Main:bigenough2 from A

Average Error: 0.0 → 0.0

Time: 1.8s

Precision: binary64

Cost: 576

Math

\[x + y \cdot \left(z + x\right) \]

↓

\[x + \left(y \cdot z + x \cdot y\right) \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* y (+ z x))))

↓

(FPCore (x y z) :precision binary64 (+ x (+ (* y z) (* x y))))

C

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

↓

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

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 + (y * (z + x))
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 + ((y * z) + (x * y))
end function

Java

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

↓

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

Python

def code(x, y, z):
	return x + (y * (z + x))

↓

def code(x, y, z):
	return x + ((y * z) + (x * y))

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

   \[x + y \cdot \left(z + x\right) \]

2. Taylor expanded in z around 0 0.0

   \[\leadsto x + \color{blue}{\left(y \cdot z + y \cdot x\right)} \]

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	7.3
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-83} \lor \neg \left(z \leq 8.6 \cdot 10^{-157}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot y\\ \end{array} \]

Alternative 2
Error	24.3
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-9}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3
Error	0.0
Cost	448

\[x + y \cdot \left(x + z\right) \]

Alternative 4
Error	23.4
Cost	320

\[x + x \cdot y \]

Alternative 5
Error	34.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022354 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))