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

Percentage Accurate: 94.4% → 96.3%

Time: 9.2s

Alternatives: 9

Speedup: 0.5×

• 21.4% 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: 94.4% 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: 96.3% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y / z), $MachinePrecision] + t$95$1), $MachinePrecision], (-Infinity)], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * N[(1.0 / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $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 65.6%

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

   3. Taylor expanded in y around inf 99.9%

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

      1. associate-*r/ 65.6%

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

   5. Simplified 65.6%

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

      1. clear-num 65.6%

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

      2. un-div-inv 69.2%

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

   7. Applied egg-rr 69.2%

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

      1. associate-/r/ 99.9%

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

   9. Applied egg-rr 99.9%

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

       1. *-commutative 99.9%

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

       2. clear-num 99.8%

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

       3. un-div-inv 99.9%

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

   11. Applied egg-rr 99.9%

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

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

   1. Initial program 97.8%

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

      1. clear-num 97.7%

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

      2. associate-/r/ 97.8%

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

   4. Applied egg-rr 97.8%

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

4. Final simplification 98.0%

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

Alternative 2: 73.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z + -1}\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+103}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+55} \lor \neg \left(t \leq 2.2 \cdot 10^{+72}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (+ z -1.0)))))
   (if (<= t -4.4e+133)
     t_1
     (if (<= t -8.6e+103)
       (/ y (/ z x))
       (if (or (<= t -2.3e+55) (not (<= t 2.2e+72))) t_1 (/ x (/ z y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z + -1.0));
	double tmp;
	if (t <= -4.4e+133) {
		tmp = t_1;
	} else if (t <= -8.6e+103) {
		tmp = y / (z / x);
	} else if ((t <= -2.3e+55) || !(t <= 2.2e+72)) {
		tmp = t_1;
	} else {
		tmp = x / (z / y);
	}
	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 * (x / (z + (-1.0d0)))
    if (t <= (-4.4d+133)) then
        tmp = t_1
    else if (t <= (-8.6d+103)) then
        tmp = y / (z / x)
    else if ((t <= (-2.3d+55)) .or. (.not. (t <= 2.2d+72))) then
        tmp = t_1
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z + -1.0));
	double tmp;
	if (t <= -4.4e+133) {
		tmp = t_1;
	} else if (t <= -8.6e+103) {
		tmp = y / (z / x);
	} else if ((t <= -2.3e+55) || !(t <= 2.2e+72)) {
		tmp = t_1;
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z + -1.0))
	tmp = 0
	if t <= -4.4e+133:
		tmp = t_1
	elif t <= -8.6e+103:
		tmp = y / (z / x)
	elif (t <= -2.3e+55) or not (t <= 2.2e+72):
		tmp = t_1
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (t <= -4.4e+133)
		tmp = t_1;
	elseif (t <= -8.6e+103)
		tmp = Float64(y / Float64(z / x));
	elseif ((t <= -2.3e+55) || !(t <= 2.2e+72))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z + -1.0));
	tmp = 0.0;
	if (t <= -4.4e+133)
		tmp = t_1;
	elseif (t <= -8.6e+103)
		tmp = y / (z / x);
	elseif ((t <= -2.3e+55) || ~((t <= 2.2e+72)))
		tmp = t_1;
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e+133], t$95$1, If[LessEqual[t, -8.6e+103], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.3e+55], N[Not[LessEqual[t, 2.2e+72]], $MachinePrecision]], t$95$1, N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4e133 or -8.59999999999999938e103 < t < -2.29999999999999987e55 or 2.2e72 < t

   1. Initial program 94.0%

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

   3. Taylor expanded in y around 0 75.6%

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

      1. mul-1-neg 75.6%

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

      2. associate-/l* 73.7%

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

      3. distribute-rgt-neg-in 73.7%

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

      4. distribute-neg-frac2 73.7%

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

      5. neg-sub0 73.7%

         \[\leadsto t \cdot \frac{x}{\color{blue}{0 - \left(1 - z\right)}} \]

      6. associate--r- 73.7%

         \[\leadsto t \cdot \frac{x}{\color{blue}{\left(0 - 1\right) + z}} \]

      7. metadata-eval 73.7%

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

   5. Simplified 73.7%

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

   if -4.4e133 < t < -8.59999999999999938e103

   1. Initial program 99.4%

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

   3. Taylor expanded in y around inf 84.9%

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

      1. associate-*r/ 84.6%

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

   5. Simplified 84.6%

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

      1. clear-num 84.6%

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

      2. un-div-inv 84.6%

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

   7. Applied egg-rr 84.6%

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

      1. associate-/r/ 84.6%

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

   9. Applied egg-rr 84.6%

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

       1. *-commutative 84.6%

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

       2. clear-num 84.6%

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

       3. un-div-inv 84.9%

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

   11. Applied egg-rr 84.9%

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

   if -2.29999999999999987e55 < t < 2.2e72

   1. Initial program 95.5%

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

   3. Taylor expanded in y around inf 86.1%

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

      1. associate-*r/ 86.1%

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

   5. Simplified 86.1%

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

      1. clear-num 86.1%

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

      2. un-div-inv 86.6%

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

   7. Applied egg-rr 86.6%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+133}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+103}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+55} \lor \neg \left(t \leq 2.2 \cdot 10^{+72}\right):\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+308}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (<= t_1 -1e+308) (/ y (/ z x)) (* t_1 x))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= -1e+308) {
		tmp = y / (z / 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 / (z + (-1.0d0)))
    if (t_1 <= (-1d+308)) then
        tmp = y / (z / 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 / (z + -1.0));
	double tmp;
	if (t_1 <= -1e+308) {
		tmp = y / (z / x);
	} else {
		tmp = t_1 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) + (t / (z + -1.0))
	tmp = 0
	if t_1 <= -1e+308:
		tmp = y / (z / x)
	else:
		tmp = t_1 * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) + Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t_1 <= -1e+308)
		tmp = Float64(y / Float64(z / 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 / (z + -1.0));
	tmp = 0.0;
	if (t_1 <= -1e+308)
		tmp = y / (z / 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[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+308], N[(y / N[(z / x), $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))) < -1e308

   1. Initial program 67.1%

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

   3. Taylor expanded in y around inf 99.9%

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

      1. associate-*r/ 67.1%

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

   5. Simplified 67.1%

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

      1. clear-num 67.1%

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

      2. un-div-inv 70.4%

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

   7. Applied egg-rr 70.4%

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

      1. associate-/r/ 99.8%

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

   9. Applied egg-rr 99.8%

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

       1. *-commutative 99.8%

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

       2. clear-num 99.7%

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

       3. un-div-inv 99.9%

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

   11. Applied egg-rr 99.9%

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

   if -1e308 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 97.8%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -1 \cdot 10^{+308}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.6% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	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 ((z <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * ((y + t) / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf 88.7%

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

      1. associate-/l* 95.8%

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

      2. neg-mul-1 95.8%

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

      3. sub-neg 95.8%

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

      4. remove-double-neg 95.8%

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

      5. neg-mul-1 95.8%

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

      6. neg-mul-1 95.8%

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

      7. distribute-lft-in 95.8%

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

      8. neg-mul-1 95.8%

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

      9. sub-neg 95.8%

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

      10. *-commutative 95.8%

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

      11. associate-*l/ 95.8%

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

      12. *-commutative 95.8%

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

      13. associate-*r/ 95.8%

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

      14. sub-neg 95.8%

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

      15. neg-mul-1 95.8%

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

      16. distribute-lft-in 95.8%

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

      17. neg-mul-1 95.8%

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

      18. remove-double-neg 95.8%

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

      19. neg-mul-1 95.8%

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

      20. remove-double-neg 95.8%

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

      21. +-commutative 95.8%

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

   5. Simplified 95.8%

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

   if -1 < z < 1

   1. Initial program 92.0%

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

   3. Taylor expanded in z around 0 91.5%

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

4. Final simplification 93.6%

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

Alternative 5: 61.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.1 \cdot 10^{-129}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 1.1e-129) (/ (* y x) z) (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1.1e-129) {
		tmp = (y * x) / z;
	} else {
		tmp = x / (z / y);
	}
	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 (x <= 1.1d-129) then
        tmp = (y * x) / z
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1.1e-129) {
		tmp = (y * x) / z;
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 1.1e-129:
		tmp = (y * x) / z
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 1.1e-129)
		tmp = Float64(Float64(y * x) / z);
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 1.1e-129)
		tmp = (y * x) / z;
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 1.1e-129], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.10000000000000001e-129

   1. Initial program 92.9%

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

   3. Taylor expanded in y around inf 65.0%

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

   if 1.10000000000000001e-129 < x

   1. Initial program 98.7%

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

   3. Taylor expanded in y around inf 61.8%

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

      1. associate-*r/ 65.8%

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

   5. Simplified 65.8%

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

      1. clear-num 65.9%

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

      2. un-div-inv 66.3%

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

   7. Applied egg-rr 66.3%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.1 \cdot 10^{-129}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.9 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.9e+59) (/ x (/ z y)) (/ y (/ z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.9e+59) {
		tmp = x / (z / y);
	} 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) :: tmp
    if (t <= 1.9d+59) then
        tmp = x / (z / y)
    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 tmp;
	if (t <= 1.9e+59) {
		tmp = x / (z / y);
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.9e+59:
		tmp = x / (z / y)
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.9e+59)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = Float64(y / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.9e+59)
		tmp = x / (z / y);
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.9e+59], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.9e59

   1. Initial program 94.9%

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

   3. Taylor expanded in y around inf 73.5%

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

      1. associate-*r/ 72.0%

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

   5. Simplified 72.0%

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

      1. clear-num 72.0%

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

      2. un-div-inv 72.6%

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

   7. Applied egg-rr 72.6%

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

   if 1.9e59 < t

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf 32.3%

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

      1. associate-*r/ 29.5%

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

   5. Simplified 29.5%

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

      1. clear-num 29.5%

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

      2. un-div-inv 29.5%

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

   7. Applied egg-rr 29.5%

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

      1. associate-/r/ 37.0%

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

   9. Applied egg-rr 37.0%

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

       1. *-commutative 37.0%

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

       2. clear-num 37.0%

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

       3. un-div-inv 37.1%

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

   11. Applied egg-rr 37.1%

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

Alternative 7: 62.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.5e+63) (/ x (/ z y)) (* y (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.5e+63) {
		tmp = x / (z / y);
	} else {
		tmp = y * (x / z);
	}
	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 <= 2.5d+63) then
        tmp = x / (z / y)
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.5e+63) {
		tmp = x / (z / y);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 2.5e+63:
		tmp = x / (z / y)
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.5e+63)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 2.5e+63)
		tmp = x / (z / y);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 2.5e+63], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.50000000000000005e63

   1. Initial program 95.0%

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

   3. Taylor expanded in y around inf 73.2%

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

      1. associate-*r/ 71.8%

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

   5. Simplified 71.8%

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

      1. clear-num 71.8%

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

      2. un-div-inv 72.4%

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

   7. Applied egg-rr 72.4%

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

   if 2.50000000000000005e63 < t

   1. Initial program 95.1%

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

   3. Taylor expanded in y around inf 31.7%

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

      1. associate-*r/ 28.7%

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

   5. Simplified 28.7%

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

      1. clear-num 28.7%

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

      2. un-div-inv 28.7%

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

   7. Applied egg-rr 28.7%

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

      1. associate-/r/ 36.5%

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

   9. Applied egg-rr 36.5%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.3 \cdot 10^{+59}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.3e+59) (* (/ y z) x) (* y (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.3e+59) {
		tmp = (y / z) * x;
	} else {
		tmp = y * (x / z);
	}
	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 <= 2.3d+59) then
        tmp = (y / z) * x
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.3e+59) {
		tmp = (y / z) * x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 2.3e+59:
		tmp = (y / z) * x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.3e+59)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 2.3e+59)
		tmp = (y / z) * x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 2.3e+59], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.30000000000000008e59

   1. Initial program 94.9%

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

   3. Taylor expanded in y around inf 73.5%

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

      1. associate-*r/ 72.0%

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

   5. Simplified 72.0%

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

   if 2.30000000000000008e59 < t

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf 32.3%

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

      1. associate-*r/ 29.5%

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

   5. Simplified 29.5%

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

      1. clear-num 29.5%

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

      2. un-div-inv 29.5%

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

   7. Applied egg-rr 29.5%

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

      1. associate-/r/ 37.0%

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

   9. Applied egg-rr 37.0%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.3 \cdot 10^{+59}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \frac{y}{z} \cdot x \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (y / z) * 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 = (y / z) * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.0%

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

3. Taylor expanded in y around inf 63.8%

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

   1. associate-*r/ 62.0%

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

5. Simplified 62.0%

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

6. Final simplification 62.0%

   \[\leadsto \frac{y}{z} \cdot x \]
7. Add Preprocessing

Developer target: 94.9% accurate, 0.2× 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 2024111 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z)))))))

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