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

Average Error: 0.2 → 0.2

Time: 11.8s

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	0.2
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.2

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

Alternatives

Alternative 1
Error	17.0
Cost	1872

\[\begin{array}{l} t_0 := \left(x \cdot 3\right) \cdot y\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+106}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq -1 \cdot 10^{+21}:\\ \;\;\;\;-z\\ \mathbf{elif}\;t_0 \leq -1 \cdot 10^{-50}:\\ \;\;\;\;\left(3 \cdot y\right) \cdot x\\ \mathbf{elif}\;t_0 \leq 10^{-61}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 2
Error	16.8
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-56}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-104}:\\ \;\;\;\;3 \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 3
Error	16.8
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-57}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-104}:\\ \;\;\;\;\left(3 \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4
Error	0.2
Cost	448

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

Alternative 5
Error	27.6
Cost	128

\[-z \]

Reproduce

herbie shell --seed 2023010 
(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))