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

Percentage Accurate: 100.0% → 100.0%

Time: 5.7s

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-define 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. Add Preprocessing
5. Add Preprocessing

Alternative 2: 58.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+90}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -470:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-20}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+49} \lor \neg \left(z \leq 4.5 \cdot 10^{+104}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -3.3e+90)
     (* y z)
     (if (<= z -470.0)
       t_0
       (if (<= z -4.2e-119)
         (* y z)
         (if (<= z 5.7e-86)
           x
           (if (<= z 5.2e-20)
             (* y z)
             (if (<= z 1.0)
               x
               (if (or (<= z 7.5e+49) (not (<= z 4.5e+104)))
                 t_0
                 (* y z))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -3.3e+90) {
		tmp = y * z;
	} else if (z <= -470.0) {
		tmp = t_0;
	} else if (z <= -4.2e-119) {
		tmp = y * z;
	} else if (z <= 5.7e-86) {
		tmp = x;
	} else if (z <= 5.2e-20) {
		tmp = y * z;
	} else if (z <= 1.0) {
		tmp = x;
	} else if ((z <= 7.5e+49) || !(z <= 4.5e+104)) {
		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 <= (-3.3d+90)) then
        tmp = y * z
    else if (z <= (-470.0d0)) then
        tmp = t_0
    else if (z <= (-4.2d-119)) then
        tmp = y * z
    else if (z <= 5.7d-86) then
        tmp = x
    else if (z <= 5.2d-20) then
        tmp = y * z
    else if (z <= 1.0d0) then
        tmp = x
    else if ((z <= 7.5d+49) .or. (.not. (z <= 4.5d+104))) 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 <= -3.3e+90) {
		tmp = y * z;
	} else if (z <= -470.0) {
		tmp = t_0;
	} else if (z <= -4.2e-119) {
		tmp = y * z;
	} else if (z <= 5.7e-86) {
		tmp = x;
	} else if (z <= 5.2e-20) {
		tmp = y * z;
	} else if (z <= 1.0) {
		tmp = x;
	} else if ((z <= 7.5e+49) || !(z <= 4.5e+104)) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -3.3e+90:
		tmp = y * z
	elif z <= -470.0:
		tmp = t_0
	elif z <= -4.2e-119:
		tmp = y * z
	elif z <= 5.7e-86:
		tmp = x
	elif z <= 5.2e-20:
		tmp = y * z
	elif z <= 1.0:
		tmp = x
	elif (z <= 7.5e+49) or not (z <= 4.5e+104):
		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 <= -3.3e+90)
		tmp = Float64(y * z);
	elseif (z <= -470.0)
		tmp = t_0;
	elseif (z <= -4.2e-119)
		tmp = Float64(y * z);
	elseif (z <= 5.7e-86)
		tmp = x;
	elseif (z <= 5.2e-20)
		tmp = Float64(y * z);
	elseif (z <= 1.0)
		tmp = x;
	elseif ((z <= 7.5e+49) || !(z <= 4.5e+104))
		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 <= -3.3e+90)
		tmp = y * z;
	elseif (z <= -470.0)
		tmp = t_0;
	elseif (z <= -4.2e-119)
		tmp = y * z;
	elseif (z <= 5.7e-86)
		tmp = x;
	elseif (z <= 5.2e-20)
		tmp = y * z;
	elseif (z <= 1.0)
		tmp = x;
	elseif ((z <= 7.5e+49) || ~((z <= 4.5e+104)))
		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, -3.3e+90], N[(y * z), $MachinePrecision], If[LessEqual[z, -470.0], t$95$0, If[LessEqual[z, -4.2e-119], N[(y * z), $MachinePrecision], If[LessEqual[z, 5.7e-86], x, If[LessEqual[z, 5.2e-20], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.0], x, If[Or[LessEqual[z, 7.5e+49], N[Not[LessEqual[z, 4.5e+104]], $MachinePrecision]], t$95$0, N[(y * z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.30000000000000008e90 or -470 < z < -4.2e-119 or 5.7000000000000004e-86 < z < 5.1999999999999999e-20 or 7.4999999999999995e49 < z < 4.4999999999999998e104

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 65.8%

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

   if -3.30000000000000008e90 < z < -470 or 1 < z < 7.4999999999999995e49 or 4.4999999999999998e104 < z

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. unsub-neg 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in z around inf 62.4%

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

      1. mul-1-neg 62.4%

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

      2. *-commutative 62.4%

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

      3. distribute-rgt-neg-in 62.4%

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

   8. Simplified 62.4%

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

   if -4.2e-119 < z < 5.7000000000000004e-86 or 5.1999999999999999e-20 < z < 1

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 89.3%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+90}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -470:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-20}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+49} \lor \neg \left(z \leq 4.5 \cdot 10^{+104}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot z\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-20}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.8:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) z)))
   (if (<= z -4.2e-119)
     t_0
     (if (<= z 5.6e-86)
       (* x (- 1.0 z))
       (if (<= z 9.5e-20) (* y z) (if (<= z 3.8) (- x (* x z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * z;
	double tmp;
	if (z <= -4.2e-119) {
		tmp = t_0;
	} else if (z <= 5.6e-86) {
		tmp = x * (1.0 - z);
	} else if (z <= 9.5e-20) {
		tmp = y * z;
	} else if (z <= 3.8) {
		tmp = x - (x * 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 = (y - x) * z
    if (z <= (-4.2d-119)) then
        tmp = t_0
    else if (z <= 5.6d-86) then
        tmp = x * (1.0d0 - z)
    else if (z <= 9.5d-20) then
        tmp = y * z
    else if (z <= 3.8d0) then
        tmp = x - (x * 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 = (y - x) * z;
	double tmp;
	if (z <= -4.2e-119) {
		tmp = t_0;
	} else if (z <= 5.6e-86) {
		tmp = x * (1.0 - z);
	} else if (z <= 9.5e-20) {
		tmp = y * z;
	} else if (z <= 3.8) {
		tmp = x - (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * z
	tmp = 0
	if z <= -4.2e-119:
		tmp = t_0
	elif z <= 5.6e-86:
		tmp = x * (1.0 - z)
	elif z <= 9.5e-20:
		tmp = y * z
	elif z <= 3.8:
		tmp = x - (x * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) * z)
	tmp = 0.0
	if (z <= -4.2e-119)
		tmp = t_0;
	elseif (z <= 5.6e-86)
		tmp = Float64(x * Float64(1.0 - z));
	elseif (z <= 9.5e-20)
		tmp = Float64(y * z);
	elseif (z <= 3.8)
		tmp = Float64(x - Float64(x * z));
	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 <= -4.2e-119)
		tmp = t_0;
	elseif (z <= 5.6e-86)
		tmp = x * (1.0 - z);
	elseif (z <= 9.5e-20)
		tmp = y * z;
	elseif (z <= 3.8)
		tmp = x - (x * z);
	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, -4.2e-119], t$95$0, If[LessEqual[z, 5.6e-86], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-20], N[(y * z), $MachinePrecision], If[LessEqual[z, 3.8], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.2e-119 or 3.7999999999999998 < z

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 94.4%

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

   if -4.2e-119 < z < 5.60000000000000019e-86

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 90.8%

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

      1. mul-1-neg 90.8%

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

      2. unsub-neg 90.8%

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

   5. Simplified 90.8%

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

   if 5.60000000000000019e-86 < z < 9.5e-20

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 63.1%

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

   if 9.5e-20 < z < 3.7999999999999998

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. unsub-neg 99.6%

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

   5. Simplified 99.6%

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

      1. sub-neg 99.6%

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

      2. distribute-rgt-in 100.0%

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

      3. *-un-lft-identity 100.0%

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

      4. distribute-lft-neg-in 100.0%

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

      5. unsub-neg 100.0%

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

      6. *-commutative 100.0%

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

   7. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{x - x \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-20}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.8:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot z\\ t_1 := x \cdot \left(1 - z\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-16}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 0.0086:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) z)) (t_1 (* x (- 1.0 z))))
   (if (<= z -4.2e-119)
     t_0
     (if (<= z 5.7e-86)
       t_1
       (if (<= z 1.1e-16) (* y z) (if (<= z 0.0086) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * z;
	double t_1 = x * (1.0 - z);
	double tmp;
	if (z <= -4.2e-119) {
		tmp = t_0;
	} else if (z <= 5.7e-86) {
		tmp = t_1;
	} else if (z <= 1.1e-16) {
		tmp = y * z;
	} else if (z <= 0.0086) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = (y - x) * z
    t_1 = x * (1.0d0 - z)
    if (z <= (-4.2d-119)) then
        tmp = t_0
    else if (z <= 5.7d-86) then
        tmp = t_1
    else if (z <= 1.1d-16) then
        tmp = y * z
    else if (z <= 0.0086d0) then
        tmp = t_1
    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 t_1 = x * (1.0 - z);
	double tmp;
	if (z <= -4.2e-119) {
		tmp = t_0;
	} else if (z <= 5.7e-86) {
		tmp = t_1;
	} else if (z <= 1.1e-16) {
		tmp = y * z;
	} else if (z <= 0.0086) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * z
	t_1 = x * (1.0 - z)
	tmp = 0
	if z <= -4.2e-119:
		tmp = t_0
	elif z <= 5.7e-86:
		tmp = t_1
	elif z <= 1.1e-16:
		tmp = y * z
	elif z <= 0.0086:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) * z)
	t_1 = Float64(x * Float64(1.0 - z))
	tmp = 0.0
	if (z <= -4.2e-119)
		tmp = t_0;
	elseif (z <= 5.7e-86)
		tmp = t_1;
	elseif (z <= 1.1e-16)
		tmp = Float64(y * z);
	elseif (z <= 0.0086)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) * z;
	t_1 = x * (1.0 - z);
	tmp = 0.0;
	if (z <= -4.2e-119)
		tmp = t_0;
	elseif (z <= 5.7e-86)
		tmp = t_1;
	elseif (z <= 1.1e-16)
		tmp = y * z;
	elseif (z <= 0.0086)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e-119], t$95$0, If[LessEqual[z, 5.7e-86], t$95$1, If[LessEqual[z, 1.1e-16], N[(y * z), $MachinePrecision], If[LessEqual[z, 0.0086], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e-119 or 0.0086 < z

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 94.4%

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

   if -4.2e-119 < z < 5.7000000000000004e-86 or 1.1e-16 < z < 0.0086

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 91.3%

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

      1. mul-1-neg 91.3%

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

      2. unsub-neg 91.3%

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

   5. Simplified 91.3%

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

   if 5.7000000000000004e-86 < z < 1.1e-16

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 63.1%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-16}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 0.0086:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-28} \lor \neg \left(x \leq 1.32 \cdot 10^{-120}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.95e-28) (not (<= x 1.32e-120))) (* x (- 1.0 z)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.95e-28) || !(x <= 1.32e-120)) {
		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 <= (-1.95d-28)) .or. (.not. (x <= 1.32d-120))) 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 <= -1.95e-28) || !(x <= 1.32e-120)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.95e-28) or not (x <= 1.32e-120):
		tmp = x * (1.0 - z)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.95e-28) || !(x <= 1.32e-120))
		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 <= -1.95e-28) || ~((x <= 1.32e-120)))
		tmp = x * (1.0 - z);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.95e-28], N[Not[LessEqual[x, 1.32e-120]], $MachinePrecision]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.94999999999999999e-28 or 1.32000000000000004e-120 < x

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 81.8%

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

      1. mul-1-neg 81.8%

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

      2. unsub-neg 81.8%

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

   5. Simplified 81.8%

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

   if -1.94999999999999999e-28 < x < 1.32000000000000004e-120

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 72.2%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-28} \lor \neg \left(x \leq 1.32 \cdot 10^{-120}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-123} \lor \neg \left(z \leq 4 \cdot 10^{-86}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.4e-123) (not (<= z 4e-86))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.4e-123) || !(z <= 4e-86)) {
		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 <= (-3.4d-123)) .or. (.not. (z <= 4d-86))) 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 <= -3.4e-123) || !(z <= 4e-86)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.4e-123) or not (z <= 4e-86):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.4e-123) || !(z <= 4e-86))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.4e-123) || ~((z <= 4e-86)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.4e-123], N[Not[LessEqual[z, 4e-86]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.4000000000000001e-123 or 4.00000000000000034e-86 < z

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 52.7%

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

   if -3.4000000000000001e-123 < z < 4.00000000000000034e-86

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 90.8%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-123} \lor \neg \left(z \leq 4 \cdot 10^{-86}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

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. Add Preprocessing
3. Add Preprocessing

Alternative 8: 37.3% 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. Add Preprocessing

3. Taylor expanded in z around 0 32.5%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024085 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))