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

Percentage Accurate: 100.0% → 100.0%

Time: 4.6s

Alternatives: 10

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-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: 59.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+266}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+178}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+96}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-97}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+24} \lor \neg \left(z \leq 8.5 \cdot 10^{+162}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -2.25e+266)
     t_0
     (if (<= z -1.15e+178)
       (* y z)
       (if (<= z -3.4e+96)
         t_0
         (if (<= z -7e-97)
           (* y z)
           (if (<= z 1e-118)
             x
             (if (or (<= z 6.2e+24) (not (<= z 8.5e+162))) (* y z) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -2.25e+266) {
		tmp = t_0;
	} else if (z <= -1.15e+178) {
		tmp = y * z;
	} else if (z <= -3.4e+96) {
		tmp = t_0;
	} else if (z <= -7e-97) {
		tmp = y * z;
	} else if (z <= 1e-118) {
		tmp = x;
	} else if ((z <= 6.2e+24) || !(z <= 8.5e+162)) {
		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 <= (-2.25d+266)) then
        tmp = t_0
    else if (z <= (-1.15d+178)) then
        tmp = y * z
    else if (z <= (-3.4d+96)) then
        tmp = t_0
    else if (z <= (-7d-97)) then
        tmp = y * z
    else if (z <= 1d-118) then
        tmp = x
    else if ((z <= 6.2d+24) .or. (.not. (z <= 8.5d+162))) 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 <= -2.25e+266) {
		tmp = t_0;
	} else if (z <= -1.15e+178) {
		tmp = y * z;
	} else if (z <= -3.4e+96) {
		tmp = t_0;
	} else if (z <= -7e-97) {
		tmp = y * z;
	} else if (z <= 1e-118) {
		tmp = x;
	} else if ((z <= 6.2e+24) || !(z <= 8.5e+162)) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -2.25e+266:
		tmp = t_0
	elif z <= -1.15e+178:
		tmp = y * z
	elif z <= -3.4e+96:
		tmp = t_0
	elif z <= -7e-97:
		tmp = y * z
	elif z <= 1e-118:
		tmp = x
	elif (z <= 6.2e+24) or not (z <= 8.5e+162):
		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 <= -2.25e+266)
		tmp = t_0;
	elseif (z <= -1.15e+178)
		tmp = Float64(y * z);
	elseif (z <= -3.4e+96)
		tmp = t_0;
	elseif (z <= -7e-97)
		tmp = Float64(y * z);
	elseif (z <= 1e-118)
		tmp = x;
	elseif ((z <= 6.2e+24) || !(z <= 8.5e+162))
		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 <= -2.25e+266)
		tmp = t_0;
	elseif (z <= -1.15e+178)
		tmp = y * z;
	elseif (z <= -3.4e+96)
		tmp = t_0;
	elseif (z <= -7e-97)
		tmp = y * z;
	elseif (z <= 1e-118)
		tmp = x;
	elseif ((z <= 6.2e+24) || ~((z <= 8.5e+162)))
		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, -2.25e+266], t$95$0, If[LessEqual[z, -1.15e+178], N[(y * z), $MachinePrecision], If[LessEqual[z, -3.4e+96], t$95$0, If[LessEqual[z, -7e-97], N[(y * z), $MachinePrecision], If[LessEqual[z, 1e-118], x, If[Or[LessEqual[z, 6.2e+24], N[Not[LessEqual[z, 8.5e+162]], $MachinePrecision]], N[(y * z), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.25e266 or -1.15e178 < z < -3.4000000000000001e96 or 6.20000000000000022e24 < z < 8.5000000000000003e162

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. unsub-neg 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in z around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. distribute-rgt-neg-out 74.3%

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

   8. Simplified 74.3%

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

   if -2.25e266 < z < -1.15e178 or -3.4000000000000001e96 < z < -7.00000000000000038e-97 or 9.99999999999999985e-119 < z < 6.20000000000000022e24 or 8.5000000000000003e162 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 60.2%

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

   if -7.00000000000000038e-97 < z < 9.99999999999999985e-119

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 79.9%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+266}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+178}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-97}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+24} \lor \neg \left(z \leq 8.5 \cdot 10^{+162}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{+98} \lor \neg \left(y \leq 0.205\right) \land \left(y \leq 6 \cdot 10^{+51} \lor \neg \left(y \leq 8.2 \cdot 10^{+95}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.18e+98)
         (and (not (<= y 0.205)) (or (<= y 6e+51) (not (<= y 8.2e+95)))))
   (* y z)
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.18e+98) || (!(y <= 0.205) && ((y <= 6e+51) || !(y <= 8.2e+95)))) {
		tmp = 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 ((y <= (-1.18d+98)) .or. (.not. (y <= 0.205d0)) .and. (y <= 6d+51) .or. (.not. (y <= 8.2d+95))) then
        tmp = 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 ((y <= -1.18e+98) || (!(y <= 0.205) && ((y <= 6e+51) || !(y <= 8.2e+95)))) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.18e+98) or (not (y <= 0.205) and ((y <= 6e+51) or not (y <= 8.2e+95))):
		tmp = y * z
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.18e+98) || (!(y <= 0.205) && ((y <= 6e+51) || !(y <= 8.2e+95))))
		tmp = 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 ((y <= -1.18e+98) || (~((y <= 0.205)) && ((y <= 6e+51) || ~((y <= 8.2e+95)))))
		tmp = y * z;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.18e+98], And[N[Not[LessEqual[y, 0.205]], $MachinePrecision], Or[LessEqual[y, 6e+51], N[Not[LessEqual[y, 8.2e+95]], $MachinePrecision]]]], N[(y * z), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.18000000000000002e98 or 0.204999999999999988 < y < 6e51 or 8.19999999999999972e95 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.1%

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

   if -1.18000000000000002e98 < y < 0.204999999999999988 or 6e51 < y < 8.19999999999999972e95

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.0%

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

      1. mul-1-neg 82.0%

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

      2. unsub-neg 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{+98} \lor \neg \left(y \leq 0.205\right) \land \left(y \leq 6 \cdot 10^{+51} \lor \neg \left(y \leq 8.2 \cdot 10^{+95}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot z\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-97}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.96 \cdot 10^{-118}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-52}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 95000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) z)))
   (if (<= z -5.8e-97)
     t_0
     (if (<= z 1.96e-118)
       (- x (* x z))
       (if (<= z 1.8e-52)
         (* y z)
         (if (<= z 95000000.0) (* x (- 1.0 z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * z;
	double tmp;
	if (z <= -5.8e-97) {
		tmp = t_0;
	} else if (z <= 1.96e-118) {
		tmp = x - (x * z);
	} else if (z <= 1.8e-52) {
		tmp = y * z;
	} else if (z <= 95000000.0) {
		tmp = x * (1.0 - 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 <= (-5.8d-97)) then
        tmp = t_0
    else if (z <= 1.96d-118) then
        tmp = x - (x * z)
    else if (z <= 1.8d-52) then
        tmp = y * z
    else if (z <= 95000000.0d0) then
        tmp = x * (1.0d0 - 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 <= -5.8e-97) {
		tmp = t_0;
	} else if (z <= 1.96e-118) {
		tmp = x - (x * z);
	} else if (z <= 1.8e-52) {
		tmp = y * z;
	} else if (z <= 95000000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * z
	tmp = 0
	if z <= -5.8e-97:
		tmp = t_0
	elif z <= 1.96e-118:
		tmp = x - (x * z)
	elif z <= 1.8e-52:
		tmp = y * z
	elif z <= 95000000.0:
		tmp = x * (1.0 - 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 <= -5.8e-97)
		tmp = t_0;
	elseif (z <= 1.96e-118)
		tmp = Float64(x - Float64(x * z));
	elseif (z <= 1.8e-52)
		tmp = Float64(y * z);
	elseif (z <= 95000000.0)
		tmp = Float64(x * Float64(1.0 - 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 <= -5.8e-97)
		tmp = t_0;
	elseif (z <= 1.96e-118)
		tmp = x - (x * z);
	elseif (z <= 1.8e-52)
		tmp = y * z;
	elseif (z <= 95000000.0)
		tmp = x * (1.0 - 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, -5.8e-97], t$95$0, If[LessEqual[z, 1.96e-118], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-52], N[(y * z), $MachinePrecision], If[LessEqual[z, 95000000.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.7999999999999999e-97 or 9.5e7 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 94.0%

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

   if -5.7999999999999999e-97 < z < 1.96e-118

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.9%

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

      1. mul-1-neg 79.9%

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

      2. unsub-neg 79.9%

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

   5. Simplified 79.9%

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

      1. sub-neg 79.9%

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

      2. distribute-rgt-in 79.9%

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

      3. *-un-lft-identity 79.9%

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

   7. Applied egg-rr 79.9%

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

   if 1.96e-118 < z < 1.79999999999999994e-52

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.3%

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

   if 1.79999999999999994e-52 < z < 9.5e7

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. unsub-neg 64.2%

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

   5. Simplified 64.2%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-97}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{elif}\;z \leq 1.96 \cdot 10^{-118}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-52}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 95000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot z\\ \mathbf{if}\;z \leq -7 \cdot 10^{-97}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-118}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;z \leq 4.15 \cdot 10^{-53}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 440000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) z)))
   (if (<= z -7e-97)
     t_0
     (if (<= z 2e-118)
       (- x (* x z))
       (if (<= z 4.15e-53)
         (* y z)
         (if (<= z 440000000.0) (* x (- 1.0 z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * z;
	double tmp;
	if (z <= -7e-97) {
		tmp = t_0;
	} else if (z <= 2e-118) {
		tmp = x - (x * z);
	} else if (z <= 4.15e-53) {
		tmp = y * z;
	} else if (z <= 440000000.0) {
		tmp = x * (1.0 - 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 <= (-7d-97)) then
        tmp = t_0
    else if (z <= 2d-118) then
        tmp = x - (x * z)
    else if (z <= 4.15d-53) then
        tmp = y * z
    else if (z <= 440000000.0d0) then
        tmp = x * (1.0d0 - 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 <= -7e-97) {
		tmp = t_0;
	} else if (z <= 2e-118) {
		tmp = x - (x * z);
	} else if (z <= 4.15e-53) {
		tmp = y * z;
	} else if (z <= 440000000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * z
	tmp = 0
	if z <= -7e-97:
		tmp = t_0
	elif z <= 2e-118:
		tmp = x - (x * z)
	elif z <= 4.15e-53:
		tmp = y * z
	elif z <= 440000000.0:
		tmp = x * (1.0 - 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 <= -7e-97)
		tmp = t_0;
	elseif (z <= 2e-118)
		tmp = Float64(x - Float64(x * z));
	elseif (z <= 4.15e-53)
		tmp = Float64(y * z);
	elseif (z <= 440000000.0)
		tmp = Float64(x * Float64(1.0 - 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 <= -7e-97)
		tmp = t_0;
	elseif (z <= 2e-118)
		tmp = x - (x * z);
	elseif (z <= 4.15e-53)
		tmp = y * z;
	elseif (z <= 440000000.0)
		tmp = x * (1.0 - 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, -7e-97], t$95$0, If[LessEqual[z, 2e-118], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.15e-53], N[(y * z), $MachinePrecision], If[LessEqual[z, 440000000.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.00000000000000038e-97 or 4.4e8 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 94.0%

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

   if -7.00000000000000038e-97 < z < 1.99999999999999997e-118

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 79.9%

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

      1. mul-1-neg 79.9%

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

      2. distribute-lft-neg-out 79.9%

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

      3. *-commutative 79.9%

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

   5. Simplified 79.9%

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

   if 1.99999999999999997e-118 < z < 4.1499999999999998e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.3%

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

   if 4.1499999999999998e-53 < z < 4.4e8

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. unsub-neg 64.2%

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

   5. Simplified 64.2%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-97}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-118}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;z \leq 4.15 \cdot 10^{-53}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 440000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot z\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-97}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-118}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-53}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 95000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) z)))
   (if (<= z -5.8e-97)
     t_0
     (if (<= z 1.95e-118)
       (- x (* x z))
       (if (<= z 3.9e-53)
         (* y z)
         (if (<= z 95000000.0) (* x (- 1.0 z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * z;
	double tmp;
	if (z <= -5.8e-97) {
		tmp = t_0;
	} else if (z <= 1.95e-118) {
		tmp = x - (x * z);
	} else if (z <= 3.9e-53) {
		tmp = y * z;
	} else if (z <= 95000000.0) {
		tmp = x * (1.0 - 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 <= (-5.8d-97)) then
        tmp = t_0
    else if (z <= 1.95d-118) then
        tmp = x - (x * z)
    else if (z <= 3.9d-53) then
        tmp = y * z
    else if (z <= 95000000.0d0) then
        tmp = x * (1.0d0 - 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 <= -5.8e-97) {
		tmp = t_0;
	} else if (z <= 1.95e-118) {
		tmp = x - (x * z);
	} else if (z <= 3.9e-53) {
		tmp = y * z;
	} else if (z <= 95000000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * z
	tmp = 0
	if z <= -5.8e-97:
		tmp = t_0
	elif z <= 1.95e-118:
		tmp = x - (x * z)
	elif z <= 3.9e-53:
		tmp = y * z
	elif z <= 95000000.0:
		tmp = x * (1.0 - 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 <= -5.8e-97)
		tmp = t_0;
	elseif (z <= 1.95e-118)
		tmp = Float64(x - Float64(x * z));
	elseif (z <= 3.9e-53)
		tmp = Float64(y * z);
	elseif (z <= 95000000.0)
		tmp = Float64(x * Float64(1.0 - 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 <= -5.8e-97)
		tmp = t_0;
	elseif (z <= 1.95e-118)
		tmp = x - (x * z);
	elseif (z <= 3.9e-53)
		tmp = y * z;
	elseif (z <= 95000000.0)
		tmp = x * (1.0 - 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, -5.8e-97], t$95$0, If[LessEqual[z, 1.95e-118], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e-53], N[(y * z), $MachinePrecision], If[LessEqual[z, 95000000.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.7999999999999999e-97 or 9.5e7 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 94.0%

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

   if -5.7999999999999999e-97 < z < 1.95e-118

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.9%

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

      1. mul-1-neg 79.9%

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

      2. unsub-neg 79.9%

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

   5. Simplified 79.9%

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

      1. sub-neg 79.9%

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

      2. distribute-rgt-in 79.9%

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

      3. *-un-lft-identity 79.9%

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

   7. Applied egg-rr 79.9%

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

      1. distribute-lft-neg-out 79.9%

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

      2. unsub-neg 79.9%

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

      3. *-commutative 79.9%

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

   9. Applied egg-rr 79.9%

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

   if 1.95e-118 < z < 3.9000000000000002e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.3%

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

   if 3.9000000000000002e-53 < z < 9.5e7

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. unsub-neg 64.2%

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

   5. Simplified 64.2%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-97}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-118}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-53}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 95000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot z\\ t_1 := x \cdot \left(1 - z\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-97}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-53}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 95000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) z)) (t_1 (* x (- 1.0 z))))
   (if (<= z -5.8e-97)
     t_0
     (if (<= z 2e-118)
       t_1
       (if (<= z 6.4e-53) (* y z) (if (<= z 95000000.0) 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 <= -5.8e-97) {
		tmp = t_0;
	} else if (z <= 2e-118) {
		tmp = t_1;
	} else if (z <= 6.4e-53) {
		tmp = y * z;
	} else if (z <= 95000000.0) {
		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 <= (-5.8d-97)) then
        tmp = t_0
    else if (z <= 2d-118) then
        tmp = t_1
    else if (z <= 6.4d-53) then
        tmp = y * z
    else if (z <= 95000000.0d0) 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 <= -5.8e-97) {
		tmp = t_0;
	} else if (z <= 2e-118) {
		tmp = t_1;
	} else if (z <= 6.4e-53) {
		tmp = y * z;
	} else if (z <= 95000000.0) {
		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 <= -5.8e-97:
		tmp = t_0
	elif z <= 2e-118:
		tmp = t_1
	elif z <= 6.4e-53:
		tmp = y * z
	elif z <= 95000000.0:
		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 <= -5.8e-97)
		tmp = t_0;
	elseif (z <= 2e-118)
		tmp = t_1;
	elseif (z <= 6.4e-53)
		tmp = Float64(y * z);
	elseif (z <= 95000000.0)
		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 <= -5.8e-97)
		tmp = t_0;
	elseif (z <= 2e-118)
		tmp = t_1;
	elseif (z <= 6.4e-53)
		tmp = y * z;
	elseif (z <= 95000000.0)
		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, -5.8e-97], t$95$0, If[LessEqual[z, 2e-118], t$95$1, If[LessEqual[z, 6.4e-53], N[(y * z), $MachinePrecision], If[LessEqual[z, 95000000.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.7999999999999999e-97 or 9.5e7 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 94.0%

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

   if -5.7999999999999999e-97 < z < 1.99999999999999997e-118 or 6.4000000000000002e-53 < z < 9.5e7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 77.3%

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

      1. mul-1-neg 77.3%

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

      2. unsub-neg 77.3%

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

   5. Simplified 77.3%

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

   if 1.99999999999999997e-118 < z < 6.4000000000000002e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.3%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-97}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-53}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 95000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-97} \lor \neg \left(z \leq 1.95 \cdot 10^{-118}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7e-97) (not (<= z 1.95e-118))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7e-97) || !(z <= 1.95e-118)) {
		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 <= (-7d-97)) .or. (.not. (z <= 1.95d-118))) 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 <= -7e-97) || !(z <= 1.95e-118)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7e-97) or not (z <= 1.95e-118):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7e-97) || !(z <= 1.95e-118))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7e-97) || ~((z <= 1.95e-118)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7e-97], N[Not[LessEqual[z, 1.95e-118]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.00000000000000038e-97 or 1.95e-118 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 49.7%

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

   if -7.00000000000000038e-97 < z < 1.95e-118

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 79.9%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-97} \lor \neg \left(z \leq 1.95 \cdot 10^{-118}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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 10: 35.8% 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 33.3%

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

Reproduce

herbie shell --seed 2024103 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))