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

Percentage Accurate: 100.0% → 100.0%

Time: 2.4s

Alternatives: 6

Speedup: 1.0×

• 20.1% 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: 61.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+134}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+32}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -52000000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-96}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+206}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+226}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= z -1e+134)
     t_0
     (if (<= z -8.5e+32)
       (* y z)
       (if (<= z -52000000000000.0)
         t_0
         (if (<= z -2.3e-96)
           (* y z)
           (if (<= z 1.02e-26)
             x
             (if (<= z 2.55e+206)
               (* y z)
               (if (<= z 6.4e+226) t_0 (* y z))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -1e+134) {
		tmp = t_0;
	} else if (z <= -8.5e+32) {
		tmp = y * z;
	} else if (z <= -52000000000000.0) {
		tmp = t_0;
	} else if (z <= -2.3e-96) {
		tmp = y * z;
	} else if (z <= 1.02e-26) {
		tmp = x;
	} else if (z <= 2.55e+206) {
		tmp = y * z;
	} else if (z <= 6.4e+226) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = z * -x
    if (z <= (-1d+134)) then
        tmp = t_0
    else if (z <= (-8.5d+32)) then
        tmp = y * z
    else if (z <= (-52000000000000.0d0)) then
        tmp = t_0
    else if (z <= (-2.3d-96)) then
        tmp = y * z
    else if (z <= 1.02d-26) then
        tmp = x
    else if (z <= 2.55d+206) then
        tmp = y * z
    else if (z <= 6.4d+226) then
        tmp = t_0
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -1e+134) {
		tmp = t_0;
	} else if (z <= -8.5e+32) {
		tmp = y * z;
	} else if (z <= -52000000000000.0) {
		tmp = t_0;
	} else if (z <= -2.3e-96) {
		tmp = y * z;
	} else if (z <= 1.02e-26) {
		tmp = x;
	} else if (z <= 2.55e+206) {
		tmp = y * z;
	} else if (z <= 6.4e+226) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if z <= -1e+134:
		tmp = t_0
	elif z <= -8.5e+32:
		tmp = y * z
	elif z <= -52000000000000.0:
		tmp = t_0
	elif z <= -2.3e-96:
		tmp = y * z
	elif z <= 1.02e-26:
		tmp = x
	elif z <= 2.55e+206:
		tmp = y * z
	elif z <= 6.4e+226:
		tmp = t_0
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (z <= -1e+134)
		tmp = t_0;
	elseif (z <= -8.5e+32)
		tmp = Float64(y * z);
	elseif (z <= -52000000000000.0)
		tmp = t_0;
	elseif (z <= -2.3e-96)
		tmp = Float64(y * z);
	elseif (z <= 1.02e-26)
		tmp = x;
	elseif (z <= 2.55e+206)
		tmp = Float64(y * z);
	elseif (z <= 6.4e+226)
		tmp = t_0;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (z <= -1e+134)
		tmp = t_0;
	elseif (z <= -8.5e+32)
		tmp = y * z;
	elseif (z <= -52000000000000.0)
		tmp = t_0;
	elseif (z <= -2.3e-96)
		tmp = y * z;
	elseif (z <= 1.02e-26)
		tmp = x;
	elseif (z <= 2.55e+206)
		tmp = y * z;
	elseif (z <= 6.4e+226)
		tmp = t_0;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[z, -1e+134], t$95$0, If[LessEqual[z, -8.5e+32], N[(y * z), $MachinePrecision], If[LessEqual[z, -52000000000000.0], t$95$0, If[LessEqual[z, -2.3e-96], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.02e-26], x, If[LessEqual[z, 2.55e+206], N[(y * z), $MachinePrecision], If[LessEqual[z, 6.4e+226], t$95$0, N[(y * z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.99999999999999921e133 or -8.4999999999999998e32 < z < -5.2e13 or 2.5500000000000002e206 < z < 6.39999999999999954e226

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 74.7%

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

      1. distribute-rgt1-in 74.7%

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

      2. mul-1-neg 74.7%

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

      3. cancel-sign-sub-inv 74.7%

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

   4. Simplified 74.7%

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

   5. Taylor expanded in z around inf 74.4%

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

      1. mul-1-neg 74.4%

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

      2. distribute-rgt-neg-in 74.4%

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

   7. Simplified 74.4%

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

   if -9.99999999999999921e133 < z < -8.4999999999999998e32 or -5.2e13 < z < -2.3e-96 or 1.02e-26 < z < 2.5500000000000002e206 or 6.39999999999999954e226 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 62.1%

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

   if -2.3e-96 < z < 1.02e-26

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 77.0%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+134}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+32}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -52000000000000:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-96}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+206}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+226}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-93} \lor \neg \left(z \leq 1.05 \cdot 10^{-26}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.9e-93) (not (<= z 1.05e-26))) (* (- y x) z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.9e-93) || !(z <= 1.05e-26)) {
		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 <= (-5.9d-93)) .or. (.not. (z <= 1.05d-26))) 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 <= -5.9e-93) || !(z <= 1.05e-26)) {
		tmp = (y - x) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.9e-93) or not (z <= 1.05e-26):
		tmp = (y - x) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.9e-93) || !(z <= 1.05e-26))
		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 <= -5.9e-93) || ~((z <= 1.05e-26)))
		tmp = (y - x) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.9e-93], N[Not[LessEqual[z, 1.05e-26]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.9e-93 or 1.05000000000000004e-26 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 93.1%

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

   if -5.9e-93 < z < 1.05000000000000004e-26

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 77.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-93} \lor \neg \left(z \leq 1.05 \cdot 10^{-26}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 62.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-93}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.7e-93) (* y z) (if (<= z 1.05e-26) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.7e-93) {
		tmp = y * z;
	} else if (z <= 1.05e-26) {
		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 <= (-3.7d-93)) then
        tmp = y * z
    else if (z <= 1.05d-26) 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 <= -3.7e-93) {
		tmp = y * z;
	} else if (z <= 1.05e-26) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.7e-93:
		tmp = y * z
	elif z <= 1.05e-26:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.7e-93)
		tmp = Float64(y * z);
	elseif (z <= 1.05e-26)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.7e-93)
		tmp = y * z;
	elseif (z <= 1.05e-26)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.7e-93], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.05e-26], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.70000000000000002e-93 or 1.05000000000000004e-26 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 51.3%

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

   if -3.70000000000000002e-93 < z < 1.05000000000000004e-26

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 77.0%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-93}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5: 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 6: 37.2% 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 35.6%

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

3. Final simplification 35.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023252 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))