Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B

Percentage Accurate: 100.0% → 100.0%

Time: 836.0ms

Alternatives: 5

Speedup: 1.0×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot z \end{array} \]

FPCore

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

C

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 - x) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot z \end{array} \]

FPCore

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

C

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 - x) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot z \end{array} \]

FPCore

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

C

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 - x) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - x\right) \cdot z \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot z\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-50}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.000115:\\ \;\;\;\;x + \left(x + \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) z)))
   (if (<= z -5.6e-50) t_0 (if (<= z 0.000115) (+ x (+ x (- y x))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * z;
	double tmp;
	if (z <= -5.6e-50) {
		tmp = t_0;
	} else if (z <= 0.000115) {
		tmp = x + (x + (y - x));
	} else {
		tmp = t_0;
	}
	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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y - x) * z
    if (z <= (-5.6d-50)) then
        tmp = t_0
    else if (z <= 0.000115d0) then
        tmp = x + (x + (y - x))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - x) * z;
	double tmp;
	if (z <= -5.6e-50) {
		tmp = t_0;
	} else if (z <= 0.000115) {
		tmp = x + (x + (y - x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * z
	tmp = 0
	if z <= -5.6e-50:
		tmp = t_0
	elif z <= 0.000115:
		tmp = x + (x + (y - x))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) * z)
	tmp = 0.0
	if (z <= -5.6e-50)
		tmp = t_0;
	elseif (z <= 0.000115)
		tmp = Float64(x + Float64(x + Float64(y - x)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) * z;
	tmp = 0.0;
	if (z <= -5.6e-50)
		tmp = t_0;
	elseif (z <= 0.000115)
		tmp = x + (x + (y - x));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -5.6e-50], t$95$0, If[LessEqual[z, 0.000115], N[(x + N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5999999999999996e-50 or 1.15e-4 < z

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot z\right) + y \cdot z} \]

   5. Applied rewrites 96.8%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot z} \]

   if -5.5999999999999996e-50 < z < 1.15e-4

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(-1 \cdot \left(x \cdot z\right) + y \cdot z\right)} \]

   5. Applied rewrites 3.7%

      \[\leadsto x + \color{blue}{\left(y - x\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto x + y \]

   8. Applied rewrites 51.3%

      \[\leadsto x + \left(x + \color{blue}{\left(y - x\right)}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 65.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \left(y - x\right) \cdot z \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - x\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot z\right) + y \cdot z} \]

5. Applied rewrites 64.0%

   \[\leadsto \color{blue}{\left(y - x\right) \cdot z} \]
6. Add Preprocessing

Alternative 4: 3.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \end{array} \]

FPCore

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

C

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

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 - x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - x\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto x + \color{blue}{\left(-1 \cdot \left(x \cdot z\right) + y \cdot z\right)} \]

5. Applied rewrites 3.3%

   \[\leadsto x + \color{blue}{\left(y - x\right)} \]
6. Add Preprocessing

Alternative 5: 3.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ y - x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- y x))

C

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

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 - x
end function

Java

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

Python

def code(x, y, z):
	return y - x

Julia

function code(x, y, z)
	return Float64(y - x)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - x\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot z\right) + y \cdot z} \]

5. Applied rewrites 64.0%

   \[\leadsto \color{blue}{\left(y - x\right) \cdot z} \]

6. Taylor expanded in x around 0

   \[\leadsto -1 \cdot \left(x \cdot z\right) + \color{blue}{y \cdot z} \]

8. Applied rewrites 3.3%

   \[\leadsto y - \color{blue}{x} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  :pre (TRUE)
  (+ x (* (- y x) z)))