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

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

Alternatives: 7

Speedup: 1.0×

• 21.1% 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: 59.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+247}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+189}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+67}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-123}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+80} \lor \neg \left(z \leq 8 \cdot 10^{+237}\right) \land z \leq 9.5 \cdot 10^{+261}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= z -6.6e+247)
     t_0
     (if (<= z -5e+189)
       (* y z)
       (if (<= z -2.9e+67)
         t_0
         (if (<= z -3.5e-65)
           (* y z)
           (if (<= z 1.12e-175)
             x
             (if (<= z 1.1e-123)
               (* y z)
               (if (<= z 4e-20)
                 x
                 (if (or (<= z 3.4e+80)
                         (and (not (<= z 8e+237)) (<= z 9.5e+261)))
                   (* y z)
                   t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -6.6e+247) {
		tmp = t_0;
	} else if (z <= -5e+189) {
		tmp = y * z;
	} else if (z <= -2.9e+67) {
		tmp = t_0;
	} else if (z <= -3.5e-65) {
		tmp = y * z;
	} else if (z <= 1.12e-175) {
		tmp = x;
	} else if (z <= 1.1e-123) {
		tmp = y * z;
	} else if (z <= 4e-20) {
		tmp = x;
	} else if ((z <= 3.4e+80) || (!(z <= 8e+237) && (z <= 9.5e+261))) {
		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 <= (-6.6d+247)) then
        tmp = t_0
    else if (z <= (-5d+189)) then
        tmp = y * z
    else if (z <= (-2.9d+67)) then
        tmp = t_0
    else if (z <= (-3.5d-65)) then
        tmp = y * z
    else if (z <= 1.12d-175) then
        tmp = x
    else if (z <= 1.1d-123) then
        tmp = y * z
    else if (z <= 4d-20) then
        tmp = x
    else if ((z <= 3.4d+80) .or. (.not. (z <= 8d+237)) .and. (z <= 9.5d+261)) 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 <= -6.6e+247) {
		tmp = t_0;
	} else if (z <= -5e+189) {
		tmp = y * z;
	} else if (z <= -2.9e+67) {
		tmp = t_0;
	} else if (z <= -3.5e-65) {
		tmp = y * z;
	} else if (z <= 1.12e-175) {
		tmp = x;
	} else if (z <= 1.1e-123) {
		tmp = y * z;
	} else if (z <= 4e-20) {
		tmp = x;
	} else if ((z <= 3.4e+80) || (!(z <= 8e+237) && (z <= 9.5e+261))) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if z <= -6.6e+247:
		tmp = t_0
	elif z <= -5e+189:
		tmp = y * z
	elif z <= -2.9e+67:
		tmp = t_0
	elif z <= -3.5e-65:
		tmp = y * z
	elif z <= 1.12e-175:
		tmp = x
	elif z <= 1.1e-123:
		tmp = y * z
	elif z <= 4e-20:
		tmp = x
	elif (z <= 3.4e+80) or (not (z <= 8e+237) and (z <= 9.5e+261)):
		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 <= -6.6e+247)
		tmp = t_0;
	elseif (z <= -5e+189)
		tmp = Float64(y * z);
	elseif (z <= -2.9e+67)
		tmp = t_0;
	elseif (z <= -3.5e-65)
		tmp = Float64(y * z);
	elseif (z <= 1.12e-175)
		tmp = x;
	elseif (z <= 1.1e-123)
		tmp = Float64(y * z);
	elseif (z <= 4e-20)
		tmp = x;
	elseif ((z <= 3.4e+80) || (!(z <= 8e+237) && (z <= 9.5e+261)))
		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 <= -6.6e+247)
		tmp = t_0;
	elseif (z <= -5e+189)
		tmp = y * z;
	elseif (z <= -2.9e+67)
		tmp = t_0;
	elseif (z <= -3.5e-65)
		tmp = y * z;
	elseif (z <= 1.12e-175)
		tmp = x;
	elseif (z <= 1.1e-123)
		tmp = y * z;
	elseif (z <= 4e-20)
		tmp = x;
	elseif ((z <= 3.4e+80) || (~((z <= 8e+237)) && (z <= 9.5e+261)))
		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, -6.6e+247], t$95$0, If[LessEqual[z, -5e+189], N[(y * z), $MachinePrecision], If[LessEqual[z, -2.9e+67], t$95$0, If[LessEqual[z, -3.5e-65], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.12e-175], x, If[LessEqual[z, 1.1e-123], N[(y * z), $MachinePrecision], If[LessEqual[z, 4e-20], x, If[Or[LessEqual[z, 3.4e+80], And[N[Not[LessEqual[z, 8e+237]], $MachinePrecision], LessEqual[z, 9.5e+261]]], N[(y * z), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.60000000000000003e247 or -5.0000000000000004e189 < z < -2.90000000000000023e67 or 3.39999999999999992e80 < z < 7.99999999999999952e237 or 9.50000000000000085e261 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

   3. Taylor expanded in y around 0 72.1%

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

      1. mul-1-neg 72.1%

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

      2. distribute-rgt-neg-out 72.1%

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

   5. Simplified 72.1%

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

   if -6.60000000000000003e247 < z < -5.0000000000000004e189 or -2.90000000000000023e67 < z < -3.50000000000000005e-65 or 1.1200000000000001e-175 < z < 1.10000000000000003e-123 or 3.99999999999999978e-20 < z < 3.39999999999999992e80 or 7.99999999999999952e237 < z < 9.50000000000000085e261

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 68.6%

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

   if -3.50000000000000005e-65 < z < 1.1200000000000001e-175 or 1.10000000000000003e-123 < z < 3.99999999999999978e-20

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 76.4%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+247}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+189}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+67}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-123}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+80} \lor \neg \left(z \leq 8 \cdot 10^{+237}\right) \land z \leq 9.5 \cdot 10^{+261}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot z\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{-66}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-122}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) z)))
   (if (<= z -6.8e-66)
     t_0
     (if (<= z 1.12e-175)
       x
       (if (<= z 6.2e-122) (* y z) (if (<= z 9.5e-19) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * z;
	double tmp;
	if (z <= -6.8e-66) {
		tmp = t_0;
	} else if (z <= 1.12e-175) {
		tmp = x;
	} else if (z <= 6.2e-122) {
		tmp = y * z;
	} else if (z <= 9.5e-19) {
		tmp = x;
	} 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 = (y - x) * z
    if (z <= (-6.8d-66)) then
        tmp = t_0
    else if (z <= 1.12d-175) then
        tmp = x
    else if (z <= 6.2d-122) then
        tmp = y * z
    else if (z <= 9.5d-19) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - x) * z;
	double tmp;
	if (z <= -6.8e-66) {
		tmp = t_0;
	} else if (z <= 1.12e-175) {
		tmp = x;
	} else if (z <= 6.2e-122) {
		tmp = y * z;
	} else if (z <= 9.5e-19) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * z
	tmp = 0
	if z <= -6.8e-66:
		tmp = t_0
	elif z <= 1.12e-175:
		tmp = x
	elif z <= 6.2e-122:
		tmp = y * z
	elif z <= 9.5e-19:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) * z)
	tmp = 0.0
	if (z <= -6.8e-66)
		tmp = t_0;
	elseif (z <= 1.12e-175)
		tmp = x;
	elseif (z <= 6.2e-122)
		tmp = Float64(y * z);
	elseif (z <= 9.5e-19)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) * z;
	tmp = 0.0;
	if (z <= -6.8e-66)
		tmp = t_0;
	elseif (z <= 1.12e-175)
		tmp = x;
	elseif (z <= 6.2e-122)
		tmp = y * z;
	elseif (z <= 9.5e-19)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -6.8e-66], t$95$0, If[LessEqual[z, 1.12e-175], x, If[LessEqual[z, 6.2e-122], N[(y * z), $MachinePrecision], If[LessEqual[z, 9.5e-19], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999994e-66 or 9.4999999999999995e-19 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 95.3%

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

   if -6.79999999999999994e-66 < z < 1.1200000000000001e-175 or 6.1999999999999997e-122 < z < 9.4999999999999995e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 76.4%

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

   if 1.1200000000000001e-175 < z < 6.1999999999999997e-122

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 68.2%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-66}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-122}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \end{array} \]

Alternative 4: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.00086\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.00086))) (* (- y x) z) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.00086)) {
		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 <= 0.00086d0))) 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 <= 0.00086)) {
		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 <= 0.00086):
		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 <= 0.00086))
		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 <= 0.00086)))
		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, 0.00086]], $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 8.59999999999999979e-4 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.4%

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

   if -1 < z < 8.59999999999999979e-4

   1. Initial program 100.0%

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

      1. flip-- 48.0%

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

      2. associate-*l/ 47.9%

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

      3. +-commutative 47.9%

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

   3. Applied egg-rr 47.9%

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

   4. Taylor expanded in y around inf 98.9%

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

      1. *-commutative 98.9%

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

   6. Simplified 98.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.00086\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 5: 54.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+72}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5e+66) x (if (<= x 8.5e+72) (* y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5e+66) {
		tmp = x;
	} else if (x <= 8.5e+72) {
		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 (x <= (-5.5d+66)) then
        tmp = x
    else if (x <= 8.5d+72) 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 (x <= -5.5e+66) {
		tmp = x;
	} else if (x <= 8.5e+72) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5e+66:
		tmp = x
	elif x <= 8.5e+72:
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5e+66)
		tmp = x;
	elseif (x <= 8.5e+72)
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5e+66)
		tmp = x;
	elseif (x <= 8.5e+72)
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5e+66], x, If[LessEqual[x, 8.5e+72], N[(y * z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e66 or 8.5000000000000004e72 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 50.0%

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

   if -5.5e66 < x < 8.5000000000000004e72

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 65.5%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+72}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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: 36.2% 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 32.2%

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

3. Final simplification 32.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023182 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))