Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, B

Average Error: 0.1 → 0.1

Time: 6.1s

Precision: binary64

Cost: 448

Math

\[\left(x \cdot 3\right) \cdot y - z \]

↓

\[\left(x \cdot 3\right) \cdot y - z \]

FPCore

(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))

↓

(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))

C

double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

↓

double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * 3.0d0) * y) - z
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * 3.0d0) * y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

↓

public static double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Python

def code(x, y, z):
	return ((x * 3.0) * y) - z

↓

def code(x, y, z):
	return ((x * 3.0) * y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * 3.0) * y) - z)
end

↓

function code(x, y, z)
	return Float64(Float64(Float64(x * 3.0) * y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * 3.0) * y) - z;
end

↓

function tmp = code(x, y, z)
	tmp = ((x * 3.0) * y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]

Target

Original	0.1
Target	0.1
Herbie	0.1

\[x \cdot \left(3 \cdot y\right) - z \]

Derivation

1. Initial program 0.1

   \[\left(x \cdot 3\right) \cdot y - z \]

2. Final simplification 0.1

   \[\leadsto \left(x \cdot 3\right) \cdot y - z \]

Alternatives

Alternative 1
Error	15.3
Cost	1873

\[\begin{array}{l} t_0 := \left(x \cdot 3\right) \cdot y\\ \mathbf{if}\;t_0 \leq -5000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{-12} \lor \neg \left(t_0 \leq 5000000000000\right) \land t_0 \leq 2 \cdot 10^{+46}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \end{array} \]

Alternative 2
Error	17.1
Cost	849

\[\begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-63}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-21} \lor \neg \left(z \leq 1.45 \cdot 10^{+78}\right) \land z \leq 1.32 \cdot 10^{+101}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 3
Error	17.1
Cost	848

\[\begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-64}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+78}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+101}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4
Error	0.1
Cost	448

\[x \cdot \left(3 \cdot y\right) - z \]

Alternative 5
Error	27.2
Cost	128

\[-z \]

Reproduce

herbie shell --seed 2023046 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (* x (* 3.0 y)) z)

  (- (* (* x 3.0) y) z))