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

Percentage Accurate: 100.0% → 100.0%

Time: 5.6s

Alternatives: 8

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, 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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 60.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+256}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+213}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+46}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -920 \lor \neg \left(z \leq 0.0068\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -2.8e+256)
     (* y z)
     (if (<= z -2.3e+213)
       t_0
       (if (<= z -7.5e+46)
         (* y z)
         (if (or (<= z -920.0) (not (<= z 0.0068))) t_0 x))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -2.8e+256) {
		tmp = y * z;
	} else if (z <= -2.3e+213) {
		tmp = t_0;
	} else if (z <= -7.5e+46) {
		tmp = y * z;
	} else if ((z <= -920.0) || !(z <= 0.0068)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * -z
    if (z <= (-2.8d+256)) then
        tmp = y * z
    else if (z <= (-2.3d+213)) then
        tmp = t_0
    else if (z <= (-7.5d+46)) then
        tmp = y * z
    else if ((z <= (-920.0d0)) .or. (.not. (z <= 0.0068d0))) then
        tmp = t_0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -2.8e+256) {
		tmp = y * z;
	} else if (z <= -2.3e+213) {
		tmp = t_0;
	} else if (z <= -7.5e+46) {
		tmp = y * z;
	} else if ((z <= -920.0) || !(z <= 0.0068)) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -2.8e+256:
		tmp = y * z
	elif z <= -2.3e+213:
		tmp = t_0
	elif z <= -7.5e+46:
		tmp = y * z
	elif (z <= -920.0) or not (z <= 0.0068):
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -2.8e+256)
		tmp = Float64(y * z);
	elseif (z <= -2.3e+213)
		tmp = t_0;
	elseif (z <= -7.5e+46)
		tmp = Float64(y * z);
	elseif ((z <= -920.0) || !(z <= 0.0068))
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (z <= -2.8e+256)
		tmp = y * z;
	elseif (z <= -2.3e+213)
		tmp = t_0;
	elseif (z <= -7.5e+46)
		tmp = y * z;
	elseif ((z <= -920.0) || ~((z <= 0.0068)))
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -2.8e+256], N[(y * z), $MachinePrecision], If[LessEqual[z, -2.3e+213], t$95$0, If[LessEqual[z, -7.5e+46], N[(y * z), $MachinePrecision], If[Or[LessEqual[z, -920.0], N[Not[LessEqual[z, 0.0068]], $MachinePrecision]], t$95$0, x]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.79999999999999988e256 or -2.29999999999999998e213 < z < -7.5000000000000003e46

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 73.4%

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

   if -2.79999999999999988e256 < z < -2.29999999999999998e213 or -7.5000000000000003e46 < z < -920 or 0.00679999999999999962 < z

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 98.7%

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

   4. Applied egg-rr 98.7%

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

   5. Taylor expanded in y around 0 61.0%

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

      1. associate-*r* 61.0%

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

      2. mul-1-neg 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in z around inf 59.8%

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

      1. mul-1-neg 59.8%

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

      2. *-commutative 59.8%

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

      3. distribute-rgt-neg-in 59.8%

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

   10. Simplified 59.8%

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

   if -920 < z < 0.00679999999999999962

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 70.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+256}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+213}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+46}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -920 \lor \neg \left(z \leq 0.0068\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+50} \lor \neg \left(y \leq 3.4 \cdot 10^{+167}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.6e+50) (not (<= y 3.4e+167))) (* y z) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.6e+50) || !(y <= 3.4e+167)) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - 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 <= (-3.6d+50)) .or. (.not. (y <= 3.4d+167))) then
        tmp = y * z
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.6e+50) || !(y <= 3.4e+167)) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.6e+50) or not (y <= 3.4e+167):
		tmp = y * z
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.6e+50) || !(y <= 3.4e+167))
		tmp = Float64(y * z);
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.6e+50) || ~((y <= 3.4e+167)))
		tmp = y * z;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.6e+50], N[Not[LessEqual[y, 3.4e+167]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.59999999999999986e50 or 3.4e167 < y

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 75.9%

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

   if -3.59999999999999986e50 < y < 3.4e167

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

   5. Simplified 80.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+50} \lor \neg \left(y \leq 3.4 \cdot 10^{+167}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.08 \lor \neg \left(z \leq 0.00034\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.08) (not (<= z 0.00034))) (* (- y x) z) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.08) || !(z <= 0.00034)) {
		tmp = (y - x) * z;
	} else {
		tmp = x * (1.0 - 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 <= (-0.08d0)) .or. (.not. (z <= 0.00034d0))) then
        tmp = (y - x) * z
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.08) || !(z <= 0.00034)) {
		tmp = (y - x) * z;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.08) or not (z <= 0.00034):
		tmp = (y - x) * z
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.08) || !(z <= 0.00034))
		tmp = Float64(Float64(y - x) * z);
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.08) || ~((z <= 0.00034)))
		tmp = (y - x) * z;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.08], N[Not[LessEqual[z, 0.00034]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0800000000000000017 or 3.4e-4 < z

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.0%

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

   if -0.0800000000000000017 < z < 3.4e-4

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 72.6%

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

      1. mul-1-neg 72.6%

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

      2. unsub-neg 72.6%

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

   5. Simplified 72.6%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.08 \lor \neg \left(z \leq 0.00034\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2700000 \lor \neg \left(z \leq 0.0068\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2700000.0) (not (<= z 0.0068))) (* (- y x) z) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2700000.0) || !(z <= 0.0068)) {
		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 <= (-2700000.0d0)) .or. (.not. (z <= 0.0068d0))) 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 <= -2700000.0) || !(z <= 0.0068)) {
		tmp = (y - x) * z;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2700000.0) or not (z <= 0.0068):
		tmp = (y - x) * z
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2700000.0) || !(z <= 0.0068))
		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 <= -2700000.0) || ~((z <= 0.0068)))
		tmp = (y - x) * z;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2700000.0], N[Not[LessEqual[z, 0.0068]], $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 < -2.7e6 or 0.00679999999999999962 < z

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.0%

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

   if -2.7e6 < z < 0.00679999999999999962

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf 99.2%

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

      1. *-commutative 99.2%

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

   7. Simplified 99.2%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2700000 \lor \neg \left(z \leq 0.0068\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.08 \lor \neg \left(z \leq 2.4 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.08) (not (<= z 2.4e-9))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.08) || !(z <= 2.4e-9)) {
		tmp = y * 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 <= (-0.08d0)) .or. (.not. (z <= 2.4d-9))) then
        tmp = y * 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 <= -0.08) || !(z <= 2.4e-9)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.08) or not (z <= 2.4e-9):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.08) || !(z <= 2.4e-9))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.08) || ~((z <= 2.4e-9)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.08], N[Not[LessEqual[z, 2.4e-9]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.0800000000000000017 or 2.4e-9 < z

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 50.6%

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

   if -0.0800000000000000017 < z < 2.4e-9

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 71.8%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.08 \lor \neg \left(z \leq 2.4 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto x + \left(y - x\right) \cdot z \]
4. Add Preprocessing

Alternative 8: 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. Add Preprocessing

3. Taylor expanded in z around 0 40.4%

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

4. Final simplification 40.4%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024026 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))