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

Percentage Accurate: 100.0% → 100.0%

Time: 5.8s

Alternatives: 8

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 99.9%

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

   1. +-commutative 99.9%

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

   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: 72.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-58} \lor \neg \left(x \leq -9.9 \cdot 10^{-144} \lor \neg \left(x \leq -1.3 \cdot 10^{-189}\right) \land \left(x \leq 4.6 \cdot 10^{-200} \lor \neg \left(x \leq 1.3 \cdot 10^{-119}\right) \land x \leq 2.7 \cdot 10^{-13}\right)\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.15e-58)
         (not
          (or (<= x -9.9e-144)
              (and (not (<= x -1.3e-189))
                   (or (<= x 4.6e-200)
                       (and (not (<= x 1.3e-119)) (<= x 2.7e-13)))))))
   (* x (- 1.0 z))
   (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.15e-58) || !((x <= -9.9e-144) || (!(x <= -1.3e-189) && ((x <= 4.6e-200) || (!(x <= 1.3e-119) && (x <= 2.7e-13)))))) {
		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 <= (-1.15d-58)) .or. (.not. (x <= (-9.9d-144)) .or. (.not. (x <= (-1.3d-189))) .and. (x <= 4.6d-200) .or. (.not. (x <= 1.3d-119)) .and. (x <= 2.7d-13))) 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 <= -1.15e-58) || !((x <= -9.9e-144) || (!(x <= -1.3e-189) && ((x <= 4.6e-200) || (!(x <= 1.3e-119) && (x <= 2.7e-13)))))) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.15e-58) or not ((x <= -9.9e-144) or (not (x <= -1.3e-189) and ((x <= 4.6e-200) or (not (x <= 1.3e-119) and (x <= 2.7e-13))))):
		tmp = x * (1.0 - z)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.15e-58) || !((x <= -9.9e-144) || (!(x <= -1.3e-189) && ((x <= 4.6e-200) || (!(x <= 1.3e-119) && (x <= 2.7e-13))))))
		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 <= -1.15e-58) || ~(((x <= -9.9e-144) || (~((x <= -1.3e-189)) && ((x <= 4.6e-200) || (~((x <= 1.3e-119)) && (x <= 2.7e-13)))))))
		tmp = x * (1.0 - z);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.15e-58], N[Not[Or[LessEqual[x, -9.9e-144], And[N[Not[LessEqual[x, -1.3e-189]], $MachinePrecision], Or[LessEqual[x, 4.6e-200], And[N[Not[LessEqual[x, 1.3e-119]], $MachinePrecision], LessEqual[x, 2.7e-13]]]]]], $MachinePrecision]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1499999999999999e-58 or -9.90000000000000042e-144 < x < -1.2999999999999999e-189 or 4.60000000000000015e-200 < x < 1.30000000000000006e-119 or 2.70000000000000011e-13 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 84.6%

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

      1. mul-1-neg 84.6%

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

      2. unsub-neg 84.6%

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

   5. Simplified 84.6%

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

   if -1.1499999999999999e-58 < x < -9.90000000000000042e-144 or -1.2999999999999999e-189 < x < 4.60000000000000015e-200 or 1.30000000000000006e-119 < x < 2.70000000000000011e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 89.9%

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

      1. *-commutative 89.9%

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

   5. Simplified 89.9%

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

   6. Taylor expanded in y around inf 89.9%

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

   7. Taylor expanded in y around inf 79.9%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-58} \lor \neg \left(x \leq -9.9 \cdot 10^{-144} \lor \neg \left(x \leq -1.3 \cdot 10^{-189}\right) \land \left(x \leq 4.6 \cdot 10^{-200} \lor \neg \left(x \leq 1.3 \cdot 10^{-119}\right) \land x \leq 2.7 \cdot 10^{-13}\right)\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+53}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-60}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-164}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-170}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -1.7e+53)
     t_0
     (if (<= z -5.2e-60)
       (* y z)
       (if (<= z -5.8e-164)
         x
         (if (<= z -2.2e-170)
           (* y z)
           (if (<= z 1.0) x (if (<= z 1.15e+171) t_0 (* y z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -1.7e+53) {
		tmp = t_0;
	} else if (z <= -5.2e-60) {
		tmp = y * z;
	} else if (z <= -5.8e-164) {
		tmp = x;
	} else if (z <= -2.2e-170) {
		tmp = y * z;
	} else if (z <= 1.0) {
		tmp = x;
	} else if (z <= 1.15e+171) {
		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 <= (-1.7d+53)) then
        tmp = t_0
    else if (z <= (-5.2d-60)) then
        tmp = y * z
    else if (z <= (-5.8d-164)) then
        tmp = x
    else if (z <= (-2.2d-170)) then
        tmp = y * z
    else if (z <= 1.0d0) then
        tmp = x
    else if (z <= 1.15d+171) 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 <= -1.7e+53) {
		tmp = t_0;
	} else if (z <= -5.2e-60) {
		tmp = y * z;
	} else if (z <= -5.8e-164) {
		tmp = x;
	} else if (z <= -2.2e-170) {
		tmp = y * z;
	} else if (z <= 1.0) {
		tmp = x;
	} else if (z <= 1.15e+171) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -1.7e+53:
		tmp = t_0
	elif z <= -5.2e-60:
		tmp = y * z
	elif z <= -5.8e-164:
		tmp = x
	elif z <= -2.2e-170:
		tmp = y * z
	elif z <= 1.0:
		tmp = x
	elif z <= 1.15e+171:
		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 <= -1.7e+53)
		tmp = t_0;
	elseif (z <= -5.2e-60)
		tmp = Float64(y * z);
	elseif (z <= -5.8e-164)
		tmp = x;
	elseif (z <= -2.2e-170)
		tmp = Float64(y * z);
	elseif (z <= 1.0)
		tmp = x;
	elseif (z <= 1.15e+171)
		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 <= -1.7e+53)
		tmp = t_0;
	elseif (z <= -5.2e-60)
		tmp = y * z;
	elseif (z <= -5.8e-164)
		tmp = x;
	elseif (z <= -2.2e-170)
		tmp = y * z;
	elseif (z <= 1.0)
		tmp = x;
	elseif (z <= 1.15e+171)
		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, -1.7e+53], t$95$0, If[LessEqual[z, -5.2e-60], N[(y * z), $MachinePrecision], If[LessEqual[z, -5.8e-164], x, If[LessEqual[z, -2.2e-170], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.0], x, If[LessEqual[z, 1.15e+171], t$95$0, N[(y * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.69999999999999999e53 or 1 < z < 1.15000000000000009e171

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. associate--l+ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around inf 98.7%

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

      1. mul-1-neg 98.7%

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

   8. Simplified 98.7%

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

   9. Taylor expanded in y around 0 63.3%

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

       1. associate-*r* 63.3%

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

       2. mul-1-neg 63.3%

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

   11. Simplified 63.3%

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

   if -1.69999999999999999e53 < z < -5.1999999999999995e-60 or -5.8e-164 < z < -2.20000000000000015e-170 or 1.15000000000000009e171 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 75.1%

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

      1. *-commutative 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in y around inf 73.4%

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

   7. Taylor expanded in y around inf 69.2%

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

   if -5.1999999999999995e-60 < z < -5.8e-164 or -2.20000000000000015e-170 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 70.8%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-60}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-164}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-170}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (y - x) * z
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. associate--l+ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 98.5%

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

      1. mul-1-neg 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in z around 0 98.5%

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

   if -1 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.0%

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

      1. *-commutative 99.0%

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

   5. Simplified 99.0%

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

4. Final simplification 98.7%

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

Alternative 5: 81.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -840 \lor \neg \left(x \leq 7.2 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -840.0) (not (<= x 7.2e-13))) (* x (- 1.0 z)) (* (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -840.0) || !(x <= 7.2e-13)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = (y - x) * 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 <= (-840.0d0)) .or. (.not. (x <= 7.2d-13))) then
        tmp = x * (1.0d0 - z)
    else
        tmp = (y - x) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -840.0) || !(x <= 7.2e-13)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = (y - x) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -840.0) or not (x <= 7.2e-13):
		tmp = x * (1.0 - z)
	else:
		tmp = (y - x) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -840.0) || !(x <= 7.2e-13))
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(Float64(y - x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -840.0) || ~((x <= 7.2e-13)))
		tmp = x * (1.0 - z);
	else
		tmp = (y - x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -840.0], N[Not[LessEqual[x, 7.2e-13]], $MachinePrecision]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -840 or 7.1999999999999996e-13 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 89.8%

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

      1. mul-1-neg 89.8%

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

      2. unsub-neg 89.8%

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

   5. Simplified 89.8%

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

   if -840 < x < 7.1999999999999996e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. associate--l+ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around inf 83.5%

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

      1. mul-1-neg 83.5%

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

   8. Simplified 83.5%

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

   9. Taylor expanded in z around 0 83.5%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -840 \lor \neg \left(x \leq 7.2 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -60000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-13}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -60000.0) x (if (<= x 5.2e-13) (* y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -60000.0) {
		tmp = x;
	} else if (x <= 5.2e-13) {
		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 <= (-60000.0d0)) then
        tmp = x
    else if (x <= 5.2d-13) 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 <= -60000.0) {
		tmp = x;
	} else if (x <= 5.2e-13) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -60000.0:
		tmp = x
	elif x <= 5.2e-13:
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -60000.0)
		tmp = x;
	elseif (x <= 5.2e-13)
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -60000.0)
		tmp = x;
	elseif (x <= 5.2e-13)
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -60000.0], x, If[LessEqual[x, 5.2e-13], N[(y * z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -6e4 or 5.2000000000000001e-13 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 50.7%

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

   if -6e4 < x < 5.2000000000000001e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 82.7%

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

      1. *-commutative 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in y around inf 82.6%

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

   7. Taylor expanded in y around inf 67.1%

      \[\leadsto \color{blue}{y \cdot z} \]
3. Recombined 2 regimes into one program.
4. 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 99.9%

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

Alternative 8: 35.7% 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 99.9%

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

3. Taylor expanded in z around 0 33.7%

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

Reproduce

herbie shell --seed 2024088 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))