Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Percentage Accurate: 67.7% → 90.7%

Time: 27.8s

Alternatives: 28

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-274}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{elif}\;t_2 \leq 10^{+261}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- y x) (- a t)) (- t z))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-274)
       t_2
       (if (<= t_2 0.0)
         (- y (/ (- y x) (/ t (- z a))))
         (if (<= t_2 1e+261) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) / (a - t)) * (t - z));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-274) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - ((y - x) / (t / (z - a)));
	} else if (t_2 <= 1e+261) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) / (a - t)) * (t - z));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-274) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - ((y - x) / (t / (z - a)));
	} else if (t_2 <= 1e+261) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - x) / (a - t)) * (t - z))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-274:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y - ((y - x) / (t / (z - a)))
	elif t_2 <= 1e+261:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) / Float64(a - t)) * Float64(t - z)))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-274)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y - Float64(Float64(y - x) / Float64(t / Float64(z - a))));
	elseif (t_2 <= 1e+261)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - x) / (a - t)) * (t - z));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-274)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y - ((y - x) / (t / (z - a)));
	elseif (t_2 <= 1e+261)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-274], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y - N[(N[(y - x), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+261], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 9.9999999999999993e260 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 43.3%

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

      1. associate-*l/ 81.5%

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

   3. Simplified 81.5%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.99999999999999966e-275 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999993e260

   1. Initial program 98.3%

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

   if -9.99999999999999966e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.1%

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

      1. associate-/l* 4.1%

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

   3. Simplified 4.1%

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

   4. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. div-sub 99.8%

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

      5. distribute-lft-out-- 99.8%

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

      6. associate-*r/ 99.8%

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

      7. mul-1-neg 99.8%

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

      8. unsub-neg 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

      10. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-274}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+261}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 2: 90.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-274}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 -1e-274)
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (if (<= t_1 0.0)
       (+ y (/ (- x y) (/ t (- z a))))
       (fma (/ (- z t) (- a t)) (- y x) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -1e-274) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else if (t_1 <= 0.0) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -1e-274)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-274], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.99999999999999966e-275

   1. Initial program 75.7%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   if -9.99999999999999966e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.1%

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

      1. associate-/l* 4.1%

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

   3. Simplified 4.1%

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

   4. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. div-sub 99.8%

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

      5. distribute-lft-out-- 99.8%

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

      6. associate-*r/ 99.8%

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

      7. mul-1-neg 99.8%

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

      8. unsub-neg 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

      10. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 76.3%

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

      1. +-commutative 76.3%

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

      2. *-commutative 76.3%

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

      3. associate-/l* 84.3%

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

      4. associate-/r/ 89.5%

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

      5. fma-def 89.5%

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

   3. Simplified 89.5%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-274}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \]

Alternative 3: 90.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-274}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t} - \frac{t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 -1e-274)
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (if (<= t_1 0.0)
       (- y (/ (- y x) (/ t (- z a))))
       (- x (/ (- x y) (- (/ a (- z t)) (/ t (- z t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -1e-274) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else if (t_1 <= 0.0) {
		tmp = y - ((y - x) / (t / (z - a)));
	} else {
		tmp = x - ((x - y) / ((a / (z - t)) - (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) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * (z - t)) / (a - t))
    if (t_1 <= (-1d-274)) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else if (t_1 <= 0.0d0) then
        tmp = y - ((y - x) / (t / (z - a)))
    else
        tmp = x - ((x - y) / ((a / (z - t)) - (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 t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -1e-274) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else if (t_1 <= 0.0) {
		tmp = y - ((y - x) / (t / (z - a)));
	} else {
		tmp = x - ((x - y) / ((a / (z - t)) - (t / (z - t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -1e-274:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	elif t_1 <= 0.0:
		tmp = y - ((y - x) / (t / (z - a)))
	else:
		tmp = x - ((x - y) / ((a / (z - t)) - (t / (z - t))))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -1e-274)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	elseif (t_1 <= 0.0)
		tmp = Float64(y - Float64(Float64(y - x) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a / Float64(z - t)) - Float64(t / Float64(z - t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -1e-274)
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	elseif (t_1 <= 0.0)
		tmp = y - ((y - x) / (t / (z - a)));
	else
		tmp = x - ((x - y) / ((a / (z - t)) - (t / (z - t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-274], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y - N[(N[(y - x), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision] - N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.99999999999999966e-275

   1. Initial program 75.7%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   if -9.99999999999999966e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.1%

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

      1. associate-/l* 4.1%

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

   3. Simplified 4.1%

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

   4. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. div-sub 99.8%

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

      5. distribute-lft-out-- 99.8%

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

      6. associate-*r/ 99.8%

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

      7. mul-1-neg 99.8%

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

      8. unsub-neg 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

      10. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 76.3%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

      1. div-sub 89.4%

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

   5. Applied egg-rr 89.4%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-274}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t} - \frac{t}{z - t}}\\ \end{array} \]

Alternative 4: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-274} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -1e-274) (not (<= t_1 0.0)))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (/ (- x y) (/ t (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-274) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + ((x - y) / (t / (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) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * (z - t)) / (a - t))
    if ((t_1 <= (-1d-274)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + ((x - y) / (t / (z - a)))
    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 - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-274) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if (t_1 <= -1e-274) or not (t_1 <= 0.0):
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + ((x - y) / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -1e-274) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -1e-274) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + ((x - y) / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-274], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.99999999999999966e-275 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 76.0%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   if -9.99999999999999966e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.1%

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

      1. associate-/l* 4.1%

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

   3. Simplified 4.1%

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

   4. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. div-sub 99.8%

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

      5. distribute-lft-out-- 99.8%

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

      6. associate-*r/ 99.8%

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

      7. mul-1-neg 99.8%

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

      8. unsub-neg 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

      10. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-274} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 5: 64.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{a - t}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ t_3 := x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-82}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+62}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z (- a t))))
        (t_2 (* y (/ (- z t) (- a t))))
        (t_3 (+ x (/ z (/ a (- y x))))))
   (if (<= t -3.9e+136)
     t_2
     (if (<= t -7.5e-19)
       t_1
       (if (<= t -2.35e-82)
         (* (- z t) (/ y (- a t)))
         (if (<= t 2.8e-84)
           t_3
           (if (<= t 5e-15) t_1 (if (<= t 3.9e+62) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) * (z / (a - t));
	double t_2 = y * ((z - t) / (a - t));
	double t_3 = x + (z / (a / (y - x)));
	double tmp;
	if (t <= -3.9e+136) {
		tmp = t_2;
	} else if (t <= -7.5e-19) {
		tmp = t_1;
	} else if (t <= -2.35e-82) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 2.8e-84) {
		tmp = t_3;
	} else if (t <= 5e-15) {
		tmp = t_1;
	} else if (t <= 3.9e+62) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = (y - x) * (z / (a - t))
    t_2 = y * ((z - t) / (a - t))
    t_3 = x + (z / (a / (y - x)))
    if (t <= (-3.9d+136)) then
        tmp = t_2
    else if (t <= (-7.5d-19)) then
        tmp = t_1
    else if (t <= (-2.35d-82)) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= 2.8d-84) then
        tmp = t_3
    else if (t <= 5d-15) then
        tmp = t_1
    else if (t <= 3.9d+62) then
        tmp = t_3
    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 = (y - x) * (z / (a - t));
	double t_2 = y * ((z - t) / (a - t));
	double t_3 = x + (z / (a / (y - x)));
	double tmp;
	if (t <= -3.9e+136) {
		tmp = t_2;
	} else if (t <= -7.5e-19) {
		tmp = t_1;
	} else if (t <= -2.35e-82) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 2.8e-84) {
		tmp = t_3;
	} else if (t <= 5e-15) {
		tmp = t_1;
	} else if (t <= 3.9e+62) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - x) * (z / (a - t))
	t_2 = y * ((z - t) / (a - t))
	t_3 = x + (z / (a / (y - x)))
	tmp = 0
	if t <= -3.9e+136:
		tmp = t_2
	elif t <= -7.5e-19:
		tmp = t_1
	elif t <= -2.35e-82:
		tmp = (z - t) * (y / (a - t))
	elif t <= 2.8e-84:
		tmp = t_3
	elif t <= 5e-15:
		tmp = t_1
	elif t <= 3.9e+62:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - x) * Float64(z / Float64(a - t)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_3 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	tmp = 0.0
	if (t <= -3.9e+136)
		tmp = t_2;
	elseif (t <= -7.5e-19)
		tmp = t_1;
	elseif (t <= -2.35e-82)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= 2.8e-84)
		tmp = t_3;
	elseif (t <= 5e-15)
		tmp = t_1;
	elseif (t <= 3.9e+62)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - x) * (z / (a - t));
	t_2 = y * ((z - t) / (a - t));
	t_3 = x + (z / (a / (y - x)));
	tmp = 0.0;
	if (t <= -3.9e+136)
		tmp = t_2;
	elseif (t <= -7.5e-19)
		tmp = t_1;
	elseif (t <= -2.35e-82)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= 2.8e-84)
		tmp = t_3;
	elseif (t <= 5e-15)
		tmp = t_1;
	elseif (t <= 3.9e+62)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+136], t$95$2, If[LessEqual[t, -7.5e-19], t$95$1, If[LessEqual[t, -2.35e-82], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-84], t$95$3, If[LessEqual[t, 5e-15], t$95$1, If[LessEqual[t, 3.9e+62], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.90000000000000019e136 or 3.9e62 < t

   1. Initial program 39.6%

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

      1. associate-/l* 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in x around 0 43.7%

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

      1. associate-*r/ 71.5%

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

   6. Simplified 71.5%

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

   if -3.90000000000000019e136 < t < -7.49999999999999957e-19 or 2.79999999999999982e-84 < t < 4.99999999999999999e-15

   1. Initial program 78.2%

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

      1. associate-/l* 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in z around inf 61.1%

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

      1. div-sub 61.1%

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

      2. associate-*r/ 58.4%

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

      3. associate-/l* 61.8%

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

   6. Simplified 61.8%

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

      1. associate-/r/ 63.1%

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

   8. Applied egg-rr 63.1%

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

   if -7.49999999999999957e-19 < t < -2.35e-82

   1. Initial program 80.8%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

      1. div-sub 87.0%

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

   5. Applied egg-rr 87.0%

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

   6. Taylor expanded in x around 0 61.1%

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

      1. div-sub 61.1%

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

      2. associate-/r/ 61.2%

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

      3. *-commutative 61.2%

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

   8. Simplified 61.2%

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

   if -2.35e-82 < t < 2.79999999999999982e-84 or 4.99999999999999999e-15 < t < 3.9e62

   1. Initial program 89.6%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in t around 0 75.9%

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

      1. associate-/l* 80.4%

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

   6. Simplified 80.4%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+136}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-19}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-82}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-15}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 6: 64.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{a - t}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-82}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z (- a t)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -3.2e+130)
     t_2
     (if (<= t -1.45e-15)
       t_1
       (if (<= t -2.3e-82)
         (* (- z t) (/ y (- a t)))
         (if (<= t 7e-84)
           (+ x (/ z (/ a (- y x))))
           (if (<= t 5.4e-9)
             t_1
             (if (<= t 7e+61) (+ x (/ (- y x) (/ a z))) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) * (z / (a - t));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -3.2e+130) {
		tmp = t_2;
	} else if (t <= -1.45e-15) {
		tmp = t_1;
	} else if (t <= -2.3e-82) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 7e-84) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 5.4e-9) {
		tmp = t_1;
	} else if (t <= 7e+61) {
		tmp = x + ((y - x) / (a / z));
	} 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 = (y - x) * (z / (a - t))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-3.2d+130)) then
        tmp = t_2
    else if (t <= (-1.45d-15)) then
        tmp = t_1
    else if (t <= (-2.3d-82)) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= 7d-84) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= 5.4d-9) then
        tmp = t_1
    else if (t <= 7d+61) then
        tmp = x + ((y - x) / (a / z))
    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 = (y - x) * (z / (a - t));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -3.2e+130) {
		tmp = t_2;
	} else if (t <= -1.45e-15) {
		tmp = t_1;
	} else if (t <= -2.3e-82) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 7e-84) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 5.4e-9) {
		tmp = t_1;
	} else if (t <= 7e+61) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - x) * (z / (a - t))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -3.2e+130:
		tmp = t_2
	elif t <= -1.45e-15:
		tmp = t_1
	elif t <= -2.3e-82:
		tmp = (z - t) * (y / (a - t))
	elif t <= 7e-84:
		tmp = x + (z / (a / (y - x)))
	elif t <= 5.4e-9:
		tmp = t_1
	elif t <= 7e+61:
		tmp = x + ((y - x) / (a / z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - x) * Float64(z / Float64(a - t)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -3.2e+130)
		tmp = t_2;
	elseif (t <= -1.45e-15)
		tmp = t_1;
	elseif (t <= -2.3e-82)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= 7e-84)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= 5.4e-9)
		tmp = t_1;
	elseif (t <= 7e+61)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - x) * (z / (a - t));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -3.2e+130)
		tmp = t_2;
	elseif (t <= -1.45e-15)
		tmp = t_1;
	elseif (t <= -2.3e-82)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= 7e-84)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= 5.4e-9)
		tmp = t_1;
	elseif (t <= 7e+61)
		tmp = x + ((y - x) / (a / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e+130], t$95$2, If[LessEqual[t, -1.45e-15], t$95$1, If[LessEqual[t, -2.3e-82], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-84], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e-9], t$95$1, If[LessEqual[t, 7e+61], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.2e130 or 7.00000000000000036e61 < t

   1. Initial program 39.6%

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

      1. associate-/l* 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in x around 0 43.7%

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

      1. associate-*r/ 71.5%

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

   6. Simplified 71.5%

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

   if -3.2e130 < t < -1.45000000000000009e-15 or 7.0000000000000002e-84 < t < 5.4000000000000004e-9

   1. Initial program 78.2%

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

      1. associate-/l* 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in z around inf 61.1%

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

      1. div-sub 61.1%

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

      2. associate-*r/ 58.4%

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

      3. associate-/l* 61.8%

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

   6. Simplified 61.8%

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

      1. associate-/r/ 63.1%

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

   8. Applied egg-rr 63.1%

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

   if -1.45000000000000009e-15 < t < -2.29999999999999997e-82

   1. Initial program 80.8%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

      1. div-sub 87.0%

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

   5. Applied egg-rr 87.0%

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

   6. Taylor expanded in x around 0 61.1%

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

      1. div-sub 61.1%

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

      2. associate-/r/ 61.2%

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

      3. *-commutative 61.2%

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

   8. Simplified 61.2%

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

   if -2.29999999999999997e-82 < t < 7.0000000000000002e-84

   1. Initial program 92.7%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in t around 0 79.3%

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

      1. associate-/l* 83.7%

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

   6. Simplified 83.7%

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

   if 5.4000000000000004e-9 < t < 7.00000000000000036e61

   1. Initial program 74.4%

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

      1. associate-/l* 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in t around 0 64.5%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+130}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-15}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-82}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-9}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 7: 52.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - y \cdot \frac{z}{t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-267}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{-x}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* y (/ z t)))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -8.5e-51)
     t_2
     (if (<= a -9e-128)
       t_1
       (if (<= a -2.35e-267)
         (* (/ z t) (- x y))
         (if (<= a 5.5e-156)
           t_1
           (if (<= a 9.5e-42)
             (/ (- x) (/ (- a t) z))
             (if (<= a 3.3e+57) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (y * (z / t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -8.5e-51) {
		tmp = t_2;
	} else if (a <= -9e-128) {
		tmp = t_1;
	} else if (a <= -2.35e-267) {
		tmp = (z / t) * (x - y);
	} else if (a <= 5.5e-156) {
		tmp = t_1;
	} else if (a <= 9.5e-42) {
		tmp = -x / ((a - t) / z);
	} else if (a <= 3.3e+57) {
		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 = y - (y * (z / t))
    t_2 = x + (y / (a / z))
    if (a <= (-8.5d-51)) then
        tmp = t_2
    else if (a <= (-9d-128)) then
        tmp = t_1
    else if (a <= (-2.35d-267)) then
        tmp = (z / t) * (x - y)
    else if (a <= 5.5d-156) then
        tmp = t_1
    else if (a <= 9.5d-42) then
        tmp = -x / ((a - t) / z)
    else if (a <= 3.3d+57) 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 = y - (y * (z / t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -8.5e-51) {
		tmp = t_2;
	} else if (a <= -9e-128) {
		tmp = t_1;
	} else if (a <= -2.35e-267) {
		tmp = (z / t) * (x - y);
	} else if (a <= 5.5e-156) {
		tmp = t_1;
	} else if (a <= 9.5e-42) {
		tmp = -x / ((a - t) / z);
	} else if (a <= 3.3e+57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (y * (z / t))
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -8.5e-51:
		tmp = t_2
	elif a <= -9e-128:
		tmp = t_1
	elif a <= -2.35e-267:
		tmp = (z / t) * (x - y)
	elif a <= 5.5e-156:
		tmp = t_1
	elif a <= 9.5e-42:
		tmp = -x / ((a - t) / z)
	elif a <= 3.3e+57:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(y * Float64(z / t)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -8.5e-51)
		tmp = t_2;
	elseif (a <= -9e-128)
		tmp = t_1;
	elseif (a <= -2.35e-267)
		tmp = Float64(Float64(z / t) * Float64(x - y));
	elseif (a <= 5.5e-156)
		tmp = t_1;
	elseif (a <= 9.5e-42)
		tmp = Float64(Float64(-x) / Float64(Float64(a - t) / z));
	elseif (a <= 3.3e+57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (y * (z / t));
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -8.5e-51)
		tmp = t_2;
	elseif (a <= -9e-128)
		tmp = t_1;
	elseif (a <= -2.35e-267)
		tmp = (z / t) * (x - y);
	elseif (a <= 5.5e-156)
		tmp = t_1;
	elseif (a <= 9.5e-42)
		tmp = -x / ((a - t) / z);
	elseif (a <= 3.3e+57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.5e-51], t$95$2, If[LessEqual[a, -9e-128], t$95$1, If[LessEqual[a, -2.35e-267], N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-156], t$95$1, If[LessEqual[a, 9.5e-42], N[((-x) / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+57], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.50000000000000036e-51 or 3.3000000000000001e57 < a

   1. Initial program 76.1%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around inf 81.6%

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

   5. Taylor expanded in t around 0 60.0%

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

      1. associate-/l* 63.4%

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

   7. Simplified 63.4%

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

   if -8.50000000000000036e-51 < a < -8.9999999999999998e-128 or -2.3500000000000001e-267 < a < 5.4999999999999998e-156 or 9.49999999999999948e-42 < a < 3.3000000000000001e57

   1. Initial program 66.3%

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

      1. associate-/l* 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in t around inf 71.1%

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

      1. associate--l+ 71.1%

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

      2. associate-*r/ 71.1%

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

      3. associate-*r/ 71.1%

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

      4. div-sub 72.5%

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

      5. distribute-lft-out-- 72.5%

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

      6. associate-*r/ 72.5%

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

      7. mul-1-neg 72.5%

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

      8. unsub-neg 72.5%

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

      9. distribute-rgt-out-- 72.5%

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

      10. associate-/l* 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in z around inf 76.8%

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

   8. Taylor expanded in y around inf 56.3%

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

      1. associate-*r/ 63.1%

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

   10. Simplified 63.1%

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

   if -8.9999999999999998e-128 < a < -2.3500000000000001e-267

   1. Initial program 62.7%

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

      1. associate-/l* 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in t around inf 68.8%

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

      1. associate--l+ 68.8%

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

      2. associate-*r/ 68.8%

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

      3. associate-*r/ 68.8%

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

      4. div-sub 72.0%

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

      5. distribute-lft-out-- 72.0%

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

      6. associate-*r/ 72.0%

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

      7. mul-1-neg 72.0%

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

      8. unsub-neg 72.0%

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

      9. distribute-rgt-out-- 72.0%

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

      10. associate-/l* 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in z around inf 74.7%

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

   8. Taylor expanded in t around 0 43.5%

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

      1. mul-1-neg 43.5%

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

      2. associate-*l/ 52.6%

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

      3. *-commutative 52.6%

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

      4. distribute-rgt-neg-in 52.6%

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

      5. distribute-neg-frac 52.6%

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

   10. Simplified 52.6%

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

   if 5.4999999999999998e-156 < a < 9.49999999999999948e-42

   1. Initial program 70.3%

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

      1. associate-/l* 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in z around inf 70.0%

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

      1. div-sub 73.1%

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

      2. associate-*r/ 67.2%

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

      3. associate-/l* 73.1%

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

   6. Simplified 73.1%

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

   7. Taylor expanded in y around 0 55.4%

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

      1. mul-1-neg 55.4%

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

      2. associate-/l* 58.1%

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

   9. Simplified 58.1%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-51}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-128}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-267}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-156}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{-x}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+57}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 8: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-133}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-40}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ y (- a t)) (- t z)))))
   (if (<= a -1.65e-41)
     t_1
     (if (<= a 9.2e-133)
       (+ y (/ (- x y) (/ t z)))
       (if (<= a 2e-40)
         (/ z (/ (- a t) (- y x)))
         (if (<= a 7.6e+59) (* y (/ (- z t) (- a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (a <= -1.65e-41) {
		tmp = t_1;
	} else if (a <= 9.2e-133) {
		tmp = y + ((x - y) / (t / z));
	} else if (a <= 2e-40) {
		tmp = z / ((a - t) / (y - x));
	} else if (a <= 7.6e+59) {
		tmp = y * ((z - 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) :: tmp
    t_1 = x - ((y / (a - t)) * (t - z))
    if (a <= (-1.65d-41)) then
        tmp = t_1
    else if (a <= 9.2d-133) then
        tmp = y + ((x - y) / (t / z))
    else if (a <= 2d-40) then
        tmp = z / ((a - t) / (y - x))
    else if (a <= 7.6d+59) then
        tmp = y * ((z - 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 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (a <= -1.65e-41) {
		tmp = t_1;
	} else if (a <= 9.2e-133) {
		tmp = y + ((x - y) / (t / z));
	} else if (a <= 2e-40) {
		tmp = z / ((a - t) / (y - x));
	} else if (a <= 7.6e+59) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y / (a - t)) * (t - z))
	tmp = 0
	if a <= -1.65e-41:
		tmp = t_1
	elif a <= 9.2e-133:
		tmp = y + ((x - y) / (t / z))
	elif a <= 2e-40:
		tmp = z / ((a - t) / (y - x))
	elif a <= 7.6e+59:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)))
	tmp = 0.0
	if (a <= -1.65e-41)
		tmp = t_1;
	elseif (a <= 9.2e-133)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	elseif (a <= 2e-40)
		tmp = Float64(z / Float64(Float64(a - t) / Float64(y - x)));
	elseif (a <= 7.6e+59)
		tmp = Float64(y * Float64(Float64(z - t) / 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 / (a - t)) * (t - z));
	tmp = 0.0;
	if (a <= -1.65e-41)
		tmp = t_1;
	elseif (a <= 9.2e-133)
		tmp = y + ((x - y) / (t / z));
	elseif (a <= 2e-40)
		tmp = z / ((a - t) / (y - x));
	elseif (a <= 7.6e+59)
		tmp = y * ((z - t) / (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[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e-41], t$95$1, If[LessEqual[a, 9.2e-133], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e-40], N[(z / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e+59], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.65000000000000012e-41 or 7.6000000000000002e59 < a

   1. Initial program 75.2%

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

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around inf 81.8%

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

   if -1.65000000000000012e-41 < a < 9.2000000000000001e-133

   1. Initial program 65.9%

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

      1. associate-/l* 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in t around inf 76.3%

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

      1. associate--l+ 76.4%

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

      2. associate-*r/ 76.4%

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

      3. associate-*r/ 76.4%

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

      4. div-sub 78.5%

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

      5. distribute-lft-out-- 78.5%

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

      6. associate-*r/ 78.5%

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

      7. mul-1-neg 78.5%

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

      8. unsub-neg 78.5%

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

      9. distribute-rgt-out-- 78.5%

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

      10. associate-/l* 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in z around inf 82.0%

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

   if 9.2000000000000001e-133 < a < 1.9999999999999999e-40

   1. Initial program 70.8%

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

      1. associate-/l* 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in z around inf 70.3%

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

      1. div-sub 74.1%

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

      2. associate-*r/ 66.9%

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

      3. associate-/l* 74.1%

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

   6. Simplified 74.1%

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

   if 1.9999999999999999e-40 < a < 7.6000000000000002e59

   1. Initial program 69.0%

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

      1. associate-/l* 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in x around 0 53.6%

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

      1. associate-*r/ 63.3%

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

   6. Simplified 63.3%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-41}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-133}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-40}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 9: 51.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+131}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+49}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-291}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-283}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+133}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))))
   (if (<= t -3.6e+131)
     y
     (if (<= t -1.05e+49)
       (* (- z a) (/ x t))
       (if (<= t -6.5e-291)
         t_1
         (if (<= t 1.8e-283)
           (* z (/ (- y x) a))
           (if (<= t 2.2e-61) t_1 (if (<= t 1.02e+133) (+ x y) y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (t <= -3.6e+131) {
		tmp = y;
	} else if (t <= -1.05e+49) {
		tmp = (z - a) * (x / t);
	} else if (t <= -6.5e-291) {
		tmp = t_1;
	} else if (t <= 1.8e-283) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.2e-61) {
		tmp = t_1;
	} else if (t <= 1.02e+133) {
		tmp = x + y;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    if (t <= (-3.6d+131)) then
        tmp = y
    else if (t <= (-1.05d+49)) then
        tmp = (z - a) * (x / t)
    else if (t <= (-6.5d-291)) then
        tmp = t_1
    else if (t <= 1.8d-283) then
        tmp = z * ((y - x) / a)
    else if (t <= 2.2d-61) then
        tmp = t_1
    else if (t <= 1.02d+133) then
        tmp = x + y
    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 t_1 = x + (y / (a / z));
	double tmp;
	if (t <= -3.6e+131) {
		tmp = y;
	} else if (t <= -1.05e+49) {
		tmp = (z - a) * (x / t);
	} else if (t <= -6.5e-291) {
		tmp = t_1;
	} else if (t <= 1.8e-283) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.2e-61) {
		tmp = t_1;
	} else if (t <= 1.02e+133) {
		tmp = x + y;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	tmp = 0
	if t <= -3.6e+131:
		tmp = y
	elif t <= -1.05e+49:
		tmp = (z - a) * (x / t)
	elif t <= -6.5e-291:
		tmp = t_1
	elif t <= 1.8e-283:
		tmp = z * ((y - x) / a)
	elif t <= 2.2e-61:
		tmp = t_1
	elif t <= 1.02e+133:
		tmp = x + y
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (t <= -3.6e+131)
		tmp = y;
	elseif (t <= -1.05e+49)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif (t <= -6.5e-291)
		tmp = t_1;
	elseif (t <= 1.8e-283)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 2.2e-61)
		tmp = t_1;
	elseif (t <= 1.02e+133)
		tmp = Float64(x + y);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	tmp = 0.0;
	if (t <= -3.6e+131)
		tmp = y;
	elseif (t <= -1.05e+49)
		tmp = (z - a) * (x / t);
	elseif (t <= -6.5e-291)
		tmp = t_1;
	elseif (t <= 1.8e-283)
		tmp = z * ((y - x) / a);
	elseif (t <= 2.2e-61)
		tmp = t_1;
	elseif (t <= 1.02e+133)
		tmp = x + y;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+131], y, If[LessEqual[t, -1.05e+49], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e-291], t$95$1, If[LessEqual[t, 1.8e-283], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e-61], t$95$1, If[LessEqual[t, 1.02e+133], N[(x + y), $MachinePrecision], y]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.60000000000000031e131 or 1.02e133 < t

   1. Initial program 32.9%

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

      1. associate-/l* 68.3%

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

   3. Simplified 68.3%

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

   4. Taylor expanded in t around inf 60.7%

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

   if -3.60000000000000031e131 < t < -1.05000000000000005e49

   1. Initial program 72.6%

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

      1. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in t around inf 73.6%

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

      1. associate--l+ 73.6%

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

      2. associate-*r/ 73.6%

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

      3. associate-*r/ 73.6%

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

      4. div-sub 73.6%

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

      5. distribute-lft-out-- 73.6%

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

      6. associate-*r/ 73.6%

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

      7. mul-1-neg 73.6%

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

      8. unsub-neg 73.6%

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

      9. distribute-rgt-out-- 73.6%

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

      10. associate-/l* 82.4%

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

   6. Simplified 82.4%

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

   7. Taylor expanded in y around 0 56.0%

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

      1. associate-/l* 64.7%

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

      2. associate-/r/ 64.5%

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

   9. Simplified 64.5%

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

   if -1.05000000000000005e49 < t < -6.50000000000000002e-291 or 1.8e-283 < t < 2.20000000000000009e-61

   1. Initial program 88.3%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in y around inf 70.9%

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

   5. Taylor expanded in t around 0 55.1%

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

      1. associate-/l* 58.9%

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

   7. Simplified 58.9%

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

   if -6.50000000000000002e-291 < t < 1.8e-283

   1. Initial program 99.7%

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

      1. associate-/l* 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in z around inf 71.5%

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

   5. Taylor expanded in t around 0 71.5%

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

      1. div-sub 81.5%

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

   7. Simplified 81.5%

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

   if 2.20000000000000009e-61 < t < 1.02e133

   1. Initial program 73.9%

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

      1. associate-*l/ 82.8%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in y around inf 63.7%

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

   5. Taylor expanded in t around inf 42.4%

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

      1. +-commutative 42.4%

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

   7. Simplified 42.4%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+131}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+49}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-291}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-283}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-61}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+133}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 10: 60.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-53}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -2.1e+120)
     t_2
     (if (<= a -2.8e-111)
       t_1
       (if (<= a 5.5e-53) (+ y (* z (/ x t))) (if (<= a 9.2e+60) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -2.1e+120) {
		tmp = t_2;
	} else if (a <= -2.8e-111) {
		tmp = t_1;
	} else if (a <= 5.5e-53) {
		tmp = y + (z * (x / t));
	} else if (a <= 9.2e+60) {
		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 = y * ((z - t) / (a - t))
    t_2 = x + (y / (a / z))
    if (a <= (-2.1d+120)) then
        tmp = t_2
    else if (a <= (-2.8d-111)) then
        tmp = t_1
    else if (a <= 5.5d-53) then
        tmp = y + (z * (x / t))
    else if (a <= 9.2d+60) 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 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -2.1e+120) {
		tmp = t_2;
	} else if (a <= -2.8e-111) {
		tmp = t_1;
	} else if (a <= 5.5e-53) {
		tmp = y + (z * (x / t));
	} else if (a <= 9.2e+60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -2.1e+120:
		tmp = t_2
	elif a <= -2.8e-111:
		tmp = t_1
	elif a <= 5.5e-53:
		tmp = y + (z * (x / t))
	elif a <= 9.2e+60:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -2.1e+120)
		tmp = t_2;
	elseif (a <= -2.8e-111)
		tmp = t_1;
	elseif (a <= 5.5e-53)
		tmp = Float64(y + Float64(z * Float64(x / t)));
	elseif (a <= 9.2e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -2.1e+120)
		tmp = t_2;
	elseif (a <= -2.8e-111)
		tmp = t_1;
	elseif (a <= 5.5e-53)
		tmp = y + (z * (x / t));
	elseif (a <= 9.2e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+120], t$95$2, If[LessEqual[a, -2.8e-111], t$95$1, If[LessEqual[a, 5.5e-53], N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e+60], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1e120 or 9.20000000000000068e60 < a

   1. Initial program 75.1%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in y around inf 85.4%

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

   5. Taylor expanded in t around 0 68.5%

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

      1. associate-/l* 71.1%

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

   7. Simplified 71.1%

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

   if -2.1e120 < a < -2.79999999999999995e-111 or 5.50000000000000023e-53 < a < 9.20000000000000068e60

   1. Initial program 72.3%

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

      1. associate-/l* 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in x around 0 46.5%

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

      1. associate-*r/ 62.3%

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

   6. Simplified 62.3%

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

   if -2.79999999999999995e-111 < a < 5.50000000000000023e-53

   1. Initial program 65.8%

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

      1. associate-/l* 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in t around inf 72.4%

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

      1. associate--l+ 72.5%

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

      2. associate-*r/ 72.5%

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

      3. associate-*r/ 72.5%

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

      4. div-sub 73.5%

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

      5. distribute-lft-out-- 73.5%

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

      6. associate-*r/ 73.5%

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

      7. mul-1-neg 73.5%

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

      8. unsub-neg 73.5%

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

      9. distribute-rgt-out-- 73.5%

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

      10. associate-/l* 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in z around inf 78.6%

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

   8. Taylor expanded in y around 0 60.5%

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

      1. mul-1-neg 60.5%

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

      2. associate-/l* 66.3%

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

      3. associate-/r/ 64.5%

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

      4. distribute-rgt-neg-in 64.5%

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

   10. Simplified 64.5%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+120}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-111}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-53}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 11: 58.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-42}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -1.1e+124)
     t_2
     (if (<= a -1.75e-143)
       t_1
       (if (<= a 6.6e-42)
         (* (- y x) (/ z (- a t)))
         (if (<= a 1.85e+60) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -1.1e+124) {
		tmp = t_2;
	} else if (a <= -1.75e-143) {
		tmp = t_1;
	} else if (a <= 6.6e-42) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 1.85e+60) {
		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 = y * ((z - t) / (a - t))
    t_2 = x + (y / (a / z))
    if (a <= (-1.1d+124)) then
        tmp = t_2
    else if (a <= (-1.75d-143)) then
        tmp = t_1
    else if (a <= 6.6d-42) then
        tmp = (y - x) * (z / (a - t))
    else if (a <= 1.85d+60) 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 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -1.1e+124) {
		tmp = t_2;
	} else if (a <= -1.75e-143) {
		tmp = t_1;
	} else if (a <= 6.6e-42) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 1.85e+60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -1.1e+124:
		tmp = t_2
	elif a <= -1.75e-143:
		tmp = t_1
	elif a <= 6.6e-42:
		tmp = (y - x) * (z / (a - t))
	elif a <= 1.85e+60:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -1.1e+124)
		tmp = t_2;
	elseif (a <= -1.75e-143)
		tmp = t_1;
	elseif (a <= 6.6e-42)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (a <= 1.85e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -1.1e+124)
		tmp = t_2;
	elseif (a <= -1.75e-143)
		tmp = t_1;
	elseif (a <= 6.6e-42)
		tmp = (y - x) * (z / (a - t));
	elseif (a <= 1.85e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.1e+124], t$95$2, If[LessEqual[a, -1.75e-143], t$95$1, If[LessEqual[a, 6.6e-42], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+60], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.1e124 or 1.84999999999999994e60 < a

   1. Initial program 75.1%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in y around inf 85.4%

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

   5. Taylor expanded in t around 0 68.5%

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

      1. associate-/l* 71.1%

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

   7. Simplified 71.1%

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

   if -1.1e124 < a < -1.75000000000000003e-143 or 6.6000000000000005e-42 < a < 1.84999999999999994e60

   1. Initial program 73.0%

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

      1. associate-/l* 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in x around 0 49.3%

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

      1. associate-*r/ 63.8%

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

   6. Simplified 63.8%

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

   if -1.75000000000000003e-143 < a < 6.6000000000000005e-42

   1. Initial program 64.7%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in z around inf 60.7%

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

      1. div-sub 62.8%

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

      2. associate-*r/ 58.6%

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

      3. associate-/l* 63.2%

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

   6. Simplified 63.2%

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

      1. associate-/r/ 63.7%

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

   8. Applied egg-rr 63.7%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+124}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-143}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-42}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 12: 61.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -8 \cdot 10^{+120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-41}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* (- z t) (/ y a)))))
   (if (<= a -8e+120)
     t_2
     (if (<= a -8.5e-142)
       t_1
       (if (<= a 1.25e-41)
         (* (- y x) (/ z (- a t)))
         (if (<= a 6e+66) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((z - t) * (y / a));
	double tmp;
	if (a <= -8e+120) {
		tmp = t_2;
	} else if (a <= -8.5e-142) {
		tmp = t_1;
	} else if (a <= 1.25e-41) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 6e+66) {
		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 = y * ((z - t) / (a - t))
    t_2 = x + ((z - t) * (y / a))
    if (a <= (-8d+120)) then
        tmp = t_2
    else if (a <= (-8.5d-142)) then
        tmp = t_1
    else if (a <= 1.25d-41) then
        tmp = (y - x) * (z / (a - t))
    else if (a <= 6d+66) 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 = y * ((z - t) / (a - t));
	double t_2 = x + ((z - t) * (y / a));
	double tmp;
	if (a <= -8e+120) {
		tmp = t_2;
	} else if (a <= -8.5e-142) {
		tmp = t_1;
	} else if (a <= 1.25e-41) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 6e+66) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + ((z - t) * (y / a))
	tmp = 0
	if a <= -8e+120:
		tmp = t_2
	elif a <= -8.5e-142:
		tmp = t_1
	elif a <= 1.25e-41:
		tmp = (y - x) * (z / (a - t))
	elif a <= 6e+66:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(Float64(z - t) * Float64(y / a)))
	tmp = 0.0
	if (a <= -8e+120)
		tmp = t_2;
	elseif (a <= -8.5e-142)
		tmp = t_1;
	elseif (a <= 1.25e-41)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (a <= 6e+66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + ((z - t) * (y / a));
	tmp = 0.0;
	if (a <= -8e+120)
		tmp = t_2;
	elseif (a <= -8.5e-142)
		tmp = t_1;
	elseif (a <= 1.25e-41)
		tmp = (y - x) * (z / (a - t));
	elseif (a <= 6e+66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e+120], t$95$2, If[LessEqual[a, -8.5e-142], t$95$1, If[LessEqual[a, 1.25e-41], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+66], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.9999999999999998e120 or 6.00000000000000005e66 < a

   1. Initial program 74.5%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in y around inf 85.0%

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

   5. Taylor expanded in a around inf 80.3%

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

   if -7.9999999999999998e120 < a < -8.4999999999999996e-142 or 1.2499999999999999e-41 < a < 6.00000000000000005e66

   1. Initial program 73.7%

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

      1. associate-/l* 84.7%

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

   3. Simplified 84.7%

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

   4. Taylor expanded in x around 0 49.3%

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

      1. associate-*r/ 63.5%

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

   6. Simplified 63.5%

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

   if -8.4999999999999996e-142 < a < 1.2499999999999999e-41

   1. Initial program 64.7%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in z around inf 60.7%

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

      1. div-sub 62.8%

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

      2. associate-*r/ 58.6%

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

      3. associate-/l* 63.2%

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

   6. Simplified 63.2%

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

      1. associate-/r/ 63.7%

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

   8. Applied egg-rr 63.7%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+120}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-142}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-41}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 13: 61.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{+120}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.68 \cdot 10^{-40}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= a -1.2e+120)
     (+ x (/ y (/ a (- z t))))
     (if (<= a -2.1e-143)
       t_1
       (if (<= a 1.68e-40)
         (* (- y x) (/ z (- a t)))
         (if (<= a 1.05e+67) t_1 (+ x (* (- z t) (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -1.2e+120) {
		tmp = x + (y / (a / (z - t)));
	} else if (a <= -2.1e-143) {
		tmp = t_1;
	} else if (a <= 1.68e-40) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 1.05e+67) {
		tmp = t_1;
	} else {
		tmp = x + ((z - t) * (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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (a <= (-1.2d+120)) then
        tmp = x + (y / (a / (z - t)))
    else if (a <= (-2.1d-143)) then
        tmp = t_1
    else if (a <= 1.68d-40) then
        tmp = (y - x) * (z / (a - t))
    else if (a <= 1.05d+67) then
        tmp = t_1
    else
        tmp = x + ((z - t) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -1.2e+120) {
		tmp = x + (y / (a / (z - t)));
	} else if (a <= -2.1e-143) {
		tmp = t_1;
	} else if (a <= 1.68e-40) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 1.05e+67) {
		tmp = t_1;
	} else {
		tmp = x + ((z - t) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if a <= -1.2e+120:
		tmp = x + (y / (a / (z - t)))
	elif a <= -2.1e-143:
		tmp = t_1
	elif a <= 1.68e-40:
		tmp = (y - x) * (z / (a - t))
	elif a <= 1.05e+67:
		tmp = t_1
	else:
		tmp = x + ((z - t) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (a <= -1.2e+120)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (a <= -2.1e-143)
		tmp = t_1;
	elseif (a <= 1.68e-40)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (a <= 1.05e+67)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (a <= -1.2e+120)
		tmp = x + (y / (a / (z - t)));
	elseif (a <= -2.1e-143)
		tmp = t_1;
	elseif (a <= 1.68e-40)
		tmp = (y - x) * (z / (a - t));
	elseif (a <= 1.05e+67)
		tmp = t_1;
	else
		tmp = x + ((z - t) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e+120], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.1e-143], t$95$1, If[LessEqual[a, 1.68e-40], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+67], t$95$1, N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.2e120

   1. Initial program 77.0%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in y around inf 88.0%

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

   5. Taylor expanded in a around inf 69.1%

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

      1. associate-/l* 80.7%

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

   7. Simplified 80.7%

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

   if -1.2e120 < a < -2.1000000000000001e-143 or 1.6800000000000001e-40 < a < 1.0500000000000001e67

   1. Initial program 73.7%

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

      1. associate-/l* 84.7%

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

   3. Simplified 84.7%

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

   4. Taylor expanded in x around 0 49.3%

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

      1. associate-*r/ 63.5%

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

   6. Simplified 63.5%

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

   if -2.1000000000000001e-143 < a < 1.6800000000000001e-40

   1. Initial program 64.7%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in z around inf 60.7%

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

      1. div-sub 62.8%

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

      2. associate-*r/ 58.6%

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

      3. associate-/l* 63.2%

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

   6. Simplified 63.2%

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

      1. associate-/r/ 63.7%

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

   8. Applied egg-rr 63.7%

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

   if 1.0500000000000001e67 < a

   1. Initial program 73.3%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in y around inf 83.7%

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

   5. Taylor expanded in a around inf 80.1%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+120}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-143}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.68 \cdot 10^{-40}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 14: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1250:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-132}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-40}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1250.0)
   (+ x (/ (- y x) (/ a z)))
   (if (<= a 3e-132)
     (+ y (/ (- x y) (/ t z)))
     (if (<= a 6.4e-40)
       (* (- y x) (/ z (- a t)))
       (if (<= a 1.25e+67)
         (* y (/ (- z t) (- a t)))
         (+ x (* (- z t) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1250.0) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= 3e-132) {
		tmp = y + ((x - y) / (t / z));
	} else if (a <= 6.4e-40) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 1.25e+67) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((z - t) * (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 (a <= (-1250.0d0)) then
        tmp = x + ((y - x) / (a / z))
    else if (a <= 3d-132) then
        tmp = y + ((x - y) / (t / z))
    else if (a <= 6.4d-40) then
        tmp = (y - x) * (z / (a - t))
    else if (a <= 1.25d+67) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + ((z - t) * (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 (a <= -1250.0) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= 3e-132) {
		tmp = y + ((x - y) / (t / z));
	} else if (a <= 6.4e-40) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 1.25e+67) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((z - t) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1250.0:
		tmp = x + ((y - x) / (a / z))
	elif a <= 3e-132:
		tmp = y + ((x - y) / (t / z))
	elif a <= 6.4e-40:
		tmp = (y - x) * (z / (a - t))
	elif a <= 1.25e+67:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + ((z - t) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1250.0)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (a <= 3e-132)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	elseif (a <= 6.4e-40)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (a <= 1.25e+67)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1250.0)
		tmp = x + ((y - x) / (a / z));
	elseif (a <= 3e-132)
		tmp = y + ((x - y) / (t / z));
	elseif (a <= 6.4e-40)
		tmp = (y - x) * (z / (a - t));
	elseif (a <= 1.25e+67)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + ((z - t) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1250.0], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e-132], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.4e-40], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+67], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1250

   1. Initial program 75.8%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in t around 0 70.3%

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

   if -1250 < a < 3e-132

   1. Initial program 66.6%

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

      1. associate-/l* 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in t around inf 74.7%

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

      1. associate--l+ 74.7%

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

      2. associate-*r/ 74.7%

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

      3. associate-*r/ 74.7%

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

      4. div-sub 76.7%

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

      5. distribute-lft-out-- 76.7%

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

      6. associate-*r/ 76.7%

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

      7. mul-1-neg 76.7%

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

      8. unsub-neg 76.7%

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

      9. distribute-rgt-out-- 76.7%

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

      10. associate-/l* 85.3%

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

   6. Simplified 85.3%

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

   7. Taylor expanded in z around inf 80.1%

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

   if 3e-132 < a < 6.40000000000000004e-40

   1. Initial program 70.8%

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

      1. associate-/l* 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in z around inf 70.3%

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

      1. div-sub 74.1%

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

      2. associate-*r/ 66.9%

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

      3. associate-/l* 74.1%

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

   6. Simplified 74.1%

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

      1. associate-/r/ 70.4%

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

   8. Applied egg-rr 70.4%

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

   if 6.40000000000000004e-40 < a < 1.24999999999999994e67

   1. Initial program 71.1%

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

      1. associate-/l* 77.1%

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

   3. Simplified 77.1%

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

   4. Taylor expanded in x around 0 53.5%

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

      1. associate-*r/ 62.5%

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

   6. Simplified 62.5%

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

   if 1.24999999999999994e67 < a

   1. Initial program 73.3%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in y around inf 83.7%

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

   5. Taylor expanded in a around inf 80.1%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1250:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-132}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-40}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 15: 68.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -102000:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-133}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-40}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -102000.0)
   (+ x (/ (- y x) (/ a z)))
   (if (<= a 3.5e-133)
     (+ y (/ (- x y) (/ t z)))
     (if (<= a 2.7e-40)
       (/ z (/ (- a t) (- y x)))
       (if (<= a 4.8e+66)
         (* y (/ (- z t) (- a t)))
         (+ x (* (- z t) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -102000.0) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= 3.5e-133) {
		tmp = y + ((x - y) / (t / z));
	} else if (a <= 2.7e-40) {
		tmp = z / ((a - t) / (y - x));
	} else if (a <= 4.8e+66) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((z - t) * (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 (a <= (-102000.0d0)) then
        tmp = x + ((y - x) / (a / z))
    else if (a <= 3.5d-133) then
        tmp = y + ((x - y) / (t / z))
    else if (a <= 2.7d-40) then
        tmp = z / ((a - t) / (y - x))
    else if (a <= 4.8d+66) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + ((z - t) * (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 (a <= -102000.0) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= 3.5e-133) {
		tmp = y + ((x - y) / (t / z));
	} else if (a <= 2.7e-40) {
		tmp = z / ((a - t) / (y - x));
	} else if (a <= 4.8e+66) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((z - t) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -102000.0:
		tmp = x + ((y - x) / (a / z))
	elif a <= 3.5e-133:
		tmp = y + ((x - y) / (t / z))
	elif a <= 2.7e-40:
		tmp = z / ((a - t) / (y - x))
	elif a <= 4.8e+66:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + ((z - t) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -102000.0)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (a <= 3.5e-133)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	elseif (a <= 2.7e-40)
		tmp = Float64(z / Float64(Float64(a - t) / Float64(y - x)));
	elseif (a <= 4.8e+66)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -102000.0)
		tmp = x + ((y - x) / (a / z));
	elseif (a <= 3.5e-133)
		tmp = y + ((x - y) / (t / z));
	elseif (a <= 2.7e-40)
		tmp = z / ((a - t) / (y - x));
	elseif (a <= 4.8e+66)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + ((z - t) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -102000.0], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-133], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-40], N[(z / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e+66], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -102000

   1. Initial program 75.8%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in t around 0 70.3%

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

   if -102000 < a < 3.50000000000000003e-133

   1. Initial program 66.6%

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

      1. associate-/l* 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in t around inf 74.7%

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

      1. associate--l+ 74.7%

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

      2. associate-*r/ 74.7%

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

      3. associate-*r/ 74.7%

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

      4. div-sub 76.7%

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

      5. distribute-lft-out-- 76.7%

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

      6. associate-*r/ 76.7%

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

      7. mul-1-neg 76.7%

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

      8. unsub-neg 76.7%

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

      9. distribute-rgt-out-- 76.7%

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

      10. associate-/l* 85.3%

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

   6. Simplified 85.3%

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

   7. Taylor expanded in z around inf 80.1%

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

   if 3.50000000000000003e-133 < a < 2.7e-40

   1. Initial program 70.8%

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

      1. associate-/l* 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in z around inf 70.3%

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

      1. div-sub 74.1%

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

      2. associate-*r/ 66.9%

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

      3. associate-/l* 74.1%

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

   6. Simplified 74.1%

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

   if 2.7e-40 < a < 4.8000000000000003e66

   1. Initial program 71.1%

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

      1. associate-/l* 77.1%

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

   3. Simplified 77.1%

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

   4. Taylor expanded in x around 0 53.5%

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

      1. associate-*r/ 62.5%

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

   6. Simplified 62.5%

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

   if 4.8000000000000003e66 < a

   1. Initial program 73.3%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in y around inf 83.7%

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

   5. Taylor expanded in a around inf 80.1%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -102000:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-133}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-40}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 16: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+124} \lor \neg \left(t \leq 1.6 \cdot 10^{+130}\right):\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4e+124) (not (<= t 1.6e+130)))
   (- y (/ (- y x) (/ t (- z a))))
   (- x (* (/ (- y x) (- a t)) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e+124) || !(t <= 1.6e+130)) {
		tmp = y - ((y - x) / (t / (z - a)));
	} else {
		tmp = x - (((y - x) / (a - t)) * (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 <= (-4d+124)) .or. (.not. (t <= 1.6d+130))) then
        tmp = y - ((y - x) / (t / (z - a)))
    else
        tmp = x - (((y - x) / (a - t)) * (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 <= -4e+124) || !(t <= 1.6e+130)) {
		tmp = y - ((y - x) / (t / (z - a)));
	} else {
		tmp = x - (((y - x) / (a - t)) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4e+124) or not (t <= 1.6e+130):
		tmp = y - ((y - x) / (t / (z - a)))
	else:
		tmp = x - (((y - x) / (a - t)) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4e+124) || !(t <= 1.6e+130))
		tmp = Float64(y - Float64(Float64(y - x) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x - Float64(Float64(Float64(y - x) / Float64(a - t)) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4e+124) || ~((t <= 1.6e+130)))
		tmp = y - ((y - x) / (t / (z - a)));
	else
		tmp = x - (((y - x) / (a - t)) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4e+124], N[Not[LessEqual[t, 1.6e+130]], $MachinePrecision]], N[(y - N[(N[(y - x), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.99999999999999979e124 or 1.6e130 < t

   1. Initial program 32.4%

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

      1. associate-/l* 67.3%

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

   3. Simplified 67.3%

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

   4. Taylor expanded in t around inf 55.8%

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

      1. associate--l+ 55.8%

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

      2. associate-*r/ 55.8%

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

      3. associate-*r/ 55.8%

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

      4. div-sub 55.8%

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

      5. distribute-lft-out-- 55.8%

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

      6. associate-*r/ 55.8%

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

      7. mul-1-neg 55.8%

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

      8. unsub-neg 55.8%

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

      9. distribute-rgt-out-- 55.9%

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

      10. associate-/l* 85.6%

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

   6. Simplified 85.6%

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

   if -3.99999999999999979e124 < t < 1.6e130

   1. Initial program 84.5%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+124} \lor \neg \left(t \leq 1.6 \cdot 10^{+130}\right):\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 17: 41.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+136}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-151}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+130}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9e+136)
   y
   (if (<= t -5.5e-17)
     (* z (/ x t))
     (if (<= t -2.1e-151)
       (+ x y)
       (if (<= t 8.5e-114)
         (* z (/ (- y x) a))
         (if (<= t 5.6e+130) (+ x y) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9e+136) {
		tmp = y;
	} else if (t <= -5.5e-17) {
		tmp = z * (x / t);
	} else if (t <= -2.1e-151) {
		tmp = x + y;
	} else if (t <= 8.5e-114) {
		tmp = z * ((y - x) / a);
	} else if (t <= 5.6e+130) {
		tmp = x + y;
	} 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 (t <= (-9d+136)) then
        tmp = y
    else if (t <= (-5.5d-17)) then
        tmp = z * (x / t)
    else if (t <= (-2.1d-151)) then
        tmp = x + y
    else if (t <= 8.5d-114) then
        tmp = z * ((y - x) / a)
    else if (t <= 5.6d+130) then
        tmp = x + y
    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 (t <= -9e+136) {
		tmp = y;
	} else if (t <= -5.5e-17) {
		tmp = z * (x / t);
	} else if (t <= -2.1e-151) {
		tmp = x + y;
	} else if (t <= 8.5e-114) {
		tmp = z * ((y - x) / a);
	} else if (t <= 5.6e+130) {
		tmp = x + y;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9e+136:
		tmp = y
	elif t <= -5.5e-17:
		tmp = z * (x / t)
	elif t <= -2.1e-151:
		tmp = x + y
	elif t <= 8.5e-114:
		tmp = z * ((y - x) / a)
	elif t <= 5.6e+130:
		tmp = x + y
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9e+136)
		tmp = y;
	elseif (t <= -5.5e-17)
		tmp = Float64(z * Float64(x / t));
	elseif (t <= -2.1e-151)
		tmp = Float64(x + y);
	elseif (t <= 8.5e-114)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 5.6e+130)
		tmp = Float64(x + y);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9e+136)
		tmp = y;
	elseif (t <= -5.5e-17)
		tmp = z * (x / t);
	elseif (t <= -2.1e-151)
		tmp = x + y;
	elseif (t <= 8.5e-114)
		tmp = z * ((y - x) / a);
	elseif (t <= 5.6e+130)
		tmp = x + y;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9e+136], y, If[LessEqual[t, -5.5e-17], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.1e-151], N[(x + y), $MachinePrecision], If[LessEqual[t, 8.5e-114], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+130], N[(x + y), $MachinePrecision], y]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.9999999999999999e136 or 5.5999999999999997e130 < t

   1. Initial program 32.9%

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

      1. associate-/l* 68.3%

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

   3. Simplified 68.3%

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

   4. Taylor expanded in t around inf 60.7%

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

   if -8.9999999999999999e136 < t < -5.50000000000000001e-17

   1. Initial program 71.5%

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

      1. associate-/l* 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in t around inf 59.5%

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

      1. associate--l+ 59.5%

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

      2. associate-*r/ 59.5%

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

      3. associate-*r/ 59.5%

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

      4. div-sub 59.5%

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

      5. distribute-lft-out-- 59.5%

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

      6. associate-*r/ 59.5%

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

      7. mul-1-neg 59.5%

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

      8. unsub-neg 59.5%

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

      9. distribute-rgt-out-- 59.5%

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

      10. associate-/l* 63.5%

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

   6. Simplified 63.5%

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

   7. Taylor expanded in z around inf 55.3%

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

   8. Taylor expanded in y around 0 35.3%

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

      1. associate-*l/ 39.2%

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

   10. Simplified 39.2%

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

   if -5.50000000000000001e-17 < t < -2.0999999999999999e-151 or 8.5000000000000006e-114 < t < 5.5999999999999997e130

   1. Initial program 79.5%

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

      1. associate-*l/ 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in y around inf 70.5%

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

   5. Taylor expanded in t around inf 41.5%

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

      1. +-commutative 41.5%

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

   7. Simplified 41.5%

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

   if -2.0999999999999999e-151 < t < 8.5000000000000006e-114

   1. Initial program 93.5%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around inf 56.7%

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

   5. Taylor expanded in t around 0 51.2%

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

      1. div-sub 52.6%

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

   7. Simplified 52.6%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+136}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-151}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+130}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 18: 52.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - y \cdot \frac{z}{t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.25 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* y (/ z t)))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -1.15e-51)
     t_2
     (if (<= a 3.25e-161)
       t_1
       (if (<= a 5e-52) (* z (/ x t)) (if (<= a 6.6e+57) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (y * (z / t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -1.15e-51) {
		tmp = t_2;
	} else if (a <= 3.25e-161) {
		tmp = t_1;
	} else if (a <= 5e-52) {
		tmp = z * (x / t);
	} else if (a <= 6.6e+57) {
		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 = y - (y * (z / t))
    t_2 = x + (y / (a / z))
    if (a <= (-1.15d-51)) then
        tmp = t_2
    else if (a <= 3.25d-161) then
        tmp = t_1
    else if (a <= 5d-52) then
        tmp = z * (x / t)
    else if (a <= 6.6d+57) 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 = y - (y * (z / t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -1.15e-51) {
		tmp = t_2;
	} else if (a <= 3.25e-161) {
		tmp = t_1;
	} else if (a <= 5e-52) {
		tmp = z * (x / t);
	} else if (a <= 6.6e+57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (y * (z / t))
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -1.15e-51:
		tmp = t_2
	elif a <= 3.25e-161:
		tmp = t_1
	elif a <= 5e-52:
		tmp = z * (x / t)
	elif a <= 6.6e+57:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(y * Float64(z / t)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -1.15e-51)
		tmp = t_2;
	elseif (a <= 3.25e-161)
		tmp = t_1;
	elseif (a <= 5e-52)
		tmp = Float64(z * Float64(x / t));
	elseif (a <= 6.6e+57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (y * (z / t));
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -1.15e-51)
		tmp = t_2;
	elseif (a <= 3.25e-161)
		tmp = t_1;
	elseif (a <= 5e-52)
		tmp = z * (x / t);
	elseif (a <= 6.6e+57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e-51], t$95$2, If[LessEqual[a, 3.25e-161], t$95$1, If[LessEqual[a, 5e-52], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.6e+57], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.15000000000000001e-51 or 6.6000000000000002e57 < a

   1. Initial program 76.1%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around inf 81.6%

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

   5. Taylor expanded in t around 0 60.0%

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

      1. associate-/l* 63.4%

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

   7. Simplified 63.4%

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

   if -1.15000000000000001e-51 < a < 3.25000000000000004e-161 or 5e-52 < a < 6.6000000000000002e57

   1. Initial program 65.7%

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

      1. associate-/l* 74.6%

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

   3. Simplified 74.6%

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

   4. Taylor expanded in t around inf 68.1%

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

      1. associate--l+ 68.1%

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

      2. associate-*r/ 68.1%

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

      3. associate-*r/ 68.1%

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

      4. div-sub 69.8%

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

      5. distribute-lft-out-- 69.8%

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

      6. associate-*r/ 69.8%

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

      7. mul-1-neg 69.8%

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

      8. unsub-neg 69.8%

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

      9. distribute-rgt-out-- 69.8%

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

      10. associate-/l* 80.4%

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

   6. Simplified 80.4%

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

   7. Taylor expanded in z around inf 74.4%

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

   8. Taylor expanded in y around inf 49.6%

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

      1. associate-*r/ 55.1%

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

   10. Simplified 55.1%

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

   if 3.25000000000000004e-161 < a < 5e-52

   1. Initial program 69.5%

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

      1. associate-/l* 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in t around inf 61.4%

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

      1. associate--l+ 61.4%

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

      2. associate-*r/ 61.4%

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

      3. associate-*r/ 61.4%

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

      4. div-sub 61.4%

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

      5. distribute-lft-out-- 61.4%

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

      6. associate-*r/ 61.4%

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

      7. mul-1-neg 61.4%

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

      8. unsub-neg 61.4%

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

      9. distribute-rgt-out-- 61.4%

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

      10. associate-/l* 68.0%

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

   6. Simplified 68.0%

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

   7. Taylor expanded in z around inf 68.2%

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

   8. Taylor expanded in y around 0 45.0%

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

      1. associate-*l/ 48.4%

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

   10. Simplified 48.4%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-51}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 3.25 \cdot 10^{-161}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+57}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 19: 53.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - y \cdot \frac{z}{t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{-x}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* y (/ z t)))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -8.5e-51)
     t_2
     (if (<= a 5.8e-162)
       t_1
       (if (<= a 1.8e-41)
         (/ (- x) (/ (- a t) z))
         (if (<= a 6e+57) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (y * (z / t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -8.5e-51) {
		tmp = t_2;
	} else if (a <= 5.8e-162) {
		tmp = t_1;
	} else if (a <= 1.8e-41) {
		tmp = -x / ((a - t) / z);
	} else if (a <= 6e+57) {
		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 = y - (y * (z / t))
    t_2 = x + (y / (a / z))
    if (a <= (-8.5d-51)) then
        tmp = t_2
    else if (a <= 5.8d-162) then
        tmp = t_1
    else if (a <= 1.8d-41) then
        tmp = -x / ((a - t) / z)
    else if (a <= 6d+57) 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 = y - (y * (z / t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -8.5e-51) {
		tmp = t_2;
	} else if (a <= 5.8e-162) {
		tmp = t_1;
	} else if (a <= 1.8e-41) {
		tmp = -x / ((a - t) / z);
	} else if (a <= 6e+57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (y * (z / t))
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -8.5e-51:
		tmp = t_2
	elif a <= 5.8e-162:
		tmp = t_1
	elif a <= 1.8e-41:
		tmp = -x / ((a - t) / z)
	elif a <= 6e+57:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(y * Float64(z / t)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -8.5e-51)
		tmp = t_2;
	elseif (a <= 5.8e-162)
		tmp = t_1;
	elseif (a <= 1.8e-41)
		tmp = Float64(Float64(-x) / Float64(Float64(a - t) / z));
	elseif (a <= 6e+57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (y * (z / t));
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -8.5e-51)
		tmp = t_2;
	elseif (a <= 5.8e-162)
		tmp = t_1;
	elseif (a <= 1.8e-41)
		tmp = -x / ((a - t) / z);
	elseif (a <= 6e+57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.5e-51], t$95$2, If[LessEqual[a, 5.8e-162], t$95$1, If[LessEqual[a, 1.8e-41], N[((-x) / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+57], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.50000000000000036e-51 or 5.9999999999999999e57 < a

   1. Initial program 76.1%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around inf 81.6%

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

   5. Taylor expanded in t around 0 60.0%

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

      1. associate-/l* 63.4%

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

   7. Simplified 63.4%

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

   if -8.50000000000000036e-51 < a < 5.8000000000000002e-162 or 1.8e-41 < a < 5.9999999999999999e57

   1. Initial program 65.3%

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

      1. associate-/l* 74.6%

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

   3. Simplified 74.6%

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

   4. Taylor expanded in t around inf 70.5%

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

      1. associate--l+ 70.5%

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

      2. associate-*r/ 70.5%

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

      3. associate-*r/ 70.5%

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

      4. div-sub 72.3%

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

      5. distribute-lft-out-- 72.3%

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

      6. associate-*r/ 72.3%

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

      7. mul-1-neg 72.3%

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

      8. unsub-neg 72.3%

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

      9. distribute-rgt-out-- 72.3%

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

      10. associate-/l* 82.4%

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

   6. Simplified 82.4%

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

   7. Taylor expanded in z around inf 76.2%

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

   8. Taylor expanded in y around inf 50.3%

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

      1. associate-*r/ 56.1%

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

   10. Simplified 56.1%

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

   if 5.8000000000000002e-162 < a < 1.8e-41

   1. Initial program 70.3%

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

      1. associate-/l* 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in z around inf 70.0%

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

      1. div-sub 73.1%

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

      2. associate-*r/ 67.2%

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

      3. associate-/l* 73.1%

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

   6. Simplified 73.1%

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

   7. Taylor expanded in y around 0 55.4%

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

      1. mul-1-neg 55.4%

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

      2. associate-/l* 58.1%

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

   9. Simplified 58.1%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-51}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-162}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{-x}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+57}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 20: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+51} \lor \neg \left(t \leq 2.5 \cdot 10^{+63}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.4e+51) (not (<= t 2.5e+63)))
   (+ y (/ (- x y) (/ t z)))
   (- x (/ (- x y) (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.4e+51) || !(t <= 2.5e+63)) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x - ((x - y) / ((a - 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 <= (-6.4d+51)) .or. (.not. (t <= 2.5d+63))) then
        tmp = y + ((x - y) / (t / z))
    else
        tmp = x - ((x - y) / ((a - 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 <= -6.4e+51) || !(t <= 2.5e+63)) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x - ((x - y) / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.4e+51) or not (t <= 2.5e+63):
		tmp = y + ((x - y) / (t / z))
	else:
		tmp = x - ((x - y) / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.4e+51) || !(t <= 2.5e+63))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.4e+51) || ~((t <= 2.5e+63)))
		tmp = y + ((x - y) / (t / z));
	else
		tmp = x - ((x - y) / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.4e+51], N[Not[LessEqual[t, 2.5e+63]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.4000000000000005e51 or 2.50000000000000005e63 < t

   1. Initial program 42.8%

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

      1. associate-/l* 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in t around inf 57.7%

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

      1. associate--l+ 57.7%

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

      2. associate-*r/ 57.7%

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

      3. associate-*r/ 57.7%

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

      4. div-sub 57.7%

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

      5. distribute-lft-out-- 57.7%

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

      6. associate-*r/ 57.7%

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

      7. mul-1-neg 57.7%

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

      8. unsub-neg 57.7%

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

      9. distribute-rgt-out-- 57.7%

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

      10. associate-/l* 81.2%

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

   6. Simplified 81.2%

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

   7. Taylor expanded in z around inf 76.9%

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

   if -6.4000000000000005e51 < t < 2.50000000000000005e63

   1. Initial program 86.8%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in z around inf 80.2%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+51} \lor \neg \left(t \leq 2.5 \cdot 10^{+63}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 21: 81.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+53} \lor \neg \left(t \leq 5 \cdot 10^{+61}\right):\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.7e+53) (not (<= t 5e+61)))
   (- y (/ (- y x) (/ t (- z a))))
   (- x (/ (- x y) (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.7e+53) || !(t <= 5e+61)) {
		tmp = y - ((y - x) / (t / (z - a)));
	} else {
		tmp = x - ((x - y) / ((a - 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 <= (-1.7d+53)) .or. (.not. (t <= 5d+61))) then
        tmp = y - ((y - x) / (t / (z - a)))
    else
        tmp = x - ((x - y) / ((a - 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 <= -1.7e+53) || !(t <= 5e+61)) {
		tmp = y - ((y - x) / (t / (z - a)));
	} else {
		tmp = x - ((x - y) / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.7e+53) or not (t <= 5e+61):
		tmp = y - ((y - x) / (t / (z - a)))
	else:
		tmp = x - ((x - y) / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.7e+53) || !(t <= 5e+61))
		tmp = Float64(y - Float64(Float64(y - x) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.7e+53) || ~((t <= 5e+61)))
		tmp = y - ((y - x) / (t / (z - a)));
	else
		tmp = x - ((x - y) / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.7e+53], N[Not[LessEqual[t, 5e+61]], $MachinePrecision]], N[(y - N[(N[(y - x), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.69999999999999999e53 or 5.00000000000000018e61 < t

   1. Initial program 42.8%

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

      1. associate-/l* 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in t around inf 57.7%

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

      1. associate--l+ 57.7%

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

      2. associate-*r/ 57.7%

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

      3. associate-*r/ 57.7%

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

      4. div-sub 57.7%

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

      5. distribute-lft-out-- 57.7%

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

      6. associate-*r/ 57.7%

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

      7. mul-1-neg 57.7%

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

      8. unsub-neg 57.7%

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

      9. distribute-rgt-out-- 57.7%

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

      10. associate-/l* 81.2%

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

   6. Simplified 81.2%

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

   if -1.69999999999999999e53 < t < 5.00000000000000018e61

   1. Initial program 86.8%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in z around inf 80.2%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+53} \lor \neg \left(t \leq 5 \cdot 10^{+61}\right):\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 22: 42.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+131}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+46}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+132}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.6e+131)
   y
   (if (<= t -5.5e+46)
     (* (- z a) (/ x t))
     (if (<= t 5.2e-114) (* z (/ (- y x) a)) (if (<= t 5.1e+132) (+ x y) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.6e+131) {
		tmp = y;
	} else if (t <= -5.5e+46) {
		tmp = (z - a) * (x / t);
	} else if (t <= 5.2e-114) {
		tmp = z * ((y - x) / a);
	} else if (t <= 5.1e+132) {
		tmp = x + y;
	} 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 (t <= (-7.6d+131)) then
        tmp = y
    else if (t <= (-5.5d+46)) then
        tmp = (z - a) * (x / t)
    else if (t <= 5.2d-114) then
        tmp = z * ((y - x) / a)
    else if (t <= 5.1d+132) then
        tmp = x + y
    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 (t <= -7.6e+131) {
		tmp = y;
	} else if (t <= -5.5e+46) {
		tmp = (z - a) * (x / t);
	} else if (t <= 5.2e-114) {
		tmp = z * ((y - x) / a);
	} else if (t <= 5.1e+132) {
		tmp = x + y;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.6e+131:
		tmp = y
	elif t <= -5.5e+46:
		tmp = (z - a) * (x / t)
	elif t <= 5.2e-114:
		tmp = z * ((y - x) / a)
	elif t <= 5.1e+132:
		tmp = x + y
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.6e+131)
		tmp = y;
	elseif (t <= -5.5e+46)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif (t <= 5.2e-114)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 5.1e+132)
		tmp = Float64(x + y);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.6e+131)
		tmp = y;
	elseif (t <= -5.5e+46)
		tmp = (z - a) * (x / t);
	elseif (t <= 5.2e-114)
		tmp = z * ((y - x) / a);
	elseif (t <= 5.1e+132)
		tmp = x + y;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.6e+131], y, If[LessEqual[t, -5.5e+46], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-114], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.1e+132], N[(x + y), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.6000000000000007e131 or 5.1000000000000001e132 < t

   1. Initial program 32.9%

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

      1. associate-/l* 68.3%

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

   3. Simplified 68.3%

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

   4. Taylor expanded in t around inf 60.7%

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

   if -7.6000000000000007e131 < t < -5.4999999999999998e46

   1. Initial program 72.6%

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

      1. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in t around inf 73.6%

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

      1. associate--l+ 73.6%

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

      2. associate-*r/ 73.6%

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

      3. associate-*r/ 73.6%

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

      4. div-sub 73.6%

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

      5. distribute-lft-out-- 73.6%

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

      6. associate-*r/ 73.6%

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

      7. mul-1-neg 73.6%

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

      8. unsub-neg 73.6%

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

      9. distribute-rgt-out-- 73.6%

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

      10. associate-/l* 82.4%

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

   6. Simplified 82.4%

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

   7. Taylor expanded in y around 0 56.0%

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

      1. associate-/l* 64.7%

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

      2. associate-/r/ 64.5%

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

   9. Simplified 64.5%

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

   if -5.4999999999999998e46 < t < 5.20000000000000026e-114

   1. Initial program 88.8%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around inf 54.0%

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

   5. Taylor expanded in t around 0 44.9%

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

      1. div-sub 45.8%

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

   7. Simplified 45.8%

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

   if 5.20000000000000026e-114 < t < 5.1000000000000001e132

   1. Initial program 77.9%

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

      1. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in y around inf 66.9%

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

   5. Taylor expanded in t around inf 40.3%

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

      1. +-commutative 40.3%

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

   7. Simplified 40.3%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+131}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+46}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+132}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 23: 57.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2400000000000 \lor \neg \left(a \leq 9.2 \cdot 10^{+53}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2400000000000.0) (not (<= a 9.2e+53)))
   (+ x (/ y (/ a z)))
   (+ y (* z (/ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2400000000000.0) || !(a <= 9.2e+53)) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + (z * (x / 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 <= (-2400000000000.0d0)) .or. (.not. (a <= 9.2d+53))) then
        tmp = x + (y / (a / z))
    else
        tmp = y + (z * (x / 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 <= -2400000000000.0) || !(a <= 9.2e+53)) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + (z * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2400000000000.0) or not (a <= 9.2e+53):
		tmp = x + (y / (a / z))
	else:
		tmp = y + (z * (x / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2400000000000.0) || !(a <= 9.2e+53))
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(y + Float64(z * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2400000000000.0) || ~((a <= 9.2e+53)))
		tmp = x + (y / (a / z));
	else
		tmp = y + (z * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2400000000000.0], N[Not[LessEqual[a, 9.2e+53]], $MachinePrecision]], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.4e12 or 9.20000000000000079e53 < a

   1. Initial program 75.4%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around inf 83.2%

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

   5. Taylor expanded in t around 0 62.0%

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

      1. associate-/l* 65.5%

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

   7. Simplified 65.5%

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

   if -2.4e12 < a < 9.20000000000000079e53

   1. Initial program 67.3%

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

      1. associate-/l* 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in t around inf 65.9%

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

      1. associate--l+ 65.9%

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

      2. associate-*r/ 65.9%

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

      3. associate-*r/ 65.9%

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

      4. div-sub 67.2%

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

      5. distribute-lft-out-- 67.2%

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

      6. associate-*r/ 67.2%

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

      7. mul-1-neg 67.2%

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

      8. unsub-neg 67.2%

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

      9. distribute-rgt-out-- 67.2%

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

      10. associate-/l* 76.6%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in z around inf 72.1%

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

   8. Taylor expanded in y around 0 55.0%

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

      1. mul-1-neg 55.0%

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

      2. associate-/l* 60.7%

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

      3. associate-/r/ 59.5%

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

      4. distribute-rgt-neg-in 59.5%

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

   10. Simplified 59.5%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2400000000000 \lor \neg \left(a \leq 9.2 \cdot 10^{+53}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]

Alternative 24: 35.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-108}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{+67}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.25e-108)
   (+ x y)
   (if (<= a 4.5e-53) (* z (/ x t)) (if (<= a 9.4e+67) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.25e-108) {
		tmp = x + y;
	} else if (a <= 4.5e-53) {
		tmp = z * (x / t);
	} else if (a <= 9.4e+67) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.25d-108)) then
        tmp = x + y
    else if (a <= 4.5d-53) then
        tmp = z * (x / t)
    else if (a <= 9.4d+67) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.25e-108) {
		tmp = x + y;
	} else if (a <= 4.5e-53) {
		tmp = z * (x / t);
	} else if (a <= 9.4e+67) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.25e-108:
		tmp = x + y
	elif a <= 4.5e-53:
		tmp = z * (x / t)
	elif a <= 9.4e+67:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.25e-108)
		tmp = Float64(x + y);
	elseif (a <= 4.5e-53)
		tmp = Float64(z * Float64(x / t));
	elseif (a <= 9.4e+67)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.25e-108)
		tmp = x + y;
	elseif (a <= 4.5e-53)
		tmp = z * (x / t);
	elseif (a <= 9.4e+67)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.25e-108], N[(x + y), $MachinePrecision], If[LessEqual[a, 4.5e-53], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.4e+67], y, x]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.25e-108

   1. Initial program 74.3%

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

      1. associate-*l/ 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in y around inf 75.3%

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

   5. Taylor expanded in t around inf 52.1%

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

      1. +-commutative 52.1%

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

   7. Simplified 52.1%

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

   if -1.25e-108 < a < 4.49999999999999985e-53

   1. Initial program 66.4%

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

      1. associate-/l* 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in t around inf 73.0%

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

      1. associate--l+ 73.0%

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

      2. associate-*r/ 73.0%

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

      3. associate-*r/ 73.0%

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

      4. div-sub 74.0%

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

      5. distribute-lft-out-- 74.0%

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

      6. associate-*r/ 74.0%

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

      7. mul-1-neg 74.0%

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

      8. unsub-neg 74.0%

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

      9. distribute-rgt-out-- 74.0%

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

      10. associate-/l* 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in z around inf 79.1%

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

   8. Taylor expanded in y around 0 35.5%

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

      1. associate-*l/ 38.3%

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

   10. Simplified 38.3%

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

   if 4.49999999999999985e-53 < a < 9.40000000000000035e67

   1. Initial program 72.5%

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

      1. associate-/l* 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in t around inf 33.4%

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

   if 9.40000000000000035e67 < a

   1. Initial program 72.8%

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

      1. associate-/l* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in a around inf 58.1%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-108}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{+67}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 25: 38.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.82 \cdot 10^{+68}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.5e+123) x (if (<= a 1.82e+68) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+123) {
		tmp = x;
	} else if (a <= 1.82e+68) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.5d+123)) then
        tmp = x
    else if (a <= 1.82d+68) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+123) {
		tmp = x;
	} else if (a <= 1.82e+68) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.5e+123:
		tmp = x
	elif a <= 1.82e+68:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.5e+123)
		tmp = x;
	elseif (a <= 1.82e+68)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.5e+123)
		tmp = x;
	elseif (a <= 1.82e+68)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.5e+123], x, If[LessEqual[a, 1.82e+68], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.5e123 or 1.81999999999999991e68 < a

   1. Initial program 74.2%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in a around inf 59.2%

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

   if -3.5e123 < a < 1.81999999999999991e68

   1. Initial program 69.1%

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

      1. associate-/l* 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in t around inf 32.5%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.82 \cdot 10^{+68}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 26: 37.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-52}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3.25 \cdot 10^{+68}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.6e-52) (+ x y) (if (<= a 3.25e+68) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e-52) {
		tmp = x + y;
	} else if (a <= 3.25e+68) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.6d-52)) then
        tmp = x + y
    else if (a <= 3.25d+68) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e-52) {
		tmp = x + y;
	} else if (a <= 3.25e+68) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.6e-52:
		tmp = x + y
	elif a <= 3.25e+68:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.6e-52)
		tmp = Float64(x + y);
	elseif (a <= 3.25e+68)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.6e-52)
		tmp = x + y;
	elseif (a <= 3.25e+68)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.6e-52], N[(x + y), $MachinePrecision], If[LessEqual[a, 3.25e+68], y, x]]

Derivation

1. Split input into 3 regimes

2. if a < -5.59999999999999989e-52

   1. Initial program 77.5%

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

      1. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around inf 78.5%

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

   5. Taylor expanded in t around inf 53.8%

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

      1. +-commutative 53.8%

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

   7. Simplified 53.8%

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

   if -5.59999999999999989e-52 < a < 3.2500000000000002e68

   1. Initial program 67.3%

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

      1. associate-/l* 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in t around inf 32.5%

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

   if 3.2500000000000002e68 < a

   1. Initial program 72.8%

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

      1. associate-/l* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in a around inf 58.1%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-52}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3.25 \cdot 10^{+68}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 27: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 70.7%

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

   1. associate-/l* 84.3%

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

3. Simplified 84.3%

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

4. Taylor expanded in z around 0 37.4%

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

   1. mul-1-neg 37.4%

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

   2. unsub-neg 37.4%

      \[\leadsto \color{blue}{x - \frac{t \cdot \left(y - x\right)}{a - t}} \]

   3. associate-/l* 43.6%

      \[\leadsto x - \color{blue}{\frac{t}{\frac{a - t}{y - x}}} \]

6. Simplified 43.6%

   \[\leadsto \color{blue}{x - \frac{t}{\frac{a - t}{y - x}}} \]

7. Taylor expanded in y around 0 24.8%

   \[\leadsto \color{blue}{x - -1 \cdot \frac{t \cdot x}{a - t}} \]
8. Step-by-step derivation

   1. sub-neg 24.8%

      \[\leadsto \color{blue}{x + \left(--1 \cdot \frac{t \cdot x}{a - t}\right)} \]

   2. mul-1-neg 24.8%

      \[\leadsto x + \left(-\color{blue}{\left(-\frac{t \cdot x}{a - t}\right)}\right) \]

   3. remove-double-neg 24.8%

      \[\leadsto x + \color{blue}{\frac{t \cdot x}{a - t}} \]

   4. associate-/l* 26.9%

      \[\leadsto x + \color{blue}{\frac{t}{\frac{a - t}{x}}} \]

9. Simplified 26.9%

   \[\leadsto \color{blue}{x + \frac{t}{\frac{a - t}{x}}} \]

10. Taylor expanded in t around inf 2.8%

    \[\leadsto \color{blue}{x + -1 \cdot x} \]
11. Step-by-step derivation

    1. distribute-rgt1-in 2.8%

       \[\leadsto \color{blue}{\left(-1 + 1\right) \cdot x} \]

    2. metadata-eval 2.8%

       \[\leadsto \color{blue}{0} \cdot x \]

    3. mul0-lft 2.8%

       \[\leadsto \color{blue}{0} \]

12. Simplified 2.8%

    \[\leadsto \color{blue}{0} \]

13. Final simplification 2.8%

    \[\leadsto 0 \]

Alternative 28: 25.4% 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 70.7%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-/l* 84.3%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

3. Simplified 84.3%

   \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

4. Taylor expanded in a around inf 25.6%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 25.6%

   \[\leadsto x \]

Developer target: 86.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} 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 - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    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 - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023320 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))