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

Percentage Accurate: 100.0% → 100.0%

Time: 3.6s

Alternatives: 8

Speedup: 1.0×

• 20.3% 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: 61.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+149}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.032:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+126}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+144}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -4e+149)
     (* y z)
     (if (<= z -1.0)
       t_0
       (if (<= z 0.032)
         x
         (if (<= z 1.5e+126) (* y z) (if (<= z 1.1e+144) t_0 (* y z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -4e+149) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 0.032) {
		tmp = x;
	} else if (z <= 1.5e+126) {
		tmp = y * z;
	} else if (z <= 1.1e+144) {
		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 = x * -z
    if (z <= (-4d+149)) then
        tmp = y * z
    else if (z <= (-1.0d0)) then
        tmp = t_0
    else if (z <= 0.032d0) then
        tmp = x
    else if (z <= 1.5d+126) then
        tmp = y * z
    else if (z <= 1.1d+144) 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 = x * -z;
	double tmp;
	if (z <= -4e+149) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 0.032) {
		tmp = x;
	} else if (z <= 1.5e+126) {
		tmp = y * z;
	} else if (z <= 1.1e+144) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -4e+149:
		tmp = y * z
	elif z <= -1.0:
		tmp = t_0
	elif z <= 0.032:
		tmp = x
	elif z <= 1.5e+126:
		tmp = y * z
	elif z <= 1.1e+144:
		tmp = t_0
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -4e+149)
		tmp = Float64(y * z);
	elseif (z <= -1.0)
		tmp = t_0;
	elseif (z <= 0.032)
		tmp = x;
	elseif (z <= 1.5e+126)
		tmp = Float64(y * z);
	elseif (z <= 1.1e+144)
		tmp = t_0;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (z <= -4e+149)
		tmp = y * z;
	elseif (z <= -1.0)
		tmp = t_0;
	elseif (z <= 0.032)
		tmp = x;
	elseif (z <= 1.5e+126)
		tmp = y * z;
	elseif (z <= 1.1e+144)
		tmp = t_0;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -4e+149], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.0], t$95$0, If[LessEqual[z, 0.032], x, If[LessEqual[z, 1.5e+126], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.1e+144], t$95$0, N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0000000000000002e149 or 0.032000000000000001 < z < 1.5000000000000001e126 or 1.09999999999999994e144 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 98.3%

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

   3. Taylor expanded in y around inf 67.3%

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

      1. *-commutative 67.3%

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

   5. Simplified 67.3%

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

   if -4.0000000000000002e149 < z < -1 or 1.5000000000000001e126 < z < 1.09999999999999994e144

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 95.0%

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

   3. Taylor expanded in y around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. distribute-rgt-neg-out 69.2%

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

   5. Simplified 69.2%

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

   if -1 < z < 0.032000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 71.1%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+149}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 0.032:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+126}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-24} \lor \neg \left(z \leq 54000000000\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.6e-24) (not (<= z 54000000000.0)))
   (* (- y x) z)
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.6e-24) || !(z <= 54000000000.0)) {
		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 <= (-2.6d-24)) .or. (.not. (z <= 54000000000.0d0))) 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 <= -2.6e-24) || !(z <= 54000000000.0)) {
		tmp = (y - x) * z;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.6e-24) or not (z <= 54000000000.0):
		tmp = (y - x) * z
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.6e-24) || !(z <= 54000000000.0))
		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 <= -2.6e-24) || ~((z <= 54000000000.0)))
		tmp = (y - x) * z;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.6e-24], N[Not[LessEqual[z, 54000000000.0]], $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 < -2.6e-24 or 5.4e10 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 98.4%

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

   if -2.6e-24 < z < 5.4e10

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 73.2%

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

      1. distribute-rgt1-in 73.1%

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

      2. mul-1-neg 73.1%

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

      3. cancel-sign-sub-inv 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in x around 0 73.2%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-24} \lor \neg \left(z \leq 54000000000\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 4: 99.1% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		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 <= 1.0d0))) 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 <= 1.0)) {
		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 <= 1.0):
		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 <= 1.0))
		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 <= 1.0)))
		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, 1.0]], $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 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 97.3%

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

   if -1 < z < 1

   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 29.9%

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

   4. Simplified 99.2%

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

4. Final simplification 98.2%

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

Alternative 5: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+33}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.4e+33) (* y z) (if (<= y 1.55e+46) (* x (- 1.0 z)) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.4e+33) {
		tmp = y * z;
	} else if (y <= 1.55e+46) {
		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 <= (-6.4d+33)) then
        tmp = y * z
    else if (y <= 1.55d+46) 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 <= -6.4e+33) {
		tmp = y * z;
	} else if (y <= 1.55e+46) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.4e+33:
		tmp = y * z
	elif y <= 1.55e+46:
		tmp = x * (1.0 - z)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.4e+33)
		tmp = Float64(y * z);
	elseif (y <= 1.55e+46)
		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 <= -6.4e+33)
		tmp = y * z;
	elseif (y <= 1.55e+46)
		tmp = x * (1.0 - z);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.4e+33], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.55e+46], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.40000000000000034e33 or 1.54999999999999988e46 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 85.6%

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

   3. Taylor expanded in y around inf 80.3%

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

      1. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   if -6.40000000000000034e33 < y < 1.54999999999999988e46

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 84.3%

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

      1. distribute-rgt1-in 84.3%

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

      2. mul-1-neg 84.3%

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

      3. cancel-sign-sub-inv 84.3%

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

   4. Simplified 84.3%

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

   5. Taylor expanded in x around 0 84.3%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+33}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 6: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-11}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 0.032:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.1e-11) (* y z) (if (<= z 0.032) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.1e-11) {
		tmp = y * z;
	} else if (z <= 0.032) {
		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 <= (-3.1d-11)) then
        tmp = y * z
    else if (z <= 0.032d0) 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 <= -3.1e-11) {
		tmp = y * z;
	} else if (z <= 0.032) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.1e-11:
		tmp = y * z
	elif z <= 0.032:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.1e-11)
		tmp = Float64(y * z);
	elseif (z <= 0.032)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.1e-11)
		tmp = y * z;
	elseif (z <= 0.032)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.1e-11], N[(y * z), $MachinePrecision], If[LessEqual[z, 0.032], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.10000000000000028e-11 or 0.032000000000000001 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 97.3%

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

   3. Taylor expanded in y around inf 56.8%

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

      1. *-commutative 56.8%

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

   5. Simplified 56.8%

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

   if -3.10000000000000028e-11 < z < 0.032000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 71.7%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-11}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 0.032:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

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. Final simplification 100.0%

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

Alternative 8: 37.1% 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 z around 0 35.5%

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

3. Final simplification 35.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023200 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))