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

Percentage Accurate: 100.0% → 100.0%

Time: 4.6s

Alternatives: 8

Speedup: 1.0×

• 21.2% 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: 61.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+156}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-10}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+44}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+280}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -7e+156)
     t_0
     (if (<= z -4.2e-10)
       (* y z)
       (if (<= z 7.2e-38)
         x
         (if (<= z 2.45e+44) (* y z) (if (<= z 6e+280) t_0 (* y z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -7e+156) {
		tmp = t_0;
	} else if (z <= -4.2e-10) {
		tmp = y * z;
	} else if (z <= 7.2e-38) {
		tmp = x;
	} else if (z <= 2.45e+44) {
		tmp = y * z;
	} else if (z <= 6e+280) {
		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 <= (-7d+156)) then
        tmp = t_0
    else if (z <= (-4.2d-10)) then
        tmp = y * z
    else if (z <= 7.2d-38) then
        tmp = x
    else if (z <= 2.45d+44) then
        tmp = y * z
    else if (z <= 6d+280) 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 <= -7e+156) {
		tmp = t_0;
	} else if (z <= -4.2e-10) {
		tmp = y * z;
	} else if (z <= 7.2e-38) {
		tmp = x;
	} else if (z <= 2.45e+44) {
		tmp = y * z;
	} else if (z <= 6e+280) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -7e+156:
		tmp = t_0
	elif z <= -4.2e-10:
		tmp = y * z
	elif z <= 7.2e-38:
		tmp = x
	elif z <= 2.45e+44:
		tmp = y * z
	elif z <= 6e+280:
		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 <= -7e+156)
		tmp = t_0;
	elseif (z <= -4.2e-10)
		tmp = Float64(y * z);
	elseif (z <= 7.2e-38)
		tmp = x;
	elseif (z <= 2.45e+44)
		tmp = Float64(y * z);
	elseif (z <= 6e+280)
		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 <= -7e+156)
		tmp = t_0;
	elseif (z <= -4.2e-10)
		tmp = y * z;
	elseif (z <= 7.2e-38)
		tmp = x;
	elseif (z <= 2.45e+44)
		tmp = y * z;
	elseif (z <= 6e+280)
		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, -7e+156], t$95$0, If[LessEqual[z, -4.2e-10], N[(y * z), $MachinePrecision], If[LessEqual[z, 7.2e-38], x, If[LessEqual[z, 2.45e+44], N[(y * z), $MachinePrecision], If[LessEqual[z, 6e+280], t$95$0, N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.0000000000000006e156 or 2.45000000000000018e44 < z < 6.0000000000000002e280

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 64.8%

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

   3. Taylor expanded in z around inf 64.8%

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

      1. associate-*r* 64.8%

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

      2. mul-1-neg 64.8%

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

   5. Simplified 64.8%

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

   if -7.0000000000000006e156 < z < -4.2e-10 or 7.2000000000000001e-38 < z < 2.45000000000000018e44 or 6.0000000000000002e280 < 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 -4.2e-10 < z < 7.2000000000000001e-38

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 72.0%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+156}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-10}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+44}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+280}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-49} \lor \neg \left(x \leq -3.8 \cdot 10^{-187} \lor \neg \left(x \leq -7 \cdot 10^{-240}\right) \land x \leq 3.2 \cdot 10^{-112}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.5e-49)
         (not
          (or (<= x -3.8e-187) (and (not (<= x -7e-240)) (<= x 3.2e-112)))))
   (* x (- 1.0 z))
   (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.5e-49) || !((x <= -3.8e-187) || (!(x <= -7e-240) && (x <= 3.2e-112)))) {
		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 ((x <= (-2.5d-49)) .or. (.not. (x <= (-3.8d-187)) .or. (.not. (x <= (-7d-240))) .and. (x <= 3.2d-112))) 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 ((x <= -2.5e-49) || !((x <= -3.8e-187) || (!(x <= -7e-240) && (x <= 3.2e-112)))) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.5e-49) or not ((x <= -3.8e-187) or (not (x <= -7e-240) and (x <= 3.2e-112))):
		tmp = x * (1.0 - z)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.5e-49) || !((x <= -3.8e-187) || (!(x <= -7e-240) && (x <= 3.2e-112))))
		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 ((x <= -2.5e-49) || ~(((x <= -3.8e-187) || (~((x <= -7e-240)) && (x <= 3.2e-112)))))
		tmp = x * (1.0 - z);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.5e-49], N[Not[Or[LessEqual[x, -3.8e-187], And[N[Not[LessEqual[x, -7e-240]], $MachinePrecision], LessEqual[x, 3.2e-112]]]], $MachinePrecision]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4999999999999999e-49 or -3.80000000000000025e-187 < x < -7.00000000000000032e-240 or 3.19999999999999993e-112 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 80.4%

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

      1. distribute-rgt1-in 80.4%

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

      2. mul-1-neg 80.4%

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

      3. cancel-sign-sub-inv 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in x around 0 80.4%

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

   if -2.4999999999999999e-49 < x < -3.80000000000000025e-187 or -7.00000000000000032e-240 < x < 3.19999999999999993e-112

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.2%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-49} \lor \neg \left(x \leq -3.8 \cdot 10^{-187} \lor \neg \left(x \leq -7 \cdot 10^{-240}\right) \land x \leq 3.2 \cdot 10^{-112}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-8} \lor \neg \left(z \leq 13.5\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5e-8) (not (<= z 13.5))) (* (- y x) z) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5e-8) || !(z <= 13.5)) {
		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 <= (-5d-8)) .or. (.not. (z <= 13.5d0))) 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 <= -5e-8) || !(z <= 13.5)) {
		tmp = (y - x) * z;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5e-8) or not (z <= 13.5):
		tmp = (y - x) * z
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5e-8) || !(z <= 13.5))
		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 <= -5e-8) || ~((z <= 13.5)))
		tmp = (y - x) * z;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5e-8], N[Not[LessEqual[z, 13.5]], $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 < -4.9999999999999998e-8 or 13.5 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.5%

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

   if -4.9999999999999998e-8 < z < 13.5

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 70.8%

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

      1. distribute-rgt1-in 70.8%

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

      2. mul-1-neg 70.8%

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

      3. cancel-sign-sub-inv 70.8%

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

   4. Simplified 70.8%

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

   5. Taylor expanded in x around 0 70.8%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-8} \lor \neg \left(z \leq 13.5\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 5: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6200000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6200000000.0) (not (<= z 1.0))) (* (- y x) z) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6200000000.0) || !(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 <= (-6200000000.0d0)) .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 <= -6200000000.0) || !(z <= 1.0)) {
		tmp = (y - x) * z;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6200000000.0) 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 <= -6200000000.0) || !(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 <= -6200000000.0) || ~((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, -6200000000.0], 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 < -6.2e9 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 98.8%

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

   if -6.2e9 < z < 1

   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-- 49.4%

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

      3. associate-*r/ 49.4%

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

      4. +-commutative 49.4%

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

   3. Applied egg-rr 49.4%

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

      1. associate-*l/ 47.0%

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

      2. +-commutative 47.0%

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

   5. Simplified 47.0%

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

   6. Taylor expanded in y around inf 98.9%

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

      1. *-commutative 98.9%

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

   8. Simplified 98.9%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6200000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 6: 61.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-8}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.3e-8) (* y z) (if (<= z 5.3e-36) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.3e-8) {
		tmp = y * z;
	} else if (z <= 5.3e-36) {
		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 <= (-2.3d-8)) then
        tmp = y * z
    else if (z <= 5.3d-36) 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 <= -2.3e-8) {
		tmp = y * z;
	} else if (z <= 5.3e-36) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.3e-8:
		tmp = y * z
	elif z <= 5.3e-36:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.3e-8)
		tmp = Float64(y * z);
	elseif (z <= 5.3e-36)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.3e-8)
		tmp = y * z;
	elseif (z <= 5.3e-36)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.3e-8], N[(y * z), $MachinePrecision], If[LessEqual[z, 5.3e-36], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3000000000000001e-8 or 5.2999999999999998e-36 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 46.6%

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

   if -2.3000000000000001e-8 < z < 5.2999999999999998e-36

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 72.0%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-8}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

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: 36.2% 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 37.8%

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

3. Final simplification 37.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023230 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))