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

Percentage Accurate: 94.2% → 94.2%

Time: 7.7s

Alternatives: 11

Speedup: 1.0×

• 20.8% 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: 94.2% 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: 94.2% 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]

Derivation

1. Initial program 94.6%

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

2. Final simplification 94.6%

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

Alternative 2: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z + -1}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \leq 0.00146 \lor \neg \left(t \leq 7.1 \cdot 10^{+105}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (+ z -1.0)))))
   (if (<= t -5e+107)
     t_1
     (if (<= t 3.6e-66)
       (/ (* x y) z)
       (if (or (<= t 0.00146) (not (<= t 7.1e+105))) t_1 (* y (/ x z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z + -1.0));
	double tmp;
	if (t <= -5e+107) {
		tmp = t_1;
	} else if (t <= 3.6e-66) {
		tmp = (x * y) / z;
	} else if ((t <= 0.00146) || !(t <= 7.1e+105)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t / (z + (-1.0d0)))
    if (t <= (-5d+107)) then
        tmp = t_1
    else if (t <= 3.6d-66) then
        tmp = (x * y) / z
    else if ((t <= 0.00146d0) .or. (.not. (t <= 7.1d+105))) then
        tmp = t_1
    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 t_1 = x * (t / (z + -1.0));
	double tmp;
	if (t <= -5e+107) {
		tmp = t_1;
	} else if (t <= 3.6e-66) {
		tmp = (x * y) / z;
	} else if ((t <= 0.00146) || !(t <= 7.1e+105)) {
		tmp = t_1;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / (z + -1.0))
	tmp = 0
	if t <= -5e+107:
		tmp = t_1
	elif t <= 3.6e-66:
		tmp = (x * y) / z
	elif (t <= 0.00146) or not (t <= 7.1e+105):
		tmp = t_1
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t <= -5e+107)
		tmp = t_1;
	elseif (t <= 3.6e-66)
		tmp = Float64(Float64(x * y) / z);
	elseif ((t <= 0.00146) || !(t <= 7.1e+105))
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / z));
	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 <= -5e+107)
		tmp = t_1;
	elseif (t <= 3.6e-66)
		tmp = (x * y) / z;
	elseif ((t <= 0.00146) || ~((t <= 7.1e+105)))
		tmp = t_1;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+107], t$95$1, If[LessEqual[t, 3.6e-66], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[t, 0.00146], N[Not[LessEqual[t, 7.1e+105]], $MachinePrecision]], t$95$1, N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.0000000000000002e107 or 3.60000000000000012e-66 < t < 0.0014599999999999999 or 7.1000000000000003e105 < t

   1. Initial program 98.8%

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

   2. Taylor expanded in y around 0 80.7%

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

      1. associate-*r/ 80.7%

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

      2. mul-1-neg 80.7%

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

      3. *-commutative 80.7%

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

      4. distribute-rgt-neg-in 80.7%

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

      5. associate-*r/ 86.8%

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

      6. neg-mul-1 86.8%

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

      7. *-commutative 86.8%

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

      8. associate-*r/ 86.8%

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

      9. metadata-eval 86.8%

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

      10. associate-/r* 86.8%

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

      11. neg-mul-1 86.8%

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

      12. associate-*r/ 86.8%

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

      13. *-rgt-identity 86.8%

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

      14. neg-sub0 86.8%

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

      15. associate--r- 86.8%

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

      16. metadata-eval 86.8%

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

   4. Simplified 86.8%

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

   if -5.0000000000000002e107 < t < 3.60000000000000012e-66

   1. Initial program 92.3%

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

   2. Taylor expanded in y around inf 85.3%

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

   if 0.0014599999999999999 < t < 7.1000000000000003e105

   1. Initial program 91.7%

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

   2. Taylor expanded in y around inf 63.0%

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

      1. associate-*l/ 59.0%

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

   4. Simplified 59.0%

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

      1. *-commutative 59.0%

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

      2. clear-num 58.9%

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

      3. un-div-inv 59.0%

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

   6. Applied egg-rr 59.0%

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

      1. associate-/r/ 67.2%

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

   8. Simplified 67.2%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \leq 0.00146 \lor \neg \left(t \leq 7.1 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 3: 67.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{+114}:\\ \;\;\;\;-x \cdot t\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -2.9e+174)
     t_1
     (if (<= t -4.9e+114)
       (- (* x t))
       (if (<= t -1.9e+25)
         (* y (/ x z))
         (if (<= t 5.7e+62) (* x (/ y z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -2.9e+174) {
		tmp = t_1;
	} else if (t <= -4.9e+114) {
		tmp = -(x * t);
	} else if (t <= -1.9e+25) {
		tmp = y * (x / z);
	} else if (t <= 5.7e+62) {
		tmp = x * (y / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-2.9d+174)) then
        tmp = t_1
    else if (t <= (-4.9d+114)) then
        tmp = -(x * t)
    else if (t <= (-1.9d+25)) then
        tmp = y * (x / z)
    else if (t <= 5.7d+62) then
        tmp = x * (y / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -2.9e+174) {
		tmp = t_1;
	} else if (t <= -4.9e+114) {
		tmp = -(x * t);
	} else if (t <= -1.9e+25) {
		tmp = y * (x / z);
	} else if (t <= 5.7e+62) {
		tmp = x * (y / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -2.9e+174:
		tmp = t_1
	elif t <= -4.9e+114:
		tmp = -(x * t)
	elif t <= -1.9e+25:
		tmp = y * (x / z)
	elif t <= 5.7e+62:
		tmp = x * (y / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -2.9e+174)
		tmp = t_1;
	elseif (t <= -4.9e+114)
		tmp = Float64(-Float64(x * t));
	elseif (t <= -1.9e+25)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= 5.7e+62)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -2.9e+174)
		tmp = t_1;
	elseif (t <= -4.9e+114)
		tmp = -(x * t);
	elseif (t <= -1.9e+25)
		tmp = y * (x / z);
	elseif (t <= 5.7e+62)
		tmp = x * (y / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+174], t$95$1, If[LessEqual[t, -4.9e+114], (-N[(x * t), $MachinePrecision]), If[LessEqual[t, -1.9e+25], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.7e+62], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9e174 or 5.69999999999999998e62 < t

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 60.0%

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

      1. cancel-sign-sub-inv 60.0%

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

      2. metadata-eval 60.0%

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

      3. *-lft-identity 60.0%

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

   4. Simplified 60.0%

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

   5. Taylor expanded in y around 0 47.6%

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

      1. *-commutative 47.6%

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

      2. *-lft-identity 47.6%

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

      3. times-frac 56.1%

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

      4. /-rgt-identity 56.1%

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

   7. Simplified 56.1%

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

   if -2.9e174 < t < -4.9000000000000001e114

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.7%

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

      1. associate-*r/ 99.7%

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

      2. mul-1-neg 99.7%

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

      3. *-commutative 99.7%

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

      4. distribute-rgt-neg-in 99.7%

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

      5. associate-*r/ 99.5%

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

      6. neg-mul-1 99.5%

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

      7. *-commutative 99.5%

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

      8. associate-*r/ 99.5%

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

      9. metadata-eval 99.5%

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

      10. associate-/r* 99.5%

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

      11. neg-mul-1 99.5%

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

      12. associate-*r/ 99.5%

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

      13. *-rgt-identity 99.5%

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

      14. neg-sub0 99.5%

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

      15. associate--r- 99.5%

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

      16. metadata-eval 99.5%

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

   4. Simplified 99.5%

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

      1. clear-num 99.2%

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

      2. un-div-inv 99.1%

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

      3. +-commutative 99.1%

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

   6. Applied egg-rr 99.1%

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

   7. Taylor expanded in z around 0 73.6%

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

      1. associate-*r* 73.6%

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

      2. neg-mul-1 73.6%

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

   9. Simplified 73.6%

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

   if -4.9000000000000001e114 < t < -1.9e25

   1. Initial program 88.1%

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

   2. Taylor expanded in y around inf 58.7%

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

      1. associate-*l/ 47.1%

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

   4. Simplified 47.1%

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

      1. *-commutative 47.1%

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

      2. clear-num 47.2%

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

      3. un-div-inv 50.3%

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

   6. Applied egg-rr 50.3%

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

      1. associate-/r/ 53.0%

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

   8. Simplified 53.0%

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

   if -1.9e25 < t < 5.69999999999999998e62

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf 81.1%

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

      1. associate-*l/ 81.3%

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

   4. Simplified 81.3%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{+114}:\\ \;\;\;\;-x \cdot t\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 4: 67.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{+114}:\\ \;\;\;\;-x \cdot t\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z t))))
   (if (<= t -1.1e+174)
     t_1
     (if (<= t -4.9e+114)
       (- (* x t))
       (if (<= t -1.3e+26)
         (* y (/ x z))
         (if (<= t 2.7e+62) (* x (/ y z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -1.1e+174) {
		tmp = t_1;
	} else if (t <= -4.9e+114) {
		tmp = -(x * t);
	} else if (t <= -1.3e+26) {
		tmp = y * (x / z);
	} else if (t <= 2.7e+62) {
		tmp = x * (y / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z / t)
    if (t <= (-1.1d+174)) then
        tmp = t_1
    else if (t <= (-4.9d+114)) then
        tmp = -(x * t)
    else if (t <= (-1.3d+26)) then
        tmp = y * (x / z)
    else if (t <= 2.7d+62) then
        tmp = x * (y / 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 / (z / t);
	double tmp;
	if (t <= -1.1e+174) {
		tmp = t_1;
	} else if (t <= -4.9e+114) {
		tmp = -(x * t);
	} else if (t <= -1.3e+26) {
		tmp = y * (x / z);
	} else if (t <= 2.7e+62) {
		tmp = x * (y / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / t)
	tmp = 0
	if t <= -1.1e+174:
		tmp = t_1
	elif t <= -4.9e+114:
		tmp = -(x * t)
	elif t <= -1.3e+26:
		tmp = y * (x / z)
	elif t <= 2.7e+62:
		tmp = x * (y / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (t <= -1.1e+174)
		tmp = t_1;
	elseif (t <= -4.9e+114)
		tmp = Float64(-Float64(x * t));
	elseif (t <= -1.3e+26)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= 2.7e+62)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / t);
	tmp = 0.0;
	if (t <= -1.1e+174)
		tmp = t_1;
	elseif (t <= -4.9e+114)
		tmp = -(x * t);
	elseif (t <= -1.3e+26)
		tmp = y * (x / z);
	elseif (t <= 2.7e+62)
		tmp = x * (y / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e+174], t$95$1, If[LessEqual[t, -4.9e+114], (-N[(x * t), $MachinePrecision]), If[LessEqual[t, -1.3e+26], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+62], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.1000000000000001e174 or 2.7e62 < t

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 54.0%

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

      1. *-commutative 54.0%

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

      2. associate-/l* 60.3%

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

      3. neg-mul-1 60.3%

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

   4. Simplified 60.3%

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

   5. Taylor expanded in y around 0 56.4%

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

   if -1.1000000000000001e174 < t < -4.9000000000000001e114

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.7%

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

      1. associate-*r/ 99.7%

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

      2. mul-1-neg 99.7%

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

      3. *-commutative 99.7%

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

      4. distribute-rgt-neg-in 99.7%

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

      5. associate-*r/ 99.5%

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

      6. neg-mul-1 99.5%

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

      7. *-commutative 99.5%

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

      8. associate-*r/ 99.5%

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

      9. metadata-eval 99.5%

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

      10. associate-/r* 99.5%

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

      11. neg-mul-1 99.5%

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

      12. associate-*r/ 99.5%

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

      13. *-rgt-identity 99.5%

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

      14. neg-sub0 99.5%

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

      15. associate--r- 99.5%

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

      16. metadata-eval 99.5%

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

   4. Simplified 99.5%

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

      1. clear-num 99.2%

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

      2. un-div-inv 99.1%

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

      3. +-commutative 99.1%

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

   6. Applied egg-rr 99.1%

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

   7. Taylor expanded in z around 0 73.6%

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

      1. associate-*r* 73.6%

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

      2. neg-mul-1 73.6%

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

   9. Simplified 73.6%

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

   if -4.9000000000000001e114 < t < -1.30000000000000001e26

   1. Initial program 88.1%

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

   2. Taylor expanded in y around inf 58.7%

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

      1. associate-*l/ 47.1%

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

   4. Simplified 47.1%

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

      1. *-commutative 47.1%

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

      2. clear-num 47.2%

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

      3. un-div-inv 50.3%

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

   6. Applied egg-rr 50.3%

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

      1. associate-/r/ 53.0%

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

   8. Simplified 53.0%

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

   if -1.30000000000000001e26 < t < 2.7e62

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf 81.1%

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

      1. associate-*l/ 81.3%

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

   4. Simplified 81.3%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{+114}:\\ \;\;\;\;-x \cdot t\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 5: 67.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;t \leq -4 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+114}:\\ \;\;\;\;-x \cdot t\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z t))))
   (if (<= t -4e+174)
     t_1
     (if (<= t -5.2e+114)
       (- (* x t))
       (if (<= t -5.2e+107)
         (* x (/ t z))
         (if (<= t 9.5e+63) (/ x (/ z y)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -4e+174) {
		tmp = t_1;
	} else if (t <= -5.2e+114) {
		tmp = -(x * t);
	} else if (t <= -5.2e+107) {
		tmp = x * (t / z);
	} else if (t <= 9.5e+63) {
		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 / (z / t)
    if (t <= (-4d+174)) then
        tmp = t_1
    else if (t <= (-5.2d+114)) then
        tmp = -(x * t)
    else if (t <= (-5.2d+107)) then
        tmp = x * (t / z)
    else if (t <= 9.5d+63) 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 / (z / t);
	double tmp;
	if (t <= -4e+174) {
		tmp = t_1;
	} else if (t <= -5.2e+114) {
		tmp = -(x * t);
	} else if (t <= -5.2e+107) {
		tmp = x * (t / z);
	} else if (t <= 9.5e+63) {
		tmp = x / (z / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / t)
	tmp = 0
	if t <= -4e+174:
		tmp = t_1
	elif t <= -5.2e+114:
		tmp = -(x * t)
	elif t <= -5.2e+107:
		tmp = x * (t / z)
	elif t <= 9.5e+63:
		tmp = x / (z / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (t <= -4e+174)
		tmp = t_1;
	elseif (t <= -5.2e+114)
		tmp = Float64(-Float64(x * t));
	elseif (t <= -5.2e+107)
		tmp = Float64(x * Float64(t / z));
	elseif (t <= 9.5e+63)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / t);
	tmp = 0.0;
	if (t <= -4e+174)
		tmp = t_1;
	elseif (t <= -5.2e+114)
		tmp = -(x * t);
	elseif (t <= -5.2e+107)
		tmp = x * (t / z);
	elseif (t <= 9.5e+63)
		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 / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e+174], t$95$1, If[LessEqual[t, -5.2e+114], (-N[(x * t), $MachinePrecision]), If[LessEqual[t, -5.2e+107], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+63], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.00000000000000028e174 or 9.5000000000000003e63 < t

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 54.0%

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

      1. *-commutative 54.0%

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

      2. associate-/l* 60.3%

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

      3. neg-mul-1 60.3%

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

   4. Simplified 60.3%

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

   5. Taylor expanded in y around 0 56.4%

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

   if -4.00000000000000028e174 < t < -5.2000000000000001e114

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.7%

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

      1. associate-*r/ 99.7%

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

      2. mul-1-neg 99.7%

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

      3. *-commutative 99.7%

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

      4. distribute-rgt-neg-in 99.7%

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

      5. associate-*r/ 99.5%

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

      6. neg-mul-1 99.5%

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

      7. *-commutative 99.5%

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

      8. associate-*r/ 99.5%

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

      9. metadata-eval 99.5%

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

      10. associate-/r* 99.5%

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

      11. neg-mul-1 99.5%

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

      12. associate-*r/ 99.5%

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

      13. *-rgt-identity 99.5%

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

      14. neg-sub0 99.5%

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

      15. associate--r- 99.5%

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

      16. metadata-eval 99.5%

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

   4. Simplified 99.5%

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

      1. clear-num 99.2%

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

      2. un-div-inv 99.1%

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

      3. +-commutative 99.1%

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

   6. Applied egg-rr 99.1%

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

   7. Taylor expanded in z around 0 73.6%

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

      1. associate-*r* 73.6%

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

      2. neg-mul-1 73.6%

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

   9. Simplified 73.6%

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

   if -5.2000000000000001e114 < t < -5.2000000000000002e107

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. metadata-eval 100.0%

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

      3. *-lft-identity 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. *-lft-identity 100.0%

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

      3. times-frac 100.0%

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

      4. /-rgt-identity 100.0%

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

   7. Simplified 100.0%

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

   if -5.2000000000000002e107 < t < 9.5000000000000003e63

   1. Initial program 93.0%

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

   2. Taylor expanded in z around inf 86.7%

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

      1. *-commutative 86.7%

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

      2. associate-/l* 81.7%

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

      3. neg-mul-1 81.7%

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

   4. Simplified 81.7%

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

   5. Taylor expanded in y around inf 78.7%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+114}:\\ \;\;\;\;-x \cdot t\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 6: 67.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{+111}:\\ \;\;\;\;-x \cdot t\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z t))))
   (if (<= t -1.7e+174)
     t_1
     (if (<= t -2.25e+111)
       (- (* x t))
       (if (<= t -8e+107)
         (* x (/ t z))
         (if (<= t 7.5e+106) (/ (* x y) z) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -1.7e+174) {
		tmp = t_1;
	} else if (t <= -2.25e+111) {
		tmp = -(x * t);
	} else if (t <= -8e+107) {
		tmp = x * (t / z);
	} else if (t <= 7.5e+106) {
		tmp = (x * y) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z / t)
    if (t <= (-1.7d+174)) then
        tmp = t_1
    else if (t <= (-2.25d+111)) then
        tmp = -(x * t)
    else if (t <= (-8d+107)) then
        tmp = x * (t / z)
    else if (t <= 7.5d+106) then
        tmp = (x * y) / 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 / (z / t);
	double tmp;
	if (t <= -1.7e+174) {
		tmp = t_1;
	} else if (t <= -2.25e+111) {
		tmp = -(x * t);
	} else if (t <= -8e+107) {
		tmp = x * (t / z);
	} else if (t <= 7.5e+106) {
		tmp = (x * y) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / t)
	tmp = 0
	if t <= -1.7e+174:
		tmp = t_1
	elif t <= -2.25e+111:
		tmp = -(x * t)
	elif t <= -8e+107:
		tmp = x * (t / z)
	elif t <= 7.5e+106:
		tmp = (x * y) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (t <= -1.7e+174)
		tmp = t_1;
	elseif (t <= -2.25e+111)
		tmp = Float64(-Float64(x * t));
	elseif (t <= -8e+107)
		tmp = Float64(x * Float64(t / z));
	elseif (t <= 7.5e+106)
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / t);
	tmp = 0.0;
	if (t <= -1.7e+174)
		tmp = t_1;
	elseif (t <= -2.25e+111)
		tmp = -(x * t);
	elseif (t <= -8e+107)
		tmp = x * (t / z);
	elseif (t <= 7.5e+106)
		tmp = (x * y) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+174], t$95$1, If[LessEqual[t, -2.25e+111], (-N[(x * t), $MachinePrecision]), If[LessEqual[t, -8e+107], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+106], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.7000000000000001e174 or 7.50000000000000058e106 < t

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 47.0%

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

      1. *-commutative 47.0%

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

      2. associate-/l* 55.9%

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

      3. neg-mul-1 55.9%

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

   4. Simplified 55.9%

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

   5. Taylor expanded in y around 0 55.9%

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

   if -1.7000000000000001e174 < t < -2.25e111

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.7%

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

      1. associate-*r/ 99.7%

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

      2. mul-1-neg 99.7%

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

      3. *-commutative 99.7%

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

      4. distribute-rgt-neg-in 99.7%

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

      5. associate-*r/ 99.5%

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

      6. neg-mul-1 99.5%

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

      7. *-commutative 99.5%

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

      8. associate-*r/ 99.5%

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

      9. metadata-eval 99.5%

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

      10. associate-/r* 99.5%

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

      11. neg-mul-1 99.5%

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

      12. associate-*r/ 99.5%

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

      13. *-rgt-identity 99.5%

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

      14. neg-sub0 99.5%

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

      15. associate--r- 99.5%

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

      16. metadata-eval 99.5%

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

   4. Simplified 99.5%

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

      1. clear-num 99.2%

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

      2. un-div-inv 99.1%

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

      3. +-commutative 99.1%

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

   6. Applied egg-rr 99.1%

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

   7. Taylor expanded in z around 0 73.6%

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

      1. associate-*r* 73.6%

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

      2. neg-mul-1 73.6%

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

   9. Simplified 73.6%

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

   if -2.25e111 < t < -7.9999999999999998e107

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. metadata-eval 100.0%

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

      3. *-lft-identity 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. *-lft-identity 100.0%

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

      3. times-frac 100.0%

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

      4. /-rgt-identity 100.0%

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

   7. Simplified 100.0%

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

   if -7.9999999999999998e107 < t < 7.50000000000000058e106

   1. Initial program 93.0%

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

   2. Taylor expanded in y around inf 78.0%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{+111}:\\ \;\;\;\;-x \cdot t\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 7: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+201}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 82:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+215}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e+201)
   (/ (* x y) z)
   (if (<= z -2.1e+44)
     (* x (/ t z))
     (if (<= z 82.0)
       (* x (- (/ y z) t))
       (if (<= z 3.4e+215) (/ x (/ z t)) (* x (/ y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+201) {
		tmp = (x * y) / z;
	} else if (z <= -2.1e+44) {
		tmp = x * (t / z);
	} else if (z <= 82.0) {
		tmp = x * ((y / z) - t);
	} else if (z <= 3.4e+215) {
		tmp = x / (z / t);
	} else {
		tmp = x * (y / 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 (z <= (-1.6d+201)) then
        tmp = (x * y) / z
    else if (z <= (-2.1d+44)) then
        tmp = x * (t / z)
    else if (z <= 82.0d0) then
        tmp = x * ((y / z) - t)
    else if (z <= 3.4d+215) then
        tmp = x / (z / t)
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+201) {
		tmp = (x * y) / z;
	} else if (z <= -2.1e+44) {
		tmp = x * (t / z);
	} else if (z <= 82.0) {
		tmp = x * ((y / z) - t);
	} else if (z <= 3.4e+215) {
		tmp = x / (z / t);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e+201:
		tmp = (x * y) / z
	elif z <= -2.1e+44:
		tmp = x * (t / z)
	elif z <= 82.0:
		tmp = x * ((y / z) - t)
	elif z <= 3.4e+215:
		tmp = x / (z / t)
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e+201)
		tmp = Float64(Float64(x * y) / z);
	elseif (z <= -2.1e+44)
		tmp = Float64(x * Float64(t / z));
	elseif (z <= 82.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 3.4e+215)
		tmp = Float64(x / Float64(z / t));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e+201)
		tmp = (x * y) / z;
	elseif (z <= -2.1e+44)
		tmp = x * (t / z);
	elseif (z <= 82.0)
		tmp = x * ((y / z) - t);
	elseif (z <= 3.4e+215)
		tmp = x / (z / t);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e+201], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -2.1e+44], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 82.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+215], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.6e201

   1. Initial program 87.6%

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

   2. Taylor expanded in y around inf 72.3%

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

   if -1.6e201 < z < -2.09999999999999987e44

   1. Initial program 97.0%

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

   2. Taylor expanded in z around inf 97.0%

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

      1. cancel-sign-sub-inv 97.0%

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

      2. metadata-eval 97.0%

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

      3. *-lft-identity 97.0%

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

   4. Simplified 97.0%

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

   5. Taylor expanded in y around 0 68.9%

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

      1. *-commutative 68.9%

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

      2. *-lft-identity 68.9%

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

      3. times-frac 74.0%

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

      4. /-rgt-identity 74.0%

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

   7. Simplified 74.0%

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

   if -2.09999999999999987e44 < z < 82

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 91.3%

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

      1. associate-*l/ 88.4%

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

      2. associate-*r* 88.4%

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

      3. neg-mul-1 88.4%

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

      4. distribute-rgt-out 90.7%

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

      5. unsub-neg 90.7%

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

   4. Simplified 90.7%

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

   if 82 < z < 3.40000000000000018e215

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 89.3%

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

      1. *-commutative 89.3%

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

      2. associate-/l* 94.0%

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

      3. neg-mul-1 94.0%

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

   4. Simplified 94.0%

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

   5. Taylor expanded in y around 0 67.0%

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

   if 3.40000000000000018e215 < z

   1. Initial program 95.4%

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

   2. Taylor expanded in y around inf 77.6%

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

      1. associate-*l/ 81.8%

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

   4. Simplified 81.8%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+201}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 82:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+215}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 8: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+200} \lor \neg \left(z \leq -1150000\right) \land z \leq 92000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.02e+200) (and (not (<= z -1150000.0)) (<= z 92000.0)))
   (* y (/ x z))
   (* x (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.02e+200) || (!(z <= -1150000.0) && (z <= 92000.0))) {
		tmp = y * (x / z);
	} else {
		tmp = x * (t / 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 ((z <= (-1.02d+200)) .or. (.not. (z <= (-1150000.0d0))) .and. (z <= 92000.0d0)) then
        tmp = y * (x / z)
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.02e+200) || (!(z <= -1150000.0) && (z <= 92000.0))) {
		tmp = y * (x / z);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.02e+200) or (not (z <= -1150000.0) and (z <= 92000.0)):
		tmp = y * (x / z)
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.02e+200) || (!(z <= -1150000.0) && (z <= 92000.0)))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.02e+200) || (~((z <= -1150000.0)) && (z <= 92000.0)))
		tmp = y * (x / z);
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.02e+200], And[N[Not[LessEqual[z, -1150000.0]], $MachinePrecision], LessEqual[z, 92000.0]]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.02000000000000001e200 or -1.15e6 < z < 92000

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf 69.9%

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

      1. associate-*l/ 66.7%

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

   4. Simplified 66.7%

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

      1. *-commutative 66.7%

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

      2. clear-num 66.7%

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

      3. un-div-inv 67.0%

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

   6. Applied egg-rr 67.0%

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

      1. associate-/r/ 67.4%

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

   8. Simplified 67.4%

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

   if -1.02000000000000001e200 < z < -1.15e6 or 92000 < z

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 95.2%

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

      1. cancel-sign-sub-inv 95.2%

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

      2. metadata-eval 95.2%

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

      3. *-lft-identity 95.2%

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

   4. Simplified 95.2%

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

   5. Taylor expanded in y around 0 59.8%

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

      1. *-commutative 59.8%

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

      2. *-lft-identity 59.8%

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

      3. times-frac 63.1%

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

      4. /-rgt-identity 63.1%

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

   7. Simplified 63.1%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+200} \lor \neg \left(z \leq -1150000\right) \land z \leq 92000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 9: 93.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3000 \lor \neg \left(z \leq 9 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3000.0) (not (<= z 9e-5)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3000.0) || !(z <= 9e-5)) {
		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 <= (-3000.0d0)) .or. (.not. (z <= 9d-5))) 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 <= -3000.0) || !(z <= 9e-5)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3000.0) or not (z <= 9e-5):
		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 <= -3000.0) || !(z <= 9e-5))
		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 <= -3000.0) || ~((z <= 9e-5)))
		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, -3000.0], N[Not[LessEqual[z, 9e-5]], $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 < -3e3 or 9.00000000000000057e-5 < z

   1. Initial program 95.4%

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

   2. Taylor expanded in z around inf 93.9%

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

      1. cancel-sign-sub-inv 93.9%

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

      2. metadata-eval 93.9%

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

      3. *-lft-identity 93.9%

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

   4. Simplified 93.9%

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

   if -3e3 < z < 9.00000000000000057e-5

   1. Initial program 93.8%

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

   2. Taylor expanded in z around 0 94.1%

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

      1. associate-*l/ 91.1%

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

      2. associate-*r* 91.1%

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

      3. neg-mul-1 91.1%

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

      4. distribute-rgt-out 93.5%

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

      5. unsub-neg 93.5%

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

   4. Simplified 93.5%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3000 \lor \neg \left(z \leq 9 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 10: 44.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{-12} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;-x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.06e-12) (not (<= z 1.0))) (* x (/ t z)) (- (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.06e-12) || !(z <= 1.0)) {
		tmp = x * (t / z);
	} else {
		tmp = -(x * 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 <= (-1.06d-12)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * (t / z)
    else
        tmp = -(x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.06e-12) || !(z <= 1.0)) {
		tmp = x * (t / z);
	} else {
		tmp = -(x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.06e-12) or not (z <= 1.0):
		tmp = x * (t / z)
	else:
		tmp = -(x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.06e-12) || !(z <= 1.0))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(-Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.06e-12) || ~((z <= 1.0)))
		tmp = x * (t / z);
	else
		tmp = -(x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.06e-12], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], (-N[(x * t), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if z < -1.0599999999999999e-12 or 1 < z

   1. Initial program 95.5%

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

   2. Taylor expanded in z around inf 93.9%

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

      1. cancel-sign-sub-inv 93.9%

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

      2. metadata-eval 93.9%

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

      3. *-lft-identity 93.9%

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

   4. Simplified 93.9%

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

   5. Taylor expanded in y around 0 56.1%

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

      1. *-commutative 56.1%

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

      2. *-lft-identity 56.1%

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

      3. times-frac 58.7%

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

      4. /-rgt-identity 58.7%

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

   7. Simplified 58.7%

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

   if -1.0599999999999999e-12 < z < 1

   1. Initial program 93.7%

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

   2. Taylor expanded in y around 0 37.0%

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

      1. associate-*r/ 37.0%

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

      2. mul-1-neg 37.0%

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

      3. *-commutative 37.0%

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

      4. distribute-rgt-neg-in 37.0%

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

      5. associate-*r/ 37.1%

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

      6. neg-mul-1 37.1%

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

      7. *-commutative 37.1%

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

      8. associate-*r/ 37.1%

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

      9. metadata-eval 37.1%

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

      10. associate-/r* 37.1%

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

      11. neg-mul-1 37.1%

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

      12. associate-*r/ 37.1%

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

      13. *-rgt-identity 37.1%

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

      14. neg-sub0 37.1%

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

      15. associate--r- 37.1%

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

      16. metadata-eval 37.1%

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

   4. Simplified 37.1%

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

      1. clear-num 37.0%

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

      2. un-div-inv 36.9%

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

      3. +-commutative 36.9%

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

   6. Applied egg-rr 36.9%

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

   7. Taylor expanded in z around 0 36.8%

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

      1. associate-*r* 36.8%

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

      2. neg-mul-1 36.8%

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

   9. Simplified 36.8%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{-12} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;-x \cdot t\\ \end{array} \]

Alternative 11: 22.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ -x \cdot t \end{array} \]

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 94.6%

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

2. Taylor expanded in y around 0 47.8%

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

   1. associate-*r/ 47.8%

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

   2. mul-1-neg 47.8%

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

   3. *-commutative 47.8%

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

   4. distribute-rgt-neg-in 47.8%

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

   5. associate-*r/ 49.2%

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

   6. neg-mul-1 49.2%

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

   7. *-commutative 49.2%

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

   8. associate-*r/ 49.1%

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

   9. metadata-eval 49.1%

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

   10. associate-/r* 49.1%

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

   11. neg-mul-1 49.1%

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

   12. associate-*r/ 49.2%

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

   13. *-rgt-identity 49.2%

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

   14. neg-sub0 49.2%

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

   15. associate--r- 49.2%

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

   16. metadata-eval 49.2%

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

4. Simplified 49.2%

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

   1. clear-num 48.7%

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

   2. un-div-inv 48.7%

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

   3. +-commutative 48.7%

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

6. Applied egg-rr 48.7%

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

7. Taylor expanded in z around 0 24.3%

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

   1. associate-*r* 24.3%

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

   2. neg-mul-1 24.3%

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

9. Simplified 24.3%

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

10. Final simplification 24.3%

    \[\leadsto -x \cdot t \]

Developer target: 94.7% 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 2023240 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (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)))))