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

Percentage Accurate: 100.0% → 100.0%

Time: 2.4s

Alternatives: 7

Speedup: 1.0×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - x\right) \cdot z \]
2. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 61.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-7}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+44}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5e-7)
   (* y z)
   (if (<= z 3e-71) x (if (<= z 3.35e+44) (* y z) (* z (- x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e-7) {
		tmp = y * z;
	} else if (z <= 3e-71) {
		tmp = x;
	} else if (z <= 3.35e+44) {
		tmp = y * z;
	} else {
		tmp = z * -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
    real(8) :: tmp
    if (z <= (-5d-7)) then
        tmp = y * z
    else if (z <= 3d-71) then
        tmp = x
    else if (z <= 3.35d+44) then
        tmp = y * z
    else
        tmp = z * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e-7) {
		tmp = y * z;
	} else if (z <= 3e-71) {
		tmp = x;
	} else if (z <= 3.35e+44) {
		tmp = y * z;
	} else {
		tmp = z * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5e-7:
		tmp = y * z
	elif z <= 3e-71:
		tmp = x
	elif z <= 3.35e+44:
		tmp = y * z
	else:
		tmp = z * -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5e-7)
		tmp = Float64(y * z);
	elseif (z <= 3e-71)
		tmp = x;
	elseif (z <= 3.35e+44)
		tmp = Float64(y * z);
	else
		tmp = Float64(z * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5e-7)
		tmp = y * z;
	elseif (z <= 3e-71)
		tmp = x;
	elseif (z <= 3.35e+44)
		tmp = y * z;
	else
		tmp = z * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5e-7], N[(y * z), $MachinePrecision], If[LessEqual[z, 3e-71], x, If[LessEqual[z, 3.35e+44], N[(y * z), $MachinePrecision], N[(z * (-x)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.99999999999999977e-7 or 3.0000000000000001e-71 < z < 3.35000000000000018e44

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in z around inf 93.5%

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

   3. Taylor expanded in y around inf 56.4%

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

      1. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   if -4.99999999999999977e-7 < z < 3.0000000000000001e-71

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in z around 0 76.9%

      \[\leadsto \color{blue}{x} \]

   if 3.35000000000000018e44 < z

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in z around inf 100.0%

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

   3. Taylor expanded in y around 0 61.2%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot x\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 61.2%

         \[\leadsto \color{blue}{-z \cdot x} \]

      2. distribute-rgt-neg-out 61.2%

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

   5. Simplified 61.2%

      \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-7}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+44}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-7} \lor \neg \left(z \leq 2.2 \cdot 10^{-71}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.8e-7) (not (<= z 2.2e-71))) (* (- y x) z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e-7) || !(z <= 2.2e-71)) {
		tmp = (y - x) * 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
    real(8) :: tmp
    if ((z <= (-4.8d-7)) .or. (.not. (z <= 2.2d-71))) then
        tmp = (y - x) * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e-7) || !(z <= 2.2e-71)) {
		tmp = (y - x) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.8e-7) or not (z <= 2.2e-71):
		tmp = (y - x) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.8e-7) || !(z <= 2.2e-71))
		tmp = Float64(Float64(y - x) * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.8e-7) || ~((z <= 2.2e-71)))
		tmp = (y - x) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.8e-7], N[Not[LessEqual[z, 2.2e-71]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999957e-7 or 2.19999999999999997e-71 < z

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in z around inf 96.4%

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

   if -4.79999999999999957e-7 < z < 2.19999999999999997e-71

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in z around 0 76.9%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-7} \lor \neg \left(z \leq 2.2 \cdot 10^{-71}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1100000000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1100000000000.0) (not (<= z 1.0)))
   (* (- y x) z)
   (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1100000000000.0) || !(z <= 1.0)) {
		tmp = (y - x) * z;
	} else {
		tmp = x + (y * z);
	}
	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) :: tmp
    if ((z <= (-1100000000000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (y - x) * z
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1100000000000.0) || !(z <= 1.0)) {
		tmp = (y - x) * z;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1100000000000.0) or not (z <= 1.0):
		tmp = (y - x) * z
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1100000000000.0) || !(z <= 1.0))
		tmp = Float64(Float64(y - x) * z);
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1100000000000.0) || ~((z <= 1.0)))
		tmp = (y - x) * z;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1100000000000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e12 or 1 < z

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in z around inf 100.0%

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

   if -1.1e12 < z < 1

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in y around inf 97.8%

      \[\leadsto x + \color{blue}{y \cdot z} \]
   3. Step-by-step derivation

      1. *-commutative 29.1%

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

   4. Simplified 97.8%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1100000000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 5: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-7}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.6e-7) (* y z) (if (<= z 2.6e-71) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.6e-7) {
		tmp = y * z;
	} else if (z <= 2.6e-71) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	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) :: tmp
    if (z <= (-7.6d-7)) then
        tmp = y * z
    else if (z <= 2.6d-71) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.6e-7) {
		tmp = y * z;
	} else if (z <= 2.6e-71) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.6e-7:
		tmp = y * z
	elif z <= 2.6e-71:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.6e-7)
		tmp = Float64(y * z);
	elseif (z <= 2.6e-71)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.6e-7)
		tmp = y * z;
	elseif (z <= 2.6e-71)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.6e-7], N[(y * z), $MachinePrecision], If[LessEqual[z, 2.6e-71], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.60000000000000029e-7 or 2.5999999999999999e-71 < z

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in z around inf 96.4%

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

   3. Taylor expanded in y around inf 51.9%

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

      1. *-commutative 51.9%

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

   5. Simplified 51.9%

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

   if -7.60000000000000029e-7 < z < 2.5999999999999999e-71

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in z around 0 76.9%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-7}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 6: 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. Final simplification 100.0%

   \[\leadsto x + \left(y - x\right) \cdot z \]

Alternative 7: 37.1% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

   \[x + \left(y - x\right) \cdot z \]

2. Taylor expanded in z around 0 38.2%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 38.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023171 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))