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

Percentage Accurate: 93.0% → 99.9%

Time: 6.4s

Alternatives: 3

Speedup: 1.1×

• 25.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \frac{y \cdot y}{z} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y \cdot y}{z} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{z}{y}} \end{array} \]

FPCore

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

C

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 / (z / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

   \[x + \frac{y \cdot y}{z} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate-/l* N/A

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

   2. clear-num N/A

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{z}{y}}} \]

   3. un-div-inv N/A

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

   4. lower-/.f64 N/A

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

   5. lower-/.f64 99.9

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

4. Applied egg-rr 99.9%

   \[\leadsto x + \color{blue}{\frac{y}{\frac{z}{y}}} \]
5. Add Preprocessing

Alternative 2: 99.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{y}{z}, y, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (/ y z) y x))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 91.8%

   \[x + \frac{y \cdot y}{z} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. +-commutative N/A

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

   4. lift-/.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. associate-*l/ N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 99.9

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

4. Applied egg-rr 99.9%

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

Alternative 3: 51.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ y \cdot \frac{y}{z} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return y * (y / 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 = y * (y / z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

   \[x + \frac{y \cdot y}{z} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{{y}^{2}}{z}} \]
4. Step-by-step derivation

   1. lower-/.f64 N/A

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

   2. unpow2 N/A

      \[\leadsto \frac{\color{blue}{y \cdot y}}{z} \]

   3. lower-*.f64 43.2

      \[\leadsto \frac{\color{blue}{y \cdot y}}{z} \]

5. Simplified 43.2%

   \[\leadsto \color{blue}{\frac{y \cdot y}{z}} \]
6. Step-by-step derivation

   1. associate-*l/ N/A

      \[\leadsto \color{blue}{\frac{y}{z} \cdot y} \]

   2. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{y}{z}} \cdot y \]

   3. lower-*.f64 49.8

      \[\leadsto \color{blue}{\frac{y}{z} \cdot y} \]

7. Applied egg-rr 49.8%

   \[\leadsto \color{blue}{\frac{y}{z} \cdot y} \]

8. Final simplification 49.8%

   \[\leadsto y \cdot \frac{y}{z} \]
9. Add Preprocessing

Developer Target 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \frac{y}{z} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024207 
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (* y (/ y z))))

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