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

Percentage Accurate: 100.0% → 100.0%

Time: 4.4s

Alternatives: 8

Speedup: 1.0×

• 21.8% 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: 60.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+241}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+200}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+47}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -760000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-39}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+14} \lor \neg \left(z \leq 3.4 \cdot 10^{+26}\right) \land z \leq 8.6 \cdot 10^{+200}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -8e+241)
     t_0
     (if (<= z -1.6e+200)
       (* y z)
       (if (<= z -1e+81)
         t_0
         (if (<= z -2.4e+47)
           (* y z)
           (if (<= z -760000000000.0)
             t_0
             (if (<= z -1.2e-39)
               (* y z)
               (if (<= z 3.9e-98)
                 x
                 (if (or (<= z 3.3e+14)
                         (and (not (<= z 3.4e+26)) (<= z 8.6e+200)))
                   (* y z)
                   t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -8e+241) {
		tmp = t_0;
	} else if (z <= -1.6e+200) {
		tmp = y * z;
	} else if (z <= -1e+81) {
		tmp = t_0;
	} else if (z <= -2.4e+47) {
		tmp = y * z;
	} else if (z <= -760000000000.0) {
		tmp = t_0;
	} else if (z <= -1.2e-39) {
		tmp = y * z;
	} else if (z <= 3.9e-98) {
		tmp = x;
	} else if ((z <= 3.3e+14) || (!(z <= 3.4e+26) && (z <= 8.6e+200))) {
		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 = x * -z
    if (z <= (-8d+241)) then
        tmp = t_0
    else if (z <= (-1.6d+200)) then
        tmp = y * z
    else if (z <= (-1d+81)) then
        tmp = t_0
    else if (z <= (-2.4d+47)) then
        tmp = y * z
    else if (z <= (-760000000000.0d0)) then
        tmp = t_0
    else if (z <= (-1.2d-39)) then
        tmp = y * z
    else if (z <= 3.9d-98) then
        tmp = x
    else if ((z <= 3.3d+14) .or. (.not. (z <= 3.4d+26)) .and. (z <= 8.6d+200)) 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 = x * -z;
	double tmp;
	if (z <= -8e+241) {
		tmp = t_0;
	} else if (z <= -1.6e+200) {
		tmp = y * z;
	} else if (z <= -1e+81) {
		tmp = t_0;
	} else if (z <= -2.4e+47) {
		tmp = y * z;
	} else if (z <= -760000000000.0) {
		tmp = t_0;
	} else if (z <= -1.2e-39) {
		tmp = y * z;
	} else if (z <= 3.9e-98) {
		tmp = x;
	} else if ((z <= 3.3e+14) || (!(z <= 3.4e+26) && (z <= 8.6e+200))) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -8e+241:
		tmp = t_0
	elif z <= -1.6e+200:
		tmp = y * z
	elif z <= -1e+81:
		tmp = t_0
	elif z <= -2.4e+47:
		tmp = y * z
	elif z <= -760000000000.0:
		tmp = t_0
	elif z <= -1.2e-39:
		tmp = y * z
	elif z <= 3.9e-98:
		tmp = x
	elif (z <= 3.3e+14) or (not (z <= 3.4e+26) and (z <= 8.6e+200)):
		tmp = y * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -8e+241)
		tmp = t_0;
	elseif (z <= -1.6e+200)
		tmp = Float64(y * z);
	elseif (z <= -1e+81)
		tmp = t_0;
	elseif (z <= -2.4e+47)
		tmp = Float64(y * z);
	elseif (z <= -760000000000.0)
		tmp = t_0;
	elseif (z <= -1.2e-39)
		tmp = Float64(y * z);
	elseif (z <= 3.9e-98)
		tmp = x;
	elseif ((z <= 3.3e+14) || (!(z <= 3.4e+26) && (z <= 8.6e+200)))
		tmp = Float64(y * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (z <= -8e+241)
		tmp = t_0;
	elseif (z <= -1.6e+200)
		tmp = y * z;
	elseif (z <= -1e+81)
		tmp = t_0;
	elseif (z <= -2.4e+47)
		tmp = y * z;
	elseif (z <= -760000000000.0)
		tmp = t_0;
	elseif (z <= -1.2e-39)
		tmp = y * z;
	elseif (z <= 3.9e-98)
		tmp = x;
	elseif ((z <= 3.3e+14) || (~((z <= 3.4e+26)) && (z <= 8.6e+200)))
		tmp = y * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -8e+241], t$95$0, If[LessEqual[z, -1.6e+200], N[(y * z), $MachinePrecision], If[LessEqual[z, -1e+81], t$95$0, If[LessEqual[z, -2.4e+47], N[(y * z), $MachinePrecision], If[LessEqual[z, -760000000000.0], t$95$0, If[LessEqual[z, -1.2e-39], N[(y * z), $MachinePrecision], If[LessEqual[z, 3.9e-98], x, If[Or[LessEqual[z, 3.3e+14], And[N[Not[LessEqual[z, 3.4e+26]], $MachinePrecision], LessEqual[z, 8.6e+200]]], N[(y * z), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.0000000000000004e241 or -1.60000000000000016e200 < z < -9.99999999999999921e80 or -2.40000000000000019e47 < z < -7.6e11 or 3.3e14 < z < 3.4000000000000003e26 or 8.60000000000000062e200 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 77.0%

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

      1. mul-1-neg 77.0%

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

      2. unsub-neg 77.0%

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

   4. Simplified 77.0%

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

   5. Taylor expanded in z around inf 76.6%

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

      1. associate-*r* 76.6%

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

      2. mul-1-neg 76.6%

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

   7. Simplified 76.6%

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

   if -8.0000000000000004e241 < z < -1.60000000000000016e200 or -9.99999999999999921e80 < z < -2.40000000000000019e47 or -7.6e11 < z < -1.20000000000000008e-39 or 3.89999999999999971e-98 < z < 3.3e14 or 3.4000000000000003e26 < z < 8.60000000000000062e200

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.9%

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

      1. *-commutative 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in x around 0 68.9%

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

      1. *-commutative 68.9%

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

   7. Simplified 68.9%

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

   if -1.20000000000000008e-39 < z < 3.89999999999999971e-98

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 77.3%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+241}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+200}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+47}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -760000000000:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-39}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+14} \lor \neg \left(z \leq 3.4 \cdot 10^{+26}\right) \land z \leq 8.6 \cdot 10^{+200}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 3: 76.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-88} \lor \neg \left(x \leq 1.95 \cdot 10^{-42}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.8e-88) (not (<= x 1.95e-42))) (* x (- 1.0 z)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.8e-88) || !(x <= 1.95e-42)) {
		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 <= (-8.8d-88)) .or. (.not. (x <= 1.95d-42))) 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 <= -8.8e-88) || !(x <= 1.95e-42)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.8e-88) or not (x <= 1.95e-42):
		tmp = x * (1.0 - z)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.8e-88) || !(x <= 1.95e-42))
		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 <= -8.8e-88) || ~((x <= 1.95e-42)))
		tmp = x * (1.0 - z);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.8e-88], N[Not[LessEqual[x, 1.95e-42]], $MachinePrecision]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.8000000000000002e-88 or 1.9500000000000001e-42 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 80.9%

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

      1. mul-1-neg 80.9%

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

      2. unsub-neg 80.9%

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

   4. Simplified 80.9%

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

   if -8.8000000000000002e-88 < x < 1.9500000000000001e-42

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 96.1%

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

      1. *-commutative 96.1%

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

   4. Simplified 96.1%

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

   5. Taylor expanded in x around 0 75.8%

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

      1. *-commutative 75.8%

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

   7. Simplified 75.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-88} \lor \neg \left(x \leq 1.95 \cdot 10^{-42}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-39} \lor \neg \left(x \leq 8.5 \cdot 10^{+56}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.5e-39) (not (<= x 8.5e+56))) (* x (- 1.0 z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.5e-39) || !(x <= 8.5e+56)) {
		tmp = x * (1.0 - 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 ((x <= (-6.5d-39)) .or. (.not. (x <= 8.5d+56))) then
        tmp = x * (1.0d0 - 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 ((x <= -6.5e-39) || !(x <= 8.5e+56)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.5e-39) or not (x <= 8.5e+56):
		tmp = x * (1.0 - z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.5e-39) || !(x <= 8.5e+56))
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.5e-39) || ~((x <= 8.5e+56)))
		tmp = x * (1.0 - z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.5e-39], N[Not[LessEqual[x, 8.5e+56]], $MachinePrecision]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.50000000000000027e-39 or 8.4999999999999998e56 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 86.6%

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

      1. mul-1-neg 86.6%

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

      2. unsub-neg 86.6%

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

   4. Simplified 86.6%

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

   if -6.50000000000000027e-39 < x < 8.4999999999999998e56

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 95.3%

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

      1. *-commutative 95.3%

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

   4. Simplified 95.3%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-39} \lor \neg \left(x \leq 8.5 \cdot 10^{+56}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 5: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-39}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.5e-39)
   (- x (* x z))
   (if (<= x 4.9e+58) (+ x (* y z)) (* x (- 1.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.5e-39) {
		tmp = x - (x * z);
	} else if (x <= 4.9e+58) {
		tmp = x + (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 (x <= (-6.5d-39)) then
        tmp = x - (x * z)
    else if (x <= 4.9d+58) then
        tmp = x + (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 (x <= -6.5e-39) {
		tmp = x - (x * z);
	} else if (x <= 4.9e+58) {
		tmp = x + (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.5e-39:
		tmp = x - (x * z)
	elif x <= 4.9e+58:
		tmp = x + (y * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.5e-39)
		tmp = Float64(x - Float64(x * z));
	elseif (x <= 4.9e+58)
		tmp = Float64(x + 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 (x <= -6.5e-39)
		tmp = x - (x * z);
	elseif (x <= 4.9e+58)
		tmp = x + (y * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.5e-39], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.9e+58], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.50000000000000027e-39

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 86.1%

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

      1. mul-1-neg 86.1%

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

      2. unsub-neg 86.1%

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

   4. Simplified 86.1%

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

   5. Taylor expanded in z around 0 86.1%

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

      1. mul-1-neg 86.1%

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

      2. sub-neg 86.1%

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

   7. Simplified 86.1%

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

   if -6.50000000000000027e-39 < x < 4.90000000000000018e58

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 95.3%

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

      1. *-commutative 95.3%

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

   4. Simplified 95.3%

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

   if 4.90000000000000018e58 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 87.3%

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

      1. mul-1-neg 87.3%

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

      2. unsub-neg 87.3%

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

   4. Simplified 87.3%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-39}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 6: 60.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-39} \lor \neg \left(z \leq 1.4 \cdot 10^{-101}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.26e-39) (not (<= z 1.4e-101))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.26e-39) || !(z <= 1.4e-101)) {
		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 <= (-1.26d-39)) .or. (.not. (z <= 1.4d-101))) 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 <= -1.26e-39) || !(z <= 1.4e-101)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.26e-39) or not (z <= 1.4e-101):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.26e-39) || !(z <= 1.4e-101))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.26e-39) || ~((z <= 1.4e-101)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.26e-39], N[Not[LessEqual[z, 1.4e-101]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.26e-39 or 1.39999999999999995e-101 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 61.8%

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

      1. *-commutative 61.8%

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

   4. Simplified 61.8%

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

   5. Taylor expanded in x around 0 54.5%

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

      1. *-commutative 54.5%

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

   7. Simplified 54.5%

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

   if -1.26e-39 < z < 1.39999999999999995e-101

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 77.3%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-39} \lor \neg \left(z \leq 1.4 \cdot 10^{-101}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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 38.1%

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

3. Final simplification 38.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023311 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))