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

Percentage Accurate: 100.0% → 100.0%

Time: 2.9s

Alternatives: 5

Speedup: 1.0×

• 20.6% 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: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{-49} \lor \neg \left(x \leq 9.5 \cdot 10^{+58}\right):\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.1e-49) (not (<= x 9.5e+58))) (- x (* x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.1e-49) || !(x <= 9.5e+58)) {
		tmp = x - (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 ((x <= (-6.1d-49)) .or. (.not. (x <= 9.5d+58))) then
        tmp = x - (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 ((x <= -6.1e-49) || !(x <= 9.5e+58)) {
		tmp = x - (x * z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.1e-49) or not (x <= 9.5e+58):
		tmp = x - (x * z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.1e-49) || !(x <= 9.5e+58))
		tmp = Float64(x - Float64(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 ((x <= -6.1e-49) || ~((x <= 9.5e+58)))
		tmp = x - (x * z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.1e-49], N[Not[LessEqual[x, 9.5e+58]], $MachinePrecision]], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.09999999999999963e-49 or 9.5000000000000002e58 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 88.3%

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

      1. mul-1-neg 88.3%

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

      2. distribute-rgt-neg-out 88.3%

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

   4. Simplified 88.3%

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

   5. Taylor expanded in x around 0 88.3%

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

      1. neg-mul-1 88.3%

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

      2. distribute-rgt1-in 88.3%

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

      3. cancel-sign-sub-inv 88.3%

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

   7. Simplified 88.3%

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

   if -6.09999999999999963e-49 < x < 9.5000000000000002e58

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 89.7%

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

      1. *-commutative 89.7%

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

   4. Simplified 89.7%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{-49} \lor \neg \left(x \leq 9.5 \cdot 10^{+58}\right):\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 3: 61.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.41 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.41) (not (<= z 1.0))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.41) || !(z <= 1.0)) {
		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 <= (-0.41d0)) .or. (.not. (z <= 1.0d0))) 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 <= -0.41) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.41) or not (z <= 1.0):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.41) || !(z <= 1.0))
		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 <= -0.41) || ~((z <= 1.0)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.41], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.409999999999999976 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 53.9%

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

      1. mul-1-neg 53.9%

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

      2. distribute-rgt-neg-out 53.9%

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

   4. Simplified 53.9%

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

   5. Taylor expanded in z around inf 53.7%

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

      1. mul-1-neg 53.7%

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

      2. distribute-rgt-neg-in 53.7%

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

   7. Simplified 53.7%

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

   if -0.409999999999999976 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. distribute-rgt-neg-out 68.8%

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

   4. Simplified 68.8%

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

   5. Taylor expanded in z around 0 67.7%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.41 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 300000000000:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 300000000000.0) (+ x (* y z)) (* x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 300000000000.0) {
		tmp = x + (y * z);
	} else {
		tmp = 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 (z <= 300000000000.0d0) then
        tmp = x + (y * z)
    else
        tmp = x * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 300000000000.0) {
		tmp = x + (y * z);
	} else {
		tmp = x * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 300000000000.0:
		tmp = x + (y * z)
	else:
		tmp = x * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 300000000000.0)
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 300000000000.0)
		tmp = x + (y * z);
	else
		tmp = x * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 300000000000.0], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3e11

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 86.9%

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

      1. *-commutative 86.9%

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

   4. Simplified 86.9%

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

   if 3e11 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. distribute-rgt-neg-out 58.4%

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

   4. Simplified 58.4%

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

   5. Taylor expanded in z around inf 58.0%

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

      1. mul-1-neg 58.0%

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

      2. distribute-rgt-neg-in 58.0%

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

   7. Simplified 58.0%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 300000000000:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 5: 36.1% 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 y around 0 62.1%

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

   1. mul-1-neg 62.1%

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

   2. distribute-rgt-neg-out 62.1%

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

4. Simplified 62.1%

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

5. Taylor expanded in z around 0 38.2%

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

6. Final simplification 38.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023185 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))