associate-*l*
8×pow1
5×rem-sqrt-square
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×associate-/r*
2×frac-times cbrt-undiv sqrt-pow1 pow1/2 div-exp associate-*l/ prod-exp cbrt-unprod associate-/l/
1×clear-num frac-2neg pow-prod-down associate-*r/ *-commutative hypot-def
Counts
4 → 577
Calls
4 calls:
132.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
293.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
746.0ms
(* (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1)))))
182.0ms
(sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))

series549.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
100.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
164.0ms
(* (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1)))))
218.0ms
(sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))

simplify2.4s

Counts
589 → 589
Iterations
IterNodes
done2000
12000
0948

prune12.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.1b

regimes149.0ms

Accuracy

38.6% (1.5b remaining)

Error of 2.7b against oracle of 1.2b and baseline of 3.6b

bsearch63.0ms

Steps
ItersRangePoint
5
1.3154968375234933e+114
3.987194372781887e+114
3.9275252152036123e+114

simplify5.0ms

Iterations
IterNodes
done36
136
027

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.4s8000×body80valid
362.0ms8000×pre80true