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

Percentage Accurate: 100.0% → 100.0%

Time: 7.7s

Alternatives: 6

Speedup: 1.0×

• 20.9% 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: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+198}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+50}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2060000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -0.115:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+87}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= z -2.2e+198)
     t_0
     (if (<= z -9e+50)
       (* y z)
       (if (<= z -2060000.0)
         t_0
         (if (<= z -0.115)
           (* y z)
           (if (<= z 1.65e-68) x (if (<= z 9.5e+87) (* y z) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -2.2e+198) {
		tmp = t_0;
	} else if (z <= -9e+50) {
		tmp = y * z;
	} else if (z <= -2060000.0) {
		tmp = t_0;
	} else if (z <= -0.115) {
		tmp = y * z;
	} else if (z <= 1.65e-68) {
		tmp = x;
	} else if (z <= 9.5e+87) {
		tmp = y * z;
	} 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 = z * -x
    if (z <= (-2.2d+198)) then
        tmp = t_0
    else if (z <= (-9d+50)) then
        tmp = y * z
    else if (z <= (-2060000.0d0)) then
        tmp = t_0
    else if (z <= (-0.115d0)) then
        tmp = y * z
    else if (z <= 1.65d-68) then
        tmp = x
    else if (z <= 9.5d+87) then
        tmp = y * z
    else
        tmp = t_0
    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 <= -2.2e+198) {
		tmp = t_0;
	} else if (z <= -9e+50) {
		tmp = y * z;
	} else if (z <= -2060000.0) {
		tmp = t_0;
	} else if (z <= -0.115) {
		tmp = y * z;
	} else if (z <= 1.65e-68) {
		tmp = x;
	} else if (z <= 9.5e+87) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if z <= -2.2e+198:
		tmp = t_0
	elif z <= -9e+50:
		tmp = y * z
	elif z <= -2060000.0:
		tmp = t_0
	elif z <= -0.115:
		tmp = y * z
	elif z <= 1.65e-68:
		tmp = x
	elif z <= 9.5e+87:
		tmp = y * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (z <= -2.2e+198)
		tmp = t_0;
	elseif (z <= -9e+50)
		tmp = Float64(y * z);
	elseif (z <= -2060000.0)
		tmp = t_0;
	elseif (z <= -0.115)
		tmp = Float64(y * z);
	elseif (z <= 1.65e-68)
		tmp = x;
	elseif (z <= 9.5e+87)
		tmp = Float64(y * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (z <= -2.2e+198)
		tmp = t_0;
	elseif (z <= -9e+50)
		tmp = y * z;
	elseif (z <= -2060000.0)
		tmp = t_0;
	elseif (z <= -0.115)
		tmp = y * z;
	elseif (z <= 1.65e-68)
		tmp = x;
	elseif (z <= 9.5e+87)
		tmp = y * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[z, -2.2e+198], t$95$0, If[LessEqual[z, -9e+50], N[(y * z), $MachinePrecision], If[LessEqual[z, -2060000.0], t$95$0, If[LessEqual[z, -0.115], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.65e-68], x, If[LessEqual[z, 9.5e+87], N[(y * z), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2e198 or -9.00000000000000027e50 < z < -2.06e6 or 9.4999999999999992e87 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. distribute-lft-neg-out 68.1%

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

      3. *-commutative 68.1%

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

   4. Simplified 68.1%

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

   5. Taylor expanded in z around inf 67.0%

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

      1. associate-*r* 67.0%

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

      2. mul-1-neg 67.0%

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

   7. Simplified 67.0%

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

   if -2.2e198 < z < -9.00000000000000027e50 or -2.06e6 < z < -0.115000000000000005 or 1.6499999999999999e-68 < z < 9.4999999999999992e87

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 76.5%

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

      1. *-commutative 76.5%

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

   4. Simplified 76.5%

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

   5. Taylor expanded in x around 0 72.0%

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

   if -0.115000000000000005 < z < 1.6499999999999999e-68

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.2%

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

      1. *-commutative 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in x around inf 78.3%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+198}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+50}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2060000:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -0.115:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+87}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+191} \lor \neg \left(z \leq 2.4 \cdot 10^{+82}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.9e+191) (not (<= z 2.4e+82))) (* z (- x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9e+191) || !(z <= 2.4e+82)) {
		tmp = z * -x;
	} 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 <= (-1.9d+191)) .or. (.not. (z <= 2.4d+82))) then
        tmp = z * -x
    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 <= -1.9e+191) || !(z <= 2.4e+82)) {
		tmp = z * -x;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.9e+191) or not (z <= 2.4e+82):
		tmp = z * -x
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.9e+191) || !(z <= 2.4e+82))
		tmp = Float64(z * Float64(-x));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.9e+191) || ~((z <= 2.4e+82)))
		tmp = z * -x;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.9e+191], N[Not[LessEqual[z, 2.4e+82]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e191 or 2.39999999999999998e82 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 66.1%

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

      1. mul-1-neg 66.1%

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

      2. distribute-lft-neg-out 66.1%

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

      3. *-commutative 66.1%

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

   4. Simplified 66.1%

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

   5. Taylor expanded in z around inf 66.1%

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

      1. associate-*r* 66.1%

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

      2. mul-1-neg 66.1%

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

   7. Simplified 66.1%

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

   if -1.8999999999999999e191 < z < 2.39999999999999998e82

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 89.6%

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

      1. *-commutative 89.6%

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

   4. Simplified 89.6%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+191} \lor \neg \left(z \leq 2.4 \cdot 10^{+82}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 4: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+23} \lor \neg \left(y \leq 1.08 \cdot 10^{-182}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.4e+23) (not (<= y 1.08e-182))) (+ x (* y z)) (- x (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.4e+23) || !(y <= 1.08e-182)) {
		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 <= (-5.4d+23)) .or. (.not. (y <= 1.08d-182))) 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 <= -5.4e+23) || !(y <= 1.08e-182)) {
		tmp = x + (y * z);
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.4e+23) or not (y <= 1.08e-182):
		tmp = x + (y * z)
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.4e+23) || !(y <= 1.08e-182))
		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 <= -5.4e+23) || ~((y <= 1.08e-182)))
		tmp = x + (y * z);
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.4e+23], N[Not[LessEqual[y, 1.08e-182]], $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 < -5.3999999999999997e23 or 1.08000000000000003e-182 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 87.9%

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

      1. *-commutative 87.9%

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

   4. Simplified 87.9%

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

   if -5.3999999999999997e23 < y < 1.08000000000000003e-182

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 90.7%

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

      1. mul-1-neg 90.7%

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

      2. distribute-lft-neg-out 90.7%

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

      3. *-commutative 90.7%

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

   4. Simplified 90.7%

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

      1. distribute-rgt-neg-out 90.7%

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

      2. unsub-neg 90.7%

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

      3. *-commutative 90.7%

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

   6. Applied egg-rr 90.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+23} \lor \neg \left(y \leq 1.08 \cdot 10^{-182}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]

Alternative 5: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.115:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.115) (* y z) (if (<= z 3.8e-69) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.115) {
		tmp = y * z;
	} else if (z <= 3.8e-69) {
		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 <= (-0.115d0)) then
        tmp = y * z
    else if (z <= 3.8d-69) 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 <= -0.115) {
		tmp = y * z;
	} else if (z <= 3.8e-69) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.115:
		tmp = y * z
	elif z <= 3.8e-69:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.115)
		tmp = Float64(y * z);
	elseif (z <= 3.8e-69)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.115)
		tmp = y * z;
	elseif (z <= 3.8e-69)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.115], N[(y * z), $MachinePrecision], If[LessEqual[z, 3.8e-69], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.115000000000000005 or 3.7999999999999998e-69 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 54.6%

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

      1. *-commutative 54.6%

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

   4. Simplified 54.6%

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

   5. Taylor expanded in x around 0 52.3%

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

   if -0.115000000000000005 < z < 3.7999999999999998e-69

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.2%

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

      1. *-commutative 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in x around inf 78.3%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.115:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 6: 36.9% 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 inf 76.6%

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

   1. *-commutative 76.6%

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

4. Simplified 76.6%

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

5. Taylor expanded in x around inf 41.1%

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

6. Final simplification 41.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))