Average Error: 0.0 → 0.0
Time: 38.8s
Precision: 64
Internal Precision: 128
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[c \cdot i + \left(\left(z \cdot t + x \cdot y\right) + a \cdot b\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]

  2. Final simplification0.0

    \[\leadsto c \cdot i + \left(\left(z \cdot t + x \cdot y\right) + a \cdot b\right)\]

Reproduce

herbie shell --seed 2019008 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

Details

Time bar (total: 37.5s)Debug log

sample135.0ms

Algorithm
intervals

simplify54.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

54.0ms
(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x y) (* z t)) (* a b))
0.0b
(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))
0.0b
(+ (* x y) (* z t))

rewrite50.0ms

Algorithm
rewrite-expression-head
Counts
3 → 38
Calls

3 calls. Slowest were:

30.0ms
(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))
17.0ms
(+ (+ (* x y) (* z t)) (* a b))
2.0ms
(+ (* x y) (* z t))

series309.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

219.0ms
(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))
54.0ms
(+ (+ (* x y) (* z t)) (* a b))
36.0ms
(+ (* x y) (* z t))

simplify673.0ms

Counts
17 → 47
Calls

17 calls. Slowest were:

204.0ms
(* (* (* (exp (* x y)) (exp (* z t))) (exp (* a b))) (exp (* c i)))
144.0ms
(* (exp (+ (+ (* x y) (* z t)) (* a b))) (exp (* c i)))
116.0ms
(* (* (exp (+ (* x y) (* z t))) (exp (* a b))) (exp (* c i)))

prune786.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

2.2b
(cbrt (+ (* x y) (* z t)))
2.2b
(cbrt (+ (* x y) (* z t)))
2.2b
(cbrt (+ (* x y) (* z t)))
0.5b
(* (cbrt (+ (* x y) (* z t))) (cbrt (+ (* x y) (* z t))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
4 → 75
Calls

4 calls. Slowest were:

8.0ms
(* (cbrt (+ (* x y) (* z t))) (cbrt (+ (* x y) (* z t))))
1.0ms
(cbrt (+ (* x y) (* z t)))
1.0ms
(cbrt (+ (* x y) (* z t)))

series558.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

186.0ms
(* (cbrt (+ (* x y) (* z t))) (cbrt (+ (* x y) (* z t))))
151.0ms
(cbrt (+ (* x y) (* z t)))
118.0ms
(cbrt (+ (* x y) (* z t)))
103.0ms
(cbrt (+ (* x y) (* z t)))

simplify7.5s

Counts
59 → 87
Calls

59 calls. Slowest were:

400.0ms
(* (cbrt (+ (* (* x y) (* x y)) (- (* (* z t) (* z t)) (* (* x y) (* z t))))) (cbrt (- (* x y) (* z t))))
393.0ms
(* (cbrt (+ (pow (* x y) 3) (pow (* z t) 3))) (cbrt (- (* (* x y) (* x y)) (* (* z t) (* z t)))))
393.0ms
(* (cbrt (- (* x y) (* z t))) (cbrt (+ (* (* x y) (* x y)) (- (* (* z t) (* z t)) (* (* x y) (* z t))))))

prune1.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.5b
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.5b
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.5b
(* (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))

rewrite187.0ms

Algorithm
rewrite-expression-head
Counts
4 → 75
Calls

4 calls. Slowest were:

109.0ms
(* (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
35.0ms
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
21.0ms
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

series693.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

226.0ms
(* (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
173.0ms
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
159.0ms
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
135.0ms
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

simplify8.8s

Counts
59 → 87
Calls

59 calls. Slowest were:

1.0s
(cbrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)))
816.0ms
(* (cbrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3))) (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
729.0ms
(cbrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)))

prune1.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize4.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.5b
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.5b
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.5b
(* (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Counts
4 → 75
Calls

4 calls. Slowest were:

79.0ms
(* (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
16.0ms
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
15.0ms
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

series652.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

219.0ms
(* (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
169.0ms
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
134.0ms
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
129.0ms
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

simplify8.3s

Counts
59 → 87
Calls

59 calls. Slowest were:

797.0ms
(cbrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)))
787.0ms
(* (cbrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3))) (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
768.0ms
(cbrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)))

prune1.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes1.1s

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch2.0ms

end0.0ms

sample3.3s

Algorithm
intervals