Main:bigenough2 from A

Average Error: 0.0 → 0.0

Time: 6.0s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = (y * z) + ((y * x) + x)
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 (y * z) + ((y * x) + x);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Taylor expanded in z around 0 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	11.9
Cost	584

\[\begin{array}{l} t_0 := y \cdot \left(z + x\right)\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	11.9
Cost	584

\[\begin{array}{l} t_0 := y \cdot \left(z + x\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-53}:\\ \;\;\;\;\left(1 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	0.8
Cost	584

\[\begin{array}{l} t_0 := y \cdot \left(z + x\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-10}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	24.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 5
Error	23.3
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-25}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 6
Error	0.0
Cost	448

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

Alternative 7
Error	34.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023075 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))