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

Percentage Accurate: 100.0% → 100.0%

Time: 2.4s

Alternatives: 5

Speedup: 1.0×

• 21.8% 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, 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 2: 75.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+20} \lor \neg \left(z \leq 3.9 \cdot 10^{+60}\right) \land \left(z \leq 5.5 \cdot 10^{+137} \lor \neg \left(z \leq 1.85 \cdot 10^{+213}\right)\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.6e+20)
         (and (not (<= z 3.9e+60))
              (or (<= z 5.5e+137) (not (<= z 1.85e+213)))))
   (* x (- z))
   (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.6e+20) || (!(z <= 3.9e+60) && ((z <= 5.5e+137) || !(z <= 1.85e+213)))) {
		tmp = 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 <= (-5.6d+20)) .or. (.not. (z <= 3.9d+60)) .and. (z <= 5.5d+137) .or. (.not. (z <= 1.85d+213))) then
        tmp = 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 <= -5.6e+20) || (!(z <= 3.9e+60) && ((z <= 5.5e+137) || !(z <= 1.85e+213)))) {
		tmp = x * -z;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.6e+20) or (not (z <= 3.9e+60) and ((z <= 5.5e+137) or not (z <= 1.85e+213))):
		tmp = x * -z
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.6e+20) || (!(z <= 3.9e+60) && ((z <= 5.5e+137) || !(z <= 1.85e+213))))
		tmp = Float64(x * Float64(-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 <= -5.6e+20) || (~((z <= 3.9e+60)) && ((z <= 5.5e+137) || ~((z <= 1.85e+213)))))
		tmp = x * -z;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.6e+20], And[N[Not[LessEqual[z, 3.9e+60]], $MachinePrecision], Or[LessEqual[z, 5.5e+137], N[Not[LessEqual[z, 1.85e+213]], $MachinePrecision]]]], N[(x * (-z)), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.6e20 or 3.9000000000000003e60 < z < 5.5000000000000002e137 or 1.84999999999999996e213 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. distribute-rgt-neg-out 67.8%

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

   4. Simplified 67.8%

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

   5. Taylor expanded in z around inf 67.8%

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

      1. associate-*r* 67.8%

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

      2. mul-1-neg 67.8%

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

   7. Simplified 67.8%

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

   if -5.6e20 < z < 3.9000000000000003e60 or 5.5000000000000002e137 < z < 1.84999999999999996e213

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 93.6%

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

      1. *-commutative 93.6%

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

   4. Simplified 93.6%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+20} \lor \neg \left(z \leq 3.9 \cdot 10^{+60}\right) \land \left(z \leq 5.5 \cdot 10^{+137} \lor \neg \left(z \leq 1.85 \cdot 10^{+213}\right)\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 3: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-30} \lor \neg \left(y \leq 2.45 \cdot 10^{-8}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.2e-30) (not (<= y 2.45e-8))) (+ x (* y z)) (- x (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.2e-30) || !(y <= 2.45e-8)) {
		tmp = x + (y * z);
	} else {
		tmp = x - (x * 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 ((y <= (-9.2d-30)) .or. (.not. (y <= 2.45d-8))) then
        tmp = x + (y * z)
    else
        tmp = x - (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.2e-30) || !(y <= 2.45e-8)) {
		tmp = x + (y * z);
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.2e-30) or not (y <= 2.45e-8):
		tmp = x + (y * z)
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.2e-30) || !(y <= 2.45e-8))
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -9.2e-30) || ~((y <= 2.45e-8)))
		tmp = x + (y * z);
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9.2e-30], N[Not[LessEqual[y, 2.45e-8]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.19999999999999937e-30 or 2.4500000000000001e-8 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 89.2%

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

      1. *-commutative 89.2%

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

   4. Simplified 89.2%

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

   if -9.19999999999999937e-30 < y < 2.4500000000000001e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 92.0%

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

      1. mul-1-neg 92.0%

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

      2. distribute-rgt-neg-out 92.0%

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

   4. Simplified 92.0%

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

      1. distribute-rgt-neg-out 92.0%

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

      2. unsub-neg 92.0%

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

      3. *-commutative 92.0%

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

   6. Applied egg-rr 92.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-30} \lor \neg \left(y \leq 2.45 \cdot 10^{-8}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]

Alternative 4: 60.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 300000\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 300000.0))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 300000.0)) {
		tmp = 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 <= (-1.0d0)) .or. (.not. (z <= 300000.0d0))) then
        tmp = 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 <= -1.0) || !(z <= 300000.0)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 300000.0):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 300000.0))
		tmp = Float64(x * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 300000.0)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 300000.0]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 3e5 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 55.1%

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

      1. mul-1-neg 55.1%

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

      2. distribute-rgt-neg-out 55.1%

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

   4. Simplified 55.1%

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

   5. Taylor expanded in z around inf 54.3%

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

      1. associate-*r* 54.3%

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

      2. mul-1-neg 54.3%

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

   7. Simplified 54.3%

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

   if -1 < z < 3e5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. distribute-rgt-neg-out 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in z around 0 69.6%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 300000\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 35.9% 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 y around 0 62.6%

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

   1. mul-1-neg 62.6%

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

   2. distribute-rgt-neg-out 62.6%

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

4. Simplified 62.6%

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

5. Taylor expanded in z around 0 36.5%

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

6. Final simplification 36.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023195 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))