Details

Time bar (total: 9.6s)

sample24.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify86.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113
done500113

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.3b

localize12.0ms

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))
3.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

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-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 expm1-log1p-u fma-def log1p-expm1-u associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 475
Calls
4 calls:
29.0ms
(+ (+ alpha beta) (* beta alpha))
309.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
452.0ms
(/ (/ (/ (+ (+ (+ 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))
272.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series415.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(+ (+ alpha beta) (* beta alpha))
145.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
164.0ms
(/ (/ (/ (+ (+ (+ 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))
85.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify123.0ms

Counts
487 → 487
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0153413079
1500112129
done500112129

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.1b

localize23.0ms

Local error

Found 4 expressions with local error:

3.3b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
13.3b
(/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

rewrite547.0ms

Algorithm
rewrite-expression-head
Rules
2015×times-frac
891×*-un-lft-identity
741×add-sqr-sqrt add-cube-cbrt
300×cbrt-prod
120×div-inv
86×associate-/r*
75×distribute-lft-out
61×add-exp-log
57×associate-/r/
42×div-exp
31×add-cbrt-cube
27×flip3-+ flip-+
24×cbrt-undiv
7×associate-/l*
6×cbrt-div 1-exp prod-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 cbrt-unprod
1×frac-2neg clear-num associate-/l/
Counts
4 → 781
Calls
4 calls:
55.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
55.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
56.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
305.0ms
(/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

series363.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
65.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
71.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
158.0ms
(/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

simplify305.0ms

Counts
793 → 793
Iterations

Useful iterations: 1 (73.0ms)

IterNodesCost
0409734252
1500132790
done500132790

prune2.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ beta (+ alpha (fma alpha beta 1.0)))
0.0b
(* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))
0.1b
(/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))) (fma 1.0 2.0 (+ alpha beta)))
16.6b
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0)))))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
58×times-frac
31×add-sqr-sqrt
29×add-cube-cbrt
24×distribute-lft-out
20×add-exp-log add-cbrt-cube
16×associate-/l*
12×associate-*r/
10×associate-/r/
9×add-log-exp
8×flip3-+ flip-+
7×cbrt-undiv div-exp
6×pow1 div-inv
5×associate-*r*
4×expm1-log1p-u associate-/r* log1p-expm1-u
3×fma-def associate-*l* prod-exp sum-log cbrt-unprod associate-/l/
2×frac-2neg clear-num
1×+-commutative distribute-rgt-in associate-+r+ distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
4 → 143
Calls
4 calls:
15.0ms
(+ beta (+ alpha (fma alpha beta 1.0)))
52.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))
73.0ms
(/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))) (fma 1.0 2.0 (+ alpha beta)))
65.0ms
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0)))))

series381.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(+ beta (+ alpha (fma alpha beta 1.0)))
40.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))
177.0ms
(/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))) (fma 1.0 2.0 (+ alpha beta)))
144.0ms
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0)))))

simplify90.0ms

Counts
155 → 155
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06082076
129241860
250011859
done50011859

prune450.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))
0.1b
(/ (/ (+ alpha (+ beta 1.0)) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))) (fma 1.0 2.0 (+ alpha beta)))
16.4b
(/ (+ alpha (+ beta 1.0)) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0)))))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity
58×times-frac
29×add-sqr-sqrt
27×add-cube-cbrt
21×distribute-lft-out
19×add-exp-log add-cbrt-cube
16×associate-/l*
12×associate-*r/
10×associate-/r/
7×cbrt-undiv flip3-+ div-exp flip-+
6×div-inv
5×pow1 associate-*r*
4×associate-/r*
3×expm1-log1p-u associate-*l* prod-exp cbrt-unprod log1p-expm1-u associate-/l/ add-log-exp
2×frac-2neg clear-num
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
3 → 123
Calls
3 calls:
51.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))
73.0ms
(/ (/ (+ alpha (+ beta 1.0)) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))) (fma 1.0 2.0 (+ alpha beta)))
66.0ms
(/ (+ alpha (+ beta 1.0)) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0)))))

series251.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))
112.0ms
(/ (/ (+ alpha (+ beta 1.0)) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))) (fma 1.0 2.0 (+ alpha beta)))
93.0ms
(/ (+ alpha (+ beta 1.0)) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0)))))

simplify82.0ms

Counts
132 → 132
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
05651856
127831661
250011660
done50011660

prune334.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.1b

regimes75.0ms

Accuracy

20.8% (2.4b remaining)

Error of 3.4b against oracle of 1.0b and baseline of 4.1b

bsearch65.0ms

Steps
ItersRangePoint
10
3.5796156622935226e+33
2.6285194651538273e+45
2.6010178709356358e+45

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03025
13025
done3025

end0.0ms

sample558.0ms

Algorithm
intervals
Results
287.0ms8000×body80valid
90.0ms8000×pre80true