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

Percentage Accurate: 68.7% → 91.4%

Time: 26.8s

Alternatives: 27

Speedup: 0.7×

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: 68.7% 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: 91.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ t_2 := \sqrt[3]{x - \left(y - x\right) \cdot \frac{t}{a - t}}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-209}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;{\left(\sqrt[3]{t_2 \cdot {t_2}^{2} + \frac{z}{\frac{a - t}{y - x}}}\right)}^{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t))))
        (t_2 (cbrt (- x (* (- y x) (/ t (- a t)))))))
   (if (<= t_1 -5e-209)
     (- x (/ (- x y) (/ (- a t) (- z t))))
     (if (<= t_1 0.0)
       (+ y (/ (* (- z a) (- x y)) t))
       (if (<= t_1 5e+307)
         (+ x (* (* (- y x) (- z t)) (/ 1.0 (- a t))))
         (pow
          (cbrt (+ (* t_2 (pow t_2 2.0)) (/ z (/ (- a t) (- y x)))))
          3.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double t_2 = cbrt((x - ((y - x) * (t / (a - t)))));
	double tmp;
	if (t_1 <= -5e-209) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else if (t_1 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_1 <= 5e+307) {
		tmp = x + (((y - x) * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = pow(cbrt(((t_2 * pow(t_2, 2.0)) + (z / ((a - t) / (y - x))))), 3.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double t_2 = Math.cbrt((x - ((y - x) * (t / (a - t)))));
	double tmp;
	if (t_1 <= -5e-209) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else if (t_1 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_1 <= 5e+307) {
		tmp = x + (((y - x) * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = Math.pow(Math.cbrt(((t_2 * Math.pow(t_2, 2.0)) + (z / ((a - t) / (y - x))))), 3.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	t_2 = cbrt(Float64(x - Float64(Float64(y - x) * Float64(t / Float64(a - t)))))
	tmp = 0.0
	if (t_1 <= -5e-209)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / Float64(z - t))));
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	elseif (t_1 <= 5e+307)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = cbrt(Float64(Float64(t_2 * (t_2 ^ 2.0)) + Float64(z / Float64(Float64(a - t) / Float64(y - x))))) ^ 3.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[N[(x - N[(N[(y - x), $MachinePrecision] * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]}, If[LessEqual[t$95$1, -5e-209], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+307], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[Power[N[(N[(t$95$2 * N[Power[t$95$2, 2.0], $MachinePrecision]), $MachinePrecision] + N[(z / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000005e-209

   1. Initial program 70.2%

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

      1. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   if -5.0000000000000005e-209 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.5%

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

      1. associate-*l/ 3.8%

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

   3. Simplified 3.8%

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

   4. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. div-sub 99.9%

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

      5. distribute-lft-out-- 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-neg-frac 99.9%

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

      8. unsub-neg 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   6. Simplified 99.9%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5e307

   1. Initial program 98.2%

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

      1. clear-num 98.0%

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

      2. associate-/r/ 98.2%

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

   3. Applied egg-rr 98.2%

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

   if 5e307 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 43.1%

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

      1. associate-*l/ 86.1%

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

   3. Simplified 86.1%

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

      1. add-cube-cbrt 85.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \cdot \sqrt[3]{x + \frac{y - x}{a - t} \cdot \left(z - t\right)}\right) \cdot \sqrt[3]{x + \frac{y - x}{a - t} \cdot \left(z - t\right)}} \]

      2. pow3 85.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{y - x}{a - t} \cdot \left(z - t\right)}\right)}^{3}} \]

      3. +-commutative 85.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x}}\right)}^{3} \]

      4. associate-/r/ 85.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x}\right)}^{3} \]

      5. div-inv 85.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x}\right)}^{3} \]

      6. fma-def 85.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, \frac{1}{\frac{a - t}{z - t}}, x\right)}}\right)}^{3} \]

      7. clear-num 85.4%

         \[\leadsto {\left(\sqrt[3]{\mathsf{fma}\left(y - x, \color{blue}{\frac{z - t}{a - t}}, x\right)}\right)}^{3} \]

   5. Applied egg-rr 85.4%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}\right)}^{3}} \]

   6. Taylor expanded in z around -inf 42.5%

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

      1. associate-+r+ 42.5%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x + -1 \cdot \frac{t \cdot \left(y - x\right)}{a - t}\right) + \frac{z \cdot \left(y - x\right)}{a - t}}}\right)}^{3} \]

      2. mul-1-neg 42.5%

         \[\leadsto {\left(\sqrt[3]{\left(x + \color{blue}{\left(-\frac{t \cdot \left(y - x\right)}{a - t}\right)}\right) + \frac{z \cdot \left(y - x\right)}{a - t}}\right)}^{3} \]

      3. unsub-neg 42.5%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x - \frac{t \cdot \left(y - x\right)}{a - t}\right)} + \frac{z \cdot \left(y - x\right)}{a - t}}\right)}^{3} \]

      4. associate-/l* 62.6%

         \[\leadsto {\left(\sqrt[3]{\left(x - \color{blue}{\frac{t}{\frac{a - t}{y - x}}}\right) + \frac{z \cdot \left(y - x\right)}{a - t}}\right)}^{3} \]

      5. associate-/l* 81.7%

         \[\leadsto {\left(\sqrt[3]{\left(x - \frac{t}{\frac{a - t}{y - x}}\right) + \color{blue}{\frac{z}{\frac{a - t}{y - x}}}}\right)}^{3} \]

   8. Simplified 81.7%

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

      1. add-cube-cbrt 81.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(\sqrt[3]{x - \frac{t}{\frac{a - t}{y - x}}} \cdot \sqrt[3]{x - \frac{t}{\frac{a - t}{y - x}}}\right) \cdot \sqrt[3]{x - \frac{t}{\frac{a - t}{y - x}}}} + \frac{z}{\frac{a - t}{y - x}}}\right)}^{3} \]

      2. pow2 81.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{{\left(\sqrt[3]{x - \frac{t}{\frac{a - t}{y - x}}}\right)}^{2}} \cdot \sqrt[3]{x - \frac{t}{\frac{a - t}{y - x}}} + \frac{z}{\frac{a - t}{y - x}}}\right)}^{3} \]

      3. associate-/r/ 81.4%

         \[\leadsto {\left(\sqrt[3]{{\left(\sqrt[3]{x - \color{blue}{\frac{t}{a - t} \cdot \left(y - x\right)}}\right)}^{2} \cdot \sqrt[3]{x - \frac{t}{\frac{a - t}{y - x}}} + \frac{z}{\frac{a - t}{y - x}}}\right)}^{3} \]

      4. associate-/r/ 90.6%

         \[\leadsto {\left(\sqrt[3]{{\left(\sqrt[3]{x - \frac{t}{a - t} \cdot \left(y - x\right)}\right)}^{2} \cdot \sqrt[3]{x - \color{blue}{\frac{t}{a - t} \cdot \left(y - x\right)}} + \frac{z}{\frac{a - t}{y - x}}}\right)}^{3} \]

   10. Applied egg-rr 90.6%

       \[\leadsto {\left(\sqrt[3]{\color{blue}{{\left(\sqrt[3]{x - \frac{t}{a - t} \cdot \left(y - x\right)}\right)}^{2} \cdot \sqrt[3]{x - \frac{t}{a - t} \cdot \left(y - x\right)}} + \frac{z}{\frac{a - t}{y - x}}}\right)}^{3} \]
3. Recombined 4 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -5 \cdot 10^{-209}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 5 \cdot 10^{+307}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;{\left(\sqrt[3]{\sqrt[3]{x - \left(y - x\right) \cdot \frac{t}{a - t}} \cdot {\left(\sqrt[3]{x - \left(y - x\right) \cdot \frac{t}{a - t}}\right)}^{2} + \frac{z}{\frac{a - t}{y - x}}}\right)}^{3}\\ \end{array} \]

Alternative 2: 89.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+185} \lor \neg \left(t \leq 7.4 \cdot 10^{+120}\right):\\ \;\;\;\;{\left(\sqrt[3]{y + \frac{x - y}{\frac{t}{z - a}}}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e+185) (not (<= t 7.4e+120)))
   (pow (cbrt (+ y (/ (- x y) (/ t (- z a))))) 3.0)
   (- x (/ (- x y) (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+185) || !(t <= 7.4e+120)) {
		tmp = pow(cbrt((y + ((x - y) / (t / (z - a))))), 3.0);
	} else {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+185) || !(t <= 7.4e+120)) {
		tmp = Math.pow(Math.cbrt((y + ((x - y) / (t / (z - a))))), 3.0);
	} else {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e+185) || !(t <= 7.4e+120))
		tmp = cbrt(Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))))) ^ 3.0;
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e+185], N[Not[LessEqual[t, 7.4e+120]], $MachinePrecision]], N[Power[N[Power[N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.39999999999999989e185 or 7.40000000000000048e120 < t

   1. Initial program 28.0%

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

      1. associate-*l/ 57.7%

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

   3. Simplified 57.7%

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

      1. add-cube-cbrt 56.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \cdot \sqrt[3]{x + \frac{y - x}{a - t} \cdot \left(z - t\right)}\right) \cdot \sqrt[3]{x + \frac{y - x}{a - t} \cdot \left(z - t\right)}} \]

      2. pow3 56.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{y - x}{a - t} \cdot \left(z - t\right)}\right)}^{3}} \]

      3. +-commutative 56.7%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x}}\right)}^{3} \]

      4. associate-/r/ 61.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x}\right)}^{3} \]

      5. div-inv 61.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x}\right)}^{3} \]

      6. fma-def 61.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, \frac{1}{\frac{a - t}{z - t}}, x\right)}}\right)}^{3} \]

      7. clear-num 61.1%

         \[\leadsto {\left(\sqrt[3]{\mathsf{fma}\left(y - x, \color{blue}{\frac{z - t}{a - t}}, x\right)}\right)}^{3} \]

   5. Applied egg-rr 61.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}\right)}^{3}} \]

   6. Taylor expanded in t around -inf 68.6%

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

      1. mul-1-neg 68.6%

         \[\leadsto {\left(\sqrt[3]{y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)}}\right)}^{3} \]

      2. unsub-neg 68.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}}}\right)}^{3} \]

      3. associate-/l* 90.1%

         \[\leadsto {\left(\sqrt[3]{y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}}}\right)}^{3} \]

   8. Simplified 90.1%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{y - \frac{y - x}{\frac{t}{z - a}}}}\right)}^{3} \]

   if -2.39999999999999989e185 < t < 7.40000000000000048e120

   1. Initial program 80.1%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+185} \lor \neg \left(t \leq 7.4 \cdot 10^{+120}\right):\\ \;\;\;\;{\left(\sqrt[3]{y + \frac{x - y}{\frac{t}{z - a}}}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 3: 90.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+259}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) (- a t)))))
        (t_2 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-209)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (* (- z a) (- x y)) t))
         (if (<= t_2 5e+259) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-209) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_2 <= 5e+259) {
		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 + ((z - t) * ((y - x) / (a - t)));
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e-209) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_2 <= 5e+259) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) / (a - t)))
	t_2 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e-209:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + (((z - a) * (x - y)) / t)
	elif t_2 <= 5e+259:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))))
	t_2 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-209)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	elseif (t_2 <= 5e+259)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) / (a - t)));
	t_2 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e-209)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + (((z - a) * (x - y)) / t);
	elseif (t_2 <= 5e+259)
		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[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-209], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+259], 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 5.00000000000000033e259 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 39.8%

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

      1. associate-*l/ 82.0%

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

   3. Simplified 82.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000005e-209 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5.00000000000000033e259

   1. Initial program 97.1%

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

   if -5.0000000000000005e-209 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.5%

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

      1. associate-*l/ 3.8%

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

   3. Simplified 3.8%

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

   4. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. div-sub 99.9%

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

      5. distribute-lft-out-- 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-neg-frac 99.9%

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

      8. unsub-neg 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -5 \cdot 10^{-209}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 5 \cdot 10^{+259}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 4: 90.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-209} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (or (<= t_1 -5e-209) (not (<= t_1 0.0)))
     (- x (/ (- x y) (/ (- a t) (- z t))))
     (+ y (/ (* (- z a) (- x y)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-209) || !(t_1 <= 0.0)) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((z - a) * (x - y)) / 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) * (t - z)) / (a - t))
    if ((t_1 <= (-5d-209)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x - ((x - y) / ((a - t) / (z - t)))
    else
        tmp = y + (((z - a) * (x - y)) / 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) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-209) || !(t_1 <= 0.0)) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((z - a) * (x - y)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if (t_1 <= -5e-209) or not (t_1 <= 0.0):
		tmp = x - ((x - y) / ((a - t) / (z - t)))
	else:
		tmp = y + (((z - a) * (x - y)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -5e-209) || !(t_1 <= 0.0))
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -5e-209) || ~((t_1 <= 0.0)))
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	else
		tmp = y + (((z - a) * (x - y)) / 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[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-209], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000005e-209 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 72.2%

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

      1. associate-/l* 89.0%

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

   3. Simplified 89.0%

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

   if -5.0000000000000005e-209 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.5%

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

      1. associate-*l/ 3.8%

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

   3. Simplified 3.8%

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

   4. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. div-sub 99.9%

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

      5. distribute-lft-out-- 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-neg-frac 99.9%

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

      8. unsub-neg 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -5 \cdot 10^{-209} \lor \neg \left(x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \end{array} \]

Alternative 5: 62.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{a}{\frac{t}{y - x}}\\ t_2 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+50}:\\ \;\;\;\;x - x \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-52}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+201}:\\ \;\;\;\;\frac{t}{\frac{t - a}{y}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+228}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ a (/ t (- y x))))) (t_2 (* z (/ (- y x) (- a t)))))
   (if (<= t -2.8e+167)
     t_1
     (if (<= t -2.7e+50)
       (- x (* x (/ z (- a t))))
       (if (<= t -1.1e+25)
         t_1
         (if (<= t 3.3e-52)
           (- x (/ (- x y) (/ a z)))
           (if (<= t 6.2e+63)
             (/ (* y (- z t)) (- a t))
             (if (<= t 3.1e+132)
               t_2
               (if (<= t 1.7e+201)
                 (/ t (/ (- t a) y))
                 (if (<= t 1.05e+228) t_2 t_1))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (a / (t / (y - x)));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (t <= -2.8e+167) {
		tmp = t_1;
	} else if (t <= -2.7e+50) {
		tmp = x - (x * (z / (a - t)));
	} else if (t <= -1.1e+25) {
		tmp = t_1;
	} else if (t <= 3.3e-52) {
		tmp = x - ((x - y) / (a / z));
	} else if (t <= 6.2e+63) {
		tmp = (y * (z - t)) / (a - t);
	} else if (t <= 3.1e+132) {
		tmp = t_2;
	} else if (t <= 1.7e+201) {
		tmp = t / ((t - a) / y);
	} else if (t <= 1.05e+228) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (a / (t / (y - x)))
    t_2 = z * ((y - x) / (a - t))
    if (t <= (-2.8d+167)) then
        tmp = t_1
    else if (t <= (-2.7d+50)) then
        tmp = x - (x * (z / (a - t)))
    else if (t <= (-1.1d+25)) then
        tmp = t_1
    else if (t <= 3.3d-52) then
        tmp = x - ((x - y) / (a / z))
    else if (t <= 6.2d+63) then
        tmp = (y * (z - t)) / (a - t)
    else if (t <= 3.1d+132) then
        tmp = t_2
    else if (t <= 1.7d+201) then
        tmp = t / ((t - a) / y)
    else if (t <= 1.05d+228) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (a / (t / (y - x)));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (t <= -2.8e+167) {
		tmp = t_1;
	} else if (t <= -2.7e+50) {
		tmp = x - (x * (z / (a - t)));
	} else if (t <= -1.1e+25) {
		tmp = t_1;
	} else if (t <= 3.3e-52) {
		tmp = x - ((x - y) / (a / z));
	} else if (t <= 6.2e+63) {
		tmp = (y * (z - t)) / (a - t);
	} else if (t <= 3.1e+132) {
		tmp = t_2;
	} else if (t <= 1.7e+201) {
		tmp = t / ((t - a) / y);
	} else if (t <= 1.05e+228) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (a / (t / (y - x)))
	t_2 = z * ((y - x) / (a - t))
	tmp = 0
	if t <= -2.8e+167:
		tmp = t_1
	elif t <= -2.7e+50:
		tmp = x - (x * (z / (a - t)))
	elif t <= -1.1e+25:
		tmp = t_1
	elif t <= 3.3e-52:
		tmp = x - ((x - y) / (a / z))
	elif t <= 6.2e+63:
		tmp = (y * (z - t)) / (a - t)
	elif t <= 3.1e+132:
		tmp = t_2
	elif t <= 1.7e+201:
		tmp = t / ((t - a) / y)
	elif t <= 1.05e+228:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(a / Float64(t / Float64(y - x))))
	t_2 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.8e+167)
		tmp = t_1;
	elseif (t <= -2.7e+50)
		tmp = Float64(x - Float64(x * Float64(z / Float64(a - t))));
	elseif (t <= -1.1e+25)
		tmp = t_1;
	elseif (t <= 3.3e-52)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	elseif (t <= 6.2e+63)
		tmp = Float64(Float64(y * Float64(z - t)) / Float64(a - t));
	elseif (t <= 3.1e+132)
		tmp = t_2;
	elseif (t <= 1.7e+201)
		tmp = Float64(t / Float64(Float64(t - a) / y));
	elseif (t <= 1.05e+228)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (a / (t / (y - x)));
	t_2 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (t <= -2.8e+167)
		tmp = t_1;
	elseif (t <= -2.7e+50)
		tmp = x - (x * (z / (a - t)));
	elseif (t <= -1.1e+25)
		tmp = t_1;
	elseif (t <= 3.3e-52)
		tmp = x - ((x - y) / (a / z));
	elseif (t <= 6.2e+63)
		tmp = (y * (z - t)) / (a - t);
	elseif (t <= 3.1e+132)
		tmp = t_2;
	elseif (t <= 1.7e+201)
		tmp = t / ((t - a) / y);
	elseif (t <= 1.05e+228)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+167], t$95$1, If[LessEqual[t, -2.7e+50], N[(x - N[(x * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.1e+25], t$95$1, If[LessEqual[t, 3.3e-52], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+63], N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e+132], t$95$2, If[LessEqual[t, 1.7e+201], N[(t / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+228], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.7999999999999999e167 or -2.7e50 < t < -1.1e25 or 1.04999999999999997e228 < t

   1. Initial program 26.3%

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

      1. associate-/l* 64.1%

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

   3. Simplified 64.1%

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

   4. Taylor expanded in z around 0 54.6%

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

      1. associate-*r/ 54.6%

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

      2. neg-mul-1 54.6%

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

   6. Simplified 54.6%

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

   7. Taylor expanded in a around 0 64.9%

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

      1. associate-/l* 75.1%

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

   9. Simplified 75.1%

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

   if -2.7999999999999999e167 < t < -2.7e50

   1. Initial program 68.1%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in x around inf 49.1%

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

      1. distribute-lft-in 49.1%

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

      2. mul-1-neg 49.1%

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

      3. distribute-rgt-neg-in 49.1%

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

      4. unsub-neg 49.1%

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

      5. *-rgt-identity 49.1%

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

   6. Simplified 49.1%

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

   7. Taylor expanded in z around inf 49.8%

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

   if -1.1e25 < t < 3.29999999999999995e-52

   1. Initial program 90.6%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in t around 0 75.1%

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

   if 3.29999999999999995e-52 < t < 6.2000000000000001e63

   1. Initial program 74.9%

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

      1. associate-*l/ 74.7%

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

   3. Simplified 74.7%

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

   4. Taylor expanded in x around 0 57.1%

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

   if 6.2000000000000001e63 < t < 3.0999999999999998e132 or 1.7e201 < t < 1.04999999999999997e228

   1. Initial program 29.8%

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

      1. associate-*l/ 58.9%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in z around inf 63.3%

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

      1. div-sub 63.3%

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

   6. Simplified 63.3%

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

   if 3.0999999999999998e132 < t < 1.7e201

   1. Initial program 62.5%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in z around 0 70.5%

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

      1. associate-*r/ 70.5%

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

      2. neg-mul-1 70.5%

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

   6. Simplified 70.5%

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

   7. Taylor expanded in x around 0 43.0%

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

      1. associate-/l* 80.0%

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

   9. Simplified 80.0%

      \[\leadsto \color{blue}{\frac{t}{\frac{t - a}{y}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+167}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+50}:\\ \;\;\;\;x - x \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+25}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-52}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+132}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+201}:\\ \;\;\;\;\frac{t}{\frac{t - a}{y}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+228}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 6: 58.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{a}{\frac{t}{y - x}}\\ t_2 := z \cdot \frac{y - x}{a - t}\\ t_3 := x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+90}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-188}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-135}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 210000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ a (/ t (- y x)))))
        (t_2 (* z (/ (- y x) (- a t))))
        (t_3 (- x (/ (- x y) (/ a z)))))
   (if (<= a -8.2e+90)
     t_3
     (if (<= a -1.2e-24)
       t_1
       (if (<= a 6.6e-188)
         (/ (* (- y x) z) (- a t))
         (if (<= a 5.3e-135)
           y
           (if (<= a 1.15e-40)
             t_2
             (if (<= a 210000000.0) t_1 (if (<= a 6.8e+14) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (a / (t / (y - x)));
	double t_2 = z * ((y - x) / (a - t));
	double t_3 = x - ((x - y) / (a / z));
	double tmp;
	if (a <= -8.2e+90) {
		tmp = t_3;
	} else if (a <= -1.2e-24) {
		tmp = t_1;
	} else if (a <= 6.6e-188) {
		tmp = ((y - x) * z) / (a - t);
	} else if (a <= 5.3e-135) {
		tmp = y;
	} else if (a <= 1.15e-40) {
		tmp = t_2;
	} else if (a <= 210000000.0) {
		tmp = t_1;
	} else if (a <= 6.8e+14) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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 + (a / (t / (y - x)))
    t_2 = z * ((y - x) / (a - t))
    t_3 = x - ((x - y) / (a / z))
    if (a <= (-8.2d+90)) then
        tmp = t_3
    else if (a <= (-1.2d-24)) then
        tmp = t_1
    else if (a <= 6.6d-188) then
        tmp = ((y - x) * z) / (a - t)
    else if (a <= 5.3d-135) then
        tmp = y
    else if (a <= 1.15d-40) then
        tmp = t_2
    else if (a <= 210000000.0d0) then
        tmp = t_1
    else if (a <= 6.8d+14) then
        tmp = t_2
    else
        tmp = t_3
    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 + (a / (t / (y - x)));
	double t_2 = z * ((y - x) / (a - t));
	double t_3 = x - ((x - y) / (a / z));
	double tmp;
	if (a <= -8.2e+90) {
		tmp = t_3;
	} else if (a <= -1.2e-24) {
		tmp = t_1;
	} else if (a <= 6.6e-188) {
		tmp = ((y - x) * z) / (a - t);
	} else if (a <= 5.3e-135) {
		tmp = y;
	} else if (a <= 1.15e-40) {
		tmp = t_2;
	} else if (a <= 210000000.0) {
		tmp = t_1;
	} else if (a <= 6.8e+14) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (a / (t / (y - x)))
	t_2 = z * ((y - x) / (a - t))
	t_3 = x - ((x - y) / (a / z))
	tmp = 0
	if a <= -8.2e+90:
		tmp = t_3
	elif a <= -1.2e-24:
		tmp = t_1
	elif a <= 6.6e-188:
		tmp = ((y - x) * z) / (a - t)
	elif a <= 5.3e-135:
		tmp = y
	elif a <= 1.15e-40:
		tmp = t_2
	elif a <= 210000000.0:
		tmp = t_1
	elif a <= 6.8e+14:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(a / Float64(t / Float64(y - x))))
	t_2 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	t_3 = Float64(x - Float64(Float64(x - y) / Float64(a / z)))
	tmp = 0.0
	if (a <= -8.2e+90)
		tmp = t_3;
	elseif (a <= -1.2e-24)
		tmp = t_1;
	elseif (a <= 6.6e-188)
		tmp = Float64(Float64(Float64(y - x) * z) / Float64(a - t));
	elseif (a <= 5.3e-135)
		tmp = y;
	elseif (a <= 1.15e-40)
		tmp = t_2;
	elseif (a <= 210000000.0)
		tmp = t_1;
	elseif (a <= 6.8e+14)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (a / (t / (y - x)));
	t_2 = z * ((y - x) / (a - t));
	t_3 = x - ((x - y) / (a / z));
	tmp = 0.0;
	if (a <= -8.2e+90)
		tmp = t_3;
	elseif (a <= -1.2e-24)
		tmp = t_1;
	elseif (a <= 6.6e-188)
		tmp = ((y - x) * z) / (a - t);
	elseif (a <= 5.3e-135)
		tmp = y;
	elseif (a <= 1.15e-40)
		tmp = t_2;
	elseif (a <= 210000000.0)
		tmp = t_1;
	elseif (a <= 6.8e+14)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.2e+90], t$95$3, If[LessEqual[a, -1.2e-24], t$95$1, If[LessEqual[a, 6.6e-188], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.3e-135], y, If[LessEqual[a, 1.15e-40], t$95$2, If[LessEqual[a, 210000000.0], t$95$1, If[LessEqual[a, 6.8e+14], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -8.20000000000000083e90 or 6.8e14 < a

   1. Initial program 71.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 t around 0 81.0%

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

   if -8.20000000000000083e90 < a < -1.1999999999999999e-24 or 1.15e-40 < a < 2.1e8

   1. Initial program 58.2%

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

      1. associate-/l* 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in z around 0 57.3%

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

      1. associate-*r/ 57.3%

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

      2. neg-mul-1 57.3%

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

   6. Simplified 57.3%

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

   7. Taylor expanded in a around 0 61.6%

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

      1. associate-/l* 70.8%

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

   9. Simplified 70.8%

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

   if -1.1999999999999999e-24 < a < 6.6000000000000005e-188

   1. Initial program 68.3%

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

      1. associate-*l/ 69.7%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in z around -inf 60.0%

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

   if 6.6000000000000005e-188 < a < 5.3e-135

   1. Initial program 46.1%

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

      1. associate-*l/ 61.5%

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

   3. Simplified 61.5%

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

   4. Taylor expanded in t around inf 59.8%

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

   if 5.3e-135 < a < 1.15e-40 or 2.1e8 < a < 6.8e14

   1. Initial program 71.6%

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

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around inf 64.8%

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

      1. div-sub 64.8%

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

   6. Simplified 64.8%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+90}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-24}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-188}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-135}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-40}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 210000000:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \]

Alternative 7: 82.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;t \leq -6 \cdot 10^{+192}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-250}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+212}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) (- a t))))))
   (if (<= t -6e+192)
     (+ y (/ a (/ t (- y x))))
     (if (<= t -8.5e-196)
       t_1
       (if (<= t 2.8e-250)
         (- x (/ (- x y) (/ a z)))
         (if (<= t 1.75e+212) t_1 (+ y (/ (* (- z a) (- x y)) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double tmp;
	if (t <= -6e+192) {
		tmp = y + (a / (t / (y - x)));
	} else if (t <= -8.5e-196) {
		tmp = t_1;
	} else if (t <= 2.8e-250) {
		tmp = x - ((x - y) / (a / z));
	} else if (t <= 1.75e+212) {
		tmp = t_1;
	} else {
		tmp = y + (((z - a) * (x - y)) / 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 + ((z - t) * ((y - x) / (a - t)))
    if (t <= (-6d+192)) then
        tmp = y + (a / (t / (y - x)))
    else if (t <= (-8.5d-196)) then
        tmp = t_1
    else if (t <= 2.8d-250) then
        tmp = x - ((x - y) / (a / z))
    else if (t <= 1.75d+212) then
        tmp = t_1
    else
        tmp = y + (((z - a) * (x - y)) / 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 + ((z - t) * ((y - x) / (a - t)));
	double tmp;
	if (t <= -6e+192) {
		tmp = y + (a / (t / (y - x)));
	} else if (t <= -8.5e-196) {
		tmp = t_1;
	} else if (t <= 2.8e-250) {
		tmp = x - ((x - y) / (a / z));
	} else if (t <= 1.75e+212) {
		tmp = t_1;
	} else {
		tmp = y + (((z - a) * (x - y)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) / (a - t)))
	tmp = 0
	if t <= -6e+192:
		tmp = y + (a / (t / (y - x)))
	elif t <= -8.5e-196:
		tmp = t_1
	elif t <= 2.8e-250:
		tmp = x - ((x - y) / (a / z))
	elif t <= 1.75e+212:
		tmp = t_1
	else:
		tmp = y + (((z - a) * (x - y)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))))
	tmp = 0.0
	if (t <= -6e+192)
		tmp = Float64(y + Float64(a / Float64(t / Float64(y - x))));
	elseif (t <= -8.5e-196)
		tmp = t_1;
	elseif (t <= 2.8e-250)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	elseif (t <= 1.75e+212)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) / (a - t)));
	tmp = 0.0;
	if (t <= -6e+192)
		tmp = y + (a / (t / (y - x)));
	elseif (t <= -8.5e-196)
		tmp = t_1;
	elseif (t <= 2.8e-250)
		tmp = x - ((x - y) / (a / z));
	elseif (t <= 1.75e+212)
		tmp = t_1;
	else
		tmp = y + (((z - a) * (x - y)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+192], N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.5e-196], t$95$1, If[LessEqual[t, 2.8e-250], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e+212], t$95$1, N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6e192

   1. Initial program 22.1%

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

      1. associate-/l* 63.2%

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

   3. Simplified 63.2%

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

   4. Taylor expanded in z around 0 59.1%

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

      1. associate-*r/ 59.1%

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

      2. neg-mul-1 59.1%

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

   6. Simplified 59.1%

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

   7. Taylor expanded in a around 0 72.1%

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

      1. associate-/l* 85.5%

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

   9. Simplified 85.5%

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

   if -6e192 < t < -8.50000000000000004e-196 or 2.80000000000000028e-250 < t < 1.74999999999999994e212

   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/ 86.1%

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

   3. Simplified 86.1%

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

   if -8.50000000000000004e-196 < t < 2.80000000000000028e-250

   1. Initial program 91.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 94.1%

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

   if 1.74999999999999994e212 < t

   1. Initial program 19.8%

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

      1. associate-*l/ 43.7%

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

   3. Simplified 43.7%

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

   4. Taylor expanded in t around inf 77.5%

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

      1. associate--l+ 77.5%

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

      2. associate-*r/ 77.5%

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

      3. associate-*r/ 77.5%

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

      4. div-sub 77.5%

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

      5. distribute-lft-out-- 77.5%

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

      6. mul-1-neg 77.5%

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

      7. distribute-neg-frac 77.5%

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

      8. unsub-neg 77.5%

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

      9. distribute-rgt-out-- 77.5%

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

   6. Simplified 77.5%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+192}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-196}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-250}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+212}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \end{array} \]

Alternative 8: 72.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y}{a - t}\\ t_2 := y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{if}\;t \leq -8 \cdot 10^{+191}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-162}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+215}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ y (- a t))))) (t_2 (+ y (/ a (/ t (- y x))))))
   (if (<= t -8e+191)
     t_2
     (if (<= t -1.95e-112)
       t_1
       (if (<= t 1.45e-162)
         (- x (/ (- x y) (/ a z)))
         (if (<= t 1.05e+215) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * (y / (a - t)));
	double t_2 = y + (a / (t / (y - x)));
	double tmp;
	if (t <= -8e+191) {
		tmp = t_2;
	} else if (t <= -1.95e-112) {
		tmp = t_1;
	} else if (t <= 1.45e-162) {
		tmp = x - ((x - y) / (a / z));
	} else if (t <= 1.05e+215) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z - t) * (y / (a - t)))
    t_2 = y + (a / (t / (y - x)))
    if (t <= (-8d+191)) then
        tmp = t_2
    else if (t <= (-1.95d-112)) then
        tmp = t_1
    else if (t <= 1.45d-162) then
        tmp = x - ((x - y) / (a / z))
    else if (t <= 1.05d+215) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * (y / (a - t)));
	double t_2 = y + (a / (t / (y - x)));
	double tmp;
	if (t <= -8e+191) {
		tmp = t_2;
	} else if (t <= -1.95e-112) {
		tmp = t_1;
	} else if (t <= 1.45e-162) {
		tmp = x - ((x - y) / (a / z));
	} else if (t <= 1.05e+215) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * (y / (a - t)))
	t_2 = y + (a / (t / (y - x)))
	tmp = 0
	if t <= -8e+191:
		tmp = t_2
	elif t <= -1.95e-112:
		tmp = t_1
	elif t <= 1.45e-162:
		tmp = x - ((x - y) / (a / z))
	elif t <= 1.05e+215:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))))
	t_2 = Float64(y + Float64(a / Float64(t / Float64(y - x))))
	tmp = 0.0
	if (t <= -8e+191)
		tmp = t_2;
	elseif (t <= -1.95e-112)
		tmp = t_1;
	elseif (t <= 1.45e-162)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	elseif (t <= 1.05e+215)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * (y / (a - t)));
	t_2 = y + (a / (t / (y - x)));
	tmp = 0.0;
	if (t <= -8e+191)
		tmp = t_2;
	elseif (t <= -1.95e-112)
		tmp = t_1;
	elseif (t <= 1.45e-162)
		tmp = x - ((x - y) / (a / z));
	elseif (t <= 1.05e+215)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e+191], t$95$2, If[LessEqual[t, -1.95e-112], t$95$1, If[LessEqual[t, 1.45e-162], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+215], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.00000000000000058e191 or 1.0500000000000001e215 < t

   1. Initial program 21.6%

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

      1. associate-/l* 58.6%

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

   3. Simplified 58.6%

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

   4. Taylor expanded in z around 0 53.8%

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

      1. associate-*r/ 53.8%

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

      2. neg-mul-1 53.8%

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

   6. Simplified 53.8%

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

   7. Taylor expanded in a around 0 69.4%

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

      1. associate-/l* 78.0%

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

   9. Simplified 78.0%

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

   if -8.00000000000000058e191 < t < -1.9500000000000001e-112 or 1.4500000000000001e-162 < t < 1.0500000000000001e215

   1. Initial program 70.6%

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

      1. associate-*l/ 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in y around inf 64.8%

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

   if -1.9500000000000001e-112 < t < 1.4500000000000001e-162

   1. Initial program 91.0%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in t around 0 86.0%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+191}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-112}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-162}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+215}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 9: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y}{a - t}\\ t_2 := y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-42}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+214}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ y (- a t))))) (t_2 (+ y (/ a (/ t (- y x))))))
   (if (<= t -9.2e+192)
     t_2
     (if (<= t -1.5e-112)
       t_1
       (if (<= t 1.35e-42)
         (- x (/ (- x y) (/ a (- z t))))
         (if (<= t 8e+214) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * (y / (a - t)));
	double t_2 = y + (a / (t / (y - x)));
	double tmp;
	if (t <= -9.2e+192) {
		tmp = t_2;
	} else if (t <= -1.5e-112) {
		tmp = t_1;
	} else if (t <= 1.35e-42) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else if (t <= 8e+214) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z - t) * (y / (a - t)))
    t_2 = y + (a / (t / (y - x)))
    if (t <= (-9.2d+192)) then
        tmp = t_2
    else if (t <= (-1.5d-112)) then
        tmp = t_1
    else if (t <= 1.35d-42) then
        tmp = x - ((x - y) / (a / (z - t)))
    else if (t <= 8d+214) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * (y / (a - t)));
	double t_2 = y + (a / (t / (y - x)));
	double tmp;
	if (t <= -9.2e+192) {
		tmp = t_2;
	} else if (t <= -1.5e-112) {
		tmp = t_1;
	} else if (t <= 1.35e-42) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else if (t <= 8e+214) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * (y / (a - t)))
	t_2 = y + (a / (t / (y - x)))
	tmp = 0
	if t <= -9.2e+192:
		tmp = t_2
	elif t <= -1.5e-112:
		tmp = t_1
	elif t <= 1.35e-42:
		tmp = x - ((x - y) / (a / (z - t)))
	elif t <= 8e+214:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))))
	t_2 = Float64(y + Float64(a / Float64(t / Float64(y - x))))
	tmp = 0.0
	if (t <= -9.2e+192)
		tmp = t_2;
	elseif (t <= -1.5e-112)
		tmp = t_1;
	elseif (t <= 1.35e-42)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / Float64(z - t))));
	elseif (t <= 8e+214)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * (y / (a - t)));
	t_2 = y + (a / (t / (y - x)));
	tmp = 0.0;
	if (t <= -9.2e+192)
		tmp = t_2;
	elseif (t <= -1.5e-112)
		tmp = t_1;
	elseif (t <= 1.35e-42)
		tmp = x - ((x - y) / (a / (z - t)));
	elseif (t <= 8e+214)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2e+192], t$95$2, If[LessEqual[t, -1.5e-112], t$95$1, If[LessEqual[t, 1.35e-42], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+214], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.1999999999999997e192 or 7.9999999999999996e214 < t

   1. Initial program 21.6%

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

      1. associate-/l* 58.6%

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

   3. Simplified 58.6%

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

   4. Taylor expanded in z around 0 53.8%

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

      1. associate-*r/ 53.8%

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

      2. neg-mul-1 53.8%

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

   6. Simplified 53.8%

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

   7. Taylor expanded in a around 0 69.4%

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

      1. associate-/l* 78.0%

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

   9. Simplified 78.0%

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

   if -9.1999999999999997e192 < t < -1.5e-112 or 1.35e-42 < t < 7.9999999999999996e214

   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/ 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in y around inf 64.0%

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

   if -1.5e-112 < t < 1.35e-42

   1. Initial program 89.2%

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

      1. associate-*l/ 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in a around inf 73.8%

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

      1. associate-/l* 80.5%

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

   6. Simplified 80.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+192}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-112}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-42}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+214}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 10: 72.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ t_2 := x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-159}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (* (- z a) (- x y)) t)))
        (t_2 (- x (/ (- x y) (/ a (- z t))))))
   (if (<= a -6.8e+20)
     t_2
     (if (<= a -1.5e-57)
       t_1
       (if (<= a -2.4e-159)
         (/ (* (- y x) z) (- a t))
         (if (<= a 6.2e+16) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((z - a) * (x - y)) / t);
	double t_2 = x - ((x - y) / (a / (z - t)));
	double tmp;
	if (a <= -6.8e+20) {
		tmp = t_2;
	} else if (a <= -1.5e-57) {
		tmp = t_1;
	} else if (a <= -2.4e-159) {
		tmp = ((y - x) * z) / (a - t);
	} else if (a <= 6.2e+16) {
		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 - a) * (x - y)) / t)
    t_2 = x - ((x - y) / (a / (z - t)))
    if (a <= (-6.8d+20)) then
        tmp = t_2
    else if (a <= (-1.5d-57)) then
        tmp = t_1
    else if (a <= (-2.4d-159)) then
        tmp = ((y - x) * z) / (a - t)
    else if (a <= 6.2d+16) 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 - a) * (x - y)) / t);
	double t_2 = x - ((x - y) / (a / (z - t)));
	double tmp;
	if (a <= -6.8e+20) {
		tmp = t_2;
	} else if (a <= -1.5e-57) {
		tmp = t_1;
	} else if (a <= -2.4e-159) {
		tmp = ((y - x) * z) / (a - t);
	} else if (a <= 6.2e+16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (((z - a) * (x - y)) / t)
	t_2 = x - ((x - y) / (a / (z - t)))
	tmp = 0
	if a <= -6.8e+20:
		tmp = t_2
	elif a <= -1.5e-57:
		tmp = t_1
	elif a <= -2.4e-159:
		tmp = ((y - x) * z) / (a - t)
	elif a <= 6.2e+16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t))
	t_2 = Float64(x - Float64(Float64(x - y) / Float64(a / Float64(z - t))))
	tmp = 0.0
	if (a <= -6.8e+20)
		tmp = t_2;
	elseif (a <= -1.5e-57)
		tmp = t_1;
	elseif (a <= -2.4e-159)
		tmp = Float64(Float64(Float64(y - x) * z) / Float64(a - t));
	elseif (a <= 6.2e+16)
		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 - a) * (x - y)) / t);
	t_2 = x - ((x - y) / (a / (z - t)));
	tmp = 0.0;
	if (a <= -6.8e+20)
		tmp = t_2;
	elseif (a <= -1.5e-57)
		tmp = t_1;
	elseif (a <= -2.4e-159)
		tmp = ((y - x) * z) / (a - t);
	elseif (a <= 6.2e+16)
		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[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.8e+20], t$95$2, If[LessEqual[a, -1.5e-57], t$95$1, If[LessEqual[a, -2.4e-159], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e+16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.8e20 or 6.2e16 < a

   1. Initial program 71.4%

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

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

   4. Taylor expanded in a around inf 67.8%

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

      1. associate-/l* 81.5%

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

   6. Simplified 81.5%

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

   if -6.8e20 < a < -1.5e-57 or -2.39999999999999997e-159 < a < 6.2e16

   1. Initial program 61.5%

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

      1. associate-*l/ 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in t around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. associate-*r/ 76.2%

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

      3. associate-*r/ 76.2%

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

      4. div-sub 77.0%

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

      5. distribute-lft-out-- 77.0%

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

      6. mul-1-neg 77.0%

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

      7. distribute-neg-frac 77.0%

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

      8. unsub-neg 77.0%

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

      9. distribute-rgt-out-- 77.0%

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

   6. Simplified 77.0%

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

   if -1.5e-57 < a < -2.39999999999999997e-159

   1. Initial program 85.0%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in z around -inf 67.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+20}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-57}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-159}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+16}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 11: 50.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+167}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+122}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+37}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-301}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+167)
   y
   (if (<= t -4.8e+122)
     (- x (/ t (/ a y)))
     (if (<= t -3.8e+37)
       y
       (if (<= t -1.5e-301)
         (- x (* x (/ z a)))
         (if (<= t 2.4e+47) (+ x (/ (* y z) a)) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+167) {
		tmp = y;
	} else if (t <= -4.8e+122) {
		tmp = x - (t / (a / y));
	} else if (t <= -3.8e+37) {
		tmp = y;
	} else if (t <= -1.5e-301) {
		tmp = x - (x * (z / a));
	} else if (t <= 2.4e+47) {
		tmp = x + ((y * z) / a);
	} 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 <= (-2.8d+167)) then
        tmp = y
    else if (t <= (-4.8d+122)) then
        tmp = x - (t / (a / y))
    else if (t <= (-3.8d+37)) then
        tmp = y
    else if (t <= (-1.5d-301)) then
        tmp = x - (x * (z / a))
    else if (t <= 2.4d+47) then
        tmp = x + ((y * z) / a)
    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 <= -2.8e+167) {
		tmp = y;
	} else if (t <= -4.8e+122) {
		tmp = x - (t / (a / y));
	} else if (t <= -3.8e+37) {
		tmp = y;
	} else if (t <= -1.5e-301) {
		tmp = x - (x * (z / a));
	} else if (t <= 2.4e+47) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+167:
		tmp = y
	elif t <= -4.8e+122:
		tmp = x - (t / (a / y))
	elif t <= -3.8e+37:
		tmp = y
	elif t <= -1.5e-301:
		tmp = x - (x * (z / a))
	elif t <= 2.4e+47:
		tmp = x + ((y * z) / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+167)
		tmp = y;
	elseif (t <= -4.8e+122)
		tmp = Float64(x - Float64(t / Float64(a / y)));
	elseif (t <= -3.8e+37)
		tmp = y;
	elseif (t <= -1.5e-301)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= 2.4e+47)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+167)
		tmp = y;
	elseif (t <= -4.8e+122)
		tmp = x - (t / (a / y));
	elseif (t <= -3.8e+37)
		tmp = y;
	elseif (t <= -1.5e-301)
		tmp = x - (x * (z / a));
	elseif (t <= 2.4e+47)
		tmp = x + ((y * z) / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+167], y, If[LessEqual[t, -4.8e+122], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e+37], y, If[LessEqual[t, -1.5e-301], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+47], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], y]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.7999999999999999e167 or -4.8000000000000004e122 < t < -3.7999999999999999e37 or 2.40000000000000019e47 < t

   1. Initial program 35.0%

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

      1. associate-*l/ 63.8%

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

   3. Simplified 63.8%

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

   4. Taylor expanded in t around inf 53.9%

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

   if -2.7999999999999999e167 < t < -4.8000000000000004e122

   1. Initial program 67.8%

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

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in a around inf 47.3%

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

      1. associate-/l* 57.8%

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

   6. Simplified 57.8%

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

   7. Taylor expanded in y around inf 47.8%

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

   8. Taylor expanded in z around 0 46.6%

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

      1. mul-1-neg 46.6%

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

      2. unsub-neg 46.6%

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

      3. associate-/l* 54.1%

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

   10. Simplified 54.1%

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

   if -3.7999999999999999e37 < t < -1.5e-301

   1. Initial program 86.7%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in x around inf 57.9%

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

      1. distribute-lft-in 57.8%

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

      2. mul-1-neg 57.8%

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

      3. distribute-rgt-neg-in 57.8%

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

      4. unsub-neg 57.8%

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

      5. *-rgt-identity 57.8%

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

   6. Simplified 57.8%

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

   7. Taylor expanded in t around 0 51.2%

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

   if -1.5e-301 < t < 2.40000000000000019e47

   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/ 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in a around inf 67.9%

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

      1. associate-/l* 71.6%

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

   6. Simplified 71.6%

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

   7. Taylor expanded in y around inf 61.6%

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

   8. Taylor expanded in z around inf 59.3%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+167}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+122}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+37}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-301}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 12: 50.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+167}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+122}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+39}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-300}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+167)
   y
   (if (<= t -4e+122)
     (- x (/ t (/ a y)))
     (if (<= t -1.9e+39)
       y
       (if (<= t -2.2e-300)
         (- x (/ x (/ a z)))
         (if (<= t 1.7e+47) (+ x (/ (* y z) a)) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+167) {
		tmp = y;
	} else if (t <= -4e+122) {
		tmp = x - (t / (a / y));
	} else if (t <= -1.9e+39) {
		tmp = y;
	} else if (t <= -2.2e-300) {
		tmp = x - (x / (a / z));
	} else if (t <= 1.7e+47) {
		tmp = x + ((y * z) / a);
	} 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 <= (-2.8d+167)) then
        tmp = y
    else if (t <= (-4d+122)) then
        tmp = x - (t / (a / y))
    else if (t <= (-1.9d+39)) then
        tmp = y
    else if (t <= (-2.2d-300)) then
        tmp = x - (x / (a / z))
    else if (t <= 1.7d+47) then
        tmp = x + ((y * z) / a)
    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 <= -2.8e+167) {
		tmp = y;
	} else if (t <= -4e+122) {
		tmp = x - (t / (a / y));
	} else if (t <= -1.9e+39) {
		tmp = y;
	} else if (t <= -2.2e-300) {
		tmp = x - (x / (a / z));
	} else if (t <= 1.7e+47) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+167:
		tmp = y
	elif t <= -4e+122:
		tmp = x - (t / (a / y))
	elif t <= -1.9e+39:
		tmp = y
	elif t <= -2.2e-300:
		tmp = x - (x / (a / z))
	elif t <= 1.7e+47:
		tmp = x + ((y * z) / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+167)
		tmp = y;
	elseif (t <= -4e+122)
		tmp = Float64(x - Float64(t / Float64(a / y)));
	elseif (t <= -1.9e+39)
		tmp = y;
	elseif (t <= -2.2e-300)
		tmp = Float64(x - Float64(x / Float64(a / z)));
	elseif (t <= 1.7e+47)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+167)
		tmp = y;
	elseif (t <= -4e+122)
		tmp = x - (t / (a / y));
	elseif (t <= -1.9e+39)
		tmp = y;
	elseif (t <= -2.2e-300)
		tmp = x - (x / (a / z));
	elseif (t <= 1.7e+47)
		tmp = x + ((y * z) / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+167], y, If[LessEqual[t, -4e+122], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.9e+39], y, If[LessEqual[t, -2.2e-300], N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+47], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], y]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.7999999999999999e167 or -4.00000000000000006e122 < t < -1.8999999999999999e39 or 1.6999999999999999e47 < t

   1. Initial program 35.0%

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

      1. associate-*l/ 63.8%

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

   3. Simplified 63.8%

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

   4. Taylor expanded in t around inf 53.9%

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

   if -2.7999999999999999e167 < t < -4.00000000000000006e122

   1. Initial program 67.8%

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

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in a around inf 47.3%

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

      1. associate-/l* 57.8%

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

   6. Simplified 57.8%

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

   7. Taylor expanded in y around inf 47.8%

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

   8. Taylor expanded in z around 0 46.6%

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

      1. mul-1-neg 46.6%

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

      2. unsub-neg 46.6%

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

      3. associate-/l* 54.1%

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

   10. Simplified 54.1%

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

   if -1.8999999999999999e39 < t < -2.20000000000000002e-300

   1. Initial program 86.7%

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

      1. +-commutative 86.7%

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

      2. associate-*l/ 91.0%

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

      3. fma-def 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in y around 0 57.4%

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

      1. neg-mul-1 57.4%

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

      2. distribute-neg-frac 57.4%

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

   6. Simplified 57.4%

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

   7. Taylor expanded in t around 0 46.3%

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

      1. mul-1-neg 46.3%

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

      2. unsub-neg 46.3%

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

      3. associate-/l* 51.2%

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

   9. Simplified 51.2%

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

   if -2.20000000000000002e-300 < t < 1.6999999999999999e47

   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/ 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in a around inf 67.9%

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

      1. associate-/l* 71.6%

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

   6. Simplified 71.6%

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

   7. Taylor expanded in y around inf 61.6%

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

   8. Taylor expanded in z around inf 59.3%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+167}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+122}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+39}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-300}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 13: 50.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+167}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{+122}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{+39}:\\ \;\;\;\;\frac{t}{\frac{t - a}{y}}\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-301}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+167)
   y
   (if (<= t -2.55e+122)
     (- x (/ t (/ a y)))
     (if (<= t -1.95e+39)
       (/ t (/ (- t a) y))
       (if (<= t -6.6e-301)
         (- x (/ x (/ a z)))
         (if (<= t 2.3e+45) (+ x (/ (* y z) a)) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+167) {
		tmp = y;
	} else if (t <= -2.55e+122) {
		tmp = x - (t / (a / y));
	} else if (t <= -1.95e+39) {
		tmp = t / ((t - a) / y);
	} else if (t <= -6.6e-301) {
		tmp = x - (x / (a / z));
	} else if (t <= 2.3e+45) {
		tmp = x + ((y * z) / a);
	} 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 <= (-2.8d+167)) then
        tmp = y
    else if (t <= (-2.55d+122)) then
        tmp = x - (t / (a / y))
    else if (t <= (-1.95d+39)) then
        tmp = t / ((t - a) / y)
    else if (t <= (-6.6d-301)) then
        tmp = x - (x / (a / z))
    else if (t <= 2.3d+45) then
        tmp = x + ((y * z) / a)
    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 <= -2.8e+167) {
		tmp = y;
	} else if (t <= -2.55e+122) {
		tmp = x - (t / (a / y));
	} else if (t <= -1.95e+39) {
		tmp = t / ((t - a) / y);
	} else if (t <= -6.6e-301) {
		tmp = x - (x / (a / z));
	} else if (t <= 2.3e+45) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+167:
		tmp = y
	elif t <= -2.55e+122:
		tmp = x - (t / (a / y))
	elif t <= -1.95e+39:
		tmp = t / ((t - a) / y)
	elif t <= -6.6e-301:
		tmp = x - (x / (a / z))
	elif t <= 2.3e+45:
		tmp = x + ((y * z) / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+167)
		tmp = y;
	elseif (t <= -2.55e+122)
		tmp = Float64(x - Float64(t / Float64(a / y)));
	elseif (t <= -1.95e+39)
		tmp = Float64(t / Float64(Float64(t - a) / y));
	elseif (t <= -6.6e-301)
		tmp = Float64(x - Float64(x / Float64(a / z)));
	elseif (t <= 2.3e+45)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+167)
		tmp = y;
	elseif (t <= -2.55e+122)
		tmp = x - (t / (a / y));
	elseif (t <= -1.95e+39)
		tmp = t / ((t - a) / y);
	elseif (t <= -6.6e-301)
		tmp = x - (x / (a / z));
	elseif (t <= 2.3e+45)
		tmp = x + ((y * z) / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+167], y, If[LessEqual[t, -2.55e+122], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.95e+39], N[(t / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.6e-301], N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+45], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], y]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.7999999999999999e167 or 2.30000000000000012e45 < t

   1. Initial program 31.7%

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

      1. associate-*l/ 61.7%

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

   3. Simplified 61.7%

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

   4. Taylor expanded in t around inf 54.9%

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

   if -2.7999999999999999e167 < t < -2.55e122

   1. Initial program 67.8%

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

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in a around inf 47.3%

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

      1. associate-/l* 57.8%

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

   6. Simplified 57.8%

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

   7. Taylor expanded in y around inf 47.8%

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

   8. Taylor expanded in z around 0 46.6%

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

      1. mul-1-neg 46.6%

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

      2. unsub-neg 46.6%

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

      3. associate-/l* 54.1%

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

   10. Simplified 54.1%

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

   if -2.55e122 < t < -1.95e39

   1. Initial program 55.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 z around 0 47.6%

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

      1. associate-*r/ 47.6%

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

      2. neg-mul-1 47.6%

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

   6. Simplified 47.6%

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

   7. Taylor expanded in x around 0 40.7%

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

      1. associate-/l* 55.2%

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

   9. Simplified 55.2%

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

   if -1.95e39 < t < -6.6000000000000001e-301

   1. Initial program 86.7%

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

      1. +-commutative 86.7%

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

      2. associate-*l/ 91.0%

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

      3. fma-def 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in y around 0 57.4%

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

      1. neg-mul-1 57.4%

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

      2. distribute-neg-frac 57.4%

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

   6. Simplified 57.4%

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

   7. Taylor expanded in t around 0 46.3%

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

      1. mul-1-neg 46.3%

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

      2. unsub-neg 46.3%

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

      3. associate-/l* 51.2%

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

   9. Simplified 51.2%

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

   if -6.6000000000000001e-301 < t < 2.30000000000000012e45

   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/ 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in a around inf 67.9%

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

      1. associate-/l* 71.6%

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

   6. Simplified 71.6%

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

   7. Taylor expanded in y around inf 61.6%

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

   8. Taylor expanded in z around inf 59.3%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+167}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{+122}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{+39}:\\ \;\;\;\;\frac{t}{\frac{t - a}{y}}\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-301}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 14: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{+57}:\\ \;\;\;\;x - x \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+24} \lor \neg \left(t \leq 1.45 \cdot 10^{+99}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ a (/ t (- y x))))))
   (if (<= t -2.8e+167)
     t_1
     (if (<= t -6.2e+57)
       (- x (* x (/ z (- a t))))
       (if (or (<= t -7.2e+24) (not (<= t 1.45e+99)))
         t_1
         (- x (/ (- x y) (/ a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (a / (t / (y - x)));
	double tmp;
	if (t <= -2.8e+167) {
		tmp = t_1;
	} else if (t <= -6.2e+57) {
		tmp = x - (x * (z / (a - t)));
	} else if ((t <= -7.2e+24) || !(t <= 1.45e+99)) {
		tmp = t_1;
	} else {
		tmp = x - ((x - y) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (a / (t / (y - x)))
    if (t <= (-2.8d+167)) then
        tmp = t_1
    else if (t <= (-6.2d+57)) then
        tmp = x - (x * (z / (a - t)))
    else if ((t <= (-7.2d+24)) .or. (.not. (t <= 1.45d+99))) then
        tmp = t_1
    else
        tmp = x - ((x - y) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (a / (t / (y - x)));
	double tmp;
	if (t <= -2.8e+167) {
		tmp = t_1;
	} else if (t <= -6.2e+57) {
		tmp = x - (x * (z / (a - t)));
	} else if ((t <= -7.2e+24) || !(t <= 1.45e+99)) {
		tmp = t_1;
	} else {
		tmp = x - ((x - y) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (a / (t / (y - x)))
	tmp = 0
	if t <= -2.8e+167:
		tmp = t_1
	elif t <= -6.2e+57:
		tmp = x - (x * (z / (a - t)))
	elif (t <= -7.2e+24) or not (t <= 1.45e+99):
		tmp = t_1
	else:
		tmp = x - ((x - y) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(a / Float64(t / Float64(y - x))))
	tmp = 0.0
	if (t <= -2.8e+167)
		tmp = t_1;
	elseif (t <= -6.2e+57)
		tmp = Float64(x - Float64(x * Float64(z / Float64(a - t))));
	elseif ((t <= -7.2e+24) || !(t <= 1.45e+99))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (a / (t / (y - x)));
	tmp = 0.0;
	if (t <= -2.8e+167)
		tmp = t_1;
	elseif (t <= -6.2e+57)
		tmp = x - (x * (z / (a - t)));
	elseif ((t <= -7.2e+24) || ~((t <= 1.45e+99)))
		tmp = t_1;
	else
		tmp = x - ((x - y) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+167], t$95$1, If[LessEqual[t, -6.2e+57], N[(x - N[(x * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -7.2e+24], N[Not[LessEqual[t, 1.45e+99]], $MachinePrecision]], t$95$1, N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7999999999999999e167 or -6.20000000000000026e57 < t < -7.19999999999999966e24 or 1.4500000000000001e99 < t

   1. Initial program 29.5%

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

      1. associate-/l* 65.1%

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

   3. Simplified 65.1%

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

   4. Taylor expanded in z around 0 48.9%

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

      1. associate-*r/ 48.9%

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

      2. neg-mul-1 48.9%

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

   6. Simplified 48.9%

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

   7. Taylor expanded in a around 0 58.8%

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

      1. associate-/l* 66.0%

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

   9. Simplified 66.0%

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

   if -2.7999999999999999e167 < t < -6.20000000000000026e57

   1. Initial program 68.1%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in x around inf 49.1%

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

      1. distribute-lft-in 49.1%

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

      2. mul-1-neg 49.1%

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

      3. distribute-rgt-neg-in 49.1%

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

      4. unsub-neg 49.1%

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

      5. *-rgt-identity 49.1%

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

   6. Simplified 49.1%

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

   7. Taylor expanded in z around inf 49.8%

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

   if -7.19999999999999966e24 < t < 1.4500000000000001e99

   1. Initial program 87.4%

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

      1. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in t around 0 69.7%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+167}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{+57}:\\ \;\;\;\;x - x \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+24} \lor \neg \left(t \leq 1.45 \cdot 10^{+99}\right):\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \]

Alternative 15: 61.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+167}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+122}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{\frac{t - a}{y}}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+100}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3e+167)
   y
   (if (<= t -1.7e+122)
     (- x (/ t (/ a y)))
     (if (<= t -9.6e+36)
       (/ t (/ (- t a) y))
       (if (<= t 4.9e+100) (- x (/ (- x y) (/ a z))) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3e+167) {
		tmp = y;
	} else if (t <= -1.7e+122) {
		tmp = x - (t / (a / y));
	} else if (t <= -9.6e+36) {
		tmp = t / ((t - a) / y);
	} else if (t <= 4.9e+100) {
		tmp = x - ((x - y) / (a / z));
	} 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 <= (-3d+167)) then
        tmp = y
    else if (t <= (-1.7d+122)) then
        tmp = x - (t / (a / y))
    else if (t <= (-9.6d+36)) then
        tmp = t / ((t - a) / y)
    else if (t <= 4.9d+100) then
        tmp = x - ((x - y) / (a / z))
    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 <= -3e+167) {
		tmp = y;
	} else if (t <= -1.7e+122) {
		tmp = x - (t / (a / y));
	} else if (t <= -9.6e+36) {
		tmp = t / ((t - a) / y);
	} else if (t <= 4.9e+100) {
		tmp = x - ((x - y) / (a / z));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3e+167:
		tmp = y
	elif t <= -1.7e+122:
		tmp = x - (t / (a / y))
	elif t <= -9.6e+36:
		tmp = t / ((t - a) / y)
	elif t <= 4.9e+100:
		tmp = x - ((x - y) / (a / z))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3e+167)
		tmp = y;
	elseif (t <= -1.7e+122)
		tmp = Float64(x - Float64(t / Float64(a / y)));
	elseif (t <= -9.6e+36)
		tmp = Float64(t / Float64(Float64(t - a) / y));
	elseif (t <= 4.9e+100)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3e+167)
		tmp = y;
	elseif (t <= -1.7e+122)
		tmp = x - (t / (a / y));
	elseif (t <= -9.6e+36)
		tmp = t / ((t - a) / y);
	elseif (t <= 4.9e+100)
		tmp = x - ((x - y) / (a / z));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3e+167], y, If[LessEqual[t, -1.7e+122], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.6e+36], N[(t / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.9e+100], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.00000000000000012e167 or 4.89999999999999967e100 < t

   1. Initial program 28.6%

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

      1. associate-*l/ 61.0%

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

   3. Simplified 61.0%

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

   4. Taylor expanded in t around inf 58.6%

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

   if -3.00000000000000012e167 < t < -1.7e122

   1. Initial program 67.8%

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

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in a around inf 47.3%

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

      1. associate-/l* 57.8%

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

   6. Simplified 57.8%

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

   7. Taylor expanded in y around inf 47.8%

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

   8. Taylor expanded in z around 0 46.6%

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

      1. mul-1-neg 46.6%

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

      2. unsub-neg 46.6%

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

      3. associate-/l* 54.1%

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

   10. Simplified 54.1%

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

   if -1.7e122 < t < -9.5999999999999997e36

   1. Initial program 55.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 z around 0 47.6%

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

      1. associate-*r/ 47.6%

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

      2. neg-mul-1 47.6%

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

   6. Simplified 47.6%

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

   7. Taylor expanded in x around 0 40.7%

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

      1. associate-/l* 55.2%

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

   9. Simplified 55.2%

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

   if -9.5999999999999997e36 < t < 4.89999999999999967e100

   1. Initial program 86.0%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in t around 0 68.2%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+167}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+122}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{\frac{t - a}{y}}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+100}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 16: 36.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a}\\ \mathbf{if}\;t \leq -24000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-299}:\\ \;\;\;\;z \cdot \frac{-x}{a}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) a))))
   (if (<= t -24000.0)
     y
     (if (<= t -4.9e-182)
       t_1
       (if (<= t -2.7e-299) (* z (/ (- x) a)) (if (<= t 2.05e-78) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / a);
	double tmp;
	if (t <= -24000.0) {
		tmp = y;
	} else if (t <= -4.9e-182) {
		tmp = t_1;
	} else if (t <= -2.7e-299) {
		tmp = z * (-x / a);
	} else if (t <= 2.05e-78) {
		tmp = t_1;
	} 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 = y * ((z - t) / a)
    if (t <= (-24000.0d0)) then
        tmp = y
    else if (t <= (-4.9d-182)) then
        tmp = t_1
    else if (t <= (-2.7d-299)) then
        tmp = z * (-x / a)
    else if (t <= 2.05d-78) then
        tmp = t_1
    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 = y * ((z - t) / a);
	double tmp;
	if (t <= -24000.0) {
		tmp = y;
	} else if (t <= -4.9e-182) {
		tmp = t_1;
	} else if (t <= -2.7e-299) {
		tmp = z * (-x / a);
	} else if (t <= 2.05e-78) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / a)
	tmp = 0
	if t <= -24000.0:
		tmp = y
	elif t <= -4.9e-182:
		tmp = t_1
	elif t <= -2.7e-299:
		tmp = z * (-x / a)
	elif t <= 2.05e-78:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / a))
	tmp = 0.0
	if (t <= -24000.0)
		tmp = y;
	elseif (t <= -4.9e-182)
		tmp = t_1;
	elseif (t <= -2.7e-299)
		tmp = Float64(z * Float64(Float64(-x) / a));
	elseif (t <= 2.05e-78)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / a);
	tmp = 0.0;
	if (t <= -24000.0)
		tmp = y;
	elseif (t <= -4.9e-182)
		tmp = t_1;
	elseif (t <= -2.7e-299)
		tmp = z * (-x / a);
	elseif (t <= 2.05e-78)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -24000.0], y, If[LessEqual[t, -4.9e-182], t$95$1, If[LessEqual[t, -2.7e-299], N[(z * N[((-x) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e-78], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -24000 or 2.0499999999999999e-78 < t

   1. Initial program 48.7%

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

      1. associate-*l/ 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in t around inf 44.0%

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

   if -24000 < t < -4.9000000000000003e-182 or -2.70000000000000002e-299 < t < 2.0499999999999999e-78

   1. Initial program 91.4%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in a around inf 70.4%

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

      1. associate-/l* 76.9%

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

   6. Simplified 76.9%

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

   7. Taylor expanded in y around inf 41.7%

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

      1. div-sub 41.7%

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

   9. Simplified 41.7%

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

   if -4.9000000000000003e-182 < t < -2.70000000000000002e-299

   1. Initial program 89.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 a around inf 78.2%

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

      1. associate-/l* 88.6%

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

   6. Simplified 88.6%

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

   7. Taylor expanded in z around inf 44.7%

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

      1. div-sub 48.5%

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

   9. Simplified 48.5%

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

   10. Taylor expanded in y around 0 40.7%

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

       1. associate-*r/ 40.7%

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

       2. neg-mul-1 40.7%

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

   12. Simplified 40.7%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -24000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-182}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-299}:\\ \;\;\;\;z \cdot \frac{-x}{a}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 17: 51.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{a}\\ \mathbf{if}\;t \leq -1300000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-299}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) a))))
   (if (<= t -1300000.0)
     y
     (if (<= t -3.6e-239)
       t_1
       (if (<= t -1.3e-299) (* z (/ (- y x) a)) (if (<= t 1.6e+46) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * z) / a);
	double tmp;
	if (t <= -1300000.0) {
		tmp = y;
	} else if (t <= -3.6e-239) {
		tmp = t_1;
	} else if (t <= -1.3e-299) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.6e+46) {
		tmp = t_1;
	} 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 * z) / a)
    if (t <= (-1300000.0d0)) then
        tmp = y
    else if (t <= (-3.6d-239)) then
        tmp = t_1
    else if (t <= (-1.3d-299)) then
        tmp = z * ((y - x) / a)
    else if (t <= 1.6d+46) then
        tmp = t_1
    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 * z) / a);
	double tmp;
	if (t <= -1300000.0) {
		tmp = y;
	} else if (t <= -3.6e-239) {
		tmp = t_1;
	} else if (t <= -1.3e-299) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.6e+46) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * z) / a)
	tmp = 0
	if t <= -1300000.0:
		tmp = y
	elif t <= -3.6e-239:
		tmp = t_1
	elif t <= -1.3e-299:
		tmp = z * ((y - x) / a)
	elif t <= 1.6e+46:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * z) / a))
	tmp = 0.0
	if (t <= -1300000.0)
		tmp = y;
	elseif (t <= -3.6e-239)
		tmp = t_1;
	elseif (t <= -1.3e-299)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 1.6e+46)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * z) / a);
	tmp = 0.0;
	if (t <= -1300000.0)
		tmp = y;
	elseif (t <= -3.6e-239)
		tmp = t_1;
	elseif (t <= -1.3e-299)
		tmp = z * ((y - x) / a);
	elseif (t <= 1.6e+46)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1300000.0], y, If[LessEqual[t, -3.6e-239], t$95$1, If[LessEqual[t, -1.3e-299], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+46], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3e6 or 1.5999999999999999e46 < t

   1. Initial program 41.4%

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

      1. associate-*l/ 68.5%

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

   3. Simplified 68.5%

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

   4. Taylor expanded in t around inf 47.6%

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

   if -1.3e6 < t < -3.6000000000000001e-239 or -1.2999999999999999e-299 < t < 1.5999999999999999e46

   1. Initial program 89.0%

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

      1. associate-*l/ 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in a around inf 66.6%

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

      1. associate-/l* 72.5%

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

   6. Simplified 72.5%

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

   7. Taylor expanded in y around inf 59.6%

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

   8. Taylor expanded in z around inf 56.9%

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

   if -3.6000000000000001e-239 < t < -1.2999999999999999e-299

   1. Initial program 86.5%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in a around inf 80.0%

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

      1. associate-/l* 93.3%

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

   6. Simplified 93.3%

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

   7. Taylor expanded in z around inf 59.9%

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

      1. div-sub 59.9%

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

   9. Simplified 59.9%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1300000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-239}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-299}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 18: 38.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-113}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-219}:\\ \;\;\;\;\frac{-z}{\frac{-t}{x}}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+16}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e+149)
   x
   (if (<= a -1.5e-113)
     y
     (if (<= a -1.6e-219) (/ (- z) (/ (- t) x)) (if (<= a 4.2e+16) y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e+149) {
		tmp = x;
	} else if (a <= -1.5e-113) {
		tmp = y;
	} else if (a <= -1.6e-219) {
		tmp = -z / (-t / x);
	} else if (a <= 4.2e+16) {
		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 <= (-1.6d+149)) then
        tmp = x
    else if (a <= (-1.5d-113)) then
        tmp = y
    else if (a <= (-1.6d-219)) then
        tmp = -z / (-t / x)
    else if (a <= 4.2d+16) 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 <= -1.6e+149) {
		tmp = x;
	} else if (a <= -1.5e-113) {
		tmp = y;
	} else if (a <= -1.6e-219) {
		tmp = -z / (-t / x);
	} else if (a <= 4.2e+16) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e+149:
		tmp = x
	elif a <= -1.5e-113:
		tmp = y
	elif a <= -1.6e-219:
		tmp = -z / (-t / x)
	elif a <= 4.2e+16:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e+149)
		tmp = x;
	elseif (a <= -1.5e-113)
		tmp = y;
	elseif (a <= -1.6e-219)
		tmp = Float64(Float64(-z) / Float64(Float64(-t) / x));
	elseif (a <= 4.2e+16)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e+149)
		tmp = x;
	elseif (a <= -1.5e-113)
		tmp = y;
	elseif (a <= -1.6e-219)
		tmp = -z / (-t / x);
	elseif (a <= 4.2e+16)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e+149], x, If[LessEqual[a, -1.5e-113], y, If[LessEqual[a, -1.6e-219], N[((-z) / N[((-t) / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e+16], y, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6000000000000001e149 or 4.2e16 < a

   1. Initial program 71.8%

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

      1. associate-*l/ 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in a around inf 47.9%

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

   if -1.6000000000000001e149 < a < -1.5e-113 or -1.59999999999999999e-219 < a < 4.2e16

   1. Initial program 65.2%

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

      1. associate-*l/ 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in t around inf 39.3%

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

   if -1.5e-113 < a < -1.59999999999999999e-219

   1. Initial program 67.0%

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

      1. associate-*l/ 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in z around -inf 71.0%

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

   5. Taylor expanded in a around 0 52.9%

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

      1. mul-1-neg 52.9%

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

      2. associate-/l* 56.0%

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

   7. Simplified 56.0%

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

   8. Taylor expanded in y around 0 49.7%

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

      1. associate-*r/ 49.7%

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

      2. neg-mul-1 49.7%

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

   10. Simplified 49.7%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-113}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-219}:\\ \;\;\;\;\frac{-z}{\frac{-t}{x}}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+16}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+34}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-300}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.65e+34)
   y
   (if (<= t -2.25e-300)
     (- x (* x (/ z a)))
     (if (<= t 2.4e+47) (+ x (/ (* y z) a)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.65e+34) {
		tmp = y;
	} else if (t <= -2.25e-300) {
		tmp = x - (x * (z / a));
	} else if (t <= 2.4e+47) {
		tmp = x + ((y * z) / a);
	} 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 <= (-1.65d+34)) then
        tmp = y
    else if (t <= (-2.25d-300)) then
        tmp = x - (x * (z / a))
    else if (t <= 2.4d+47) then
        tmp = x + ((y * z) / a)
    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 <= -1.65e+34) {
		tmp = y;
	} else if (t <= -2.25e-300) {
		tmp = x - (x * (z / a));
	} else if (t <= 2.4e+47) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.65e+34:
		tmp = y
	elif t <= -2.25e-300:
		tmp = x - (x * (z / a))
	elif t <= 2.4e+47:
		tmp = x + ((y * z) / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.65e+34)
		tmp = y;
	elseif (t <= -2.25e-300)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= 2.4e+47)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.65e+34)
		tmp = y;
	elseif (t <= -2.25e-300)
		tmp = x - (x * (z / a));
	elseif (t <= 2.4e+47)
		tmp = x + ((y * z) / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.65e+34], y, If[LessEqual[t, -2.25e-300], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+47], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.64999999999999994e34 or 2.40000000000000019e47 < t

   1. Initial program 37.9%

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

      1. associate-*l/ 66.0%

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

   3. Simplified 66.0%

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

   4. Taylor expanded in t around inf 49.5%

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

   if -1.64999999999999994e34 < t < -2.25e-300

   1. Initial program 86.7%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in x around inf 57.9%

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

      1. distribute-lft-in 57.8%

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

      2. mul-1-neg 57.8%

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

      3. distribute-rgt-neg-in 57.8%

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

      4. unsub-neg 57.8%

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

      5. *-rgt-identity 57.8%

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

   6. Simplified 57.8%

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

   7. Taylor expanded in t around 0 51.2%

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

   if -2.25e-300 < t < 2.40000000000000019e47

   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/ 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in a around inf 67.9%

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

      1. associate-/l* 71.6%

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

   6. Simplified 71.6%

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

   7. Taylor expanded in y around inf 61.6%

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

   8. Taylor expanded in z around inf 59.3%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+34}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-300}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 20: 54.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+149} \lor \neg \left(a \leq 1.1 \cdot 10^{+109}\right):\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.8e+149) (not (<= a 1.1e+109)))
   (+ x (/ (* y z) a))
   (* z (/ (- y x) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e+149) || !(a <= 1.1e+109)) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = z * ((y - x) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.8d+149)) .or. (.not. (a <= 1.1d+109))) then
        tmp = x + ((y * z) / a)
    else
        tmp = z * ((y - x) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e+149) || !(a <= 1.1e+109)) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = z * ((y - x) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.8e+149) or not (a <= 1.1e+109):
		tmp = x + ((y * z) / a)
	else:
		tmp = z * ((y - x) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.8e+149) || !(a <= 1.1e+109))
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.8e+149) || ~((a <= 1.1e+109)))
		tmp = x + ((y * z) / a);
	else
		tmp = z * ((y - x) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.8e+149], N[Not[LessEqual[a, 1.1e+109]], $MachinePrecision]], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.79999999999999997e149 or 1.1e109 < 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/ 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in a around inf 73.2%

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

      1. associate-/l* 91.1%

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

   6. Simplified 91.1%

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

   7. Taylor expanded in y around inf 76.6%

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

   8. Taylor expanded in z around inf 72.1%

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

   if -1.79999999999999997e149 < a < 1.1e109

   1. Initial program 64.6%

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

      1. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around inf 49.0%

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

      1. div-sub 50.1%

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

   6. Simplified 50.1%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+149} \lor \neg \left(a \leq 1.1 \cdot 10^{+109}\right):\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 21: 55.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+149} \lor \neg \left(a \leq 8.5 \cdot 10^{+107}\right):\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.6e+149) (not (<= a 8.5e+107)))
   (+ x (/ (* y (- z t)) a))
   (* z (/ (- y x) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.6e+149) || !(a <= 8.5e+107)) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = z * ((y - x) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.6d+149)) .or. (.not. (a <= 8.5d+107))) then
        tmp = x + ((y * (z - t)) / a)
    else
        tmp = z * ((y - x) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.6e+149) || !(a <= 8.5e+107)) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = z * ((y - x) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.6e+149) or not (a <= 8.5e+107):
		tmp = x + ((y * (z - t)) / a)
	else:
		tmp = z * ((y - x) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.6e+149) || !(a <= 8.5e+107))
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.6e+149) || ~((a <= 8.5e+107)))
		tmp = x + ((y * (z - t)) / a);
	else
		tmp = z * ((y - x) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.6e+149], N[Not[LessEqual[a, 8.5e+107]], $MachinePrecision]], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6000000000000001e149 or 8.4999999999999999e107 < 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/ 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in a around inf 73.2%

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

      1. associate-/l* 91.1%

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

   6. Simplified 91.1%

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

   7. Taylor expanded in y around inf 76.6%

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

   if -1.6000000000000001e149 < a < 8.4999999999999999e107

   1. Initial program 64.6%

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

      1. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around inf 49.0%

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

      1. div-sub 50.1%

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

   6. Simplified 50.1%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+149} \lor \neg \left(a \leq 8.5 \cdot 10^{+107}\right):\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 22: 65.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+24} \lor \neg \left(t \leq 1.9 \cdot 10^{+98}\right):\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.5e+24) (not (<= t 1.9e+98)))
   (+ y (/ a (/ t (- y x))))
   (- x (/ (- x y) (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.5e+24) || !(t <= 1.9e+98)) {
		tmp = y + (a / (t / (y - x)));
	} else {
		tmp = x - ((x - y) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-9.5d+24)) .or. (.not. (t <= 1.9d+98))) then
        tmp = y + (a / (t / (y - x)))
    else
        tmp = x - ((x - y) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.5e+24) || !(t <= 1.9e+98)) {
		tmp = y + (a / (t / (y - x)));
	} else {
		tmp = x - ((x - y) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9.5e+24) or not (t <= 1.9e+98):
		tmp = y + (a / (t / (y - x)))
	else:
		tmp = x - ((x - y) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9.5e+24) || !(t <= 1.9e+98))
		tmp = Float64(y + Float64(a / Float64(t / Float64(y - x))));
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9.5e+24) || ~((t <= 1.9e+98)))
		tmp = y + (a / (t / (y - x)));
	else
		tmp = x - ((x - y) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9.5e+24], N[Not[LessEqual[t, 1.9e+98]], $MachinePrecision]], N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.5000000000000001e24 or 1.89999999999999995e98 < t

   1. Initial program 36.5%

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

      1. associate-/l* 70.5%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in z around 0 50.0%

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

      1. associate-*r/ 50.0%

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

      2. neg-mul-1 50.0%

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

   6. Simplified 50.0%

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

   7. Taylor expanded in a around 0 51.6%

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

      1. associate-/l* 58.5%

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

   9. Simplified 58.5%

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

   if -9.5000000000000001e24 < t < 1.89999999999999995e98

   1. Initial program 87.4%

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

      1. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in t around 0 69.7%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+24} \lor \neg \left(t \leq 1.9 \cdot 10^{+98}\right):\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \]

Alternative 23: 55.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+149}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-42}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e+149)
   (+ x (/ (* y (- z t)) a))
   (if (<= a 3.6e-42) (* z (/ (- y x) (- a t))) (- x (/ (* z (- x y)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e+149) {
		tmp = x + ((y * (z - t)) / a);
	} else if (a <= 3.6e-42) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x - ((z * (x - 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 <= (-1.6d+149)) then
        tmp = x + ((y * (z - t)) / a)
    else if (a <= 3.6d-42) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = x - ((z * (x - 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 <= -1.6e+149) {
		tmp = x + ((y * (z - t)) / a);
	} else if (a <= 3.6e-42) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x - ((z * (x - y)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e+149:
		tmp = x + ((y * (z - t)) / a)
	elif a <= 3.6e-42:
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = x - ((z * (x - y)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e+149)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	elseif (a <= 3.6e-42)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(Float64(z * Float64(x - y)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e+149)
		tmp = x + ((y * (z - t)) / a);
	elseif (a <= 3.6e-42)
		tmp = z * ((y - x) / (a - t));
	else
		tmp = x - ((z * (x - y)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e+149], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e-42], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6000000000000001e149

   1. Initial program 71.4%

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

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in a around inf 71.1%

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

      1. associate-/l* 96.4%

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

   6. Simplified 96.4%

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

   7. Taylor expanded in y around inf 79.5%

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

   if -1.6000000000000001e149 < a < 3.6000000000000002e-42

   1. Initial program 66.1%

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

      1. associate-*l/ 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in z around inf 50.0%

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

      1. div-sub 51.3%

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

   6. Simplified 51.3%

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

   if 3.6000000000000002e-42 < a

   1. Initial program 69.9%

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

      1. associate-*l/ 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in t around 0 64.4%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+149}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-42}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \end{array} \]

Alternative 24: 41.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -700000000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -700000000.0) y (if (<= t 2.1e-78) (* z (/ (- y x) a)) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -700000000.0) {
		tmp = y;
	} else if (t <= 2.1e-78) {
		tmp = z * ((y - x) / a);
	} 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 <= (-700000000.0d0)) then
        tmp = y
    else if (t <= 2.1d-78) then
        tmp = z * ((y - x) / a)
    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 <= -700000000.0) {
		tmp = y;
	} else if (t <= 2.1e-78) {
		tmp = z * ((y - x) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -700000000.0:
		tmp = y
	elif t <= 2.1e-78:
		tmp = z * ((y - x) / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -700000000.0)
		tmp = y;
	elseif (t <= 2.1e-78)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -700000000.0)
		tmp = y;
	elseif (t <= 2.1e-78)
		tmp = z * ((y - x) / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -700000000.0], y, If[LessEqual[t, 2.1e-78], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -7e8 or 2.1000000000000001e-78 < t

   1. Initial program 48.4%

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

      1. associate-*l/ 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in t around inf 44.2%

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

   if -7e8 < t < 2.1000000000000001e-78

   1. Initial program 91.0%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in a around inf 71.6%

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

      1. associate-/l* 78.9%

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

   6. Simplified 78.9%

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

   7. Taylor expanded in z around inf 43.0%

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

      1. div-sub 44.7%

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

   9. Simplified 44.7%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -700000000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 25: 38.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+15}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.7e+149) x (if (<= a 4.2e+15) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e+149) {
		tmp = x;
	} else if (a <= 4.2e+15) {
		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 <= (-1.7d+149)) then
        tmp = x
    else if (a <= 4.2d+15) 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 <= -1.7e+149) {
		tmp = x;
	} else if (a <= 4.2e+15) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.7e+149:
		tmp = x
	elif a <= 4.2e+15:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.7e+149)
		tmp = x;
	elseif (a <= 4.2e+15)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.7e+149)
		tmp = x;
	elseif (a <= 4.2e+15)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.7e+149], x, If[LessEqual[a, 4.2e+15], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6999999999999999e149 or 4.2e15 < a

   1. Initial program 71.8%

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

      1. associate-*l/ 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in a around inf 47.9%

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

   if -1.6999999999999999e149 < a < 4.2e15

   1. Initial program 65.5%

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

      1. associate-*l/ 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in t around inf 36.9%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+15}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 26: 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 67.7%

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

   1. +-commutative 67.7%

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

   2. associate-*l/ 79.2%

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

   3. fma-def 79.3%

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

3. Simplified 79.3%

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

4. Taylor expanded in y around 0 42.0%

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

   1. neg-mul-1 42.0%

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

   2. distribute-neg-frac 42.0%

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

6. Simplified 42.0%

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

7. Taylor expanded in t around inf 2.6%

   \[\leadsto \color{blue}{x + -1 \cdot x} \]
8. Step-by-step derivation

   1. distribute-rgt1-in 2.6%

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

   2. metadata-eval 2.6%

      \[\leadsto \color{blue}{0} \cdot x \]

   3. mul0-lft 2.6%

      \[\leadsto \color{blue}{0} \]

9. Simplified 2.6%

   \[\leadsto \color{blue}{0} \]

10. Final simplification 2.6%

    \[\leadsto 0 \]

Alternative 27: 26.0% 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 67.7%

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

   1. associate-*l/ 79.2%

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

3. Simplified 79.2%

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

4. Taylor expanded in a around inf 22.2%

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

5. Final simplification 22.2%

   \[\leadsto x \]

Developer target: 87.6% 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 2023271 
(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))))