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

Average Error: 6.0 → 5.3

Time: 2.8s

Precision: binary64

Cost: 708

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \cdot y \leq 2 \cdot 10^{+302}:\\ \;\;\;\;x + \frac{y \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (if (<= (* y y) 2e+302) (+ x (/ (* y y) z)) x))

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 * y) <= 2e+302) {
		tmp = x + ((y * y) / z);
	} else {
		tmp = x;
	}
	return 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 * y) <= 2d+302) then
        tmp = x + ((y * y) / z)
    else
        tmp = x
    end if
    code = 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 * y) <= 2e+302) {
		tmp = x + ((y * y) / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	tmp = 0
	if (y * y) <= 2e+302:
		tmp = x + ((y * y) / z)
	else:
		tmp = x
	return 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 (Float64(y * y) <= 2e+302)
		tmp = Float64(x + Float64(Float64(y * y) / z));
	else
		tmp = x;
	end
	return 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 * y) <= 2e+302)
		tmp = x + ((y * y) / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_] := If[LessEqual[N[(y * y), $MachinePrecision], 2e+302], N[(x + N[(N[(y * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], x]

Target

Original	6.0
Target	0.1
Herbie	5.3

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 y y) < 2.0000000000000002e302

   1. Initial program 0.9

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

   if 2.0000000000000002e302 < (*.f64 y y)

   1. Initial program 62.0

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

   2. Taylor expanded in x around inf 53.9

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 5.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot y \leq 2 \cdot 10^{+302}:\\ \;\;\;\;x + \frac{y \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternatives

Alternative 1
Error	21.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023090 
(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)))