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

Percentage Accurate: 85.2% → 97.9%

Time: 9.2s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{+117}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(y \cdot \frac{-1}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a - t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (+ x (/ (* y (- z t)) (- a t))) -4e+117)
   (+ x (* (- z t) (* y (/ -1.0 (- t a)))))
   (fma y (/ (- z t) (- a t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x + ((y * (z - t)) / (a - t))) <= -4e+117) {
		tmp = x + ((z - t) * (y * (-1.0 / (t - a))));
	} else {
		tmp = fma(y, ((z - t) / (a - t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t))) <= -4e+117)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y * Float64(-1.0 / Float64(t - a)))));
	else
		tmp = fma(y, Float64(Float64(z - t) / Float64(a - t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -4e+117], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y * N[(-1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))) < -4.0000000000000002e117

   1. Initial program 71.7%

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

      1. div-inv 71.7%

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

      2. *-commutative 71.7%

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

      3. associate-*l* 99.9%

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

   4. Applied egg-rr 99.9%

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

   if -4.0000000000000002e117 < (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

   1. Initial program 89.0%

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

      1. +-commutative 89.0%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{+117}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(y \cdot \frac{-1}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a - t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ t_2 := x - y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+187}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.7 \cdot 10^{-68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-83} \lor \neg \left(t \leq 24\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))) (t_2 (- x (* y (/ z t)))))
   (if (<= t -1.26e+187)
     (+ x y)
     (if (<= t -2.35e+42)
       t_2
       (if (<= t -1.05e-14)
         t_1
         (if (<= t -6.7e-68)
           t_2
           (if (or (<= t -7.5e-83) (not (<= t 24.0))) (+ x y) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = x - (y * (z / t));
	double tmp;
	if (t <= -1.26e+187) {
		tmp = x + y;
	} else if (t <= -2.35e+42) {
		tmp = t_2;
	} else if (t <= -1.05e-14) {
		tmp = t_1;
	} else if (t <= -6.7e-68) {
		tmp = t_2;
	} else if ((t <= -7.5e-83) || !(t <= 24.0)) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    t_2 = x - (y * (z / t))
    if (t <= (-1.26d+187)) then
        tmp = x + y
    else if (t <= (-2.35d+42)) then
        tmp = t_2
    else if (t <= (-1.05d-14)) then
        tmp = t_1
    else if (t <= (-6.7d-68)) then
        tmp = t_2
    else if ((t <= (-7.5d-83)) .or. (.not. (t <= 24.0d0))) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = x - (y * (z / t));
	double tmp;
	if (t <= -1.26e+187) {
		tmp = x + y;
	} else if (t <= -2.35e+42) {
		tmp = t_2;
	} else if (t <= -1.05e-14) {
		tmp = t_1;
	} else if (t <= -6.7e-68) {
		tmp = t_2;
	} else if ((t <= -7.5e-83) || !(t <= 24.0)) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	t_2 = x - (y * (z / t))
	tmp = 0
	if t <= -1.26e+187:
		tmp = x + y
	elif t <= -2.35e+42:
		tmp = t_2
	elif t <= -1.05e-14:
		tmp = t_1
	elif t <= -6.7e-68:
		tmp = t_2
	elif (t <= -7.5e-83) or not (t <= 24.0):
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	t_2 = Float64(x - Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -1.26e+187)
		tmp = Float64(x + y);
	elseif (t <= -2.35e+42)
		tmp = t_2;
	elseif (t <= -1.05e-14)
		tmp = t_1;
	elseif (t <= -6.7e-68)
		tmp = t_2;
	elseif ((t <= -7.5e-83) || !(t <= 24.0))
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	t_2 = x - (y * (z / t));
	tmp = 0.0;
	if (t <= -1.26e+187)
		tmp = x + y;
	elseif (t <= -2.35e+42)
		tmp = t_2;
	elseif (t <= -1.05e-14)
		tmp = t_1;
	elseif (t <= -6.7e-68)
		tmp = t_2;
	elseif ((t <= -7.5e-83) || ~((t <= 24.0)))
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e+187], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.35e+42], t$95$2, If[LessEqual[t, -1.05e-14], t$95$1, If[LessEqual[t, -6.7e-68], t$95$2, If[Or[LessEqual[t, -7.5e-83], N[Not[LessEqual[t, 24.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.26e187 or -6.6999999999999996e-68 < t < -7.4999999999999997e-83 or 24 < t

   1. Initial program 66.1%

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

   3. Taylor expanded in t around inf 79.4%

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

      1. +-commutative 79.4%

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

   5. Simplified 79.4%

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

   if -1.26e187 < t < -2.34999999999999993e42 or -1.0499999999999999e-14 < t < -6.6999999999999996e-68

   1. Initial program 91.5%

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

   3. Taylor expanded in z around inf 81.0%

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

   4. Taylor expanded in a around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. associate-/l* 79.9%

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

      3. distribute-lft-neg-in 79.9%

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

   6. Simplified 79.9%

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

      1. add-sqr-sqrt 30.7%

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

      2. fma-define 30.7%

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

      3. distribute-lft-neg-out 30.7%

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

      4. add-sqr-sqrt 14.6%

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

      5. sqrt-unprod 21.7%

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

      6. sqr-neg 21.7%

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

      7. sqrt-unprod 9.0%

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

      8. add-sqr-sqrt 15.0%

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

      9. *-commutative 15.0%

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

      10. *-commutative 15.0%

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

      11. fma-neg 15.0%

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

      12. add-sqr-sqrt 46.2%

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

      13. add-sqr-sqrt 21.0%

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

      14. sqrt-unprod 52.2%

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

      15. sqr-neg 52.2%

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

      16. sqrt-unprod 40.1%

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

      17. add-sqr-sqrt 79.9%

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

   8. Applied egg-rr 79.9%

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

   if -2.34999999999999993e42 < t < -1.0499999999999999e-14 or -7.4999999999999997e-83 < t < 24

   1. Initial program 94.5%

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

   3. Taylor expanded in t around 0 79.4%

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

      1. associate-/l* 80.7%

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

   5. Simplified 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-*l/ 79.4%

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

   7. Applied egg-rr 79.4%

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

      1. associate-/l* 83.5%

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

   9. Applied egg-rr 83.5%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+187}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+42}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -6.7 \cdot 10^{-68}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-83} \lor \neg \left(t \leq 24\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -0.225:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+75}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ z t))))))
   (if (<= t -0.225)
     t_1
     (if (<= t -9e-15)
       (+ x (/ y (/ a (- z t))))
       (if (<= t -7.5e-83)
         t_1
         (if (<= t 5e-40)
           (+ x (/ (* y z) (- a t)))
           (if (<= t 9.5e+75) (+ x (* y (/ z (- a t)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (z / t)));
	double tmp;
	if (t <= -0.225) {
		tmp = t_1;
	} else if (t <= -9e-15) {
		tmp = x + (y / (a / (z - t)));
	} else if (t <= -7.5e-83) {
		tmp = t_1;
	} else if (t <= 5e-40) {
		tmp = x + ((y * z) / (a - t));
	} else if (t <= 9.5e+75) {
		tmp = x + (y * (z / (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) :: tmp
    t_1 = x + (y * (1.0d0 - (z / t)))
    if (t <= (-0.225d0)) then
        tmp = t_1
    else if (t <= (-9d-15)) then
        tmp = x + (y / (a / (z - t)))
    else if (t <= (-7.5d-83)) then
        tmp = t_1
    else if (t <= 5d-40) then
        tmp = x + ((y * z) / (a - t))
    else if (t <= 9.5d+75) then
        tmp = x + (y * (z / (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 = x + (y * (1.0 - (z / t)));
	double tmp;
	if (t <= -0.225) {
		tmp = t_1;
	} else if (t <= -9e-15) {
		tmp = x + (y / (a / (z - t)));
	} else if (t <= -7.5e-83) {
		tmp = t_1;
	} else if (t <= 5e-40) {
		tmp = x + ((y * z) / (a - t));
	} else if (t <= 9.5e+75) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (z / t)))
	tmp = 0
	if t <= -0.225:
		tmp = t_1
	elif t <= -9e-15:
		tmp = x + (y / (a / (z - t)))
	elif t <= -7.5e-83:
		tmp = t_1
	elif t <= 5e-40:
		tmp = x + ((y * z) / (a - t))
	elif t <= 9.5e+75:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(z / t))))
	tmp = 0.0
	if (t <= -0.225)
		tmp = t_1;
	elseif (t <= -9e-15)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (t <= -7.5e-83)
		tmp = t_1;
	elseif (t <= 5e-40)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	elseif (t <= 9.5e+75)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 - (z / t)));
	tmp = 0.0;
	if (t <= -0.225)
		tmp = t_1;
	elseif (t <= -9e-15)
		tmp = x + (y / (a / (z - t)));
	elseif (t <= -7.5e-83)
		tmp = t_1;
	elseif (t <= 5e-40)
		tmp = x + ((y * z) / (a - t));
	elseif (t <= 9.5e+75)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.225], t$95$1, If[LessEqual[t, -9e-15], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.5e-83], t$95$1, If[LessEqual[t, 5e-40], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+75], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -0.225000000000000006 or -8.9999999999999995e-15 < t < -7.4999999999999997e-83 or 9.50000000000000061e75 < t

   1. Initial program 73.4%

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

   3. Taylor expanded in a around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. unsub-neg 68.3%

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

      3. associate-/l* 91.1%

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

      4. div-sub 91.1%

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

      5. sub-neg 91.1%

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

      6. *-inverses 91.1%

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

      7. metadata-eval 91.1%

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

   5. Simplified 91.1%

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

   if -0.225000000000000006 < t < -8.9999999999999995e-15

   1. Initial program 68.7%

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

      1. associate-/l* 99.7%

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

      2. clear-num 99.5%

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

      3. un-div-inv 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in a around inf 99.2%

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

   if -7.4999999999999997e-83 < t < 4.99999999999999965e-40

   1. Initial program 95.8%

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

   3. Taylor expanded in z around inf 91.0%

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

   if 4.99999999999999965e-40 < t < 9.50000000000000061e75

   1. Initial program 94.1%

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

      1. div-inv 94.3%

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

      2. *-commutative 94.3%

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

      3. associate-*l* 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around inf 89.3%

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

      1. associate-/l* 95.1%

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

   7. Simplified 95.1%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.225:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-83}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+75}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{+38}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(y \cdot \frac{-1}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (+ x (/ (* y (- z t)) (- a t))) -5e+38)
   (+ x (* (- z t) (* y (/ -1.0 (- t a)))))
   (+ x (/ y (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x + ((y * (z - t)) / (a - t))) <= -5e+38) {
		tmp = x + ((z - t) * (y * (-1.0 / (t - a))));
	} else {
		tmp = x + (y / ((a - t) / (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 ((x + ((y * (z - t)) / (a - t))) <= (-5d+38)) then
        tmp = x + ((z - t) * (y * ((-1.0d0) / (t - a))))
    else
        tmp = x + (y / ((a - t) / (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 ((x + ((y * (z - t)) / (a - t))) <= -5e+38) {
		tmp = x + ((z - t) * (y * (-1.0 / (t - a))));
	} else {
		tmp = x + (y / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x + ((y * (z - t)) / (a - t))) <= -5e+38:
		tmp = x + ((z - t) * (y * (-1.0 / (t - a))))
	else:
		tmp = x + (y / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t))) <= -5e+38)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y * Float64(-1.0 / Float64(t - a)))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x + ((y * (z - t)) / (a - t))) <= -5e+38)
		tmp = x + ((z - t) * (y * (-1.0 / (t - a))));
	else
		tmp = x + (y / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e+38], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y * N[(-1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))) < -4.9999999999999997e38

   1. Initial program 78.0%

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

      1. div-inv 78.0%

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

      2. *-commutative 78.0%

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

      3. associate-*l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   if -4.9999999999999997e38 < (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

   1. Initial program 87.8%

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

      1. associate-/l* 99.9%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{+38}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(y \cdot \frac{-1}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-48} \lor \neg \left(z \leq 230000\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e-48) (not (<= z 230000.0)))
   (+ x (* y (/ z (- a t))))
   (+ x (* t (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-48) || !(z <= 230000.0)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (t * (y / (t - a)));
	}
	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 <= (-2.7d-48)) .or. (.not. (z <= 230000.0d0))) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = x + (t * (y / (t - a)))
    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 <= -2.7e-48) || !(z <= 230000.0)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (t * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e-48) or not (z <= 230000.0):
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + (t * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e-48) || !(z <= 230000.0))
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.7e-48) || ~((z <= 230000.0)))
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + (t * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e-48], N[Not[LessEqual[z, 230000.0]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.70000000000000011e-48 or 2.3e5 < z

   1. Initial program 84.5%

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

      1. div-inv 84.5%

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

      2. *-commutative 84.5%

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

      3. associate-*l* 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in z around inf 79.6%

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

      1. associate-/l* 83.9%

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

   7. Simplified 83.9%

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

   if -2.70000000000000011e-48 < z < 2.3e5

   1. Initial program 84.6%

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

   3. Taylor expanded in z around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. associate-/l* 91.5%

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

      3. distribute-rgt-neg-in 91.5%

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

      4. distribute-frac-neg 91.5%

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

   5. Simplified 91.5%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-48} \lor \neg \left(z \leq 230000\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+188} \lor \neg \left(t \leq 2.15 \cdot 10^{+126}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.95e+188) (not (<= t 2.15e+126)))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.95e+188) || !(t <= 2.15e+126)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.95d+188)) .or. (.not. (t <= 2.15d+126))) then
        tmp = x + y
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.95e+188) || !(t <= 2.15e+126)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.95e+188) or not (t <= 2.15e+126):
		tmp = x + y
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.95e+188) || !(t <= 2.15e+126))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.95e+188) || ~((t <= 2.15e+126)))
		tmp = x + y;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.95e+188], N[Not[LessEqual[t, 2.15e+126]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.95e188 or 2.1500000000000001e126 < t

   1. Initial program 58.0%

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

   3. Taylor expanded in t around inf 83.6%

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

      1. +-commutative 83.6%

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

   5. Simplified 83.6%

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

   if -1.95e188 < t < 2.1500000000000001e126

   1. Initial program 94.0%

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

      1. div-inv 93.9%

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

      2. *-commutative 93.9%

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

      3. associate-*l* 97.8%

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

   4. Applied egg-rr 97.8%

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

   5. Taylor expanded in z around inf 86.2%

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

      1. associate-/l* 87.5%

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

   7. Simplified 87.5%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+188} \lor \neg \left(t \leq 2.15 \cdot 10^{+126}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.01 \cdot 10^{-25}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-156}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.01e-25)
   (- x (/ (* y z) t))
   (if (<= x 1.85e-156) (* (- z t) (/ y (- a t))) (+ x (* z (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.01e-25) {
		tmp = x - ((y * z) / t);
	} else if (x <= 1.85e-156) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = x + (z * (y / a));
	}
	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 (x <= (-1.01d-25)) then
        tmp = x - ((y * z) / t)
    else if (x <= 1.85d-156) then
        tmp = (z - t) * (y / (a - t))
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.01e-25) {
		tmp = x - ((y * z) / t);
	} else if (x <= 1.85e-156) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.01e-25:
		tmp = x - ((y * z) / t)
	elif x <= 1.85e-156:
		tmp = (z - t) * (y / (a - t))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.01e-25)
		tmp = Float64(x - Float64(Float64(y * z) / t));
	elseif (x <= 1.85e-156)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.01e-25)
		tmp = x - ((y * z) / t);
	elseif (x <= 1.85e-156)
		tmp = (z - t) * (y / (a - t));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.01e-25], N[(x - N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e-156], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.01000000000000001e-25

   1. Initial program 87.7%

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

   3. Taylor expanded in z around inf 90.4%

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

   4. Taylor expanded in a around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. unsub-neg 74.4%

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

   6. Simplified 74.4%

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

   if -1.01000000000000001e-25 < x < 1.85e-156

   1. Initial program 78.7%

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

   3. Taylor expanded in x around 0 60.6%

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

      1. *-rgt-identity 60.6%

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

      2. times-frac 77.5%

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

      3. /-rgt-identity 77.5%

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

   5. Simplified 77.5%

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

   if 1.85e-156 < x

   1. Initial program 88.5%

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

   3. Taylor expanded in t around 0 72.6%

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

      1. associate-/l* 74.8%

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

   5. Simplified 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-*l/ 72.6%

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

   7. Applied egg-rr 72.6%

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

      1. associate-/l* 75.8%

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

   9. Applied egg-rr 75.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.01 \cdot 10^{-25}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-156}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.044 \lor \neg \left(t \leq 490\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.044) (not (<= t 490.0))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.044) || !(t <= 490.0)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	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 <= (-0.044d0)) .or. (.not. (t <= 490.0d0))) then
        tmp = x + y
    else
        tmp = x + (z * (y / a))
    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 <= -0.044) || !(t <= 490.0)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.044) or not (t <= 490.0):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.044) || !(t <= 490.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -0.044) || ~((t <= 490.0)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.044], N[Not[LessEqual[t, 490.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.043999999999999997 or 490 < t

   1. Initial program 72.0%

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

   3. Taylor expanded in t around inf 73.7%

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

      1. +-commutative 73.7%

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

   5. Simplified 73.7%

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

   if -0.043999999999999997 < t < 490

   1. Initial program 94.7%

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

   3. Taylor expanded in t around 0 77.5%

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

      1. associate-/l* 79.4%

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

   5. Simplified 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-*l/ 77.5%

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

   7. Applied egg-rr 77.5%

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

      1. associate-/l* 81.4%

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

   9. Applied egg-rr 81.4%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.044 \lor \neg \left(t \leq 490\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.021 \lor \neg \left(t \leq 0.205\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.021) (not (<= t 0.205))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.021) || !(t <= 0.205)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	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 <= (-0.021d0)) .or. (.not. (t <= 0.205d0))) then
        tmp = x + y
    else
        tmp = x + (y * (z / a))
    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 <= -0.021) || !(t <= 0.205)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.021) or not (t <= 0.205):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.021) || !(t <= 0.205))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -0.021) || ~((t <= 0.205)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.021], N[Not[LessEqual[t, 0.205]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.0210000000000000013 or 0.204999999999999988 < t

   1. Initial program 72.0%

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

   3. Taylor expanded in t around inf 73.7%

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

      1. +-commutative 73.7%

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

   5. Simplified 73.7%

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

   if -0.0210000000000000013 < t < 0.204999999999999988

   1. Initial program 94.7%

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

   3. Taylor expanded in t around 0 77.5%

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

      1. associate-/l* 79.4%

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

   5. Simplified 79.4%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.021 \lor \neg \left(t \leq 0.205\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-91} \lor \neg \left(t \leq 2.6 \cdot 10^{+110}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7e-91) (not (<= t 2.6e+110))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7e-91) || !(t <= 2.6e+110)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7d-91)) .or. (.not. (t <= 2.6d+110))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7e-91) || !(t <= 2.6e+110)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7e-91) or not (t <= 2.6e+110):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7e-91) || !(t <= 2.6e+110))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7e-91) || ~((t <= 2.6e+110)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7e-91], N[Not[LessEqual[t, 2.6e+110]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -6.9999999999999997e-91 or 2.6e110 < t

   1. Initial program 71.8%

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

   3. Taylor expanded in t around inf 73.5%

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

      1. +-commutative 73.5%

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

   5. Simplified 73.5%

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

   if -6.9999999999999997e-91 < t < 2.6e110

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf 52.1%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-91} \lor \neg \left(t \leq 2.6 \cdot 10^{+110}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{a - t}{z - t}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (y / ((a - t) / (z - 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 / ((a - t) / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.6%

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

   1. associate-/l* 97.6%

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

   2. clear-num 97.6%

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

   3. un-div-inv 97.6%

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

4. Applied egg-rr 97.6%

   \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]
5. Add Preprocessing

Alternative 12: 50.2% accurate, 11.0× 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 84.6%

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

3. Taylor expanded in x around inf 49.7%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{a - t}{z - t}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (y / ((a - t) / (z - 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 / ((a - t) / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (+ x (/ y (/ (- a t) (- z t))))

  (+ x (/ (* y (- z t)) (- a t))))