Main:bigenough2 from A

Average Error: 0.02% → 0.02%

Time: 2.0s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

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

Python

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

↓

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

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(x + z)))
end

MATLAB

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

↓

function tmp = code(x, y, z)
	tmp = x + (y * (x + z));
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[(x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.02

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

2. Final simplification 0.02

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

Alternatives

Alternative 1
Error	25.98%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-46} \lor \neg \left(x \leq 4.6 \cdot 10^{-113}\right):\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 2
Error	10.91%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-105} \lor \neg \left(z \leq 7.2 \cdot 10^{-147}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot y\\ \end{array} \]

Alternative 3
Error	37.9%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 20:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4
Error	39.01%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-48}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	54.54%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023089 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))