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

Average Error: 6.0 → 0.1

Time: 2.6s

Precision: binary64

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (+ x (/ 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) {
	return x + (y / (z / y));
}

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
    code = x + (y / (z / y))
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) {
	return x + (y / (z / y));
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	6.0
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 6.0

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

2. Simplified 0.1

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{y}{z}, x\right)} \]

3. Applied egg-rr 1.4

   \[\leadsto \color{blue}{\sqrt[3]{\mathsf{fma}\left(y, \frac{y}{z}, x\right)} \cdot {\left(\sqrt[3]{\mathsf{fma}\left(y, \frac{y}{z}, x\right)}\right)}^{2}} \]

4. Taylor expanded in y around 0 6.0

   \[\leadsto \color{blue}{\frac{{y}^{2}}{z} + x} \]

5. Simplified 0.1

   \[\leadsto \color{blue}{x + \frac{y}{\frac{z}{y}}} \]

6. Final simplification 0.1

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

Reproduce

herbie shell --seed 2022150 
(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)))