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

Percentage Accurate: 76.9% → 90.0%

Time: 18.7s

Alternatives: 16

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: 76.9% 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: 90.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+186}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - z}{a - t}, y, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{a}{\frac{t}{y}}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.5e+186)
   (- x (/ y (/ t (- a z))))
   (if (<= t 1.45e+76)
     (fma (/ (- t z) (- a t)) y (+ x y))
     (+ (- x (/ a (/ t y))) (/ y (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e+186) {
		tmp = x - (y / (t / (a - z)));
	} else if (t <= 1.45e+76) {
		tmp = fma(((t - z) / (a - t)), y, (x + y));
	} else {
		tmp = (x - (a / (t / y))) + (y / (t / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.5e+186)
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	elseif (t <= 1.45e+76)
		tmp = fma(Float64(Float64(t - z) / Float64(a - t)), y, Float64(x + y));
	else
		tmp = Float64(Float64(x - Float64(a / Float64(t / y))) + Float64(y / Float64(t / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.5e+186], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+76], N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * y + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.4999999999999997e186

   1. Initial program 37.5%

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

      1. associate-*l/ 57.4%

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

   3. Simplified 57.4%

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

      1. associate-*l/ 37.5%

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

      2. clear-num 37.5%

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

      3. *-commutative 37.5%

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

   6. Applied egg-rr 37.5%

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

   7. Taylor expanded in t around inf 73.0%

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

      1. associate--l+ 73.0%

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

      2. associate-*r/ 73.0%

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

      3. associate-*r/ 73.0%

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

      4. div-sub 73.0%

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

      5. distribute-lft-out-- 73.0%

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

      6. associate-*r/ 73.0%

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

      7. mul-1-neg 73.0%

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

      8. unsub-neg 73.0%

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

      9. *-commutative 73.0%

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

      10. cancel-sign-sub-inv 73.0%

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

      11. distribute-rgt-in 73.2%

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

      12. sub-neg 73.2%

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

      13. associate-/l* 96.2%

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

   9. Simplified 96.2%

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

   if -6.4999999999999997e186 < t < 1.4500000000000001e76

   1. Initial program 90.9%

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

      1. sub-neg 90.9%

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

      2. distribute-frac-neg 90.9%

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

      3. distribute-rgt-neg-out 90.9%

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

      4. +-commutative 90.9%

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

      5. associate-*l/ 92.9%

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

      6. distribute-rgt-neg-in 92.9%

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

      7. distribute-lft-neg-in 92.9%

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

      8. distribute-frac-neg 92.9%

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

      9. fma-def 93.0%

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

      10. sub-neg 93.0%

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

      11. distribute-neg-in 93.0%

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

      12. remove-double-neg 93.0%

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

      13. +-commutative 93.0%

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

      14. sub-neg 93.0%

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

   3. Simplified 93.0%

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

   if 1.4500000000000001e76 < t

   1. Initial program 56.9%

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

      1. associate-*l/ 70.4%

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

   3. Simplified 70.4%

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

   5. Taylor expanded in t around inf 75.3%

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

      1. sub-neg 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

      4. associate-/l* 83.0%

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

      5. mul-1-neg 83.0%

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

      6. remove-double-neg 83.0%

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

      7. associate-/l* 90.3%

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

   7. Simplified 90.3%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+186}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - z}{a - t}, y, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{a}{\frac{t}{y}}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+36}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-23}:\\ \;\;\;\;y + \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 0.001:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{a}{\frac{t}{y}}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ y (/ a z)))))
   (if (<= t -4.2e+36)
     (- x (/ y (/ t (- a z))))
     (if (<= t -9e-15)
       t_1
       (if (<= t -4.2e-87)
         (+ x (/ (* y z) t))
         (if (<= t 5.9e-86)
           t_1
           (if (<= t 1.02e-23)
             (+ y (* (/ y (- a t)) (- t z)))
             (if (<= t 0.001)
               (- (+ x y) (* y (/ z a)))
               (+ (- x (/ a (/ t y))) (/ y (/ t z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y / (a / z));
	double tmp;
	if (t <= -4.2e+36) {
		tmp = x - (y / (t / (a - z)));
	} else if (t <= -9e-15) {
		tmp = t_1;
	} else if (t <= -4.2e-87) {
		tmp = x + ((y * z) / t);
	} else if (t <= 5.9e-86) {
		tmp = t_1;
	} else if (t <= 1.02e-23) {
		tmp = y + ((y / (a - t)) * (t - z));
	} else if (t <= 0.001) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = (x - (a / (t / y))) + (y / (t / z));
	}
	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 / (a / z))
    if (t <= (-4.2d+36)) then
        tmp = x - (y / (t / (a - z)))
    else if (t <= (-9d-15)) then
        tmp = t_1
    else if (t <= (-4.2d-87)) then
        tmp = x + ((y * z) / t)
    else if (t <= 5.9d-86) then
        tmp = t_1
    else if (t <= 1.02d-23) then
        tmp = y + ((y / (a - t)) * (t - z))
    else if (t <= 0.001d0) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = (x - (a / (t / y))) + (y / (t / z))
    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 / (a / z));
	double tmp;
	if (t <= -4.2e+36) {
		tmp = x - (y / (t / (a - z)));
	} else if (t <= -9e-15) {
		tmp = t_1;
	} else if (t <= -4.2e-87) {
		tmp = x + ((y * z) / t);
	} else if (t <= 5.9e-86) {
		tmp = t_1;
	} else if (t <= 1.02e-23) {
		tmp = y + ((y / (a - t)) * (t - z));
	} else if (t <= 0.001) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = (x - (a / (t / y))) + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (y / (a / z))
	tmp = 0
	if t <= -4.2e+36:
		tmp = x - (y / (t / (a - z)))
	elif t <= -9e-15:
		tmp = t_1
	elif t <= -4.2e-87:
		tmp = x + ((y * z) / t)
	elif t <= 5.9e-86:
		tmp = t_1
	elif t <= 1.02e-23:
		tmp = y + ((y / (a - t)) * (t - z))
	elif t <= 0.001:
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = (x - (a / (t / y))) + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(y / Float64(a / z)))
	tmp = 0.0
	if (t <= -4.2e+36)
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	elseif (t <= -9e-15)
		tmp = t_1;
	elseif (t <= -4.2e-87)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (t <= 5.9e-86)
		tmp = t_1;
	elseif (t <= 1.02e-23)
		tmp = Float64(y + Float64(Float64(y / Float64(a - t)) * Float64(t - z)));
	elseif (t <= 0.001)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(Float64(x - Float64(a / Float64(t / y))) + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (y / (a / z));
	tmp = 0.0;
	if (t <= -4.2e+36)
		tmp = x - (y / (t / (a - z)));
	elseif (t <= -9e-15)
		tmp = t_1;
	elseif (t <= -4.2e-87)
		tmp = x + ((y * z) / t);
	elseif (t <= 5.9e-86)
		tmp = t_1;
	elseif (t <= 1.02e-23)
		tmp = y + ((y / (a - t)) * (t - z));
	elseif (t <= 0.001)
		tmp = (x + y) - (y * (z / a));
	else
		tmp = (x - (a / (t / y))) + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+36], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e-15], t$95$1, If[LessEqual[t, -4.2e-87], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.9e-86], t$95$1, If[LessEqual[t, 1.02e-23], N[(y + N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.001], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -4.20000000000000009e36

   1. Initial program 61.9%

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

      1. associate-*l/ 75.3%

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

   3. Simplified 75.3%

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

      1. associate-*l/ 61.9%

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

      2. clear-num 61.9%

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

      3. *-commutative 61.9%

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

   6. Applied egg-rr 61.9%

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

   7. Taylor expanded in t around inf 80.9%

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

      1. associate--l+ 80.9%

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

      2. associate-*r/ 80.9%

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

      3. associate-*r/ 80.9%

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

      4. div-sub 80.9%

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

      5. distribute-lft-out-- 80.9%

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

      6. associate-*r/ 80.9%

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

      7. mul-1-neg 80.9%

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

      8. unsub-neg 80.9%

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

      9. *-commutative 80.9%

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

      10. cancel-sign-sub-inv 80.9%

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

      11. distribute-rgt-in 81.2%

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

      12. sub-neg 81.2%

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

      13. associate-/l* 92.2%

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

   9. Simplified 92.2%

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

   if -4.20000000000000009e36 < t < -8.9999999999999995e-15 or -4.20000000000000014e-87 < t < 5.89999999999999998e-86

   1. Initial program 92.9%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in t around 0 86.8%

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

      1. associate-/l* 89.3%

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

   7. Simplified 89.3%

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

   if -8.9999999999999995e-15 < t < -4.20000000000000014e-87

   1. Initial program 77.5%

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

      1. associate-*l/ 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in t around inf 63.1%

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

      1. sub-neg 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. associate-/l* 55.4%

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

      5. mul-1-neg 55.4%

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

      6. remove-double-neg 55.4%

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

      7. associate-/l* 55.3%

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

   7. Simplified 55.3%

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

   8. Taylor expanded in a around 0 88.4%

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

   if 5.89999999999999998e-86 < t < 1.02000000000000005e-23

   1. Initial program 95.2%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in x around 0 79.5%

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

      1. *-commutative 79.5%

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

      2. associate-*r/ 84.2%

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

   7. Simplified 84.2%

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

   if 1.02000000000000005e-23 < t < 1e-3

   1. Initial program 84.8%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 90.8%

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

   if 1e-3 < t

   1. Initial program 61.4%

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

      1. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   5. Taylor expanded in t around inf 74.6%

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

      1. sub-neg 74.6%

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

      2. mul-1-neg 74.6%

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

      3. unsub-neg 74.6%

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

      4. associate-/l* 81.5%

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

      5. mul-1-neg 81.5%

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

      6. remove-double-neg 81.5%

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

      7. associate-/l* 88.0%

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

   7. Simplified 88.0%

      \[\leadsto \color{blue}{\left(x - \frac{a}{\frac{t}{y}}\right) + \frac{y}{\frac{t}{z}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+36}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-15}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-86}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-23}:\\ \;\;\;\;y + \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 0.001:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{a}{\frac{t}{y}}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y}{\frac{a}{z}}\\ t_2 := x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-83}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-23}:\\ \;\;\;\;y + \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 3200:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ y (/ a z)))) (t_2 (- x (/ y (/ t (- a z))))))
   (if (<= t -2.9e+39)
     t_2
     (if (<= t -8.5e-15)
       t_1
       (if (<= t -7.5e-83)
         (+ x (/ (* y z) t))
         (if (<= t 2.6e-89)
           t_1
           (if (<= t 1.7e-23)
             (+ y (* (/ y (- a t)) (- t z)))
             (if (<= t 3200.0) (- (+ x y) (* y (/ z a))) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y / (a / z));
	double t_2 = x - (y / (t / (a - z)));
	double tmp;
	if (t <= -2.9e+39) {
		tmp = t_2;
	} else if (t <= -8.5e-15) {
		tmp = t_1;
	} else if (t <= -7.5e-83) {
		tmp = x + ((y * z) / t);
	} else if (t <= 2.6e-89) {
		tmp = t_1;
	} else if (t <= 1.7e-23) {
		tmp = y + ((y / (a - t)) * (t - z));
	} else if (t <= 3200.0) {
		tmp = (x + y) - (y * (z / a));
	} 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 / (a / z))
    t_2 = x - (y / (t / (a - z)))
    if (t <= (-2.9d+39)) then
        tmp = t_2
    else if (t <= (-8.5d-15)) then
        tmp = t_1
    else if (t <= (-7.5d-83)) then
        tmp = x + ((y * z) / t)
    else if (t <= 2.6d-89) then
        tmp = t_1
    else if (t <= 1.7d-23) then
        tmp = y + ((y / (a - t)) * (t - z))
    else if (t <= 3200.0d0) then
        tmp = (x + y) - (y * (z / a))
    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 / (a / z));
	double t_2 = x - (y / (t / (a - z)));
	double tmp;
	if (t <= -2.9e+39) {
		tmp = t_2;
	} else if (t <= -8.5e-15) {
		tmp = t_1;
	} else if (t <= -7.5e-83) {
		tmp = x + ((y * z) / t);
	} else if (t <= 2.6e-89) {
		tmp = t_1;
	} else if (t <= 1.7e-23) {
		tmp = y + ((y / (a - t)) * (t - z));
	} else if (t <= 3200.0) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (y / (a / z))
	t_2 = x - (y / (t / (a - z)))
	tmp = 0
	if t <= -2.9e+39:
		tmp = t_2
	elif t <= -8.5e-15:
		tmp = t_1
	elif t <= -7.5e-83:
		tmp = x + ((y * z) / t)
	elif t <= 2.6e-89:
		tmp = t_1
	elif t <= 1.7e-23:
		tmp = y + ((y / (a - t)) * (t - z))
	elif t <= 3200.0:
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(y / Float64(a / z)))
	t_2 = Float64(x - Float64(y / Float64(t / Float64(a - z))))
	tmp = 0.0
	if (t <= -2.9e+39)
		tmp = t_2;
	elseif (t <= -8.5e-15)
		tmp = t_1;
	elseif (t <= -7.5e-83)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (t <= 2.6e-89)
		tmp = t_1;
	elseif (t <= 1.7e-23)
		tmp = Float64(y + Float64(Float64(y / Float64(a - t)) * Float64(t - z)));
	elseif (t <= 3200.0)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (y / (a / z));
	t_2 = x - (y / (t / (a - z)));
	tmp = 0.0;
	if (t <= -2.9e+39)
		tmp = t_2;
	elseif (t <= -8.5e-15)
		tmp = t_1;
	elseif (t <= -7.5e-83)
		tmp = x + ((y * z) / t);
	elseif (t <= 2.6e-89)
		tmp = t_1;
	elseif (t <= 1.7e-23)
		tmp = y + ((y / (a - t)) * (t - z));
	elseif (t <= 3200.0)
		tmp = (x + y) - (y * (z / a));
	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[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+39], t$95$2, If[LessEqual[t, -8.5e-15], t$95$1, If[LessEqual[t, -7.5e-83], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e-89], t$95$1, If[LessEqual[t, 1.7e-23], N[(y + N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3200.0], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.90000000000000029e39 or 3200 < t

   1. Initial program 61.6%

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

      1. associate-*l/ 74.4%

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

   3. Simplified 74.4%

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

      1. associate-*l/ 61.6%

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

      2. clear-num 61.6%

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

      3. *-commutative 61.6%

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

   6. Applied egg-rr 61.6%

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

   7. Taylor expanded in t around inf 77.6%

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

      1. associate--l+ 77.6%

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

      2. associate-*r/ 77.6%

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

      3. associate-*r/ 77.6%

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

      4. div-sub 77.6%

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

      5. distribute-lft-out-- 77.6%

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

      6. associate-*r/ 77.6%

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

      7. mul-1-neg 77.6%

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

      8. unsub-neg 77.6%

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

      9. *-commutative 77.6%

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

      10. cancel-sign-sub-inv 77.6%

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

      11. distribute-rgt-in 78.7%

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

      12. sub-neg 78.7%

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

      13. associate-/l* 89.1%

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

   9. Simplified 89.1%

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

   if -2.90000000000000029e39 < t < -8.50000000000000007e-15 or -7.4999999999999997e-83 < t < 2.5999999999999999e-89

   1. Initial program 92.9%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in t around 0 86.8%

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

      1. associate-/l* 89.3%

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

   7. Simplified 89.3%

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

   if -8.50000000000000007e-15 < t < -7.4999999999999997e-83

   1. Initial program 77.5%

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

      1. associate-*l/ 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in t around inf 63.1%

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

      1. sub-neg 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. associate-/l* 55.4%

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

      5. mul-1-neg 55.4%

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

      6. remove-double-neg 55.4%

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

      7. associate-/l* 55.3%

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

   7. Simplified 55.3%

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

   8. Taylor expanded in a around 0 88.4%

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

   if 2.5999999999999999e-89 < t < 1.7e-23

   1. Initial program 95.2%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in x around 0 79.5%

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

      1. *-commutative 79.5%

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

      2. associate-*r/ 84.2%

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

   7. Simplified 84.2%

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

   if 1.7e-23 < t < 3200

   1. Initial program 84.8%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 90.8%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+39}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-15}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-83}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-89}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-23}:\\ \;\;\;\;y + \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 3200:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+218}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 4.55 \cdot 10^{+80}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+182}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+206}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z a)))))
   (if (<= z -3.8e+218)
     (/ (* y z) t)
     (if (<= z 4.55e+80)
       (+ x y)
       (if (<= z 8.5e+144)
         t_1
         (if (<= z 9e+182) x (if (<= z 4.8e+206) t_1 (/ y (/ t z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / a));
	double tmp;
	if (z <= -3.8e+218) {
		tmp = (y * z) / t;
	} else if (z <= 4.55e+80) {
		tmp = x + y;
	} else if (z <= 8.5e+144) {
		tmp = t_1;
	} else if (z <= 9e+182) {
		tmp = x;
	} else if (z <= 4.8e+206) {
		tmp = t_1;
	} else {
		tmp = y / (t / z);
	}
	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 * (1.0d0 - (z / a))
    if (z <= (-3.8d+218)) then
        tmp = (y * z) / t
    else if (z <= 4.55d+80) then
        tmp = x + y
    else if (z <= 8.5d+144) then
        tmp = t_1
    else if (z <= 9d+182) then
        tmp = x
    else if (z <= 4.8d+206) then
        tmp = t_1
    else
        tmp = y / (t / z)
    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 * (1.0 - (z / a));
	double tmp;
	if (z <= -3.8e+218) {
		tmp = (y * z) / t;
	} else if (z <= 4.55e+80) {
		tmp = x + y;
	} else if (z <= 8.5e+144) {
		tmp = t_1;
	} else if (z <= 9e+182) {
		tmp = x;
	} else if (z <= 4.8e+206) {
		tmp = t_1;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / a))
	tmp = 0
	if z <= -3.8e+218:
		tmp = (y * z) / t
	elif z <= 4.55e+80:
		tmp = x + y
	elif z <= 8.5e+144:
		tmp = t_1
	elif z <= 9e+182:
		tmp = x
	elif z <= 4.8e+206:
		tmp = t_1
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (z <= -3.8e+218)
		tmp = Float64(Float64(y * z) / t);
	elseif (z <= 4.55e+80)
		tmp = Float64(x + y);
	elseif (z <= 8.5e+144)
		tmp = t_1;
	elseif (z <= 9e+182)
		tmp = x;
	elseif (z <= 4.8e+206)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / a));
	tmp = 0.0;
	if (z <= -3.8e+218)
		tmp = (y * z) / t;
	elseif (z <= 4.55e+80)
		tmp = x + y;
	elseif (z <= 8.5e+144)
		tmp = t_1;
	elseif (z <= 9e+182)
		tmp = x;
	elseif (z <= 4.8e+206)
		tmp = t_1;
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+218], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4.55e+80], N[(x + y), $MachinePrecision], If[LessEqual[z, 8.5e+144], t$95$1, If[LessEqual[z, 9e+182], x, If[LessEqual[z, 4.8e+206], t$95$1, N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.80000000000000012e218

   1. Initial program 80.1%

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

      1. associate-*l/ 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around inf 59.9%

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

      1. associate-*r/ 59.9%

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

      2. associate-*r* 59.9%

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

      3. neg-mul-1 59.9%

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

   7. Simplified 59.9%

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

   8. Taylor expanded in a around 0 51.1%

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

   if -3.80000000000000012e218 < z < 4.55000000000000007e80

   1. Initial program 79.4%

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

      1. associate-*l/ 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in a around inf 72.2%

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

      1. +-commutative 72.2%

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

   7. Simplified 72.2%

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

   if 4.55000000000000007e80 < z < 8.4999999999999998e144 or 9.00000000000000058e182 < z < 4.7999999999999999e206

   1. Initial program 78.6%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in x around 0 77.5%

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

      1. sub-neg 77.5%

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

      2. associate-*r/ 86.3%

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

      3. *-rgt-identity 86.3%

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

      4. distribute-rgt-neg-in 86.3%

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

      5. distribute-frac-neg 86.3%

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

      6. distribute-lft-in 86.2%

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

      7. distribute-frac-neg 86.2%

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

      8. sub-neg 86.2%

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

   7. Simplified 86.2%

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

   8. Taylor expanded in t around 0 69.9%

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

   if 8.4999999999999998e144 < z < 9.00000000000000058e182

   1. Initial program 65.6%

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

      1. associate-*l/ 65.3%

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

   3. Simplified 65.3%

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

   5. Taylor expanded in x around inf 62.1%

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

   if 4.7999999999999999e206 < z

   1. Initial program 80.4%

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

      1. associate-*l/ 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in z around inf 67.2%

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

      1. associate-*r/ 67.2%

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

      2. associate-*r* 67.2%

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

      3. neg-mul-1 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in a around 0 54.9%

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

      1. associate-/l* 61.3%

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

   10. Simplified 61.3%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+218}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 4.55 \cdot 10^{+80}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+144}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+182}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+206}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - y \cdot \frac{z}{a}\\ t_2 := x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 0.008:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (* y (/ z a)))) (t_2 (- x (/ y (/ t (- a z))))))
   (if (<= t -5.4e+38)
     t_2
     (if (<= t -1.05e-14)
       t_1
       (if (<= t -3.8e-88) (+ x (/ (* y z) t)) (if (<= t 0.008) 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 / (t / (a - z)));
	double tmp;
	if (t <= -5.4e+38) {
		tmp = t_2;
	} else if (t <= -1.05e-14) {
		tmp = t_1;
	} else if (t <= -3.8e-88) {
		tmp = x + ((y * z) / t);
	} else if (t <= 0.008) {
		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 / (t / (a - z)))
    if (t <= (-5.4d+38)) then
        tmp = t_2
    else if (t <= (-1.05d-14)) then
        tmp = t_1
    else if (t <= (-3.8d-88)) then
        tmp = x + ((y * z) / t)
    else if (t <= 0.008d0) 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 / (t / (a - z)));
	double tmp;
	if (t <= -5.4e+38) {
		tmp = t_2;
	} else if (t <= -1.05e-14) {
		tmp = t_1;
	} else if (t <= -3.8e-88) {
		tmp = x + ((y * z) / t);
	} else if (t <= 0.008) {
		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 / (t / (a - z)))
	tmp = 0
	if t <= -5.4e+38:
		tmp = t_2
	elif t <= -1.05e-14:
		tmp = t_1
	elif t <= -3.8e-88:
		tmp = x + ((y * z) / t)
	elif t <= 0.008:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(y * Float64(z / a)))
	t_2 = Float64(x - Float64(y / Float64(t / Float64(a - z))))
	tmp = 0.0
	if (t <= -5.4e+38)
		tmp = t_2;
	elseif (t <= -1.05e-14)
		tmp = t_1;
	elseif (t <= -3.8e-88)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (t <= 0.008)
		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 / (t / (a - z)));
	tmp = 0.0;
	if (t <= -5.4e+38)
		tmp = t_2;
	elseif (t <= -1.05e-14)
		tmp = t_1;
	elseif (t <= -3.8e-88)
		tmp = x + ((y * z) / t);
	elseif (t <= 0.008)
		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[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.4e+38], t$95$2, If[LessEqual[t, -1.05e-14], t$95$1, If[LessEqual[t, -3.8e-88], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.008], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.39999999999999992e38 or 0.0080000000000000002 < t

   1. Initial program 61.6%

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

      1. associate-*l/ 74.4%

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

   3. Simplified 74.4%

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

      1. associate-*l/ 61.6%

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

      2. clear-num 61.6%

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

      3. *-commutative 61.6%

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

   6. Applied egg-rr 61.6%

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

   7. Taylor expanded in t around inf 77.6%

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

      1. associate--l+ 77.6%

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

      2. associate-*r/ 77.6%

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

      3. associate-*r/ 77.6%

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

      4. div-sub 77.6%

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

      5. distribute-lft-out-- 77.6%

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

      6. associate-*r/ 77.6%

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

      7. mul-1-neg 77.6%

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

      8. unsub-neg 77.6%

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

      9. *-commutative 77.6%

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

      10. cancel-sign-sub-inv 77.6%

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

      11. distribute-rgt-in 78.7%

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

      12. sub-neg 78.7%

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

      13. associate-/l* 89.1%

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

   9. Simplified 89.1%

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

   if -5.39999999999999992e38 < t < -1.0499999999999999e-14 or -3.80000000000000011e-88 < t < 0.0080000000000000002

   1. Initial program 92.8%

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

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in t around 0 85.2%

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

   if -1.0499999999999999e-14 < t < -3.80000000000000011e-88

   1. Initial program 77.5%

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

      1. associate-*l/ 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in t around inf 63.1%

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

      1. sub-neg 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. associate-/l* 55.4%

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

      5. mul-1-neg 55.4%

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

      6. remove-double-neg 55.4%

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

      7. associate-/l* 55.3%

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

   7. Simplified 55.3%

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

   8. Taylor expanded in a around 0 88.4%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+38}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 0.008:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 0.72:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ t (- a z))))))
   (if (<= t -3.3e+40)
     t_1
     (if (<= t -1.05e-14)
       (- (+ x y) (/ y (/ a z)))
       (if (<= t -4e-87)
         (+ x (/ (* y z) t))
         (if (<= t 0.72) (- (+ x y) (* y (/ z a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (t / (a - z)));
	double tmp;
	if (t <= -3.3e+40) {
		tmp = t_1;
	} else if (t <= -1.05e-14) {
		tmp = (x + y) - (y / (a / z));
	} else if (t <= -4e-87) {
		tmp = x + ((y * z) / t);
	} else if (t <= 0.72) {
		tmp = (x + y) - (y * (z / a));
	} 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 / (t / (a - z)))
    if (t <= (-3.3d+40)) then
        tmp = t_1
    else if (t <= (-1.05d-14)) then
        tmp = (x + y) - (y / (a / z))
    else if (t <= (-4d-87)) then
        tmp = x + ((y * z) / t)
    else if (t <= 0.72d0) then
        tmp = (x + y) - (y * (z / a))
    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 / (t / (a - z)));
	double tmp;
	if (t <= -3.3e+40) {
		tmp = t_1;
	} else if (t <= -1.05e-14) {
		tmp = (x + y) - (y / (a / z));
	} else if (t <= -4e-87) {
		tmp = x + ((y * z) / t);
	} else if (t <= 0.72) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (t / (a - z)))
	tmp = 0
	if t <= -3.3e+40:
		tmp = t_1
	elif t <= -1.05e-14:
		tmp = (x + y) - (y / (a / z))
	elif t <= -4e-87:
		tmp = x + ((y * z) / t)
	elif t <= 0.72:
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(t / Float64(a - z))))
	tmp = 0.0
	if (t <= -3.3e+40)
		tmp = t_1;
	elseif (t <= -1.05e-14)
		tmp = Float64(Float64(x + y) - Float64(y / Float64(a / z)));
	elseif (t <= -4e-87)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (t <= 0.72)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (t / (a - z)));
	tmp = 0.0;
	if (t <= -3.3e+40)
		tmp = t_1;
	elseif (t <= -1.05e-14)
		tmp = (x + y) - (y / (a / z));
	elseif (t <= -4e-87)
		tmp = x + ((y * z) / t);
	elseif (t <= 0.72)
		tmp = (x + y) - (y * (z / a));
	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[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e+40], t$95$1, If[LessEqual[t, -1.05e-14], N[(N[(x + y), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4e-87], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.72], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.2999999999999998e40 or 0.71999999999999997 < t

   1. Initial program 61.6%

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

      1. associate-*l/ 74.4%

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

   3. Simplified 74.4%

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

      1. associate-*l/ 61.6%

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

      2. clear-num 61.6%

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

      3. *-commutative 61.6%

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

   6. Applied egg-rr 61.6%

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

   7. Taylor expanded in t around inf 77.6%

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

      1. associate--l+ 77.6%

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

      2. associate-*r/ 77.6%

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

      3. associate-*r/ 77.6%

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

      4. div-sub 77.6%

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

      5. distribute-lft-out-- 77.6%

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

      6. associate-*r/ 77.6%

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

      7. mul-1-neg 77.6%

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

      8. unsub-neg 77.6%

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

      9. *-commutative 77.6%

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

      10. cancel-sign-sub-inv 77.6%

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

      11. distribute-rgt-in 78.7%

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

      12. sub-neg 78.7%

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

      13. associate-/l* 89.1%

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

   9. Simplified 89.1%

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

   if -3.2999999999999998e40 < t < -1.0499999999999999e-14

   1. Initial program 72.3%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in t around 0 64.7%

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

      1. associate-/l* 82.3%

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

   7. Simplified 82.3%

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

   if -1.0499999999999999e-14 < t < -4.00000000000000007e-87

   1. Initial program 77.5%

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

      1. associate-*l/ 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in t around inf 63.1%

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

      1. sub-neg 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. associate-/l* 55.4%

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

      5. mul-1-neg 55.4%

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

      6. remove-double-neg 55.4%

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

      7. associate-/l* 55.3%

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

   7. Simplified 55.3%

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

   8. Taylor expanded in a around 0 88.4%

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

   if -4.00000000000000007e-87 < t < 0.71999999999999997

   1. Initial program 94.7%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in t around 0 85.5%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+40}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 0.72:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{if}\;a \leq -1.12 \cdot 10^{-131}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y t) (- z a))))
   (if (<= a -1.12e-131)
     (+ x y)
     (if (<= a 1.85e-240)
       t_1
       (if (<= a 7e-167) x (if (<= a 2.45e-64) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / t) * (z - a);
	double tmp;
	if (a <= -1.12e-131) {
		tmp = x + y;
	} else if (a <= 1.85e-240) {
		tmp = t_1;
	} else if (a <= 7e-167) {
		tmp = x;
	} else if (a <= 2.45e-64) {
		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 = (y / t) * (z - a)
    if (a <= (-1.12d-131)) then
        tmp = x + y
    else if (a <= 1.85d-240) then
        tmp = t_1
    else if (a <= 7d-167) then
        tmp = x
    else if (a <= 2.45d-64) 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 = (y / t) * (z - a);
	double tmp;
	if (a <= -1.12e-131) {
		tmp = x + y;
	} else if (a <= 1.85e-240) {
		tmp = t_1;
	} else if (a <= 7e-167) {
		tmp = x;
	} else if (a <= 2.45e-64) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / t) * (z - a)
	tmp = 0
	if a <= -1.12e-131:
		tmp = x + y
	elif a <= 1.85e-240:
		tmp = t_1
	elif a <= 7e-167:
		tmp = x
	elif a <= 2.45e-64:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / t) * Float64(z - a))
	tmp = 0.0
	if (a <= -1.12e-131)
		tmp = Float64(x + y);
	elseif (a <= 1.85e-240)
		tmp = t_1;
	elseif (a <= 7e-167)
		tmp = x;
	elseif (a <= 2.45e-64)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / t) * (z - a);
	tmp = 0.0;
	if (a <= -1.12e-131)
		tmp = x + y;
	elseif (a <= 1.85e-240)
		tmp = t_1;
	elseif (a <= 7e-167)
		tmp = x;
	elseif (a <= 2.45e-64)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.12e-131], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.85e-240], t$95$1, If[LessEqual[a, 7e-167], x, If[LessEqual[a, 2.45e-64], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.12000000000000001e-131 or 2.4500000000000001e-64 < a

   1. Initial program 79.7%

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

      1. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in a around inf 70.0%

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

      1. +-commutative 70.0%

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

   7. Simplified 70.0%

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

   if -1.12000000000000001e-131 < a < 1.8500000000000001e-240 or 6.9999999999999998e-167 < a < 2.4500000000000001e-64

   1. Initial program 77.0%

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

      1. associate-*l/ 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in t around inf 87.8%

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

      1. sub-neg 87.8%

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

      2. mul-1-neg 87.8%

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

      3. unsub-neg 87.8%

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

      4. associate-/l* 81.7%

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

      5. mul-1-neg 81.7%

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

      6. remove-double-neg 81.7%

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

      7. associate-/l* 78.7%

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

   7. Simplified 78.7%

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

   8. Taylor expanded in x around 0 57.8%

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

      1. associate-*l/ 62.3%

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

      2. associate-*r/ 56.2%

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

      3. *-commutative 56.2%

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

      4. distribute-lft-out-- 62.2%

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

   10. Simplified 62.2%

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

   if 1.8500000000000001e-240 < a < 6.9999999999999998e-167

   1. Initial program 78.0%

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

      1. associate-*l/ 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in x around inf 71.8%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-131}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-240}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-64}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+218}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+81}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+144}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.2e+218)
   (/ (* y z) t)
   (if (<= z 1.85e+81)
     (+ x y)
     (if (<= z 4.7e+144)
       (/ (- y) (/ a z))
       (if (<= z 6.2e+179) x (* y (/ z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e+218) {
		tmp = (y * z) / t;
	} else if (z <= 1.85e+81) {
		tmp = x + y;
	} else if (z <= 4.7e+144) {
		tmp = -y / (a / z);
	} else if (z <= 6.2e+179) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-6.2d+218)) then
        tmp = (y * z) / t
    else if (z <= 1.85d+81) then
        tmp = x + y
    else if (z <= 4.7d+144) then
        tmp = -y / (a / z)
    else if (z <= 6.2d+179) then
        tmp = x
    else
        tmp = 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 (z <= -6.2e+218) {
		tmp = (y * z) / t;
	} else if (z <= 1.85e+81) {
		tmp = x + y;
	} else if (z <= 4.7e+144) {
		tmp = -y / (a / z);
	} else if (z <= 6.2e+179) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.2e+218:
		tmp = (y * z) / t
	elif z <= 1.85e+81:
		tmp = x + y
	elif z <= 4.7e+144:
		tmp = -y / (a / z)
	elif z <= 6.2e+179:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.2e+218)
		tmp = Float64(Float64(y * z) / t);
	elseif (z <= 1.85e+81)
		tmp = Float64(x + y);
	elseif (z <= 4.7e+144)
		tmp = Float64(Float64(-y) / Float64(a / z));
	elseif (z <= 6.2e+179)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.2e+218)
		tmp = (y * z) / t;
	elseif (z <= 1.85e+81)
		tmp = x + y;
	elseif (z <= 4.7e+144)
		tmp = -y / (a / z);
	elseif (z <= 6.2e+179)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.2e+218], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.85e+81], N[(x + y), $MachinePrecision], If[LessEqual[z, 4.7e+144], N[((-y) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+179], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.2000000000000003e218

   1. Initial program 80.1%

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

      1. associate-*l/ 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around inf 59.9%

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

      1. associate-*r/ 59.9%

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

      2. associate-*r* 59.9%

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

      3. neg-mul-1 59.9%

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

   7. Simplified 59.9%

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

   8. Taylor expanded in a around 0 51.1%

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

   if -6.2000000000000003e218 < z < 1.85e81

   1. Initial program 79.4%

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

      1. associate-*l/ 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in a around inf 72.2%

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

      1. +-commutative 72.2%

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

   7. Simplified 72.2%

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

   if 1.85e81 < z < 4.7000000000000002e144

   1. Initial program 84.8%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in z around inf 74.9%

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

      1. associate-*r/ 74.9%

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

      2. associate-*r* 74.9%

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

      3. neg-mul-1 74.9%

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

   7. Simplified 74.9%

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

   8. Taylor expanded in a around inf 60.9%

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

      1. mul-1-neg 60.9%

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

      2. associate-/l* 68.0%

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

   10. Simplified 68.0%

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

   if 4.7000000000000002e144 < z < 6.2e179

   1. Initial program 71.8%

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

      1. associate-*l/ 71.5%

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

   3. Simplified 71.5%

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

   5. Taylor expanded in x around inf 67.8%

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

   if 6.2e179 < z

   1. Initial program 73.5%

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

      1. associate-*l/ 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in x around 0 65.2%

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

      1. sub-neg 65.2%

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

      2. associate-*r/ 77.0%

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

      3. *-rgt-identity 77.0%

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

      4. distribute-rgt-neg-in 77.0%

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

      5. distribute-frac-neg 77.0%

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

      6. distribute-lft-in 76.9%

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

      7. distribute-frac-neg 76.9%

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

      8. sub-neg 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in a around 0 55.3%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+218}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+81}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+144}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+186}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{+76}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{a}{\frac{t}{y}}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.5e+186)
   (- x (/ y (/ t (- a z))))
   (if (<= t 1.28e+76)
     (- (+ x y) (* y (/ (- z t) (- a t))))
     (+ (- x (/ a (/ t y))) (/ y (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e+186) {
		tmp = x - (y / (t / (a - z)));
	} else if (t <= 1.28e+76) {
		tmp = (x + y) - (y * ((z - t) / (a - t)));
	} else {
		tmp = (x - (a / (t / y))) + (y / (t / z));
	}
	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 <= (-6.5d+186)) then
        tmp = x - (y / (t / (a - z)))
    else if (t <= 1.28d+76) then
        tmp = (x + y) - (y * ((z - t) / (a - t)))
    else
        tmp = (x - (a / (t / y))) + (y / (t / z))
    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 <= -6.5e+186) {
		tmp = x - (y / (t / (a - z)));
	} else if (t <= 1.28e+76) {
		tmp = (x + y) - (y * ((z - t) / (a - t)));
	} else {
		tmp = (x - (a / (t / y))) + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.5e+186:
		tmp = x - (y / (t / (a - z)))
	elif t <= 1.28e+76:
		tmp = (x + y) - (y * ((z - t) / (a - t)))
	else:
		tmp = (x - (a / (t / y))) + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.5e+186)
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	elseif (t <= 1.28e+76)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(Float64(x - Float64(a / Float64(t / y))) + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.5e+186)
		tmp = x - (y / (t / (a - z)));
	elseif (t <= 1.28e+76)
		tmp = (x + y) - (y * ((z - t) / (a - t)));
	else
		tmp = (x - (a / (t / y))) + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.5e+186], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.28e+76], N[(N[(x + y), $MachinePrecision] - N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.4999999999999997e186

   1. Initial program 37.5%

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

      1. associate-*l/ 57.4%

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

   3. Simplified 57.4%

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

      1. associate-*l/ 37.5%

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

      2. clear-num 37.5%

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

      3. *-commutative 37.5%

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

   6. Applied egg-rr 37.5%

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

   7. Taylor expanded in t around inf 73.0%

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

      1. associate--l+ 73.0%

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

      2. associate-*r/ 73.0%

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

      3. associate-*r/ 73.0%

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

      4. div-sub 73.0%

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

      5. distribute-lft-out-- 73.0%

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

      6. associate-*r/ 73.0%

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

      7. mul-1-neg 73.0%

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

      8. unsub-neg 73.0%

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

      9. *-commutative 73.0%

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

      10. cancel-sign-sub-inv 73.0%

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

      11. distribute-rgt-in 73.2%

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

      12. sub-neg 73.2%

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

      13. associate-/l* 96.2%

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

   9. Simplified 96.2%

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

   if -6.4999999999999997e186 < t < 1.27999999999999994e76

   1. Initial program 90.9%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   if 1.27999999999999994e76 < t

   1. Initial program 56.9%

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

      1. associate-*l/ 70.4%

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

   3. Simplified 70.4%

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

   5. Taylor expanded in t around inf 75.3%

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

      1. sub-neg 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

      4. associate-/l* 83.0%

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

      5. mul-1-neg 83.0%

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

      6. remove-double-neg 83.0%

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

      7. associate-/l* 90.3%

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

   7. Simplified 90.3%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+186}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{+76}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{a}{\frac{t}{y}}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.76 \cdot 10^{+118} \lor \neg \left(a \leq 2900000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.76e+118) (not (<= a 2900000.0)))
   (+ x y)
   (- x (/ y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.76e+118) || !(a <= 2900000.0)) {
		tmp = x + y;
	} else {
		tmp = x - (y / (t / (a - z)));
	}
	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 <= (-1.76d+118)) .or. (.not. (a <= 2900000.0d0))) then
        tmp = x + y
    else
        tmp = x - (y / (t / (a - z)))
    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 <= -1.76e+118) || !(a <= 2900000.0)) {
		tmp = x + y;
	} else {
		tmp = x - (y / (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.76e+118) or not (a <= 2900000.0):
		tmp = x + y
	else:
		tmp = x - (y / (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.76e+118) || !(a <= 2900000.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.76e+118) || ~((a <= 2900000.0)))
		tmp = x + y;
	else
		tmp = x - (y / (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.76e+118], N[Not[LessEqual[a, 2900000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.76000000000000011e118 or 2.9e6 < a

   1. Initial program 80.6%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in a around inf 83.9%

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

      1. +-commutative 83.9%

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

   7. Simplified 83.9%

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

   if -1.76000000000000011e118 < a < 2.9e6

   1. Initial program 77.7%

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

      1. associate-*l/ 77.8%

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

   3. Simplified 77.8%

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

      1. associate-*l/ 77.7%

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

      2. clear-num 77.7%

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

      3. *-commutative 77.7%

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

   6. Applied egg-rr 77.7%

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

   7. Taylor expanded in t around inf 71.4%

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

      1. associate--l+ 71.4%

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

      2. associate-*r/ 71.4%

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

      3. associate-*r/ 71.4%

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

      4. div-sub 71.5%

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

      5. distribute-lft-out-- 71.5%

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

      6. associate-*r/ 71.5%

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

      7. mul-1-neg 71.5%

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

      8. unsub-neg 71.5%

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

      9. *-commutative 71.5%

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

      10. cancel-sign-sub-inv 71.5%

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

      11. distribute-rgt-in 71.5%

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

      12. sub-neg 71.5%

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

      13. associate-/l* 70.8%

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

   9. Simplified 70.8%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.76 \cdot 10^{+118} \lor \neg \left(a \leq 2900000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-10} \lor \neg \left(a \leq 110000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.2e-10) (not (<= a 110000000.0)))
   (+ x y)
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.2e-10) || !(a <= 110000000.0)) {
		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 <= (-2.2d-10)) .or. (.not. (a <= 110000000.0d0))) 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 <= -2.2e-10) || !(a <= 110000000.0)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.2e-10) or not (a <= 110000000.0):
		tmp = x + y
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.2e-10) || !(a <= 110000000.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.2e-10) || ~((a <= 110000000.0)))
		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, -2.2e-10], N[Not[LessEqual[a, 110000000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.1999999999999999e-10 or 1.1e8 < a

   1. Initial program 80.2%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in a around inf 74.7%

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

      1. +-commutative 74.7%

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

   7. Simplified 74.7%

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

   if -2.1999999999999999e-10 < a < 1.1e8

   1. Initial program 77.4%

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

      1. associate-*l/ 75.3%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in t around inf 79.6%

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

      1. sub-neg 79.6%

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

      2. mul-1-neg 79.6%

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

      3. unsub-neg 79.6%

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

      4. associate-/l* 76.3%

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

      5. mul-1-neg 76.3%

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

      6. remove-double-neg 76.3%

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

      7. associate-/l* 74.6%

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

   7. Simplified 74.6%

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

   8. Taylor expanded in a around 0 76.8%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-10} \lor \neg \left(a \leq 110000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+218} \lor \neg \left(z \leq 2.5 \cdot 10^{+180}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3e+218) (not (<= z 2.5e+180))) (* y (/ z t)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e+218) || !(z <= 2.5e+180)) {
		tmp = y * (z / t);
	} 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) :: tmp
    if ((z <= (-3d+218)) .or. (.not. (z <= 2.5d+180))) then
        tmp = y * (z / t)
    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 tmp;
	if ((z <= -3e+218) || !(z <= 2.5e+180)) {
		tmp = y * (z / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3e+218) or not (z <= 2.5e+180):
		tmp = y * (z / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3e+218) || !(z <= 2.5e+180))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3e+218) || ~((z <= 2.5e+180)))
		tmp = y * (z / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3e+218], N[Not[LessEqual[z, 2.5e+180]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0000000000000001e218 or 2.4999999999999998e180 < z

   1. Initial program 76.8%

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

      1. associate-*l/ 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in x around 0 62.4%

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

      1. sub-neg 62.4%

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

      2. associate-*r/ 72.0%

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

      3. *-rgt-identity 72.0%

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

      4. distribute-rgt-neg-in 72.0%

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

      5. distribute-frac-neg 72.0%

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

      6. distribute-lft-in 71.9%

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

      7. distribute-frac-neg 71.9%

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

      8. sub-neg 71.9%

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

   7. Simplified 71.9%

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

   8. Taylor expanded in a around 0 51.2%

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

   if -3.0000000000000001e218 < z < 2.4999999999999998e180

   1. Initial program 79.4%

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

      1. associate-*l/ 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in a around inf 68.3%

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

      1. +-commutative 68.3%

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

   7. Simplified 68.3%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+218} \lor \neg \left(z \leq 2.5 \cdot 10^{+180}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+218}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+180}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e+218)
   (/ (* y z) t)
   (if (<= z 2.5e+180) (+ x y) (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e+218) {
		tmp = (y * z) / t;
	} else if (z <= 2.5e+180) {
		tmp = x + y;
	} else {
		tmp = 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 (z <= (-2.9d+218)) then
        tmp = (y * z) / t
    else if (z <= 2.5d+180) then
        tmp = x + y
    else
        tmp = 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 (z <= -2.9e+218) {
		tmp = (y * z) / t;
	} else if (z <= 2.5e+180) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e+218:
		tmp = (y * z) / t
	elif z <= 2.5e+180:
		tmp = x + y
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.9e+218)
		tmp = Float64(Float64(y * z) / t);
	elseif (z <= 2.5e+180)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.9e+218)
		tmp = (y * z) / t;
	elseif (z <= 2.5e+180)
		tmp = x + y;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.9e+218], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.5e+180], N[(x + y), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8999999999999999e218

   1. Initial program 80.1%

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

      1. associate-*l/ 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around inf 59.9%

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

      1. associate-*r/ 59.9%

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

      2. associate-*r* 59.9%

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

      3. neg-mul-1 59.9%

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

   7. Simplified 59.9%

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

   8. Taylor expanded in a around 0 51.1%

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

   if -2.8999999999999999e218 < z < 2.4999999999999998e180

   1. Initial program 79.4%

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

      1. associate-*l/ 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in a around inf 68.3%

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

      1. +-commutative 68.3%

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

   7. Simplified 68.3%

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

   if 2.4999999999999998e180 < z

   1. Initial program 73.5%

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

      1. associate-*l/ 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in x around 0 65.2%

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

      1. sub-neg 65.2%

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

      2. associate-*r/ 77.0%

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

      3. *-rgt-identity 77.0%

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

      4. distribute-rgt-neg-in 77.0%

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

      5. distribute-frac-neg 77.0%

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

      6. distribute-lft-in 76.9%

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

      7. distribute-frac-neg 76.9%

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

      8. sub-neg 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in a around 0 55.3%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+218}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+180}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+135}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+170}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.8e+135) y (if (<= y 1.9e+170) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.8e+135) {
		tmp = y;
	} else if (y <= 1.9e+170) {
		tmp = x;
	} else {
		tmp = 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) :: tmp
    if (y <= (-3.8d+135)) then
        tmp = y
    else if (y <= 1.9d+170) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.8e+135) {
		tmp = y;
	} else if (y <= 1.9e+170) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.8e+135:
		tmp = y
	elif y <= 1.9e+170:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.8e+135)
		tmp = y;
	elseif (y <= 1.9e+170)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.8e+135)
		tmp = y;
	elseif (y <= 1.9e+170)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.8e+135], y, If[LessEqual[y, 1.9e+170], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8000000000000001e135 or 1.8999999999999999e170 < y

   1. Initial program 55.8%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in x around 0 54.3%

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

      1. sub-neg 54.3%

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

      2. associate-*r/ 71.4%

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

      3. *-rgt-identity 71.4%

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

      4. distribute-rgt-neg-in 71.4%

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

      5. distribute-frac-neg 71.4%

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

      6. distribute-lft-in 71.4%

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

      7. distribute-frac-neg 71.4%

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

      8. sub-neg 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in a around inf 36.7%

      \[\leadsto y \cdot \color{blue}{1} \]

   9. Taylor expanded in y around 0 36.7%

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

   if -3.8000000000000001e135 < y < 1.8999999999999999e170

   1. Initial program 87.3%

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

      1. associate-*l/ 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in x around inf 58.3%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+135}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+170}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.1% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x + y \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 78.9%

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

   1. associate-*l/ 85.0%

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

3. Simplified 85.0%

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

5. Taylor expanded in a around inf 59.7%

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

   1. +-commutative 59.7%

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

7. Simplified 59.7%

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

8. Final simplification 59.7%

   \[\leadsto x + y \]
9. Add Preprocessing

Alternative 16: 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 78.9%

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

   1. associate-*l/ 85.0%

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

3. Simplified 85.0%

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

5. Taylor expanded in x around inf 45.9%

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

6. Final simplification 45.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 88.0% 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 2024096 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (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))))