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

Percentage Accurate: 93.8% → 95.9%

Time: 8.3s

Alternatives: 12

Speedup: 0.5×

• 20.9% 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: 93.8% 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: 95.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+276}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{\mathsf{fma}\left(1 - z, y, \left(-z\right) \cdot t\right)}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 -1e+276)
     (* (/ x z) (/ (fma (- 1.0 z) y (* (- z) t)) (- 1.0 z)))
     (* x t_1))))

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 <= -1e+276) {
		tmp = (x / z) * (fma((1.0 - z), y, (-z * t)) / (1.0 - z));
	} else {
		tmp = x * t_1;
	}
	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 <= -1e+276)
		tmp = Float64(Float64(x / z) * Float64(fma(Float64(1.0 - z), y, Float64(Float64(-z) * t)) / Float64(1.0 - z)));
	else
		tmp = Float64(x * t_1);
	end
	return 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, -1e+276], N[(N[(x / z), $MachinePrecision] * N[(N[(N[(1.0 - z), $MachinePrecision] * y + N[((-z) * t), $MachinePrecision]), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -1.0000000000000001e276

   1. Initial program 76.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. frac-sub N/A

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

      7. associate-*l/ N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

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

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lower-/.f64 100.0

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

   4. Applied rewrites 100.0%

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

   if -1.0000000000000001e276 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 97.3%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -1 \cdot 10^{+276}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{\mathsf{fma}\left(1 - z, y, \left(-z\right) \cdot t\right)}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.9% accurate, 0.5× speedup

Math

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

FPCore

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

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 <= -((double) INFINITY)) {
		tmp = (x / z) * y;
	} else {
		tmp = x * t_1;
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = (x / z) * y;
	} else {
		tmp = x * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x / z) * y
	else:
		tmp = x * t_1
	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 <= Float64(-Inf))
		tmp = Float64(Float64(x / z) * y);
	else
		tmp = Float64(x * t_1);
	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 <= -Inf)
		tmp = (x / z) * y;
	else
		tmp = x * t_1;
	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, (-Infinity)], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision], N[(x * t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -inf.0

   1. Initial program 70.6%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 99.8

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

   5. Applied rewrites 99.8%

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

   7. Applied rewrites 100.0%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 97.3%

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

Alternative 3: 73.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot t}{z - 1}\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-145}:\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x t) (- z 1.0))))
   (if (<= t -4.3e+166)
     t_1
     (if (<= t -3.3e-145)
       (/ (* (+ t y) x) z)
       (if (<= t 5.6e+50) (* (/ y z) x) 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 <= -4.3e+166) {
		tmp = t_1;
	} else if (t <= -3.3e-145) {
		tmp = ((t + y) * x) / z;
	} else if (t <= 5.6e+50) {
		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 - 1.0d0)
    if (t <= (-4.3d+166)) then
        tmp = t_1
    else if (t <= (-3.3d-145)) then
        tmp = ((t + y) * x) / z
    else if (t <= 5.6d+50) 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 - 1.0);
	double tmp;
	if (t <= -4.3e+166) {
		tmp = t_1;
	} else if (t <= -3.3e-145) {
		tmp = ((t + y) * x) / z;
	} else if (t <= 5.6e+50) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * t) / (z - 1.0)
	tmp = 0
	if t <= -4.3e+166:
		tmp = t_1
	elif t <= -3.3e-145:
		tmp = ((t + y) * x) / z
	elif t <= 5.6e+50:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * t) / Float64(z - 1.0))
	tmp = 0.0
	if (t <= -4.3e+166)
		tmp = t_1;
	elseif (t <= -3.3e-145)
		tmp = Float64(Float64(Float64(t + y) * x) / z);
	elseif (t <= 5.6e+50)
		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 - 1.0);
	tmp = 0.0;
	if (t <= -4.3e+166)
		tmp = t_1;
	elseif (t <= -3.3e-145)
		tmp = ((t + y) * x) / z;
	elseif (t <= 5.6e+50)
		tmp = (y / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * t), $MachinePrecision] / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.3e+166], t$95$1, If[LessEqual[t, -3.3e-145], N[(N[(N[(t + y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 5.6e+50], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.3e166 or 5.5999999999999996e50 < t

   1. Initial program 96.4%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot x}{1 - z}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 70.7

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

   5. Applied rewrites 70.7%

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

   if -4.3e166 < t < -3.29999999999999981e-145

   1. Initial program 98.0%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 97.8

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in z around inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-commutative N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 82.4

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

   7. Applied rewrites 82.4%

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

   if -3.29999999999999981e-145 < t < 5.5999999999999996e50

   1. Initial program 93.3%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 85.6

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

   5. Applied rewrites 85.6%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+166}:\\ \;\;\;\;\frac{x \cdot t}{z - 1}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-145}:\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z - 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+174}:\\ \;\;\;\;\left(-x\right) \cdot t\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-194}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.5e+174)
   (* (- x) t)
   (if (<= t 9.2e-194)
     (/ (* x y) z)
     (if (<= t 7.4e+58) (* (/ x z) y) (* (/ t z) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.5e+174) {
		tmp = -x * t;
	} else if (t <= 9.2e-194) {
		tmp = (x * y) / z;
	} else if (t <= 7.4e+58) {
		tmp = (x / z) * y;
	} else {
		tmp = (t / 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) :: tmp
    if (t <= (-4.5d+174)) then
        tmp = -x * t
    else if (t <= 9.2d-194) then
        tmp = (x * y) / z
    else if (t <= 7.4d+58) then
        tmp = (x / z) * y
    else
        tmp = (t / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.5e+174) {
		tmp = -x * t;
	} else if (t <= 9.2e-194) {
		tmp = (x * y) / z;
	} else if (t <= 7.4e+58) {
		tmp = (x / z) * y;
	} else {
		tmp = (t / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.5e+174:
		tmp = -x * t
	elif t <= 9.2e-194:
		tmp = (x * y) / z
	elif t <= 7.4e+58:
		tmp = (x / z) * y
	else:
		tmp = (t / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.5e+174)
		tmp = Float64(Float64(-x) * t);
	elseif (t <= 9.2e-194)
		tmp = Float64(Float64(x * y) / z);
	elseif (t <= 7.4e+58)
		tmp = Float64(Float64(x / z) * y);
	else
		tmp = Float64(Float64(t / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.5e+174)
		tmp = -x * t;
	elseif (t <= 9.2e-194)
		tmp = (x * y) / z;
	elseif (t <= 7.4e+58)
		tmp = (x / z) * y;
	else
		tmp = (t / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.5e+174], N[((-x) * t), $MachinePrecision], If[LessEqual[t, 9.2e-194], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 7.4e+58], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.50000000000000042e174

   1. Initial program 97.2%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot x}{1 - z}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 73.0

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

   5. Applied rewrites 73.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 59.1%

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

   if -4.50000000000000042e174 < t < 9.2000000000000001e-194

   1. Initial program 94.7%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 77.8

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

   5. Applied rewrites 77.8%

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

   if 9.2000000000000001e-194 < t < 7.4000000000000004e58

   1. Initial program 93.6%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 70.8

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

   5. Applied rewrites 70.8%

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

   7. Applied rewrites 80.1%

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

   if 7.4000000000000004e58 < t

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 64.5

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

   5. Applied rewrites 64.5%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 56.3%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+174}:\\ \;\;\;\;\left(-x\right) \cdot t\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-194}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-x\right) \cdot t\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-194}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x) t)))
   (if (<= t -4.5e+174)
     t_1
     (if (<= t 9.2e-194)
       (/ (* x y) z)
       (if (<= t 1.2e+143) (* (/ x z) y) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x * t;
	double tmp;
	if (t <= -4.5e+174) {
		tmp = t_1;
	} else if (t <= 9.2e-194) {
		tmp = (x * y) / z;
	} else if (t <= 1.2e+143) {
		tmp = (x / z) * y;
	} 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
    if (t <= (-4.5d+174)) then
        tmp = t_1
    else if (t <= 9.2d-194) then
        tmp = (x * y) / z
    else if (t <= 1.2d+143) then
        tmp = (x / z) * y
    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;
	double tmp;
	if (t <= -4.5e+174) {
		tmp = t_1;
	} else if (t <= 9.2e-194) {
		tmp = (x * y) / z;
	} else if (t <= 1.2e+143) {
		tmp = (x / z) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x * t
	tmp = 0
	if t <= -4.5e+174:
		tmp = t_1
	elif t <= 9.2e-194:
		tmp = (x * y) / z
	elif t <= 1.2e+143:
		tmp = (x / z) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) * t)
	tmp = 0.0
	if (t <= -4.5e+174)
		tmp = t_1;
	elseif (t <= 9.2e-194)
		tmp = Float64(Float64(x * y) / z);
	elseif (t <= 1.2e+143)
		tmp = Float64(Float64(x / z) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x * t;
	tmp = 0.0;
	if (t <= -4.5e+174)
		tmp = t_1;
	elseif (t <= 9.2e-194)
		tmp = (x * y) / z;
	elseif (t <= 1.2e+143)
		tmp = (x / z) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) * t), $MachinePrecision]}, If[LessEqual[t, -4.5e+174], t$95$1, If[LessEqual[t, 9.2e-194], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 1.2e+143], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.50000000000000042e174 or 1.1999999999999999e143 < t

   1. Initial program 96.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot x}{1 - z}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 76.2

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

   5. Applied rewrites 76.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 52.1%

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

   if -4.50000000000000042e174 < t < 9.2000000000000001e-194

   1. Initial program 94.7%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 77.8

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

   5. Applied rewrites 77.8%

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

   if 9.2000000000000001e-194 < t < 1.1999999999999999e143

   1. Initial program 94.9%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 65.5

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

   5. Applied rewrites 65.5%

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

   7. Applied rewrites 72.7%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+174}:\\ \;\;\;\;\left(-x\right) \cdot t\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-194}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y}{z} \cdot x\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-9}:\\ \;\;\;\;\left(\frac{y}{z} - t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (+ t y) z) x)))
   (if (<= z -1.0) t_1 (if (<= z 2.4e-9) (* (- (/ y z) t) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((t + y) / z) * x;
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 2.4e-9) {
		tmp = ((y / z) - t) * 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 = ((t + y) / z) * x
    if (z <= (-1.0d0)) then
        tmp = t_1
    else if (z <= 2.4d-9) then
        tmp = ((y / z) - t) * 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 = ((t + y) / z) * x;
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 2.4e-9) {
		tmp = ((y / z) - t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((t + y) / z) * x
	tmp = 0
	if z <= -1.0:
		tmp = t_1
	elif z <= 2.4e-9:
		tmp = ((y / z) - t) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(t + y) / z) * x)
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= 2.4e-9)
		tmp = Float64(Float64(Float64(y / z) - t) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((t + y) / z) * x;
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= 2.4e-9)
		tmp = ((y / z) - t) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$1, If[LessEqual[z, 2.4e-9], N[(N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 2.4e-9 < z

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 97.5

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

   5. Applied rewrites 97.5%

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

   if -1 < z < 2.4e-9

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 92.2

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

   5. Applied rewrites 92.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 92.3%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;\frac{t + y}{z} \cdot x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-9}:\\ \;\;\;\;\left(\frac{y}{z} - t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(t + y\right) \cdot x}{z}\\ \mathbf{if}\;z \leq -1.1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-9}:\\ \;\;\;\;\left(\frac{y}{z} - t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* (+ t y) x) z)))
   (if (<= z -1.1) t_1 (if (<= z 2.4e-9) (* (- (/ y z) t) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((t + y) * x) / z;
	double tmp;
	if (z <= -1.1) {
		tmp = t_1;
	} else if (z <= 2.4e-9) {
		tmp = ((y / z) - t) * 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 = ((t + y) * x) / z
    if (z <= (-1.1d0)) then
        tmp = t_1
    else if (z <= 2.4d-9) then
        tmp = ((y / z) - t) * 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 = ((t + y) * x) / z;
	double tmp;
	if (z <= -1.1) {
		tmp = t_1;
	} else if (z <= 2.4e-9) {
		tmp = ((y / z) - t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((t + y) * x) / z
	tmp = 0
	if z <= -1.1:
		tmp = t_1
	elif z <= 2.4e-9:
		tmp = ((y / z) - t) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(t + y) * x) / z)
	tmp = 0.0
	if (z <= -1.1)
		tmp = t_1;
	elseif (z <= 2.4e-9)
		tmp = Float64(Float64(Float64(y / z) - t) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((t + y) * x) / z;
	tmp = 0.0;
	if (z <= -1.1)
		tmp = t_1;
	elseif (z <= 2.4e-9)
		tmp = ((y / z) - t) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.1], t$95$1, If[LessEqual[z, 2.4e-9], N[(N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1000000000000001 or 2.4e-9 < z

   1. Initial program 98.2%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 97.4

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

   4. Applied rewrites 97.4%

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

   5. Taylor expanded in z around inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-commutative N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 81.9

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

   7. Applied rewrites 81.9%

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

   if -1.1000000000000001 < z < 2.4e-9

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 92.2

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

   5. Applied rewrites 92.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 92.3%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1:\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-9}:\\ \;\;\;\;\left(\frac{y}{z} - t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot t}{z - 1}\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x t) (- z 1.0))))
   (if (<= t -2.25e+166) t_1 (if (<= t 5.6e+50) (* (/ y z) x) 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 <= -2.25e+166) {
		tmp = t_1;
	} else if (t <= 5.6e+50) {
		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 - 1.0d0)
    if (t <= (-2.25d+166)) then
        tmp = t_1
    else if (t <= 5.6d+50) 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 - 1.0);
	double tmp;
	if (t <= -2.25e+166) {
		tmp = t_1;
	} else if (t <= 5.6e+50) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * t) / (z - 1.0)
	tmp = 0
	if t <= -2.25e+166:
		tmp = t_1
	elif t <= 5.6e+50:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * t) / Float64(z - 1.0))
	tmp = 0.0
	if (t <= -2.25e+166)
		tmp = t_1;
	elseif (t <= 5.6e+50)
		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 - 1.0);
	tmp = 0.0;
	if (t <= -2.25e+166)
		tmp = t_1;
	elseif (t <= 5.6e+50)
		tmp = (y / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * t), $MachinePrecision] / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.25e+166], t$95$1, If[LessEqual[t, 5.6e+50], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.25000000000000015e166 or 5.5999999999999996e50 < t

   1. Initial program 96.4%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot x}{1 - z}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 70.7

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

   5. Applied rewrites 70.7%

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

   if -2.25000000000000015e166 < t < 5.5999999999999996e50

   1. Initial program 94.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 79.3

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

   5. Applied rewrites 79.3%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+166}:\\ \;\;\;\;\frac{x \cdot t}{z - 1}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z - 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+167}:\\ \;\;\;\;\left(-x\right) \cdot t\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+58}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.8e+167)
   (* (- x) t)
   (if (<= t 7.4e+58) (* (/ y z) x) (* (/ t z) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e+167) {
		tmp = -x * t;
	} else if (t <= 7.4e+58) {
		tmp = (y / z) * x;
	} else {
		tmp = (t / 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) :: tmp
    if (t <= (-1.8d+167)) then
        tmp = -x * t
    else if (t <= 7.4d+58) then
        tmp = (y / z) * x
    else
        tmp = (t / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e+167) {
		tmp = -x * t;
	} else if (t <= 7.4e+58) {
		tmp = (y / z) * x;
	} else {
		tmp = (t / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.8e+167:
		tmp = -x * t
	elif t <= 7.4e+58:
		tmp = (y / z) * x
	else:
		tmp = (t / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.8e+167)
		tmp = Float64(Float64(-x) * t);
	elseif (t <= 7.4e+58)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = Float64(Float64(t / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.8e+167)
		tmp = -x * t;
	elseif (t <= 7.4e+58)
		tmp = (y / z) * x;
	else
		tmp = (t / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.8e+167], N[((-x) * t), $MachinePrecision], If[LessEqual[t, 7.4e+58], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.80000000000000012e167

   1. Initial program 94.8%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot x}{1 - z}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 70.0

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

   5. Applied rewrites 70.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 56.9%

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

   if -1.80000000000000012e167 < t < 7.4000000000000004e58

   1. Initial program 94.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 78.9

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

   5. Applied rewrites 78.9%

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

   if 7.4000000000000004e58 < t

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 64.5

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

   5. Applied rewrites 64.5%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 56.3%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+167}:\\ \;\;\;\;\left(-x\right) \cdot t\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+58}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-x\right) \cdot t\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x) t)))
   (if (<= t -1.6e+178) t_1 (if (<= t 1.2e+143) (* (/ x z) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x * t;
	double tmp;
	if (t <= -1.6e+178) {
		tmp = t_1;
	} else if (t <= 1.2e+143) {
		tmp = (x / z) * y;
	} 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
    if (t <= (-1.6d+178)) then
        tmp = t_1
    else if (t <= 1.2d+143) then
        tmp = (x / z) * y
    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;
	double tmp;
	if (t <= -1.6e+178) {
		tmp = t_1;
	} else if (t <= 1.2e+143) {
		tmp = (x / z) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x * t
	tmp = 0
	if t <= -1.6e+178:
		tmp = t_1
	elif t <= 1.2e+143:
		tmp = (x / z) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) * t)
	tmp = 0.0
	if (t <= -1.6e+178)
		tmp = t_1;
	elseif (t <= 1.2e+143)
		tmp = Float64(Float64(x / z) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x * t;
	tmp = 0.0;
	if (t <= -1.6e+178)
		tmp = t_1;
	elseif (t <= 1.2e+143)
		tmp = (x / z) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) * t), $MachinePrecision]}, If[LessEqual[t, -1.6e+178], t$95$1, If[LessEqual[t, 1.2e+143], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6e178 or 1.1999999999999999e143 < t

   1. Initial program 96.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot x}{1 - z}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 76.2

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

   5. Applied rewrites 76.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 52.1%

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

   if -1.6e178 < t < 1.1999999999999999e143

   1. Initial program 94.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 72.7

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

   5. Applied rewrites 72.7%

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

   7. Applied rewrites 72.5%

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

Alternative 11: 42.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot t\\ \mathbf{if}\;z \leq -0.013:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\left(-\mathsf{fma}\left(t, z, t\right)\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) t)))
   (if (<= z -0.013) t_1 (if (<= z 1.0) (* (- (fma t z t)) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * t;
	double tmp;
	if (z <= -0.013) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = -fma(t, z, t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * t)
	tmp = 0.0
	if (z <= -0.013)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(Float64(-fma(t, z, t)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[z, -0.013], t$95$1, If[LessEqual[z, 1.0], N[((-N[(t * z + t), $MachinePrecision]) * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0129999999999999994 or 1 < z

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot x}{1 - z}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 50.2

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

   5. Applied rewrites 50.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 52.6%

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

   if -0.0129999999999999994 < z < 1

   1. Initial program 92.4%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. sub-neg N/A

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

      11. lower--.f64 29.6

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

   5. Applied rewrites 29.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 29.6%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.013:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\left(-\mathsf{fma}\left(t, z, t\right)\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 22.6% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

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 * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

3. Taylor expanded in t around inf

   \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot x}{1 - z}} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

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

   2. distribute-neg-frac2 N/A

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

   3. lower-/.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. sub-neg N/A

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

   6. mul-1-neg N/A

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

   7. +-commutative N/A

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

   8. distribute-neg-in N/A

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

   9. mul-1-neg N/A

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

   10. remove-double-neg N/A

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

   11. sub-neg N/A

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

   12. lower--.f64 40.1

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

5. Applied rewrites 40.1%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 21.3%

   \[\leadsto \left(-x\right) \cdot \color{blue}{t} \]
9. Add Preprocessing

Developer Target 1: 94.5% 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 2024255 
(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)))))