Crypto.Random.Test:calculate from crypto-random-0.0.9

Average Error: 6.8 → 0.1

Time: 1.6min

Precision: binary64

Cost: 580

Math

\[x + \frac{y \cdot y}{z} \]

↓

\[x + \begin{array}{l} \mathbf{if}\;y \ne 0:\\ \;\;\;\;\frac{y}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot y\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (+ x (if (!= y 0.0) (/ y (/ z y)) (* (/ y z) y))))

C

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

↓

double code(double x, double y, double z) {
	double tmp;
	if (y != 0.0) {
		tmp = y / (z / y);
	} else {
		tmp = (y / z) * y;
	}
	return x + tmp;
}

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 * 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
    real(8) :: tmp
    if (y /= 0.0d0) then
        tmp = y / (z / y)
    else
        tmp = (y / z) * y
    end if
    code = x + tmp
end function

Java

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

↓

public static double code(double x, double y, double z) {
	double tmp;
	if (y != 0.0) {
		tmp = y / (z / y);
	} else {
		tmp = (y / z) * y;
	}
	return x + tmp;
}

Python

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

↓

def code(x, y, z):
	tmp = 0
	if y != 0.0:
		tmp = y / (z / y)
	else:
		tmp = (y / z) * y
	return x + tmp

Julia

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

↓

function code(x, y, z)
	tmp = 0.0
	if (y != 0.0)
		tmp = Float64(y / Float64(z / y));
	else
		tmp = Float64(Float64(y / z) * y);
	end
	return Float64(x + tmp)
end

MATLAB

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

↓

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y ~= 0.0)
		tmp = y / (z / y);
	else
		tmp = (y / z) * y;
	end
	tmp_2 = x + tmp;
end

Wolfram

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

↓

code[x_, y_, z_] := N[(x + If[Unequal[y, 0.0], N[(y / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * y), $MachinePrecision]]), $MachinePrecision]

Target

Original	6.8
Target	0.1
Herbie	0.1

\[x + y \cdot \frac{y}{z} \]

Derivation

1. Initial program 6.8

   \[x + \frac{y \cdot y}{z} \]

2. Applied egg-rr 0.1

   \[\leadsto x + \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;y \ne 0:\\ \;\;\;\;\frac{y}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{{y}^{2}}{z}\\ } \end{array}} \]

3. Applied egg-rr 0.1

   \[\leadsto x + \begin{array}{l} \mathbf{if}\;y \ne 0:\\ \;\;\;\;\frac{y}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot y\\ \end{array} \]

Alternatives

Alternative 1
Error	11.8
Cost	1096

\[\begin{array}{l} t_0 := \frac{y \cdot y}{z}\\ t_1 := \frac{y}{z} \cdot y\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 2000000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	0.1
Cost	448

\[x + \frac{y}{z} \cdot y \]

Alternative 3
Error	21.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"
  :precision binary64

  :herbie-target
  (+ x (* y (/ y z)))

  (+ x (/ (* y y) z)))