Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Percentage Accurate: 77.0% → 90.4%

Time: 14.2s

Alternatives: 18

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+102}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+47}:\\ \;\;\;\;\left(x + y\right) + \frac{z - t}{\frac{t - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.4e+102)
   (- x (* y (/ (- a z) t)))
   (if (<= t 2.8e+47)
     (+ (+ x y) (/ (- z t) (/ (- t a) y)))
     (+ (- x (* a (/ y t))) (* y (/ z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e+102) {
		tmp = x - (y * ((a - z) / t));
	} else if (t <= 2.8e+47) {
		tmp = (x + y) + ((z - t) / ((t - a) / y));
	} else {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.4d+102)) then
        tmp = x - (y * ((a - z) / t))
    else if (t <= 2.8d+47) then
        tmp = (x + y) + ((z - t) / ((t - a) / y))
    else
        tmp = (x - (a * (y / t))) + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e+102) {
		tmp = x - (y * ((a - z) / t));
	} else if (t <= 2.8e+47) {
		tmp = (x + y) + ((z - t) / ((t - a) / y));
	} else {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.4e+102:
		tmp = x - (y * ((a - z) / t))
	elif t <= 2.8e+47:
		tmp = (x + y) + ((z - t) / ((t - a) / y))
	else:
		tmp = (x - (a * (y / t))) + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.4e+102)
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	elseif (t <= 2.8e+47)
		tmp = Float64(Float64(x + y) + Float64(Float64(z - t) / Float64(Float64(t - a) / y)));
	else
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.4e+102)
		tmp = x - (y * ((a - z) / t));
	elseif (t <= 2.8e+47)
		tmp = (x + y) + ((z - t) / ((t - a) / y));
	else
		tmp = (x - (a * (y / t))) + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.4e+102], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+47], N[(N[(x + y), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4e102

   1. Initial program 44.6%

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

   3. Taylor expanded in y around 0 44.6%

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

      1. associate-*l/ 56.4%

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

   5. Simplified 56.4%

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

      1. *-commutative 56.4%

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

      2. clear-num 56.8%

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

      3. un-div-inv 56.4%

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

   7. Applied egg-rr 56.4%

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

   8. Taylor expanded in t around -inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. unsub-neg 67.9%

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

      3. *-commutative 67.9%

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

      4. cancel-sign-sub-inv 67.9%

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

      5. neg-mul-1 67.9%

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

      6. distribute-rgt-in 68.0%

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

      7. associate-/l* 90.7%

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

      8. neg-mul-1 90.7%

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

      9. sub-neg 90.7%

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

   10. Simplified 90.7%

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

   if -3.4e102 < t < 2.79999999999999988e47

   1. Initial program 90.9%

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

   3. Taylor expanded in y around 0 90.9%

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

      1. associate-*l/ 94.1%

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

   5. Simplified 94.1%

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

      1. *-commutative 94.1%

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

      2. clear-num 94.1%

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

      3. un-div-inv 94.7%

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

   7. Applied egg-rr 94.7%

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

   if 2.79999999999999988e47 < t

   1. Initial program 53.6%

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

   3. Taylor expanded in y around 0 53.6%

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

      1. associate-*l/ 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in t around inf 76.7%

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

      1. sub-neg 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

      4. associate-/l* 81.7%

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

      5. mul-1-neg 81.7%

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

      6. remove-double-neg 81.7%

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

      7. associate-/l* 86.8%

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

   8. Simplified 86.8%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+102}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+47}:\\ \;\;\;\;\left(x + y\right) + \frac{z - t}{\frac{t - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{a - z}{t}\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+49}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.86 \cdot 10^{-227}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-90}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+26} \lor \neg \left(a \leq 2.2 \cdot 10^{+132}\right) \land a \leq 2.55 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- a z) t)))))
   (if (<= a -2.6e+49)
     (+ x y)
     (if (<= a -2.2e-63)
       t_1
       (if (<= a -9.5e-67)
         x
         (if (<= a -1.86e-227)
           (+ x (* y (/ z t)))
           (if (<= a 6.5e-90)
             (- x (/ (* y (- a z)) t))
             (if (or (<= a 2.35e+26)
                     (and (not (<= a 2.2e+132)) (<= a 2.55e+154)))
               t_1
               (+ x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((a - z) / t));
	double tmp;
	if (a <= -2.6e+49) {
		tmp = x + y;
	} else if (a <= -2.2e-63) {
		tmp = t_1;
	} else if (a <= -9.5e-67) {
		tmp = x;
	} else if (a <= -1.86e-227) {
		tmp = x + (y * (z / t));
	} else if (a <= 6.5e-90) {
		tmp = x - ((y * (a - z)) / t);
	} else if ((a <= 2.35e+26) || (!(a <= 2.2e+132) && (a <= 2.55e+154))) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * ((a - z) / t))
    if (a <= (-2.6d+49)) then
        tmp = x + y
    else if (a <= (-2.2d-63)) then
        tmp = t_1
    else if (a <= (-9.5d-67)) then
        tmp = x
    else if (a <= (-1.86d-227)) then
        tmp = x + (y * (z / t))
    else if (a <= 6.5d-90) then
        tmp = x - ((y * (a - z)) / t)
    else if ((a <= 2.35d+26) .or. (.not. (a <= 2.2d+132)) .and. (a <= 2.55d+154)) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((a - z) / t));
	double tmp;
	if (a <= -2.6e+49) {
		tmp = x + y;
	} else if (a <= -2.2e-63) {
		tmp = t_1;
	} else if (a <= -9.5e-67) {
		tmp = x;
	} else if (a <= -1.86e-227) {
		tmp = x + (y * (z / t));
	} else if (a <= 6.5e-90) {
		tmp = x - ((y * (a - z)) / t);
	} else if ((a <= 2.35e+26) || (!(a <= 2.2e+132) && (a <= 2.55e+154))) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((a - z) / t))
	tmp = 0
	if a <= -2.6e+49:
		tmp = x + y
	elif a <= -2.2e-63:
		tmp = t_1
	elif a <= -9.5e-67:
		tmp = x
	elif a <= -1.86e-227:
		tmp = x + (y * (z / t))
	elif a <= 6.5e-90:
		tmp = x - ((y * (a - z)) / t)
	elif (a <= 2.35e+26) or (not (a <= 2.2e+132) and (a <= 2.55e+154)):
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (a <= -2.6e+49)
		tmp = Float64(x + y);
	elseif (a <= -2.2e-63)
		tmp = t_1;
	elseif (a <= -9.5e-67)
		tmp = x;
	elseif (a <= -1.86e-227)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (a <= 6.5e-90)
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	elseif ((a <= 2.35e+26) || (!(a <= 2.2e+132) && (a <= 2.55e+154)))
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((a - z) / t));
	tmp = 0.0;
	if (a <= -2.6e+49)
		tmp = x + y;
	elseif (a <= -2.2e-63)
		tmp = t_1;
	elseif (a <= -9.5e-67)
		tmp = x;
	elseif (a <= -1.86e-227)
		tmp = x + (y * (z / t));
	elseif (a <= 6.5e-90)
		tmp = x - ((y * (a - z)) / t);
	elseif ((a <= 2.35e+26) || (~((a <= 2.2e+132)) && (a <= 2.55e+154)))
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e+49], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.2e-63], t$95$1, If[LessEqual[a, -9.5e-67], x, If[LessEqual[a, -1.86e-227], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-90], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 2.35e+26], And[N[Not[LessEqual[a, 2.2e+132]], $MachinePrecision], LessEqual[a, 2.55e+154]]], t$95$1, N[(x + y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.59999999999999989e49 or 2.3499999999999999e26 < a < 2.19999999999999989e132 or 2.55e154 < a

   1. Initial program 76.7%

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

   3. Taylor expanded in a around inf 77.1%

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

      1. +-commutative 77.1%

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

   5. Simplified 77.1%

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

   if -2.59999999999999989e49 < a < -2.2e-63 or 6.4999999999999996e-90 < a < 2.3499999999999999e26 or 2.19999999999999989e132 < a < 2.55e154

   1. Initial program 71.4%

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

   3. Taylor expanded in y around 0 71.4%

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

      1. associate-*l/ 72.1%

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

   5. Simplified 72.1%

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

      1. *-commutative 72.1%

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

      2. clear-num 72.1%

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

      3. un-div-inv 72.0%

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

   7. Applied egg-rr 72.0%

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

   8. Taylor expanded in t around -inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. unsub-neg 66.4%

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

      3. *-commutative 66.4%

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

      4. cancel-sign-sub-inv 66.4%

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

      5. neg-mul-1 66.4%

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

      6. distribute-rgt-in 66.4%

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

      7. associate-/l* 73.7%

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

      8. neg-mul-1 73.7%

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

      9. sub-neg 73.7%

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

   10. Simplified 73.7%

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

   if -2.2e-63 < a < -9.4999999999999994e-67

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   if -9.4999999999999994e-67 < a < -1.86000000000000011e-227

   1. Initial program 74.0%

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

   3. Taylor expanded in y around 0 74.0%

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

      1. associate-*l/ 82.3%

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

   5. Simplified 82.3%

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

      1. *-commutative 82.3%

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

      2. clear-num 82.2%

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

      3. un-div-inv 82.4%

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

   7. Applied egg-rr 82.4%

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

   8. Taylor expanded in t around -inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. unsub-neg 70.7%

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

      3. *-commutative 70.7%

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

      4. cancel-sign-sub-inv 70.7%

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

      5. neg-mul-1 70.7%

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

      6. distribute-rgt-in 70.7%

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

      7. associate-/l* 76.5%

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

      8. neg-mul-1 76.5%

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

      9. sub-neg 76.5%

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

   10. Simplified 76.5%

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

   11. Taylor expanded in a around 0 79.1%

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

       1. neg-mul-1 79.1%

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

       2. distribute-neg-frac2 79.1%

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

   13. Simplified 79.1%

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

       1. sub-neg 79.1%

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

       2. +-commutative 79.1%

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

       3. distribute-lft-neg-in 79.1%

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

       4. add-sqr-sqrt 63.8%

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

       5. sqrt-unprod 63.3%

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

       6. sqr-neg 63.3%

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

       7. sqrt-unprod 12.4%

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

       8. add-sqr-sqrt 60.6%

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

       9. add-sqr-sqrt 29.9%

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

       10. sqrt-unprod 66.7%

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

       11. sqr-neg 66.7%

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

       12. sqrt-unprod 42.6%

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

       13. add-sqr-sqrt 79.1%

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

   15. Applied egg-rr 79.1%

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

   if -1.86000000000000011e-227 < a < 6.4999999999999996e-90

   1. Initial program 76.4%

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

   3. Taylor expanded in t around inf 83.7%

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

      1. associate--l+ 83.7%

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

      2. distribute-lft-out-- 83.7%

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

      3. div-sub 83.7%

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

      4. mul-1-neg 83.7%

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

      5. unsub-neg 83.7%

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

      6. *-commutative 83.7%

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

      7. distribute-lft-out-- 83.7%

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

   5. Simplified 83.7%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(a - z\right)}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+49}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-63}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.86 \cdot 10^{-227}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-90}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+26} \lor \neg \left(a \leq 2.2 \cdot 10^{+132}\right) \land a \leq 2.55 \cdot 10^{+154}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{t - a}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-187}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-293}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.7 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+206} \lor \neg \left(z \leq 10^{+213}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- t a)))))
   (if (<= z -1.4e+186)
     t_1
     (if (<= z -6.6e-187)
       (+ x y)
       (if (<= z -2.8e-293)
         x
         (if (<= z 1.6e+35)
           (+ x y)
           (if (<= z 3.5e+135)
             t_1
             (if (<= z 9.7e+154)
               x
               (if (or (<= z 6.5e+206) (not (<= z 1e+213)))
                 t_1
                 (+ x y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (t - a));
	double tmp;
	if (z <= -1.4e+186) {
		tmp = t_1;
	} else if (z <= -6.6e-187) {
		tmp = x + y;
	} else if (z <= -2.8e-293) {
		tmp = x;
	} else if (z <= 1.6e+35) {
		tmp = x + y;
	} else if (z <= 3.5e+135) {
		tmp = t_1;
	} else if (z <= 9.7e+154) {
		tmp = x;
	} else if ((z <= 6.5e+206) || !(z <= 1e+213)) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y / (t - a))
    if (z <= (-1.4d+186)) then
        tmp = t_1
    else if (z <= (-6.6d-187)) then
        tmp = x + y
    else if (z <= (-2.8d-293)) then
        tmp = x
    else if (z <= 1.6d+35) then
        tmp = x + y
    else if (z <= 3.5d+135) then
        tmp = t_1
    else if (z <= 9.7d+154) then
        tmp = x
    else if ((z <= 6.5d+206) .or. (.not. (z <= 1d+213))) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (t - a));
	double tmp;
	if (z <= -1.4e+186) {
		tmp = t_1;
	} else if (z <= -6.6e-187) {
		tmp = x + y;
	} else if (z <= -2.8e-293) {
		tmp = x;
	} else if (z <= 1.6e+35) {
		tmp = x + y;
	} else if (z <= 3.5e+135) {
		tmp = t_1;
	} else if (z <= 9.7e+154) {
		tmp = x;
	} else if ((z <= 6.5e+206) || !(z <= 1e+213)) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / (t - a))
	tmp = 0
	if z <= -1.4e+186:
		tmp = t_1
	elif z <= -6.6e-187:
		tmp = x + y
	elif z <= -2.8e-293:
		tmp = x
	elif z <= 1.6e+35:
		tmp = x + y
	elif z <= 3.5e+135:
		tmp = t_1
	elif z <= 9.7e+154:
		tmp = x
	elif (z <= 6.5e+206) or not (z <= 1e+213):
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(t - a)))
	tmp = 0.0
	if (z <= -1.4e+186)
		tmp = t_1;
	elseif (z <= -6.6e-187)
		tmp = Float64(x + y);
	elseif (z <= -2.8e-293)
		tmp = x;
	elseif (z <= 1.6e+35)
		tmp = Float64(x + y);
	elseif (z <= 3.5e+135)
		tmp = t_1;
	elseif (z <= 9.7e+154)
		tmp = x;
	elseif ((z <= 6.5e+206) || !(z <= 1e+213))
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / (t - a));
	tmp = 0.0;
	if (z <= -1.4e+186)
		tmp = t_1;
	elseif (z <= -6.6e-187)
		tmp = x + y;
	elseif (z <= -2.8e-293)
		tmp = x;
	elseif (z <= 1.6e+35)
		tmp = x + y;
	elseif (z <= 3.5e+135)
		tmp = t_1;
	elseif (z <= 9.7e+154)
		tmp = x;
	elseif ((z <= 6.5e+206) || ~((z <= 1e+213)))
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+186], t$95$1, If[LessEqual[z, -6.6e-187], N[(x + y), $MachinePrecision], If[LessEqual[z, -2.8e-293], x, If[LessEqual[z, 1.6e+35], N[(x + y), $MachinePrecision], If[LessEqual[z, 3.5e+135], t$95$1, If[LessEqual[z, 9.7e+154], x, If[Or[LessEqual[z, 6.5e+206], N[Not[LessEqual[z, 1e+213]], $MachinePrecision]], t$95$1, N[(x + y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.40000000000000009e186 or 1.59999999999999991e35 < z < 3.5000000000000003e135 or 9.69999999999999987e154 < z < 6.4999999999999995e206 or 9.99999999999999984e212 < z

   1. Initial program 78.0%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   2. Step-by-step derivation

      1. sub-neg 78.0%

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

      2. +-commutative 78.0%

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

      3. distribute-frac-neg 78.0%

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

      4. distribute-rgt-neg-out 78.0%

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

      5. associate-/l* 91.8%

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

      6. fma-define 91.9%

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

      7. distribute-frac-neg 91.9%

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

      8. distribute-neg-frac2 91.9%

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

      9. sub-neg 91.9%

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

      10. distribute-neg-in 91.9%

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

      11. remove-double-neg 91.9%

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

      12. +-commutative 91.9%

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

      13. sub-neg 91.9%

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

   3. Simplified 91.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 58.1%

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

      1. associate-/l* 64.5%

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

   7. Simplified 64.5%

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

      1. associate-*r/ 58.1%

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

      2. clear-num 58.1%

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

   9. Applied egg-rr 58.1%

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

       1. clear-num 58.1%

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

       2. *-commutative 58.1%

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

       3. associate-/l* 74.7%

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

   11. Applied egg-rr 74.7%

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

   if -1.40000000000000009e186 < z < -6.6e-187 or -2.80000000000000025e-293 < z < 1.59999999999999991e35 or 6.4999999999999995e206 < z < 9.99999999999999984e212

   1. Initial program 74.9%

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

   3. Taylor expanded in a around inf 66.1%

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

      1. +-commutative 66.1%

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

   5. Simplified 66.1%

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

   if -6.6e-187 < z < -2.80000000000000025e-293 or 3.5000000000000003e135 < z < 9.69999999999999987e154

   1. Initial program 70.6%

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

   3. Taylor expanded in x around inf 93.8%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-187}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-293}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+135}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;z \leq 9.7 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+206} \lor \neg \left(z \leq 10^{+213}\right):\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t - a}\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{+119}:\\ \;\;\;\;\left(x + y\right) - y\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-187}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+37} \lor \neg \left(z \leq 8.5 \cdot 10^{+205}\right) \land z \leq 9.5 \cdot 10^{+212}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- t a)))))
   (if (<= z -1.12e+163)
     t_1
     (if (<= z -1.46e+119)
       (- (+ x y) y)
       (if (<= z -2.2e-187)
         (+ x y)
         (if (<= z -4.6e-295)
           x
           (if (or (<= z 1.95e+37) (and (not (<= z 8.5e+205)) (<= z 9.5e+212)))
             (+ x y)
             t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (t - a));
	double tmp;
	if (z <= -1.12e+163) {
		tmp = t_1;
	} else if (z <= -1.46e+119) {
		tmp = (x + y) - y;
	} else if (z <= -2.2e-187) {
		tmp = x + y;
	} else if (z <= -4.6e-295) {
		tmp = x;
	} else if ((z <= 1.95e+37) || (!(z <= 8.5e+205) && (z <= 9.5e+212))) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / (t - a))
    if (z <= (-1.12d+163)) then
        tmp = t_1
    else if (z <= (-1.46d+119)) then
        tmp = (x + y) - y
    else if (z <= (-2.2d-187)) then
        tmp = x + y
    else if (z <= (-4.6d-295)) then
        tmp = x
    else if ((z <= 1.95d+37) .or. (.not. (z <= 8.5d+205)) .and. (z <= 9.5d+212)) then
        tmp = x + 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 a) {
	double t_1 = y * (z / (t - a));
	double tmp;
	if (z <= -1.12e+163) {
		tmp = t_1;
	} else if (z <= -1.46e+119) {
		tmp = (x + y) - y;
	} else if (z <= -2.2e-187) {
		tmp = x + y;
	} else if (z <= -4.6e-295) {
		tmp = x;
	} else if ((z <= 1.95e+37) || (!(z <= 8.5e+205) && (z <= 9.5e+212))) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (t - a))
	tmp = 0
	if z <= -1.12e+163:
		tmp = t_1
	elif z <= -1.46e+119:
		tmp = (x + y) - y
	elif z <= -2.2e-187:
		tmp = x + y
	elif z <= -4.6e-295:
		tmp = x
	elif (z <= 1.95e+37) or (not (z <= 8.5e+205) and (z <= 9.5e+212)):
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(t - a)))
	tmp = 0.0
	if (z <= -1.12e+163)
		tmp = t_1;
	elseif (z <= -1.46e+119)
		tmp = Float64(Float64(x + y) - y);
	elseif (z <= -2.2e-187)
		tmp = Float64(x + y);
	elseif (z <= -4.6e-295)
		tmp = x;
	elseif ((z <= 1.95e+37) || (!(z <= 8.5e+205) && (z <= 9.5e+212)))
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (t - a));
	tmp = 0.0;
	if (z <= -1.12e+163)
		tmp = t_1;
	elseif (z <= -1.46e+119)
		tmp = (x + y) - y;
	elseif (z <= -2.2e-187)
		tmp = x + y;
	elseif (z <= -4.6e-295)
		tmp = x;
	elseif ((z <= 1.95e+37) || (~((z <= 8.5e+205)) && (z <= 9.5e+212)))
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.12e+163], t$95$1, If[LessEqual[z, -1.46e+119], N[(N[(x + y), $MachinePrecision] - y), $MachinePrecision], If[LessEqual[z, -2.2e-187], N[(x + y), $MachinePrecision], If[LessEqual[z, -4.6e-295], x, If[Or[LessEqual[z, 1.95e+37], And[N[Not[LessEqual[z, 8.5e+205]], $MachinePrecision], LessEqual[z, 9.5e+212]]], N[(x + y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.11999999999999996e163 or 1.9499999999999999e37 < z < 8.49999999999999997e205 or 9.4999999999999993e212 < z

   1. Initial program 77.6%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   2. Step-by-step derivation

      1. sub-neg 77.6%

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

      2. +-commutative 77.6%

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

      3. distribute-frac-neg 77.6%

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

      4. distribute-rgt-neg-out 77.6%

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

      5. associate-/l* 91.3%

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

      6. fma-define 91.4%

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

      7. distribute-frac-neg 91.4%

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

      8. distribute-neg-frac2 91.4%

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

      9. sub-neg 91.4%

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

      10. distribute-neg-in 91.4%

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

      11. remove-double-neg 91.4%

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

      12. +-commutative 91.4%

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

      13. sub-neg 91.4%

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

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 57.1%

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

      1. associate-/l* 62.8%

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

   7. Simplified 62.8%

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

   if -1.11999999999999996e163 < z < -1.4600000000000001e119

   1. Initial program 90.7%

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

   3. Taylor expanded in t around inf 70.5%

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

   if -1.4600000000000001e119 < z < -2.20000000000000008e-187 or -4.6e-295 < z < 1.9499999999999999e37 or 8.49999999999999997e205 < z < 9.4999999999999993e212

   1. Initial program 74.1%

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

   3. Taylor expanded in a around inf 67.1%

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

      1. +-commutative 67.1%

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

   5. Simplified 67.1%

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

   if -2.20000000000000008e-187 < z < -4.6e-295

   1. Initial program 67.7%

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

   3. Taylor expanded in x around inf 93.1%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+163}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{+119}:\\ \;\;\;\;\left(x + y\right) - y\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-187}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+37} \lor \neg \left(z \leq 8.5 \cdot 10^{+205}\right) \land z \leq 9.5 \cdot 10^{+212}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{-26}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* y z) a))))
   (if (<= t -4.6e-26)
     (- x (* y (/ (- a z) t)))
     (if (<= t -1.05e-208)
       t_1
       (if (<= t -1.8e-274)
         (* y (+ (/ (- z t) (- t a)) 1.0))
         (if (<= t 2.3e-73) t_1 (+ x (* y (- (/ z t) (/ a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * z) / a);
	double tmp;
	if (t <= -4.6e-26) {
		tmp = x - (y * ((a - z) / t));
	} else if (t <= -1.05e-208) {
		tmp = t_1;
	} else if (t <= -1.8e-274) {
		tmp = y * (((z - t) / (t - a)) + 1.0);
	} else if (t <= 2.3e-73) {
		tmp = t_1;
	} else {
		tmp = x + (y * ((z / t) - (a / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - ((y * z) / a)
    if (t <= (-4.6d-26)) then
        tmp = x - (y * ((a - z) / t))
    else if (t <= (-1.05d-208)) then
        tmp = t_1
    else if (t <= (-1.8d-274)) then
        tmp = y * (((z - t) / (t - a)) + 1.0d0)
    else if (t <= 2.3d-73) then
        tmp = t_1
    else
        tmp = x + (y * ((z / t) - (a / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * z) / a);
	double tmp;
	if (t <= -4.6e-26) {
		tmp = x - (y * ((a - z) / t));
	} else if (t <= -1.05e-208) {
		tmp = t_1;
	} else if (t <= -1.8e-274) {
		tmp = y * (((z - t) / (t - a)) + 1.0);
	} else if (t <= 2.3e-73) {
		tmp = t_1;
	} else {
		tmp = x + (y * ((z / t) - (a / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((y * z) / a)
	tmp = 0
	if t <= -4.6e-26:
		tmp = x - (y * ((a - z) / t))
	elif t <= -1.05e-208:
		tmp = t_1
	elif t <= -1.8e-274:
		tmp = y * (((z - t) / (t - a)) + 1.0)
	elif t <= 2.3e-73:
		tmp = t_1
	else:
		tmp = x + (y * ((z / t) - (a / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(y * z) / a))
	tmp = 0.0
	if (t <= -4.6e-26)
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	elseif (t <= -1.05e-208)
		tmp = t_1;
	elseif (t <= -1.8e-274)
		tmp = Float64(y * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0));
	elseif (t <= 2.3e-73)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((y * z) / a);
	tmp = 0.0;
	if (t <= -4.6e-26)
		tmp = x - (y * ((a - z) / t));
	elseif (t <= -1.05e-208)
		tmp = t_1;
	elseif (t <= -1.8e-274)
		tmp = y * (((z - t) / (t - a)) + 1.0);
	elseif (t <= 2.3e-73)
		tmp = t_1;
	else
		tmp = x + (y * ((z / t) - (a / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.6e-26], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.05e-208], t$95$1, If[LessEqual[t, -1.8e-274], N[(y * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e-73], t$95$1, N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.60000000000000018e-26

   1. Initial program 60.3%

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

   3. Taylor expanded in y around 0 60.3%

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

      1. associate-*l/ 67.8%

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

   5. Simplified 67.8%

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

      1. *-commutative 67.8%

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

      2. clear-num 68.1%

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

      3. un-div-inv 67.9%

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

   7. Applied egg-rr 67.9%

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

   8. Taylor expanded in t around -inf 73.6%

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

      1. mul-1-neg 73.6%

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

      2. unsub-neg 73.6%

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

      3. *-commutative 73.6%

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

      4. cancel-sign-sub-inv 73.6%

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

      5. neg-mul-1 73.6%

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

      6. distribute-rgt-in 73.6%

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

      7. associate-/l* 88.1%

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

      8. neg-mul-1 88.1%

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

      9. sub-neg 88.1%

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

   10. Simplified 88.1%

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

   if -4.60000000000000018e-26 < t < -1.05000000000000006e-208 or -1.79999999999999991e-274 < t < 2.29999999999999988e-73

   1. Initial program 96.1%

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

   3. Taylor expanded in t around 0 83.6%

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

   if -1.05000000000000006e-208 < t < -1.79999999999999991e-274

   1. Initial program 94.0%

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

   3. Taylor expanded in x around 0 70.0%

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

      1. sub-neg 70.0%

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

      2. *-rgt-identity 70.0%

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

      3. associate-*r/ 70.0%

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

      4. distribute-rgt-neg-in 70.0%

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

      5. mul-1-neg 70.0%

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

      6. distribute-lft-in 70.0%

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

      7. mul-1-neg 70.0%

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

      8. unsub-neg 70.0%

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

   5. Simplified 70.0%

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

   if 2.29999999999999988e-73 < t

   1. Initial program 58.4%

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

   3. Taylor expanded in y around 0 58.4%

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

      1. associate-*l/ 67.6%

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

   5. Simplified 67.6%

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

      1. *-commutative 67.6%

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

      2. clear-num 67.5%

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

      3. un-div-inv 67.5%

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

   7. Applied egg-rr 67.5%

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

   8. Taylor expanded in t around -inf 71.3%

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

      1. mul-1-neg 71.3%

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

      2. unsub-neg 71.3%

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

      3. *-commutative 71.3%

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

      4. cancel-sign-sub-inv 71.3%

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

      5. neg-mul-1 71.3%

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

      6. distribute-rgt-in 71.4%

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

      7. associate-/l* 78.4%

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

      8. neg-mul-1 78.4%

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

      9. sub-neg 78.4%

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

   10. Simplified 78.4%

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

       1. div-sub 78.4%

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

   12. Applied egg-rr 78.4%

       \[\leadsto x - y \cdot \color{blue}{\left(\frac{a}{t} - \frac{z}{t}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-26}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-208}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-73}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot z}{a}\\ t_2 := x - y \cdot \frac{a - z}{t}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-76}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* y z) a))) (t_2 (- x (* y (/ (- a z) t)))))
   (if (<= t -1.7e-21)
     t_2
     (if (<= t -1.05e-208)
       t_1
       (if (<= t -6e-274)
         (* y (+ (/ (- z t) (- t a)) 1.0))
         (if (<= t 4.2e-76) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * z) / a);
	double t_2 = x - (y * ((a - z) / t));
	double tmp;
	if (t <= -1.7e-21) {
		tmp = t_2;
	} else if (t <= -1.05e-208) {
		tmp = t_1;
	} else if (t <= -6e-274) {
		tmp = y * (((z - t) / (t - a)) + 1.0);
	} else if (t <= 4.2e-76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + y) - ((y * z) / a)
    t_2 = x - (y * ((a - z) / t))
    if (t <= (-1.7d-21)) then
        tmp = t_2
    else if (t <= (-1.05d-208)) then
        tmp = t_1
    else if (t <= (-6d-274)) then
        tmp = y * (((z - t) / (t - a)) + 1.0d0)
    else if (t <= 4.2d-76) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * z) / a);
	double t_2 = x - (y * ((a - z) / t));
	double tmp;
	if (t <= -1.7e-21) {
		tmp = t_2;
	} else if (t <= -1.05e-208) {
		tmp = t_1;
	} else if (t <= -6e-274) {
		tmp = y * (((z - t) / (t - a)) + 1.0);
	} else if (t <= 4.2e-76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((y * z) / a)
	t_2 = x - (y * ((a - z) / t))
	tmp = 0
	if t <= -1.7e-21:
		tmp = t_2
	elif t <= -1.05e-208:
		tmp = t_1
	elif t <= -6e-274:
		tmp = y * (((z - t) / (t - a)) + 1.0)
	elif t <= 4.2e-76:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(y * z) / a))
	t_2 = Float64(x - Float64(y * Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (t <= -1.7e-21)
		tmp = t_2;
	elseif (t <= -1.05e-208)
		tmp = t_1;
	elseif (t <= -6e-274)
		tmp = Float64(y * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0));
	elseif (t <= 4.2e-76)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((y * z) / a);
	t_2 = x - (y * ((a - z) / t));
	tmp = 0.0;
	if (t <= -1.7e-21)
		tmp = t_2;
	elseif (t <= -1.05e-208)
		tmp = t_1;
	elseif (t <= -6e-274)
		tmp = y * (((z - t) / (t - a)) + 1.0);
	elseif (t <= 4.2e-76)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e-21], t$95$2, If[LessEqual[t, -1.05e-208], t$95$1, If[LessEqual[t, -6e-274], N[(y * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-76], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7e-21 or 4.19999999999999985e-76 < t

   1. Initial program 59.3%

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

   3. Taylor expanded in y around 0 59.3%

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

      1. associate-*l/ 67.7%

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

   5. Simplified 67.7%

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

      1. *-commutative 67.7%

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

      2. clear-num 67.8%

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

      3. un-div-inv 67.7%

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

   7. Applied egg-rr 67.7%

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

   8. Taylor expanded in t around -inf 72.4%

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

      1. mul-1-neg 72.4%

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

      2. unsub-neg 72.4%

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

      3. *-commutative 72.4%

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

      4. cancel-sign-sub-inv 72.4%

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

      5. neg-mul-1 72.4%

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

      6. distribute-rgt-in 72.4%

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

      7. associate-/l* 82.9%

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

      8. neg-mul-1 82.9%

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

      9. sub-neg 82.9%

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

   10. Simplified 82.9%

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

   if -1.7e-21 < t < -1.05000000000000006e-208 or -5.99999999999999954e-274 < t < 4.19999999999999985e-76

   1. Initial program 96.1%

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

   3. Taylor expanded in t around 0 83.6%

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

   if -1.05000000000000006e-208 < t < -5.99999999999999954e-274

   1. Initial program 94.0%

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

   3. Taylor expanded in x around 0 70.0%

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

      1. sub-neg 70.0%

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

      2. *-rgt-identity 70.0%

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

      3. associate-*r/ 70.0%

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

      4. distribute-rgt-neg-in 70.0%

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

      5. mul-1-neg 70.0%

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

      6. distribute-lft-in 70.0%

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

      7. mul-1-neg 70.0%

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

      8. unsub-neg 70.0%

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

   5. Simplified 70.0%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-21}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-208}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-76}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{a - z}{t}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-79}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+15}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- a z) t)))))
   (if (<= t -2.8e+59)
     t_1
     (if (<= t 4.1e-79)
       (- (+ x y) (/ (* y z) a))
       (if (<= t 1.75e+15) (+ x (* y (/ z t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((a - z) / t));
	double tmp;
	if (t <= -2.8e+59) {
		tmp = t_1;
	} else if (t <= 4.1e-79) {
		tmp = (x + y) - ((y * z) / a);
	} else if (t <= 1.75e+15) {
		tmp = x + (y * (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * ((a - z) / t))
    if (t <= (-2.8d+59)) then
        tmp = t_1
    else if (t <= 4.1d-79) then
        tmp = (x + y) - ((y * z) / a)
    else if (t <= 1.75d+15) then
        tmp = x + (y * (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((a - z) / t));
	double tmp;
	if (t <= -2.8e+59) {
		tmp = t_1;
	} else if (t <= 4.1e-79) {
		tmp = (x + y) - ((y * z) / a);
	} else if (t <= 1.75e+15) {
		tmp = x + (y * (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((a - z) / t))
	tmp = 0
	if t <= -2.8e+59:
		tmp = t_1
	elif t <= 4.1e-79:
		tmp = (x + y) - ((y * z) / a)
	elif t <= 1.75e+15:
		tmp = x + (y * (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (t <= -2.8e+59)
		tmp = t_1;
	elseif (t <= 4.1e-79)
		tmp = Float64(Float64(x + y) - Float64(Float64(y * z) / a));
	elseif (t <= 1.75e+15)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((a - z) / t));
	tmp = 0.0;
	if (t <= -2.8e+59)
		tmp = t_1;
	elseif (t <= 4.1e-79)
		tmp = (x + y) - ((y * z) / a);
	elseif (t <= 1.75e+15)
		tmp = x + (y * (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+59], t$95$1, If[LessEqual[t, 4.1e-79], N[(N[(x + y), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e+15], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7999999999999998e59 or 1.75e15 < t

   1. Initial program 53.0%

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

   3. Taylor expanded in y around 0 53.0%

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

      1. associate-*l/ 62.5%

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

   5. Simplified 62.5%

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

      1. *-commutative 62.5%

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

      2. clear-num 62.7%

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

      3. un-div-inv 62.6%

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

   7. Applied egg-rr 62.6%

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

   8. Taylor expanded in t around -inf 74.2%

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

      1. mul-1-neg 74.2%

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

      2. unsub-neg 74.2%

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

      3. *-commutative 74.2%

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

      4. cancel-sign-sub-inv 74.2%

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

      5. neg-mul-1 74.2%

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

      6. distribute-rgt-in 74.4%

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

      7. associate-/l* 88.1%

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

      8. neg-mul-1 88.1%

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

      9. sub-neg 88.1%

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

   10. Simplified 88.1%

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

   if -2.7999999999999998e59 < t < 4.09999999999999994e-79

   1. Initial program 94.8%

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

   3. Taylor expanded in t around 0 77.2%

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

   if 4.09999999999999994e-79 < t < 1.75e15

   1. Initial program 73.2%

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

   3. Taylor expanded in y around 0 73.2%

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

      1. associate-*l/ 81.9%

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

   5. Simplified 81.9%

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

      1. *-commutative 81.9%

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

      2. clear-num 81.9%

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

      3. un-div-inv 82.0%

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

   7. Applied egg-rr 82.0%

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

   8. Taylor expanded in t around -inf 60.4%

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

      1. mul-1-neg 60.4%

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

      2. unsub-neg 60.4%

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

      3. *-commutative 60.4%

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

      4. cancel-sign-sub-inv 60.4%

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

      5. neg-mul-1 60.4%

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

      6. distribute-rgt-in 60.4%

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

      7. associate-/l* 60.3%

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

      8. neg-mul-1 60.3%

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

      9. sub-neg 60.3%

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

   10. Simplified 60.3%

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

   11. Taylor expanded in a around 0 75.7%

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

       1. neg-mul-1 75.7%

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

       2. distribute-neg-frac2 75.7%

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

   13. Simplified 75.7%

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

       1. sub-neg 75.7%

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

       2. +-commutative 75.7%

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

       3. distribute-lft-neg-in 75.7%

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

       4. add-sqr-sqrt 54.2%

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

       5. sqrt-unprod 60.0%

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

       6. sqr-neg 60.0%

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

       7. sqrt-unprod 16.5%

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

       8. add-sqr-sqrt 44.5%

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

       9. add-sqr-sqrt 0.0%

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

       10. sqrt-unprod 75.7%

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

       11. sqr-neg 75.7%

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

       12. sqrt-unprod 75.5%

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

       13. add-sqr-sqrt 75.7%

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

   15. Applied egg-rr 75.7%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+59}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-79}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+15}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 90.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+101}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;\left(x + y\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.7e+101)
   (- x (* y (/ (- a z) t)))
   (if (<= t 2.4e+47)
     (- (+ x y) (* (- z t) (/ y (- a t))))
     (+ (- x (* a (/ y t))) (* y (/ z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+101) {
		tmp = x - (y * ((a - z) / t));
	} else if (t <= 2.4e+47) {
		tmp = (x + y) - ((z - t) * (y / (a - t)));
	} else {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.7d+101)) then
        tmp = x - (y * ((a - z) / t))
    else if (t <= 2.4d+47) then
        tmp = (x + y) - ((z - t) * (y / (a - t)))
    else
        tmp = (x - (a * (y / t))) + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+101) {
		tmp = x - (y * ((a - z) / t));
	} else if (t <= 2.4e+47) {
		tmp = (x + y) - ((z - t) * (y / (a - t)));
	} else {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.7e+101:
		tmp = x - (y * ((a - z) / t))
	elif t <= 2.4e+47:
		tmp = (x + y) - ((z - t) * (y / (a - t)))
	else:
		tmp = (x - (a * (y / t))) + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.7e+101)
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	elseif (t <= 2.4e+47)
		tmp = Float64(Float64(x + y) - Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.7e+101)
		tmp = x - (y * ((a - z) / t));
	elseif (t <= 2.4e+47)
		tmp = (x + y) - ((z - t) * (y / (a - t)));
	else
		tmp = (x - (a * (y / t))) + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.7e+101], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+47], N[(N[(x + y), $MachinePrecision] - N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.70000000000000009e101

   1. Initial program 44.6%

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

   3. Taylor expanded in y around 0 44.6%

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

      1. associate-*l/ 56.4%

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

   5. Simplified 56.4%

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

      1. *-commutative 56.4%

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

      2. clear-num 56.8%

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

      3. un-div-inv 56.4%

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

   7. Applied egg-rr 56.4%

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

   8. Taylor expanded in t around -inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. unsub-neg 67.9%

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

      3. *-commutative 67.9%

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

      4. cancel-sign-sub-inv 67.9%

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

      5. neg-mul-1 67.9%

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

      6. distribute-rgt-in 68.0%

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

      7. associate-/l* 90.7%

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

      8. neg-mul-1 90.7%

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

      9. sub-neg 90.7%

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

   10. Simplified 90.7%

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

   if -1.70000000000000009e101 < t < 2.40000000000000019e47

   1. Initial program 90.9%

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

   3. Taylor expanded in y around 0 90.9%

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

      1. associate-*l/ 94.1%

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

   5. Simplified 94.1%

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

   if 2.40000000000000019e47 < t

   1. Initial program 53.6%

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

   3. Taylor expanded in y around 0 53.6%

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

      1. associate-*l/ 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in t around inf 76.7%

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

      1. sub-neg 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

      4. associate-/l* 81.7%

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

      5. mul-1-neg 81.7%

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

      6. remove-double-neg 81.7%

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

      7. associate-/l* 86.8%

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

   8. Simplified 86.8%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+101}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;\left(x + y\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+102}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-33}:\\ \;\;\;\;\left(x + y\right) + z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.2e+102)
   (- x (* y (/ (- a z) t)))
   (if (<= t 3.9e-33)
     (+ (+ x y) (* z (/ y (- t a))))
     (+ (- x (* a (/ y t))) (* y (/ z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.2e+102) {
		tmp = x - (y * ((a - z) / t));
	} else if (t <= 3.9e-33) {
		tmp = (x + y) + (z * (y / (t - a)));
	} else {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.2d+102)) then
        tmp = x - (y * ((a - z) / t))
    else if (t <= 3.9d-33) then
        tmp = (x + y) + (z * (y / (t - a)))
    else
        tmp = (x - (a * (y / t))) + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.2e+102) {
		tmp = x - (y * ((a - z) / t));
	} else if (t <= 3.9e-33) {
		tmp = (x + y) + (z * (y / (t - a)));
	} else {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.2e+102:
		tmp = x - (y * ((a - z) / t))
	elif t <= 3.9e-33:
		tmp = (x + y) + (z * (y / (t - a)))
	else:
		tmp = (x - (a * (y / t))) + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.2e+102)
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	elseif (t <= 3.9e-33)
		tmp = Float64(Float64(x + y) + Float64(z * Float64(y / Float64(t - a))));
	else
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.2e+102)
		tmp = x - (y * ((a - z) / t));
	elseif (t <= 3.9e-33)
		tmp = (x + y) + (z * (y / (t - a)));
	else
		tmp = (x - (a * (y / t))) + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.2e+102], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-33], N[(N[(x + y), $MachinePrecision] + N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.20000000000000007e102

   1. Initial program 44.6%

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

   3. Taylor expanded in y around 0 44.6%

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

      1. associate-*l/ 56.4%

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

   5. Simplified 56.4%

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

      1. *-commutative 56.4%

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

      2. clear-num 56.8%

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

      3. un-div-inv 56.4%

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

   7. Applied egg-rr 56.4%

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

   8. Taylor expanded in t around -inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. unsub-neg 67.9%

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

      3. *-commutative 67.9%

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

      4. cancel-sign-sub-inv 67.9%

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

      5. neg-mul-1 67.9%

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

      6. distribute-rgt-in 68.0%

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

      7. associate-/l* 90.7%

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

      8. neg-mul-1 90.7%

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

      9. sub-neg 90.7%

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

   10. Simplified 90.7%

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

   if -2.20000000000000007e102 < t < 3.89999999999999974e-33

   1. Initial program 93.0%

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

   3. Taylor expanded in y around 0 93.0%

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

      1. associate-*l/ 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in z around inf 92.6%

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

      1. associate-*l/ 95.1%

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

      2. *-commutative 95.1%

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

   8. Simplified 95.1%

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

   if 3.89999999999999974e-33 < t

   1. Initial program 56.1%

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

   3. Taylor expanded in y around 0 56.1%

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

      1. associate-*l/ 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in t around inf 73.9%

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

      1. sub-neg 73.9%

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

      2. mul-1-neg 73.9%

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

      3. unsub-neg 73.9%

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

      4. associate-/l* 78.0%

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

      5. mul-1-neg 78.0%

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

      6. remove-double-neg 78.0%

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

      7. associate-/l* 82.1%

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

   8. Simplified 82.1%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+102}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-33}:\\ \;\;\;\;\left(x + y\right) + z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+107}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-33}:\\ \;\;\;\;\left(x + y\right) + z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.8e+107)
   (- x (* y (/ (- a z) t)))
   (if (<= t 3.9e-33)
     (+ (+ x y) (* z (/ y (- t a))))
     (+ x (* y (- (/ z t) (/ a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.8e+107) {
		tmp = x - (y * ((a - z) / t));
	} else if (t <= 3.9e-33) {
		tmp = (x + y) + (z * (y / (t - a)));
	} else {
		tmp = x + (y * ((z / t) - (a / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.8d+107)) then
        tmp = x - (y * ((a - z) / t))
    else if (t <= 3.9d-33) then
        tmp = (x + y) + (z * (y / (t - a)))
    else
        tmp = x + (y * ((z / t) - (a / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.8e+107) {
		tmp = x - (y * ((a - z) / t));
	} else if (t <= 3.9e-33) {
		tmp = (x + y) + (z * (y / (t - a)));
	} else {
		tmp = x + (y * ((z / t) - (a / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.8e+107:
		tmp = x - (y * ((a - z) / t))
	elif t <= 3.9e-33:
		tmp = (x + y) + (z * (y / (t - a)))
	else:
		tmp = x + (y * ((z / t) - (a / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.8e+107)
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	elseif (t <= 3.9e-33)
		tmp = Float64(Float64(x + y) + Float64(z * Float64(y / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.8e+107)
		tmp = x - (y * ((a - z) / t));
	elseif (t <= 3.9e-33)
		tmp = (x + y) + (z * (y / (t - a)));
	else
		tmp = x + (y * ((z / t) - (a / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.8e+107], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-33], N[(N[(x + y), $MachinePrecision] + N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.7999999999999994e107

   1. Initial program 44.6%

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

   3. Taylor expanded in y around 0 44.6%

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

      1. associate-*l/ 56.4%

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

   5. Simplified 56.4%

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

      1. *-commutative 56.4%

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

      2. clear-num 56.8%

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

      3. un-div-inv 56.4%

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

   7. Applied egg-rr 56.4%

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

   8. Taylor expanded in t around -inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. unsub-neg 67.9%

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

      3. *-commutative 67.9%

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

      4. cancel-sign-sub-inv 67.9%

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

      5. neg-mul-1 67.9%

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

      6. distribute-rgt-in 68.0%

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

      7. associate-/l* 90.7%

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

      8. neg-mul-1 90.7%

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

      9. sub-neg 90.7%

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

   10. Simplified 90.7%

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

   if -6.7999999999999994e107 < t < 3.89999999999999974e-33

   1. Initial program 93.0%

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

   3. Taylor expanded in y around 0 93.0%

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

      1. associate-*l/ 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in z around inf 92.6%

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

      1. associate-*l/ 95.1%

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

      2. *-commutative 95.1%

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

   8. Simplified 95.1%

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

   if 3.89999999999999974e-33 < t

   1. Initial program 56.1%

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

   3. Taylor expanded in y around 0 56.1%

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

      1. associate-*l/ 64.2%

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

   5. Simplified 64.2%

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

      1. *-commutative 64.2%

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

      2. clear-num 64.1%

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

      3. un-div-inv 64.1%

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

   7. Applied egg-rr 64.1%

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

   8. Taylor expanded in t around -inf 73.9%

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

      1. mul-1-neg 73.9%

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

      2. unsub-neg 73.9%

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

      3. *-commutative 73.9%

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

      4. cancel-sign-sub-inv 73.9%

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

      5. neg-mul-1 73.9%

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

      6. distribute-rgt-in 74.0%

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

      7. associate-/l* 82.1%

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

      8. neg-mul-1 82.1%

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

      9. sub-neg 82.1%

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

   10. Simplified 82.1%

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

       1. div-sub 82.1%

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

   12. Applied egg-rr 82.1%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+107}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-33}:\\ \;\;\;\;\left(x + y\right) + z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+100}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-33}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.2e+100)
   (- x (* y (/ (- a z) t)))
   (if (<= t 3.9e-33)
     (+ (+ x y) (* y (/ z (- t a))))
     (+ x (* y (- (/ z t) (/ a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+100) {
		tmp = x - (y * ((a - z) / t));
	} else if (t <= 3.9e-33) {
		tmp = (x + y) + (y * (z / (t - a)));
	} else {
		tmp = x + (y * ((z / t) - (a / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7.2d+100)) then
        tmp = x - (y * ((a - z) / t))
    else if (t <= 3.9d-33) then
        tmp = (x + y) + (y * (z / (t - a)))
    else
        tmp = x + (y * ((z / t) - (a / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+100) {
		tmp = x - (y * ((a - z) / t));
	} else if (t <= 3.9e-33) {
		tmp = (x + y) + (y * (z / (t - a)));
	} else {
		tmp = x + (y * ((z / t) - (a / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.2e+100:
		tmp = x - (y * ((a - z) / t))
	elif t <= 3.9e-33:
		tmp = (x + y) + (y * (z / (t - a)))
	else:
		tmp = x + (y * ((z / t) - (a / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.2e+100)
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	elseif (t <= 3.9e-33)
		tmp = Float64(Float64(x + y) + Float64(y * Float64(z / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.2e+100)
		tmp = x - (y * ((a - z) / t));
	elseif (t <= 3.9e-33)
		tmp = (x + y) + (y * (z / (t - a)));
	else
		tmp = x + (y * ((z / t) - (a / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.2e+100], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-33], N[(N[(x + y), $MachinePrecision] + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.2e100

   1. Initial program 44.6%

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

   3. Taylor expanded in y around 0 44.6%

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

      1. associate-*l/ 56.4%

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

   5. Simplified 56.4%

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

      1. *-commutative 56.4%

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

      2. clear-num 56.8%

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

      3. un-div-inv 56.4%

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

   7. Applied egg-rr 56.4%

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

   8. Taylor expanded in t around -inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. unsub-neg 67.9%

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

      3. *-commutative 67.9%

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

      4. cancel-sign-sub-inv 67.9%

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

      5. neg-mul-1 67.9%

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

      6. distribute-rgt-in 68.0%

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

      7. associate-/l* 90.7%

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

      8. neg-mul-1 90.7%

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

      9. sub-neg 90.7%

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

   10. Simplified 90.7%

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

   if -7.2e100 < t < 3.89999999999999974e-33

   1. Initial program 93.0%

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

   3. Taylor expanded in z around inf 92.6%

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

      1. associate-/l* 91.3%

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

   5. Simplified 91.3%

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

   if 3.89999999999999974e-33 < t

   1. Initial program 56.1%

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

   3. Taylor expanded in y around 0 56.1%

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

      1. associate-*l/ 64.2%

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

   5. Simplified 64.2%

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

      1. *-commutative 64.2%

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

      2. clear-num 64.1%

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

      3. un-div-inv 64.1%

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

   7. Applied egg-rr 64.1%

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

   8. Taylor expanded in t around -inf 73.9%

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

      1. mul-1-neg 73.9%

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

      2. unsub-neg 73.9%

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

      3. *-commutative 73.9%

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

      4. cancel-sign-sub-inv 73.9%

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

      5. neg-mul-1 73.9%

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

      6. distribute-rgt-in 74.0%

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

      7. associate-/l* 82.1%

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

      8. neg-mul-1 82.1%

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

      9. sub-neg 82.1%

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

   10. Simplified 82.1%

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

       1. div-sub 82.1%

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

   12. Applied egg-rr 82.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+100}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-33}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+51} \lor \neg \left(a \leq 1.65 \cdot 10^{+21}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.6e+51) (not (<= a 1.65e+21)))
   (+ x y)
   (- x (* y (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.6e+51) || !(a <= 1.65e+21)) {
		tmp = x + y;
	} else {
		tmp = x - (y * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5.6d+51)) .or. (.not. (a <= 1.65d+21))) then
        tmp = x + y
    else
        tmp = x - (y * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.6e+51) || !(a <= 1.65e+21)) {
		tmp = x + y;
	} else {
		tmp = x - (y * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.6e+51) or not (a <= 1.65e+21):
		tmp = x + y
	else:
		tmp = x - (y * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.6e+51) || !(a <= 1.65e+21))
		tmp = Float64(x + y);
	else
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.6e+51) || ~((a <= 1.65e+21)))
		tmp = x + y;
	else
		tmp = x - (y * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.6e+51], N[Not[LessEqual[a, 1.65e+21]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.60000000000000009e51 or 1.65e21 < a

   1. Initial program 75.5%

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

   3. Taylor expanded in a around inf 75.0%

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

      1. +-commutative 75.0%

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

   5. Simplified 75.0%

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

   if -5.60000000000000009e51 < a < 1.65e21

   1. Initial program 75.3%

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

   3. Taylor expanded in y around 0 75.3%

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

      1. associate-*l/ 76.8%

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

   5. Simplified 76.8%

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

      1. *-commutative 76.8%

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

      2. clear-num 76.7%

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

      3. un-div-inv 77.4%

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

   7. Applied egg-rr 77.4%

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

   8. Taylor expanded in t around -inf 75.8%

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

      1. mul-1-neg 75.8%

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

      2. unsub-neg 75.8%

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

      3. *-commutative 75.8%

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

      4. cancel-sign-sub-inv 75.8%

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

      5. neg-mul-1 75.8%

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

      6. distribute-rgt-in 75.8%

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

      7. associate-/l* 77.0%

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

      8. neg-mul-1 77.0%

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

      9. sub-neg 77.0%

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

   10. Simplified 77.0%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+51} \lor \neg \left(a \leq 1.65 \cdot 10^{+21}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+196}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-189} \lor \neg \left(z \leq -1.02 \cdot 10^{-290}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+196)
   (* z (/ y t))
   (if (or (<= z -5.6e-189) (not (<= z -1.02e-290))) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+196) {
		tmp = z * (y / t);
	} else if ((z <= -5.6e-189) || !(z <= -1.02e-290)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.4d+196)) then
        tmp = z * (y / t)
    else if ((z <= (-5.6d-189)) .or. (.not. (z <= (-1.02d-290)))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+196) {
		tmp = z * (y / t);
	} else if ((z <= -5.6e-189) || !(z <= -1.02e-290)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+196:
		tmp = z * (y / t)
	elif (z <= -5.6e-189) or not (z <= -1.02e-290):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+196)
		tmp = Float64(z * Float64(y / t));
	elseif ((z <= -5.6e-189) || !(z <= -1.02e-290))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e+196)
		tmp = z * (y / t);
	elseif ((z <= -5.6e-189) || ~((z <= -1.02e-290)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+196], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -5.6e-189], N[Not[LessEqual[z, -1.02e-290]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4e196

   1. Initial program 77.4%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   2. Step-by-step derivation

      1. sub-neg 77.4%

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

      2. +-commutative 77.4%

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

      3. distribute-frac-neg 77.4%

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

      4. distribute-rgt-neg-out 77.4%

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

      5. associate-/l* 96.3%

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

      6. fma-define 96.5%

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

      7. distribute-frac-neg 96.5%

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

      8. distribute-neg-frac2 96.5%

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

      9. sub-neg 96.5%

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

      10. distribute-neg-in 96.5%

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

      11. remove-double-neg 96.5%

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

      12. +-commutative 96.5%

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

      13. sub-neg 96.5%

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

   3. Simplified 96.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 60.7%

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

      1. associate-/l* 76.6%

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

   7. Simplified 76.6%

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

   8. Taylor expanded in t around inf 44.2%

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

      1. *-commutative 44.2%

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

      2. associate-/l* 53.7%

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

      3. un-div-inv 53.7%

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

      4. *-commutative 53.7%

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

      5. un-div-inv 53.7%

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

   10. Applied egg-rr 53.7%

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

   if -2.4e196 < z < -5.5999999999999999e-189 or -1.02e-290 < z

   1. Initial program 75.9%

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

   3. Taylor expanded in a around inf 58.5%

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

      1. +-commutative 58.5%

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

   5. Simplified 58.5%

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

   if -5.5999999999999999e-189 < z < -1.02e-290

   1. Initial program 67.7%

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

   3. Taylor expanded in x around inf 93.1%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+196}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-189} \lor \neg \left(z \leq -1.02 \cdot 10^{-290}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+188}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-189} \lor \neg \left(z \leq -2.9 \cdot 10^{-292}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.6e+188)
   (* y (/ z t))
   (if (or (<= z -3.2e-189) (not (<= z -2.9e-292))) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+188) {
		tmp = y * (z / t);
	} else if ((z <= -3.2e-189) || !(z <= -2.9e-292)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.6d+188)) then
        tmp = y * (z / t)
    else if ((z <= (-3.2d-189)) .or. (.not. (z <= (-2.9d-292)))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+188) {
		tmp = y * (z / t);
	} else if ((z <= -3.2e-189) || !(z <= -2.9e-292)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.6e+188:
		tmp = y * (z / t)
	elif (z <= -3.2e-189) or not (z <= -2.9e-292):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.6e+188)
		tmp = Float64(y * Float64(z / t));
	elseif ((z <= -3.2e-189) || !(z <= -2.9e-292))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.6e+188)
		tmp = y * (z / t);
	elseif ((z <= -3.2e-189) || ~((z <= -2.9e-292)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.6e+188], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.2e-189], N[Not[LessEqual[z, -2.9e-292]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -6.59999999999999966e188

   1. Initial program 78.2%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   2. Step-by-step derivation

      1. sub-neg 78.2%

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

      2. +-commutative 78.2%

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

      3. distribute-frac-neg 78.2%

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

      4. distribute-rgt-neg-out 78.2%

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

      5. associate-/l* 96.4%

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

      6. fma-define 96.6%

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

      7. distribute-frac-neg 96.6%

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

      8. distribute-neg-frac2 96.6%

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

      9. sub-neg 96.6%

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

      10. distribute-neg-in 96.6%

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

      11. remove-double-neg 96.6%

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

      12. +-commutative 96.6%

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

      13. sub-neg 96.6%

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

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 62.0%

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

      1. associate-/l* 77.4%

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

   7. Simplified 77.4%

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

   8. Taylor expanded in t around inf 46.0%

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

      1. associate-/l* 52.1%

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

   10. Simplified 52.1%

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

   if -6.59999999999999966e188 < z < -3.2000000000000001e-189 or -2.89999999999999993e-292 < z

   1. Initial program 75.8%

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

   3. Taylor expanded in a around inf 58.8%

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

      1. +-commutative 58.8%

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

   5. Simplified 58.8%

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

   if -3.2000000000000001e-189 < z < -2.89999999999999993e-292

   1. Initial program 67.7%

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

   3. Taylor expanded in x around inf 93.1%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+188}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-189} \lor \neg \left(z \leq -2.9 \cdot 10^{-292}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 76.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+59} \lor \neg \left(a \leq 2 \cdot 10^{-6}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.2e+59) (not (<= a 2e-6))) (+ x y) (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.2e+59) || !(a <= 2e-6)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.2d+59)) .or. (.not. (a <= 2d-6))) then
        tmp = x + y
    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 a) {
	double tmp;
	if ((a <= -3.2e+59) || !(a <= 2e-6)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.2e+59) or not (a <= 2e-6):
		tmp = x + y
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.2e+59) || !(a <= 2e-6))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.2e+59) || ~((a <= 2e-6)))
		tmp = x + y;
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.2e+59], N[Not[LessEqual[a, 2e-6]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.19999999999999982e59 or 1.99999999999999991e-6 < a

   1. Initial program 74.8%

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

   3. Taylor expanded in a around inf 74.3%

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

      1. +-commutative 74.3%

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

   5. Simplified 74.3%

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

   if -3.19999999999999982e59 < a < 1.99999999999999991e-6

   1. Initial program 75.8%

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

   3. Taylor expanded in y around 0 75.8%

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

      1. associate-*l/ 77.3%

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

   5. Simplified 77.3%

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

      1. *-commutative 77.3%

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

      2. clear-num 77.2%

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

      3. un-div-inv 77.9%

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

   7. Applied egg-rr 77.9%

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

   8. Taylor expanded in t around -inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. unsub-neg 74.3%

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

      3. *-commutative 74.3%

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

      4. cancel-sign-sub-inv 74.3%

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

      5. neg-mul-1 74.3%

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

      6. distribute-rgt-in 74.3%

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

      7. associate-/l* 75.5%

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

      8. neg-mul-1 75.5%

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

      9. sub-neg 75.5%

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

   10. Simplified 75.5%

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

   11. Taylor expanded in a around 0 74.1%

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

       1. neg-mul-1 74.1%

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

       2. distribute-neg-frac2 74.1%

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

   13. Simplified 74.1%

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

       1. sub-neg 74.1%

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

       2. +-commutative 74.1%

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

       3. distribute-lft-neg-in 74.1%

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

       4. add-sqr-sqrt 38.4%

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

       5. sqrt-unprod 53.0%

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

       6. sqr-neg 53.0%

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

       7. sqrt-unprod 24.2%

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

       8. add-sqr-sqrt 50.3%

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

       9. add-sqr-sqrt 26.0%

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

       10. sqrt-unprod 54.6%

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

       11. sqr-neg 54.6%

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

       12. sqrt-unprod 35.7%

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

       13. add-sqr-sqrt 74.1%

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

   15. Applied egg-rr 74.1%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+59} \lor \neg \left(a \leq 2 \cdot 10^{-6}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 63.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+225}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 10^{+93}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.05e+225) x (if (<= t 1e+93) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05e+225) {
		tmp = x;
	} else if (t <= 1e+93) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.05d+225)) then
        tmp = x
    else if (t <= 1d+93) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05e+225) {
		tmp = x;
	} else if (t <= 1e+93) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.05e+225:
		tmp = x
	elif t <= 1e+93:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.05e+225)
		tmp = x;
	elseif (t <= 1e+93)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.05e+225)
		tmp = x;
	elseif (t <= 1e+93)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.05e+225], x, If[LessEqual[t, 1e+93], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e225 or 1.00000000000000004e93 < t

   1. Initial program 45.4%

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

   3. Taylor expanded in x around inf 61.6%

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

   if -1.05e225 < t < 1.00000000000000004e93

   1. Initial program 84.4%

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

   3. Taylor expanded in a around inf 58.2%

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

      1. +-commutative 58.2%

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

   5. Simplified 58.2%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+225}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 10^{+93}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+299}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -3.2e+299) y x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e+299) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.2d+299)) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e+299) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e+299:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e+299)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e+299)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e+299], y, x]

Derivation

1. Split input into 2 regimes

2. if a < -3.1999999999999999e299

   1. Initial program 82.4%

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

   3. Taylor expanded in t around 0 82.4%

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

   4. Taylor expanded in x around 0 82.4%

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

   5. Taylor expanded in z around 0 100.0%

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

   if -3.1999999999999999e299 < a

   1. Initial program 75.3%

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

   3. Taylor expanded in x around inf 49.5%

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

Alternative 18: 50.7% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

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

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 75.4%

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

3. Taylor expanded in x around inf 48.6%

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

Developer target: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (a - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

  (- (+ x y) (/ (* (- z t) y) (- a t))))