Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C

Percentage Accurate: 94.6% → 96.2%

Time: 12.0s

Alternatives: 9

Speedup: 0.9×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+305}:\\ \;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 -2e+305) (/ 1.0 (/ z (* y x))) (* t_1 x))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= -2e+305) {
		tmp = 1.0 / (z / (y * x));
	} else {
		tmp = t_1 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / z) - (t / (1.0d0 - z))
    if (t_1 <= (-2d+305)) then
        tmp = 1.0d0 / (z / (y * x))
    else
        tmp = t_1 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= -2e+305) {
		tmp = 1.0 / (z / (y * x));
	} else {
		tmp = t_1 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if t_1 <= -2e+305:
		tmp = 1.0 / (z / (y * x))
	else:
		tmp = t_1 * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) - Float64(t / Float64(1.0 - z)))
	tmp = 0.0
	if (t_1 <= -2e+305)
		tmp = Float64(1.0 / Float64(z / Float64(y * x)));
	else
		tmp = Float64(t_1 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) - (t / (1.0 - z));
	tmp = 0.0;
	if (t_1 <= -2e+305)
		tmp = 1.0 / (z / (y * x));
	else
		tmp = t_1 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+305], N[(1.0 / N[(z / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -1.9999999999999999e305

   1. Initial program 39.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 39.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 39.7%

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

      1. associate-*r/ N/A

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

      2. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{z}{x \cdot y}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{z}{x \cdot y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \left(y \cdot \color{blue}{x}\right)\right)\right) \]

      6. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{y \cdot x}}} \]

   if -1.9999999999999999e305 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 96.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -2 \cdot 10^{+305}:\\ \;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -24000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\left(y - \mathsf{fma}\left(t, z, 0\right)\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (+ y t) z))))
   (if (<= z -24000.0)
     t_1
     (if (<= z 1.0) (* (- y (fma t z 0.0)) (/ x z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + t) / z);
	double tmp;
	if (z <= -24000.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = (y - fma(t, z, 0.0)) * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y + t) / z))
	tmp = 0.0
	if (z <= -24000.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(Float64(y - fma(t, z, 0.0)) * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -24000.0], t$95$1, If[LessEqual[z, 1.0], N[(N[(y - N[(t * z + 0.0), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -24000 or 1 < z

   1. Initial program 95.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - -1 \cdot t}{z}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y - -1 \cdot t\right), \color{blue}{z}\right)\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right), z\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + 1 \cdot t\right), z\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + t\right), z\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(t + y\right), z\right)\right) \]

      6. +-lowering-+.f64 95.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, y\right), z\right)\right) \]

   5. Simplified 95.6%

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

   if -24000 < z < 1

   1. Initial program 90.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot \left(t \cdot \left(x \cdot z\right)\right) + x \cdot y\right), \color{blue}{z}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + -1 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right), z\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(t \cdot \left(x \cdot z\right)\right)\right)\right), z\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - t \cdot \left(x \cdot z\right)\right), z\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(t \cdot x\right) \cdot z\right), z\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(x \cdot t\right) \cdot z\right), z\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - x \cdot \left(t \cdot z\right)\right), z\right) \]

      8. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y - t \cdot z\right)\right), z\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y + \left(\mathsf{neg}\left(t \cdot z\right)\right)\right)\right), z\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y + -1 \cdot \left(t \cdot z\right)\right)\right), z\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + -1 \cdot \left(t \cdot z\right)\right)\right), z\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + \left(\mathsf{neg}\left(t \cdot z\right)\right)\right)\right), z\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y - t \cdot z\right)\right), z\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \left(t \cdot z\right)\right)\right), z\right) \]

      15. +-rgt-identity N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \left(t \cdot z + 0\right)\right)\right), z\right) \]

      16. accelerator-lowering-fma.f64 92.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \mathsf{fma.f64}\left(t, z, 0\right)\right)\right), z\right) \]

   5. Simplified 92.6%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - \mathsf{fma}\left(t, z, 0\right)\right)}{z}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(y - \left(t \cdot z + 0\right)\right) \cdot x}{z} \]

      2. associate-/l* N/A

         \[\leadsto \left(y - \left(t \cdot z + 0\right)\right) \cdot \color{blue}{\frac{x}{z}} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y - \left(t \cdot z + 0\right)\right), \color{blue}{\left(\frac{x}{z}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, \left(t \cdot z + 0\right)\right), \left(\frac{\color{blue}{x}}{z}\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{fma.f64}\left(t, z, 0\right)\right), \left(\frac{x}{z}\right)\right) \]

      6. /-lowering-/.f64 94.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{fma.f64}\left(t, z, 0\right)\right), \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 94.0%

      \[\leadsto \color{blue}{\left(y - \mathsf{fma}\left(t, z, 0\right)\right) \cdot \frac{x}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -24000:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\left(y - \mathsf{fma}\left(t, z, 0\right)\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -24000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \mathsf{fma}\left(t, z, t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (+ y t) z))))
   (if (<= z -24000.0) t_1 (if (<= z 1.0) (* x (- (/ y z) (fma t z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + t) / z);
	double tmp;
	if (z <= -24000.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - fma(t, z, t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y + t) / z))
	tmp = 0.0
	if (z <= -24000.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(Float64(y / z) - fma(t, z, t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -24000.0], t$95$1, If[LessEqual[z, 1.0], N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -24000 or 1 < z

   1. Initial program 95.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - -1 \cdot t}{z}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y - -1 \cdot t\right), \color{blue}{z}\right)\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right), z\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + 1 \cdot t\right), z\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + t\right), z\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(t + y\right), z\right)\right) \]

      6. +-lowering-+.f64 95.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, y\right), z\right)\right) \]

   5. Simplified 95.6%

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

   if -24000 < z < 1

   1. Initial program 90.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), \color{blue}{\left(t + t \cdot z\right)}\right)\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), \left(t \cdot z + \color{blue}{t}\right)\right)\right) \]

      2. accelerator-lowering-fma.f64 89.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), \mathsf{fma.f64}\left(t, \color{blue}{z}, t\right)\right)\right) \]

   5. Simplified 89.4%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -24000:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \mathsf{fma}\left(t, z, t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= z -5.2e+85)
     t_1
     (if (<= z 2.5e+32)
       (* x (- (/ y z) t))
       (if (<= z 1.05e+84) t_1 (* (/ y z) x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (z <= -5.2e+85) {
		tmp = t_1;
	} else if (z <= 2.5e+32) {
		tmp = x * ((y / z) - t);
	} else if (z <= 1.05e+84) {
		tmp = t_1;
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (z <= (-5.2d+85)) then
        tmp = t_1
    else if (z <= 2.5d+32) then
        tmp = x * ((y / z) - t)
    else if (z <= 1.05d+84) then
        tmp = t_1
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (z <= -5.2e+85) {
		tmp = t_1;
	} else if (z <= 2.5e+32) {
		tmp = x * ((y / z) - t);
	} else if (z <= 1.05e+84) {
		tmp = t_1;
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if z <= -5.2e+85:
		tmp = t_1
	elif z <= 2.5e+32:
		tmp = x * ((y / z) - t)
	elif z <= 1.05e+84:
		tmp = t_1
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (z <= -5.2e+85)
		tmp = t_1;
	elseif (z <= 2.5e+32)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 1.05e+84)
		tmp = t_1;
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (z <= -5.2e+85)
		tmp = t_1;
	elseif (z <= 2.5e+32)
		tmp = x * ((y / z) - t);
	elseif (z <= 1.05e+84)
		tmp = t_1;
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+85], t$95$1, If[LessEqual[z, 2.5e+32], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+84], t$95$1, N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.20000000000000021e85 or 2.4999999999999999e32 < z < 1.05000000000000009e84

   1. Initial program 94.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - -1 \cdot t}{z}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y - -1 \cdot t\right), \color{blue}{z}\right)\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right), z\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + 1 \cdot t\right), z\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + t\right), z\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(t + y\right), z\right)\right) \]

      6. +-lowering-+.f64 94.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, y\right), z\right)\right) \]

   5. Simplified 94.7%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{t}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 60.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   8. Simplified 60.1%

      \[\leadsto x \cdot \color{blue}{\frac{t}{z}} \]

   if -5.20000000000000021e85 < z < 2.4999999999999999e32

   1. Initial program 91.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), \color{blue}{t}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 84.6%

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

   if 1.05000000000000009e84 < z

   1. Initial program 95.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 65.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 65.1%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -24000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (+ y t) z))))
   (if (<= z -24000.0) t_1 (if (<= z 1.0) (* x (- (/ y z) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + t) / z);
	double tmp;
	if (z <= -24000.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y + t) / z)
    if (z <= (-24000.0d0)) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + t) / z);
	double tmp;
	if (z <= -24000.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y + t) / z)
	tmp = 0
	if z <= -24000.0:
		tmp = t_1
	elif z <= 1.0:
		tmp = x * ((y / z) - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y + t) / z))
	tmp = 0.0
	if (z <= -24000.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y + t) / z);
	tmp = 0.0;
	if (z <= -24000.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = x * ((y / z) - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -24000.0], t$95$1, If[LessEqual[z, 1.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -24000 or 1 < z

   1. Initial program 95.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - -1 \cdot t}{z}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y - -1 \cdot t\right), \color{blue}{z}\right)\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right), z\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + 1 \cdot t\right), z\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + t\right), z\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(t + y\right), z\right)\right) \]

      6. +-lowering-+.f64 95.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, y\right), z\right)\right) \]

   5. Simplified 95.6%

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

   if -24000 < z < 1

   1. Initial program 90.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), \color{blue}{t}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 88.5%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -24000:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z + -1}\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (+ z -1.0)))))
   (if (<= t -4.4e+157) t_1 (if (<= t 1.7e-52) (* y (/ x z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z + -1.0));
	double tmp;
	if (t <= -4.4e+157) {
		tmp = t_1;
	} else if (t <= 1.7e-52) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / (z + (-1.0d0)))
    if (t <= (-4.4d+157)) then
        tmp = t_1
    else if (t <= 1.7d-52) then
        tmp = y * (x / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z + -1.0));
	double tmp;
	if (t <= -4.4e+157) {
		tmp = t_1;
	} else if (t <= 1.7e-52) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / (z + -1.0))
	tmp = 0
	if t <= -4.4e+157:
		tmp = t_1
	elif t <= 1.7e-52:
		tmp = y * (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t <= -4.4e+157)
		tmp = t_1;
	elseif (t <= 1.7e-52)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / (z + -1.0));
	tmp = 0.0;
	if (t <= -4.4e+157)
		tmp = t_1;
	elseif (t <= 1.7e-52)
		tmp = y * (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e+157], t$95$1, If[LessEqual[t, 1.7e-52], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4000000000000002e157 or 1.70000000000000009e-52 < t

   1. Initial program 94.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{t}{1 - z}\right)\right)\right) \]

      2. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{t}{\color{blue}{\mathsf{neg}\left(\left(1 - z\right)\right)}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\left(1 - z\right)\right)\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + -1 \cdot z\right)\right)\right)\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\color{blue}{-1 \cdot z}\right)\right)\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      9. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + z\right)\right)\right) \]

      10. +-lowering-+.f64 72.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{+.f64}\left(-1, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 72.8%

      \[\leadsto x \cdot \color{blue}{\frac{t}{-1 + z}} \]

   if -4.4000000000000002e157 < t < 1.70000000000000009e-52

   1. Initial program 92.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 78.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 78.4%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto \frac{y \cdot x}{z} \]

      2. associate-*r/ N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{z}\right)}\right) \]

      4. /-lowering-/.f64 78.6%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right) \]

   8. Simplified 78.6%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+81}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -4.4e+157) t_1 (if (<= t 1.55e+81) (* (/ y z) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -4.4e+157) {
		tmp = t_1;
	} else if (t <= 1.55e+81) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-4.4d+157)) then
        tmp = t_1
    else if (t <= 1.55d+81) then
        tmp = (y / z) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -4.4e+157) {
		tmp = t_1;
	} else if (t <= 1.55e+81) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -4.4e+157:
		tmp = t_1
	elif t <= 1.55e+81:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -4.4e+157)
		tmp = t_1;
	elseif (t <= 1.55e+81)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -4.4e+157)
		tmp = t_1;
	elseif (t <= 1.55e+81)
		tmp = (y / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e+157], t$95$1, If[LessEqual[t, 1.55e+81], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4000000000000002e157 or 1.55e81 < t

   1. Initial program 92.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - -1 \cdot t}{z}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y - -1 \cdot t\right), \color{blue}{z}\right)\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right), z\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + 1 \cdot t\right), z\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + t\right), z\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(t + y\right), z\right)\right) \]

      6. +-lowering-+.f64 65.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, y\right), z\right)\right) \]

   5. Simplified 65.8%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{t}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 62.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   8. Simplified 62.9%

      \[\leadsto x \cdot \color{blue}{\frac{t}{z}} \]

   if -4.4000000000000002e157 < t < 1.55e81

   1. Initial program 93.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 75.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 75.1%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+81}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 45.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -0.75:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(t \cdot \left(-1 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= z -0.75) t_1 (if (<= z 1.0) (* x (* t (- -1.0 z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (z <= -0.75) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x * (t * (-1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (z <= (-0.75d0)) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = x * (t * ((-1.0d0) - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (z <= -0.75) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x * (t * (-1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if z <= -0.75:
		tmp = t_1
	elif z <= 1.0:
		tmp = x * (t * (-1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (z <= -0.75)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(t * Float64(-1.0 - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (z <= -0.75)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = x * (t * (-1.0 - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.75], t$95$1, If[LessEqual[z, 1.0], N[(x * N[(t * N[(-1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.75 or 1 < z

   1. Initial program 96.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - -1 \cdot t}{z}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y - -1 \cdot t\right), \color{blue}{z}\right)\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right), z\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + 1 \cdot t\right), z\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + t\right), z\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(t + y\right), z\right)\right) \]

      6. +-lowering-+.f64 95.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, y\right), z\right)\right) \]

   5. Simplified 95.6%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{t}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 53.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   8. Simplified 53.4%

      \[\leadsto x \cdot \color{blue}{\frac{t}{z}} \]

   if -0.75 < z < 1

   1. Initial program 90.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{z} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{1 - z}\right)\right)}\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{t}{1 - z}\right)\right) + \color{blue}{\frac{y}{z}}\right)\right) \]

      3. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{t}{\mathsf{neg}\left(\left(1 - z\right)\right)} + \frac{\color{blue}{y}}{z}\right)\right) \]

      4. div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(t \cdot \frac{1}{\mathsf{neg}\left(\left(1 - z\right)\right)} + \frac{\color{blue}{y}}{z}\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fma.f64}\left(t, \color{blue}{\left(\frac{1}{\mathsf{neg}\left(\left(1 - z\right)\right)}\right)}, \left(\frac{y}{z}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fma.f64}\left(t, \mathsf{/.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(\left(1 - z\right)\right)\right)}\right), \left(\frac{y}{z}\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fma.f64}\left(t, \mathsf{/.f64}\left(1, \left(\mathsf{neg}\left(\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right), \left(\frac{y}{z}\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fma.f64}\left(t, \mathsf{/.f64}\left(1, \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)}\right)\right), \left(\frac{y}{z}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fma.f64}\left(t, \mathsf{/.f64}\left(1, \left(-1 + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right), \left(\frac{y}{z}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fma.f64}\left(t, \mathsf{/.f64}\left(1, \left(-1 + z\right)\right), \left(\frac{y}{z}\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fma.f64}\left(t, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(-1, \color{blue}{z}\right)\right), \left(\frac{y}{z}\right)\right)\right) \]

      12. /-lowering-/.f64 90.4%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fma.f64}\left(t, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(-1, z\right)\right), \mathsf{/.f64}\left(y, z\right)\right)\right) \]

   4. Applied egg-rr 90.4%

      \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(t, \frac{1}{-1 + z}, \frac{y}{z}\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fma.f64}\left(t, \color{blue}{\left(-1 \cdot z - 1\right)}, \mathsf{/.f64}\left(y, z\right)\right)\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fma.f64}\left(t, \left(-1 \cdot z + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right), \mathsf{/.f64}\left(y, z\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fma.f64}\left(t, \left(-1 \cdot z + -1\right), \mathsf{/.f64}\left(y, z\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fma.f64}\left(t, \left(-1 + \color{blue}{-1 \cdot z}\right), \mathsf{/.f64}\left(y, z\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fma.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(z\right)\right)\right), \mathsf{/.f64}\left(y, z\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fma.f64}\left(t, \left(-1 - \color{blue}{z}\right), \mathsf{/.f64}\left(y, z\right)\right)\right) \]

      6. --lowering--.f64 89.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fma.f64}\left(t, \mathsf{\_.f64}\left(-1, \color{blue}{z}\right), \mathsf{/.f64}\left(y, z\right)\right)\right) \]

   7. Simplified 89.4%

      \[\leadsto x \cdot \mathsf{fma}\left(t, \color{blue}{-1 - z}, \frac{y}{z}\right) \]

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(t \cdot \left(1 + z\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(t \cdot \left(1 + z\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(\left(1 + z\right)\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(t \cdot \left(-1 \cdot \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(1 + z\right)\right)}\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \left(-1 \cdot 1 + \color{blue}{-1 \cdot z}\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \left(-1 + \color{blue}{-1} \cdot z\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \left(-1 - \color{blue}{z}\right)\right)\right) \]

      9. --lowering--.f64 31.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(-1, \color{blue}{z}\right)\right)\right) \]

   10. Simplified 31.7%

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

Alternative 9: 23.0% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ t \cdot \left(0 - x\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* t (- 0.0 x)))

C

double code(double x, double y, double z, double t) {
	return t * (0.0 - x);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t * (0.0d0 - x)
end function

Java

public static double code(double x, double y, double z, double t) {
	return t * (0.0 - x);
}

Python

def code(x, y, z, t):
	return t * (0.0 - x)

Julia

function code(x, y, z, t)
	return Float64(t * Float64(0.0 - x))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t * (0.0 - x);
end

Wolfram

code[x_, y_, z_, t_] := N[(t * N[(0.0 - x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.1%

   \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0

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

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot \left(t \cdot \left(x \cdot z\right)\right) + x \cdot y\right), \color{blue}{z}\right) \]

   2. +-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + -1 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right), z\right) \]

   3. mul-1-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(t \cdot \left(x \cdot z\right)\right)\right)\right), z\right) \]

   4. unsub-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - t \cdot \left(x \cdot z\right)\right), z\right) \]

   5. associate-*r* N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(t \cdot x\right) \cdot z\right), z\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(x \cdot t\right) \cdot z\right), z\right) \]

   7. associate-*l* N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - x \cdot \left(t \cdot z\right)\right), z\right) \]

   8. distribute-lft-out-- N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y - t \cdot z\right)\right), z\right) \]

   9. unsub-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y + \left(\mathsf{neg}\left(t \cdot z\right)\right)\right)\right), z\right) \]

   10. mul-1-neg N/A

       \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y + -1 \cdot \left(t \cdot z\right)\right)\right), z\right) \]

   11. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + -1 \cdot \left(t \cdot z\right)\right)\right), z\right) \]

   12. mul-1-neg N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + \left(\mathsf{neg}\left(t \cdot z\right)\right)\right)\right), z\right) \]

   13. unsub-neg N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y - t \cdot z\right)\right), z\right) \]

   14. --lowering--.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \left(t \cdot z\right)\right)\right), z\right) \]

   15. +-rgt-identity N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \left(t \cdot z + 0\right)\right)\right), z\right) \]

   16. accelerator-lowering-fma.f64 63.8%

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \mathsf{fma.f64}\left(t, z, 0\right)\right)\right), z\right) \]

5. Simplified 63.8%

   \[\leadsto \color{blue}{\frac{x \cdot \left(y - \mathsf{fma}\left(t, z, 0\right)\right)}{z}} \]

6. Taylor expanded in y around 0

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

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(t \cdot x\right) \]

   2. neg-sub0 N/A

      \[\leadsto 0 - \color{blue}{t \cdot x} \]

   3. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot x\right)}\right) \]

   4. *-lowering-*.f64 22.2%

      \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right) \]

8. Simplified 22.2%

   \[\leadsto \color{blue}{0 - t \cdot x} \]

9. Final simplification 22.2%

   \[\leadsto t \cdot \left(0 - x\right) \]
10. Add Preprocessing

Developer Target 1: 94.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t\_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))))
        (t_2 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (< t_2 -7.623226303312042e-196)
     t_1
     (if (< t_2 1.4133944927702302e-211)
       (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z))))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - (t * (1.0d0 / (1.0d0 - z))))
    t_2 = x * ((y / z) - (t / (1.0d0 - z)))
    if (t_2 < (-7.623226303312042d-196)) then
        tmp = t_1
    else if (t_2 < 1.4133944927702302d-211) then
        tmp = ((y * x) / z) + -((t * x) / (1.0d0 - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))))
	t_2 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_2 < -7.623226303312042e-196:
		tmp = t_1
	elif t_2 < 1.4133944927702302e-211:
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t * Float64(1.0 / Float64(1.0 - z)))))
	t_2 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = Float64(Float64(Float64(y * x) / z) + Float64(-Float64(Float64(t * x) / Float64(1.0 - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	t_2 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -7.623226303312042e-196], t$95$1, If[Less[t$95$2, 1.4133944927702302e-211], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] + (-N[(N[(t * x), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024193 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- (/ y z) (/ t (- 1 z)))) -3811613151656021/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* x (- (/ y z) (* t (/ 1 (- 1 z))))) (if (< (* x (- (/ y z) (/ t (- 1 z)))) 7066972463851151/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (/ (* y x) z) (- (/ (* t x) (- 1 z)))) (* x (- (/ y z) (* t (/ 1 (- 1 z))))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))