Main:bigenough2 from A

Average Error: 0.0 → 0.0

Time: 7.0s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

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));
}

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))
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));
}

Python

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	23.5
Cost	1116

\[\begin{array}{l} \mathbf{if}\;y \leq -460000000000:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-85}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+60}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+70}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+140}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+209}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 2
Error	12.3
Cost	584

\[\begin{array}{l} t_0 := y \cdot \left(z + x\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{-85}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	12.4
Cost	584

\[\begin{array}{l} t_0 := y \cdot \left(z + x\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{-85}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-13}:\\ \;\;\;\;\left(1 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	0.9
Cost	584

\[\begin{array}{l} t_0 := y \cdot \left(z + x\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-7}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	23.7
Cost	456

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

Alternative 6
Error	34.4
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023077 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))