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

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

Alternatives: 7

Speedup: 1.0×

• 21.3% 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: 77.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+94} \lor \neg \left(y \leq 0.00017\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.5e+94) (not (<= y 0.00017))) (* (- y x) z) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e+94) || !(y <= 0.00017)) {
		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 ((y <= (-5.5d+94)) .or. (.not. (y <= 0.00017d0))) 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 ((y <= -5.5e+94) || !(y <= 0.00017)) {
		tmp = (y - x) * z;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.5e+94) or not (y <= 0.00017):
		tmp = (y - x) * z
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.5e+94) || !(y <= 0.00017))
		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 ((y <= -5.5e+94) || ~((y <= 0.00017)))
		tmp = (y - x) * z;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.5e+94], N[Not[LessEqual[y, 0.00017]], $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 y < -5.4999999999999997e94 or 1.7e-4 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 84.3%

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

   if -5.4999999999999997e94 < y < 1.7e-4

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 81.0%

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

      3. associate-*r/ 76.5%

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

      4. +-commutative 76.5%

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

   3. Applied egg-rr 76.5%

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

      1. associate-/l* 80.9%

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

      2. difference-of-squares 80.9%

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

      3. +-commutative 80.9%

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

      4. associate-/r* 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around inf 87.6%

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

      1. mul-1-neg 87.6%

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

      2. sub-neg 87.6%

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

   8. Simplified 87.6%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+94} \lor \neg \left(y \leq 0.00017\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 3: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.3 \cdot 10^{-8}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.3e-8))) (* (- y x) z) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.3e-8)) {
		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 <= (-1.0d0)) .or. (.not. (z <= 1.3d-8))) 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 <= -1.0) || !(z <= 1.3e-8)) {
		tmp = (y - x) * z;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.3e-8):
		tmp = (y - x) * z
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.3e-8))
		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 <= -1.0) || ~((z <= 1.3e-8)))
		tmp = (y - x) * z;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.3e-8]], $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 < -1 or 1.3000000000000001e-8 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 97.8%

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

   if -1 < z < 1.3000000000000001e-8

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 59.4%

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

      3. associate-*r/ 57.6%

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

      4. +-commutative 57.6%

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

   3. Applied egg-rr 57.6%

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

      1. associate-/l* 59.4%

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

      2. difference-of-squares 59.7%

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

      3. +-commutative 59.7%

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

      4. associate-/r* 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around inf 99.4%

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

      1. *-commutative 99.4%

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

   8. Simplified 99.4%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.3 \cdot 10^{-8}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 4: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+94}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.8e+94) (* y z) (if (<= y 9.6e+34) (* x (- 1.0 z)) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.8e+94) {
		tmp = y * z;
	} else if (y <= 9.6e+34) {
		tmp = x * (1.0 - z);
	} 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 (y <= (-9.8d+94)) then
        tmp = y * z
    else if (y <= 9.6d+34) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.8e+94) {
		tmp = y * z;
	} else if (y <= 9.6e+34) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.8e+94:
		tmp = y * z
	elif y <= 9.6e+34:
		tmp = x * (1.0 - z)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.8e+94)
		tmp = Float64(y * z);
	elseif (y <= 9.6e+34)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.8e+94)
		tmp = y * z;
	elseif (y <= 9.6e+34)
		tmp = x * (1.0 - z);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.8e+94], N[(y * z), $MachinePrecision], If[LessEqual[y, 9.6e+34], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.7999999999999998e94 or 9.59999999999999948e34 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.8%

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

   if -9.7999999999999998e94 < y < 9.59999999999999948e34

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 81.6%

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

      3. associate-*r/ 77.4%

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

      4. +-commutative 77.4%

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

   3. Applied egg-rr 77.4%

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

      1. associate-/l* 81.5%

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

      2. difference-of-squares 81.5%

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

      3. +-commutative 81.5%

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

      4. associate-/r* 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around inf 87.0%

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

      1. mul-1-neg 87.0%

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

      2. sub-neg 87.0%

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

   8. Simplified 87.0%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+94}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5: 54.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+94}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 700:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.6e+94) (* y z) (if (<= y 700.0) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.6e+94) {
		tmp = y * z;
	} else if (y <= 700.0) {
		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 (y <= (-4.6d+94)) then
        tmp = y * z
    else if (y <= 700.0d0) 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 (y <= -4.6e+94) {
		tmp = y * z;
	} else if (y <= 700.0) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.6e+94:
		tmp = y * z
	elif y <= 700.0:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.6e+94)
		tmp = Float64(y * z);
	elseif (y <= 700.0)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.6e+94)
		tmp = y * z;
	elseif (y <= 700.0)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.6e+94], N[(y * z), $MachinePrecision], If[LessEqual[y, 700.0], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5999999999999999e94 or 700 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.4%

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

   if -4.5999999999999999e94 < y < 700

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 46.1%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+94}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 700:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 6: 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 7: 36.8% 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 34.4%

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

3. Final simplification 34.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))