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

Percentage Accurate: 68.0% → 90.9%

Time: 20.2s

Alternatives: 27

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-278}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_1 -1e-278)
     (- x (/ (- x y) (/ (- a t) (- z t))))
     (if (<= t_1 0.0)
       (+ y (/ (* (- y x) (- a z)) t))
       (fma (/ (- z t) (- a t)) (- y x) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -1e-278) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -1e-278)
		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(y - x) * Float64(a - z)) / t));
	else
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-278], 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[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.99999999999999938e-279

   1. Initial program 72.1%

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

      1. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

   if -9.99999999999999938e-279 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.6%

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

      1. associate-/l* 3.6%

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

   3. Simplified 3.6%

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

   4. Taylor expanded in t around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

      3. div-sub 99.7%

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

      4. *-commutative 99.7%

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

      5. div-sub 99.7%

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

      6. distribute-rgt-out-- 99.7%

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

   6. Simplified 99.7%

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

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

   1. Initial program 77.5%

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

      1. +-commutative 77.5%

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

      2. associate-*r/ 96.2%

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

      3. *-commutative 96.2%

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

      4. fma-def 96.2%

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

   3. Simplified 96.2%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -1 \cdot 10^{-278}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \]

Alternative 2: 84.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+289}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (* z (/ (- y x) (- a t)))
     (if (<= t_1 -1e-278)
       t_1
       (if (<= t_1 0.0)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_1 2e+289) t_1 (+ y (* (- y x) (/ (- a z) 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 <= -((double) INFINITY)) {
		tmp = z * ((y - x) / (a - t));
	} else if (t_1 <= -1e-278) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_1 <= 2e+289) {
		tmp = t_1;
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	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 tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z * ((y - x) / (a - t));
	} else if (t_1 <= -1e-278) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_1 <= 2e+289) {
		tmp = t_1;
	} else {
		tmp = y + ((y - x) * ((a - z) / 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 <= -math.inf:
		tmp = z * ((y - x) / (a - t))
	elif t_1 <= -1e-278:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t_1 <= 2e+289:
		tmp = t_1
	else:
		tmp = y + ((y - x) * ((a - z) / 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 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t_1 <= -1e-278)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_1 <= 2e+289)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / 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 <= -Inf)
		tmp = z * ((y - x) / (a - t));
	elseif (t_1 <= -1e-278)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t_1 <= 2e+289)
		tmp = t_1;
	else
		tmp = y + ((y - x) * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-278], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+289], t$95$1, N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 43.0%

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

      1. associate-/l* 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in z around inf 68.8%

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

      1. div-sub 70.6%

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

   6. Simplified 70.6%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.99999999999999938e-279 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 2.0000000000000001e289

   1. Initial program 97.8%

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

   if -9.99999999999999938e-279 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.6%

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

      1. associate-/l* 3.6%

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

   3. Simplified 3.6%

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

   4. Taylor expanded in t around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

      3. div-sub 99.7%

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

      4. *-commutative 99.7%

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

      5. div-sub 99.7%

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

      6. distribute-rgt-out-- 99.7%

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

   6. Simplified 99.7%

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

   if 2.0000000000000001e289 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 41.5%

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

      1. associate-/l* 90.8%

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

   3. Simplified 90.8%

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

      1. div-inv 90.7%

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

   5. Applied egg-rr 90.7%

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

   6. Taylor expanded in t around inf 48.3%

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

      1. +-commutative 48.3%

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

      2. *-commutative 48.3%

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

      3. associate--l+ 48.3%

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

      4. associate-*r/ 48.3%

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

      5. associate-*r/ 48.3%

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

      6. div-sub 50.7%

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

      7. distribute-lft-out-- 50.7%

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

      8. *-commutative 50.7%

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

      9. distribute-rgt-out-- 51.5%

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

      10. associate-*r/ 51.5%

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

      11. +-commutative 51.5%

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

      12. fma-def 51.5%

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

      13. associate-/l* 70.2%

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

   8. Simplified 70.2%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -1 \cdot 10^{-278}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 2 \cdot 10^{+289}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]

Alternative 3: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-278} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (or (<= t_1 -1e-278) (not (<= t_1 0.0)))
     (- x (/ (- x y) (/ (- a t) (- z t))))
     (+ y (/ (* (- y x) (- a z)) 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 <= -1e-278) || !(t_1 <= 0.0)) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - x) * (t - z)) / (a - t))
    if ((t_1 <= (-1d-278)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x - ((x - y) / ((a - t) / (z - t)))
    else
        tmp = y + (((y - x) * (a - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-278) || !(t_1 <= 0.0)) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / 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 <= -1e-278) or not (t_1 <= 0.0):
		tmp = x - ((x - y) / ((a - t) / (z - t)))
	else:
		tmp = y + (((y - x) * (a - z)) / 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 <= -1e-278) || !(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(y - x) * Float64(a - z)) / 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 <= -1e-278) || ~((t_1 <= 0.0)))
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	else
		tmp = y + (((y - x) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-278], 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[(y - x), $MachinePrecision] * N[(a - z), $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))) < -9.99999999999999938e-279 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 74.7%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   if -9.99999999999999938e-279 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.6%

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

      1. associate-/l* 3.6%

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

   3. Simplified 3.6%

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

   4. Taylor expanded in t around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

      3. div-sub 99.7%

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

      4. *-commutative 99.7%

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

      5. div-sub 99.7%

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

      6. distribute-rgt-out-- 99.7%

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

   6. Simplified 99.7%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -1 \cdot 10^{-278} \lor \neg \left(x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]

Alternative 4: 65.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := y + x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.14 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{+41}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{+100}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ y (* x (/ z t)))))
   (if (<= t -5.6e+73)
     t_1
     (if (<= t -9.6e+42)
       (- x (/ z (/ a x)))
       (if (<= t -1e-17)
         t_1
         (if (<= t 1.14e-125)
           (+ x (/ z (/ a (- y x))))
           (if (<= t 2.55e-17)
             (* z (/ (- y x) (- a t)))
             (if (<= t 1.26e+41)
               (- x (* t (/ y a)))
               (if (<= t 1.15e+66)
                 t_2
                 (if (<= t 6.7e+100)
                   (+ x y)
                   (if (<= t 1.4e+172) t_1 t_2)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = y + (x * (z / t));
	double tmp;
	if (t <= -5.6e+73) {
		tmp = t_1;
	} else if (t <= -9.6e+42) {
		tmp = x - (z / (a / x));
	} else if (t <= -1e-17) {
		tmp = t_1;
	} else if (t <= 1.14e-125) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 2.55e-17) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.26e+41) {
		tmp = x - (t * (y / a));
	} else if (t <= 1.15e+66) {
		tmp = t_2;
	} else if (t <= 6.7e+100) {
		tmp = x + y;
	} else if (t <= 1.4e+172) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = y + (x * (z / t))
    if (t <= (-5.6d+73)) then
        tmp = t_1
    else if (t <= (-9.6d+42)) then
        tmp = x - (z / (a / x))
    else if (t <= (-1d-17)) then
        tmp = t_1
    else if (t <= 1.14d-125) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= 2.55d-17) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 1.26d+41) then
        tmp = x - (t * (y / a))
    else if (t <= 1.15d+66) then
        tmp = t_2
    else if (t <= 6.7d+100) then
        tmp = x + y
    else if (t <= 1.4d+172) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = y + (x * (z / t));
	double tmp;
	if (t <= -5.6e+73) {
		tmp = t_1;
	} else if (t <= -9.6e+42) {
		tmp = x - (z / (a / x));
	} else if (t <= -1e-17) {
		tmp = t_1;
	} else if (t <= 1.14e-125) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 2.55e-17) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.26e+41) {
		tmp = x - (t * (y / a));
	} else if (t <= 1.15e+66) {
		tmp = t_2;
	} else if (t <= 6.7e+100) {
		tmp = x + y;
	} else if (t <= 1.4e+172) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = y + (x * (z / t))
	tmp = 0
	if t <= -5.6e+73:
		tmp = t_1
	elif t <= -9.6e+42:
		tmp = x - (z / (a / x))
	elif t <= -1e-17:
		tmp = t_1
	elif t <= 1.14e-125:
		tmp = x + (z / (a / (y - x)))
	elif t <= 2.55e-17:
		tmp = z * ((y - x) / (a - t))
	elif t <= 1.26e+41:
		tmp = x - (t * (y / a))
	elif t <= 1.15e+66:
		tmp = t_2
	elif t <= 6.7e+100:
		tmp = x + y
	elif t <= 1.4e+172:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(y + Float64(x * Float64(z / t)))
	tmp = 0.0
	if (t <= -5.6e+73)
		tmp = t_1;
	elseif (t <= -9.6e+42)
		tmp = Float64(x - Float64(z / Float64(a / x)));
	elseif (t <= -1e-17)
		tmp = t_1;
	elseif (t <= 1.14e-125)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= 2.55e-17)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 1.26e+41)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	elseif (t <= 1.15e+66)
		tmp = t_2;
	elseif (t <= 6.7e+100)
		tmp = Float64(x + y);
	elseif (t <= 1.4e+172)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = y + (x * (z / t));
	tmp = 0.0;
	if (t <= -5.6e+73)
		tmp = t_1;
	elseif (t <= -9.6e+42)
		tmp = x - (z / (a / x));
	elseif (t <= -1e-17)
		tmp = t_1;
	elseif (t <= 1.14e-125)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= 2.55e-17)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 1.26e+41)
		tmp = x - (t * (y / a));
	elseif (t <= 1.15e+66)
		tmp = t_2;
	elseif (t <= 6.7e+100)
		tmp = x + y;
	elseif (t <= 1.4e+172)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+73], t$95$1, If[LessEqual[t, -9.6e+42], N[(x - N[(z / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1e-17], t$95$1, If[LessEqual[t, 1.14e-125], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.55e-17], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.26e+41], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+66], t$95$2, If[LessEqual[t, 6.7e+100], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.4e+172], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -5.60000000000000016e73 or -9.5999999999999994e42 < t < -1.00000000000000007e-17 or 6.6999999999999997e100 < t < 1.4e172

   1. Initial program 59.2%

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

      1. associate-/l* 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in x around 0 53.0%

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

      1. associate-*r/ 72.8%

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

   6. Simplified 72.8%

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

   if -5.60000000000000016e73 < t < -9.5999999999999994e42

   1. Initial program 61.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 61.8%

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

      1. +-commutative 61.8%

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

      2. *-commutative 61.8%

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

      3. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 61.8%

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

      1. +-commutative 61.8%

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

      2. mul-1-neg 61.8%

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

      3. unsub-neg 61.8%

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

      4. associate-/l* 100.0%

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

   9. Simplified 100.0%

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

   if -1.00000000000000007e-17 < t < 1.13999999999999996e-125

   1. Initial program 84.8%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in t around 0 72.1%

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

      1. +-commutative 72.1%

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

      2. *-commutative 72.1%

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

      3. associate-/l* 79.0%

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

   6. Simplified 79.0%

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

   if 1.13999999999999996e-125 < t < 2.5500000000000001e-17

   1. Initial program 91.8%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 88.4%

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

      1. div-sub 88.4%

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

   6. Simplified 88.4%

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

   if 2.5500000000000001e-17 < t < 1.26000000000000001e41

   1. Initial program 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in a around inf 92.7%

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

   6. Taylor expanded in z around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-*r/ 82.0%

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

      4. distribute-rgt-neg-in 82.0%

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

      5. distribute-neg-frac 82.0%

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

   8. Simplified 82.0%

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

   if 1.26000000000000001e41 < t < 1.15e66 or 1.4e172 < t

   1. Initial program 38.3%

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

      1. associate-/l* 65.5%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in t around -inf 65.7%

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

      1. mul-1-neg 65.7%

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

      2. unsub-neg 65.7%

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

      3. div-sub 65.7%

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

      4. *-commutative 65.7%

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

      5. div-sub 65.7%

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

      6. distribute-rgt-out-- 65.7%

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

   6. Simplified 65.7%

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

   7. Taylor expanded in a around 0 68.5%

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

   8. Taylor expanded in z around 0 68.5%

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

      1. *-commutative 68.5%

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

      2. associate-*r/ 86.4%

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

   10. Simplified 86.4%

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

   11. Taylor expanded in y around 0 66.0%

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

       1. mul-1-neg 66.0%

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

       2. associate-*l/ 81.4%

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

       3. distribute-rgt-neg-out 81.4%

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

   13. Simplified 81.4%

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

   if 1.15e66 < t < 6.6999999999999997e100

   1. Initial program 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in t around inf 86.6%

      \[\leadsto x + \color{blue}{y} \]
3. Recombined 7 regimes into one program.

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.14 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{+41}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+66}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{+100}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 65.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := y + x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq -1.28 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+32}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ y (* x (/ z t)))))
   (if (<= t -1.7e+73)
     t_1
     (if (<= t -2.1e+42)
       (- x (/ z (/ a x)))
       (if (<= t -1.28e-17)
         t_1
         (if (<= t 1.06e-125)
           (+ x (/ (- y x) (/ a z)))
           (if (<= t 3.5e-17)
             (* z (/ (- y x) (- a t)))
             (if (<= t 7.5e+32)
               (- x (* t (/ y a)))
               (if (<= t 1.2e+67)
                 t_2
                 (if (<= t 1.65e+101)
                   (+ x y)
                   (if (<= t 1.35e+172) t_1 t_2)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = y + (x * (z / t));
	double tmp;
	if (t <= -1.7e+73) {
		tmp = t_1;
	} else if (t <= -2.1e+42) {
		tmp = x - (z / (a / x));
	} else if (t <= -1.28e-17) {
		tmp = t_1;
	} else if (t <= 1.06e-125) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 3.5e-17) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 7.5e+32) {
		tmp = x - (t * (y / a));
	} else if (t <= 1.2e+67) {
		tmp = t_2;
	} else if (t <= 1.65e+101) {
		tmp = x + y;
	} else if (t <= 1.35e+172) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = y + (x * (z / t))
    if (t <= (-1.7d+73)) then
        tmp = t_1
    else if (t <= (-2.1d+42)) then
        tmp = x - (z / (a / x))
    else if (t <= (-1.28d-17)) then
        tmp = t_1
    else if (t <= 1.06d-125) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 3.5d-17) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 7.5d+32) then
        tmp = x - (t * (y / a))
    else if (t <= 1.2d+67) then
        tmp = t_2
    else if (t <= 1.65d+101) then
        tmp = x + y
    else if (t <= 1.35d+172) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = y + (x * (z / t));
	double tmp;
	if (t <= -1.7e+73) {
		tmp = t_1;
	} else if (t <= -2.1e+42) {
		tmp = x - (z / (a / x));
	} else if (t <= -1.28e-17) {
		tmp = t_1;
	} else if (t <= 1.06e-125) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 3.5e-17) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 7.5e+32) {
		tmp = x - (t * (y / a));
	} else if (t <= 1.2e+67) {
		tmp = t_2;
	} else if (t <= 1.65e+101) {
		tmp = x + y;
	} else if (t <= 1.35e+172) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = y + (x * (z / t))
	tmp = 0
	if t <= -1.7e+73:
		tmp = t_1
	elif t <= -2.1e+42:
		tmp = x - (z / (a / x))
	elif t <= -1.28e-17:
		tmp = t_1
	elif t <= 1.06e-125:
		tmp = x + ((y - x) / (a / z))
	elif t <= 3.5e-17:
		tmp = z * ((y - x) / (a - t))
	elif t <= 7.5e+32:
		tmp = x - (t * (y / a))
	elif t <= 1.2e+67:
		tmp = t_2
	elif t <= 1.65e+101:
		tmp = x + y
	elif t <= 1.35e+172:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(y + Float64(x * Float64(z / t)))
	tmp = 0.0
	if (t <= -1.7e+73)
		tmp = t_1;
	elseif (t <= -2.1e+42)
		tmp = Float64(x - Float64(z / Float64(a / x)));
	elseif (t <= -1.28e-17)
		tmp = t_1;
	elseif (t <= 1.06e-125)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 3.5e-17)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 7.5e+32)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	elseif (t <= 1.2e+67)
		tmp = t_2;
	elseif (t <= 1.65e+101)
		tmp = Float64(x + y);
	elseif (t <= 1.35e+172)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = y + (x * (z / t));
	tmp = 0.0;
	if (t <= -1.7e+73)
		tmp = t_1;
	elseif (t <= -2.1e+42)
		tmp = x - (z / (a / x));
	elseif (t <= -1.28e-17)
		tmp = t_1;
	elseif (t <= 1.06e-125)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 3.5e-17)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 7.5e+32)
		tmp = x - (t * (y / a));
	elseif (t <= 1.2e+67)
		tmp = t_2;
	elseif (t <= 1.65e+101)
		tmp = x + y;
	elseif (t <= 1.35e+172)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+73], t$95$1, If[LessEqual[t, -2.1e+42], N[(x - N[(z / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.28e-17], t$95$1, If[LessEqual[t, 1.06e-125], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-17], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+32], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+67], t$95$2, If[LessEqual[t, 1.65e+101], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.35e+172], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.7000000000000001e73 or -2.09999999999999995e42 < t < -1.28e-17 or 1.65000000000000006e101 < t < 1.35e172

   1. Initial program 59.2%

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

      1. associate-/l* 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in x around 0 53.0%

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

      1. associate-*r/ 72.8%

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

   6. Simplified 72.8%

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

   if -1.7000000000000001e73 < t < -2.09999999999999995e42

   1. Initial program 61.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 61.8%

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

      1. +-commutative 61.8%

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

      2. *-commutative 61.8%

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

      3. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 61.8%

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

      1. +-commutative 61.8%

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

      2. mul-1-neg 61.8%

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

      3. unsub-neg 61.8%

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

      4. associate-/l* 100.0%

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

   9. Simplified 100.0%

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

   if -1.28e-17 < t < 1.05999999999999999e-125

   1. Initial program 84.8%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in t around 0 80.5%

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

   if 1.05999999999999999e-125 < t < 3.5000000000000002e-17

   1. Initial program 91.8%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 88.4%

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

      1. div-sub 88.4%

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

   6. Simplified 88.4%

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

   if 3.5000000000000002e-17 < t < 7.49999999999999959e32

   1. Initial program 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in a around inf 92.7%

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

   6. Taylor expanded in z around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-*r/ 82.0%

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

      4. distribute-rgt-neg-in 82.0%

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

      5. distribute-neg-frac 82.0%

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

   8. Simplified 82.0%

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

   if 7.49999999999999959e32 < t < 1.20000000000000001e67 or 1.35e172 < t

   1. Initial program 38.3%

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

      1. associate-/l* 65.5%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in t around -inf 65.7%

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

      1. mul-1-neg 65.7%

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

      2. unsub-neg 65.7%

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

      3. div-sub 65.7%

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

      4. *-commutative 65.7%

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

      5. div-sub 65.7%

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

      6. distribute-rgt-out-- 65.7%

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

   6. Simplified 65.7%

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

   7. Taylor expanded in a around 0 68.5%

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

   8. Taylor expanded in z around 0 68.5%

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

      1. *-commutative 68.5%

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

      2. associate-*r/ 86.4%

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

   10. Simplified 86.4%

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

   11. Taylor expanded in y around 0 66.0%

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

       1. mul-1-neg 66.0%

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

       2. associate-*l/ 81.4%

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

       3. distribute-rgt-neg-out 81.4%

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

   13. Simplified 81.4%

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

   if 1.20000000000000001e67 < t < 1.65000000000000006e101

   1. Initial program 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in t around inf 86.6%

      \[\leadsto x + \color{blue}{y} \]
3. Recombined 7 regimes into one program.

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq -1.28 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+32}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+67}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 6: 66.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + x \cdot \frac{z}{t}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+172}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* x (/ z t)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -5.6e+73)
     t_2
     (if (<= t -1.55e+42)
       (- x (/ z (/ a x)))
       (if (<= t -7e-19)
         t_2
         (if (<= t 1.15e-125)
           (+ x (/ (- y x) (/ a z)))
           (if (<= t 2.4e-17)
             (* z (/ (- y x) (- a t)))
             (if (<= t 2.75e+42)
               (- x (/ (- t z) (/ a y)))
               (if (<= t 3.6e+66)
                 t_1
                 (if (<= t 3.4e+101)
                   (+ x y)
                   (if (<= t 5e+172) t_2 t_1)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x * (z / t));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -5.6e+73) {
		tmp = t_2;
	} else if (t <= -1.55e+42) {
		tmp = x - (z / (a / x));
	} else if (t <= -7e-19) {
		tmp = t_2;
	} else if (t <= 1.15e-125) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 2.4e-17) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 2.75e+42) {
		tmp = x - ((t - z) / (a / y));
	} else if (t <= 3.6e+66) {
		tmp = t_1;
	} else if (t <= 3.4e+101) {
		tmp = x + y;
	} else if (t <= 5e+172) {
		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 + (x * (z / t))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-5.6d+73)) then
        tmp = t_2
    else if (t <= (-1.55d+42)) then
        tmp = x - (z / (a / x))
    else if (t <= (-7d-19)) then
        tmp = t_2
    else if (t <= 1.15d-125) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 2.4d-17) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 2.75d+42) then
        tmp = x - ((t - z) / (a / y))
    else if (t <= 3.6d+66) then
        tmp = t_1
    else if (t <= 3.4d+101) then
        tmp = x + y
    else if (t <= 5d+172) 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 + (x * (z / t));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -5.6e+73) {
		tmp = t_2;
	} else if (t <= -1.55e+42) {
		tmp = x - (z / (a / x));
	} else if (t <= -7e-19) {
		tmp = t_2;
	} else if (t <= 1.15e-125) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 2.4e-17) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 2.75e+42) {
		tmp = x - ((t - z) / (a / y));
	} else if (t <= 3.6e+66) {
		tmp = t_1;
	} else if (t <= 3.4e+101) {
		tmp = x + y;
	} else if (t <= 5e+172) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (x * (z / t))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -5.6e+73:
		tmp = t_2
	elif t <= -1.55e+42:
		tmp = x - (z / (a / x))
	elif t <= -7e-19:
		tmp = t_2
	elif t <= 1.15e-125:
		tmp = x + ((y - x) / (a / z))
	elif t <= 2.4e-17:
		tmp = z * ((y - x) / (a - t))
	elif t <= 2.75e+42:
		tmp = x - ((t - z) / (a / y))
	elif t <= 3.6e+66:
		tmp = t_1
	elif t <= 3.4e+101:
		tmp = x + y
	elif t <= 5e+172:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(x * Float64(z / t)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -5.6e+73)
		tmp = t_2;
	elseif (t <= -1.55e+42)
		tmp = Float64(x - Float64(z / Float64(a / x)));
	elseif (t <= -7e-19)
		tmp = t_2;
	elseif (t <= 1.15e-125)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 2.4e-17)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 2.75e+42)
		tmp = Float64(x - Float64(Float64(t - z) / Float64(a / y)));
	elseif (t <= 3.6e+66)
		tmp = t_1;
	elseif (t <= 3.4e+101)
		tmp = Float64(x + y);
	elseif (t <= 5e+172)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (x * (z / t));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -5.6e+73)
		tmp = t_2;
	elseif (t <= -1.55e+42)
		tmp = x - (z / (a / x));
	elseif (t <= -7e-19)
		tmp = t_2;
	elseif (t <= 1.15e-125)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 2.4e-17)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 2.75e+42)
		tmp = x - ((t - z) / (a / y));
	elseif (t <= 3.6e+66)
		tmp = t_1;
	elseif (t <= 3.4e+101)
		tmp = x + y;
	elseif (t <= 5e+172)
		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[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+73], t$95$2, If[LessEqual[t, -1.55e+42], N[(x - N[(z / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7e-19], t$95$2, If[LessEqual[t, 1.15e-125], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-17], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.75e+42], N[(x - N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+66], t$95$1, If[LessEqual[t, 3.4e+101], N[(x + y), $MachinePrecision], If[LessEqual[t, 5e+172], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -5.60000000000000016e73 or -1.5500000000000001e42 < t < -7.00000000000000031e-19 or 3.40000000000000017e101 < t < 5.0000000000000001e172

   1. Initial program 59.2%

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

      1. associate-/l* 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in x around 0 53.0%

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

      1. associate-*r/ 72.8%

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

   6. Simplified 72.8%

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

   if -5.60000000000000016e73 < t < -1.5500000000000001e42

   1. Initial program 61.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 61.8%

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

      1. +-commutative 61.8%

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

      2. *-commutative 61.8%

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

      3. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 61.8%

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

      1. +-commutative 61.8%

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

      2. mul-1-neg 61.8%

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

      3. unsub-neg 61.8%

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

      4. associate-/l* 100.0%

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

   9. Simplified 100.0%

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

   if -7.00000000000000031e-19 < t < 1.15e-125

   1. Initial program 84.8%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in t around 0 80.5%

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

   if 1.15e-125 < t < 2.39999999999999986e-17

   1. Initial program 91.8%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 88.4%

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

      1. div-sub 88.4%

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

   6. Simplified 88.4%

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

   if 2.39999999999999986e-17 < t < 2.75000000000000001e42

   1. Initial program 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in a around inf 92.7%

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

   if 2.75000000000000001e42 < t < 3.6e66 or 5.0000000000000001e172 < t

   1. Initial program 38.3%

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

      1. associate-/l* 65.5%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in t around -inf 65.7%

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

      1. mul-1-neg 65.7%

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

      2. unsub-neg 65.7%

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

      3. div-sub 65.7%

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

      4. *-commutative 65.7%

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

      5. div-sub 65.7%

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

      6. distribute-rgt-out-- 65.7%

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

   6. Simplified 65.7%

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

   7. Taylor expanded in a around 0 68.5%

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

   8. Taylor expanded in z around 0 68.5%

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

      1. *-commutative 68.5%

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

      2. associate-*r/ 86.4%

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

   10. Simplified 86.4%

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

   11. Taylor expanded in y around 0 66.0%

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

       1. mul-1-neg 66.0%

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

       2. associate-*l/ 81.4%

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

       3. distribute-rgt-neg-out 81.4%

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

   13. Simplified 81.4%

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

   if 3.6e66 < t < 3.40000000000000017e101

   1. Initial program 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in t around inf 86.6%

      \[\leadsto x + \color{blue}{y} \]
3. Recombined 7 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+66}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 7: 52.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \frac{y}{a}\\ t_2 := y + x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-197}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-125}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-18}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+106}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (/ y a)))) (t_2 (+ y (* x (/ z t)))))
   (if (<= t -1.6e-18)
     t_2
     (if (<= t -2.35e-135)
       t_1
       (if (<= t -4e-197)
         (* z (/ (- y x) a))
         (if (<= t 1.18e-125)
           (- x (/ z (/ a x)))
           (if (<= t 6e-18)
             (/ (* z (- x y)) t)
             (if (<= t 5.4e+32)
               t_1
               (if (<= t 1.22e+67)
                 t_2
                 (if (<= t 2.5e+106)
                   (+ x y)
                   (if (<= t 3.4e+152) (* y (- 1.0 (/ z t))) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (y / a));
	double t_2 = y + (x * (z / t));
	double tmp;
	if (t <= -1.6e-18) {
		tmp = t_2;
	} else if (t <= -2.35e-135) {
		tmp = t_1;
	} else if (t <= -4e-197) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.18e-125) {
		tmp = x - (z / (a / x));
	} else if (t <= 6e-18) {
		tmp = (z * (x - y)) / t;
	} else if (t <= 5.4e+32) {
		tmp = t_1;
	} else if (t <= 1.22e+67) {
		tmp = t_2;
	} else if (t <= 2.5e+106) {
		tmp = x + y;
	} else if (t <= 3.4e+152) {
		tmp = y * (1.0 - (z / t));
	} 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 - (t * (y / a))
    t_2 = y + (x * (z / t))
    if (t <= (-1.6d-18)) then
        tmp = t_2
    else if (t <= (-2.35d-135)) then
        tmp = t_1
    else if (t <= (-4d-197)) then
        tmp = z * ((y - x) / a)
    else if (t <= 1.18d-125) then
        tmp = x - (z / (a / x))
    else if (t <= 6d-18) then
        tmp = (z * (x - y)) / t
    else if (t <= 5.4d+32) then
        tmp = t_1
    else if (t <= 1.22d+67) then
        tmp = t_2
    else if (t <= 2.5d+106) then
        tmp = x + y
    else if (t <= 3.4d+152) then
        tmp = y * (1.0d0 - (z / t))
    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 - (t * (y / a));
	double t_2 = y + (x * (z / t));
	double tmp;
	if (t <= -1.6e-18) {
		tmp = t_2;
	} else if (t <= -2.35e-135) {
		tmp = t_1;
	} else if (t <= -4e-197) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.18e-125) {
		tmp = x - (z / (a / x));
	} else if (t <= 6e-18) {
		tmp = (z * (x - y)) / t;
	} else if (t <= 5.4e+32) {
		tmp = t_1;
	} else if (t <= 1.22e+67) {
		tmp = t_2;
	} else if (t <= 2.5e+106) {
		tmp = x + y;
	} else if (t <= 3.4e+152) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * (y / a))
	t_2 = y + (x * (z / t))
	tmp = 0
	if t <= -1.6e-18:
		tmp = t_2
	elif t <= -2.35e-135:
		tmp = t_1
	elif t <= -4e-197:
		tmp = z * ((y - x) / a)
	elif t <= 1.18e-125:
		tmp = x - (z / (a / x))
	elif t <= 6e-18:
		tmp = (z * (x - y)) / t
	elif t <= 5.4e+32:
		tmp = t_1
	elif t <= 1.22e+67:
		tmp = t_2
	elif t <= 2.5e+106:
		tmp = x + y
	elif t <= 3.4e+152:
		tmp = y * (1.0 - (z / t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t * Float64(y / a)))
	t_2 = Float64(y + Float64(x * Float64(z / t)))
	tmp = 0.0
	if (t <= -1.6e-18)
		tmp = t_2;
	elseif (t <= -2.35e-135)
		tmp = t_1;
	elseif (t <= -4e-197)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 1.18e-125)
		tmp = Float64(x - Float64(z / Float64(a / x)));
	elseif (t <= 6e-18)
		tmp = Float64(Float64(z * Float64(x - y)) / t);
	elseif (t <= 5.4e+32)
		tmp = t_1;
	elseif (t <= 1.22e+67)
		tmp = t_2;
	elseif (t <= 2.5e+106)
		tmp = Float64(x + y);
	elseif (t <= 3.4e+152)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t * (y / a));
	t_2 = y + (x * (z / t));
	tmp = 0.0;
	if (t <= -1.6e-18)
		tmp = t_2;
	elseif (t <= -2.35e-135)
		tmp = t_1;
	elseif (t <= -4e-197)
		tmp = z * ((y - x) / a);
	elseif (t <= 1.18e-125)
		tmp = x - (z / (a / x));
	elseif (t <= 6e-18)
		tmp = (z * (x - y)) / t;
	elseif (t <= 5.4e+32)
		tmp = t_1;
	elseif (t <= 1.22e+67)
		tmp = t_2;
	elseif (t <= 2.5e+106)
		tmp = x + y;
	elseif (t <= 3.4e+152)
		tmp = y * (1.0 - (z / t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e-18], t$95$2, If[LessEqual[t, -2.35e-135], t$95$1, If[LessEqual[t, -4e-197], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.18e-125], N[(x - N[(z / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-18], N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 5.4e+32], t$95$1, If[LessEqual[t, 1.22e+67], t$95$2, If[LessEqual[t, 2.5e+106], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.4e+152], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.6e-18 or 5.40000000000000025e32 < t < 1.22000000000000004e67 or 3.4000000000000002e152 < t

   1. Initial program 52.1%

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

      1. associate-/l* 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in t around -inf 62.1%

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

      1. mul-1-neg 62.1%

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

      2. unsub-neg 62.1%

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

      3. div-sub 62.1%

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

      4. *-commutative 62.1%

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

      5. div-sub 62.1%

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

      6. distribute-rgt-out-- 62.3%

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

   6. Simplified 62.3%

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

   7. Taylor expanded in a around 0 62.1%

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

   8. Taylor expanded in z around 0 62.1%

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

      1. *-commutative 62.1%

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

      2. associate-*r/ 73.6%

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

   10. Simplified 73.6%

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

   11. Taylor expanded in y around 0 56.8%

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

       1. mul-1-neg 56.8%

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

       2. associate-*l/ 64.0%

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

       3. distribute-rgt-neg-out 64.0%

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

   13. Simplified 64.0%

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

   if -1.6e-18 < t < -2.34999999999999988e-135 or 5.99999999999999966e-18 < t < 5.40000000000000025e32

   1. Initial program 78.3%

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

      1. *-commutative 78.3%

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

      2. associate-/l* 86.4%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in y around inf 78.8%

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

   5. Taylor expanded in a around inf 68.7%

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

   6. Taylor expanded in z around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. *-commutative 58.2%

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

      3. associate-*r/ 58.2%

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

      4. distribute-rgt-neg-in 58.2%

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

      5. distribute-neg-frac 58.2%

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

   8. Simplified 58.2%

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

   if -2.34999999999999988e-135 < t < -3.9999999999999999e-197

   1. Initial program 91.1%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around 0 69.6%

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

      1. +-commutative 69.6%

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

      2. *-commutative 69.6%

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

      3. associate-/l* 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in z around inf 69.1%

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

      1. div-sub 69.1%

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

   9. Simplified 69.1%

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

   if -3.9999999999999999e-197 < t < 1.17999999999999994e-125

   1. Initial program 88.1%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in t around 0 81.8%

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

      1. +-commutative 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-/l* 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in y around 0 65.0%

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

      1. +-commutative 65.0%

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

      2. mul-1-neg 65.0%

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

      3. unsub-neg 65.0%

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

      4. associate-/l* 68.5%

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

   9. Simplified 68.5%

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

   if 1.17999999999999994e-125 < t < 5.99999999999999966e-18

   1. Initial program 91.3%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around inf 87.7%

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

      1. div-sub 87.7%

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

      2. associate-*r/ 82.1%

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

   6. Simplified 82.1%

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

   7. Taylor expanded in a around 0 75.5%

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

      1. associate-*r/ 75.5%

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

      2. mul-1-neg 75.5%

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

      3. *-commutative 75.5%

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

   9. Simplified 75.5%

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

   if 1.22000000000000004e67 < t < 2.4999999999999999e106

   1. Initial program 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in t around inf 86.6%

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

   if 2.4999999999999999e106 < t < 3.4000000000000002e152

   1. Initial program 52.7%

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

      1. associate-/l* 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in t around -inf 84.5%

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

      1. mul-1-neg 84.5%

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

      2. unsub-neg 84.5%

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

      3. div-sub 84.5%

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

      4. *-commutative 84.5%

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

      5. div-sub 84.5%

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

      6. distribute-rgt-out-- 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in a around 0 84.5%

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

   8. Taylor expanded in y around inf 83.1%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot y} \]
3. Recombined 7 regimes into one program.

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-18}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-135}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-197}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-125}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-18}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+32}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+67}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+106}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 8: 51.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ t_2 := x - \frac{z}{\frac{a}{x}}\\ t_3 := x \cdot \frac{-z}{a - t}\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-156}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-275}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+47}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t))))
        (t_2 (- x (/ z (/ a x))))
        (t_3 (* x (/ (- z) (- a t)))))
   (if (<= a -4.1e+65)
     t_2
     (if (<= a -6.1e-31)
       t_1
       (if (<= a -4.2e-50)
         t_3
         (if (<= a -5e-123)
           t_1
           (if (<= a -2.8e-156)
             t_3
             (if (<= a 8.8e-281)
               t_1
               (if (<= a 1.25e-275)
                 (/ z (/ t x))
                 (if (<= a 9.5e+47) (- y (/ y (/ t z))) t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double t_2 = x - (z / (a / x));
	double t_3 = x * (-z / (a - t));
	double tmp;
	if (a <= -4.1e+65) {
		tmp = t_2;
	} else if (a <= -6.1e-31) {
		tmp = t_1;
	} else if (a <= -4.2e-50) {
		tmp = t_3;
	} else if (a <= -5e-123) {
		tmp = t_1;
	} else if (a <= -2.8e-156) {
		tmp = t_3;
	} else if (a <= 8.8e-281) {
		tmp = t_1;
	} else if (a <= 1.25e-275) {
		tmp = z / (t / x);
	} else if (a <= 9.5e+47) {
		tmp = y - (y / (t / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (1.0d0 - (z / t))
    t_2 = x - (z / (a / x))
    t_3 = x * (-z / (a - t))
    if (a <= (-4.1d+65)) then
        tmp = t_2
    else if (a <= (-6.1d-31)) then
        tmp = t_1
    else if (a <= (-4.2d-50)) then
        tmp = t_3
    else if (a <= (-5d-123)) then
        tmp = t_1
    else if (a <= (-2.8d-156)) then
        tmp = t_3
    else if (a <= 8.8d-281) then
        tmp = t_1
    else if (a <= 1.25d-275) then
        tmp = z / (t / x)
    else if (a <= 9.5d+47) then
        tmp = y - (y / (t / z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double t_2 = x - (z / (a / x));
	double t_3 = x * (-z / (a - t));
	double tmp;
	if (a <= -4.1e+65) {
		tmp = t_2;
	} else if (a <= -6.1e-31) {
		tmp = t_1;
	} else if (a <= -4.2e-50) {
		tmp = t_3;
	} else if (a <= -5e-123) {
		tmp = t_1;
	} else if (a <= -2.8e-156) {
		tmp = t_3;
	} else if (a <= 8.8e-281) {
		tmp = t_1;
	} else if (a <= 1.25e-275) {
		tmp = z / (t / x);
	} else if (a <= 9.5e+47) {
		tmp = y - (y / (t / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / t))
	t_2 = x - (z / (a / x))
	t_3 = x * (-z / (a - t))
	tmp = 0
	if a <= -4.1e+65:
		tmp = t_2
	elif a <= -6.1e-31:
		tmp = t_1
	elif a <= -4.2e-50:
		tmp = t_3
	elif a <= -5e-123:
		tmp = t_1
	elif a <= -2.8e-156:
		tmp = t_3
	elif a <= 8.8e-281:
		tmp = t_1
	elif a <= 1.25e-275:
		tmp = z / (t / x)
	elif a <= 9.5e+47:
		tmp = y - (y / (t / z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	t_2 = Float64(x - Float64(z / Float64(a / x)))
	t_3 = Float64(x * Float64(Float64(-z) / Float64(a - t)))
	tmp = 0.0
	if (a <= -4.1e+65)
		tmp = t_2;
	elseif (a <= -6.1e-31)
		tmp = t_1;
	elseif (a <= -4.2e-50)
		tmp = t_3;
	elseif (a <= -5e-123)
		tmp = t_1;
	elseif (a <= -2.8e-156)
		tmp = t_3;
	elseif (a <= 8.8e-281)
		tmp = t_1;
	elseif (a <= 1.25e-275)
		tmp = Float64(z / Float64(t / x));
	elseif (a <= 9.5e+47)
		tmp = Float64(y - Float64(y / Float64(t / z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / t));
	t_2 = x - (z / (a / x));
	t_3 = x * (-z / (a - t));
	tmp = 0.0;
	if (a <= -4.1e+65)
		tmp = t_2;
	elseif (a <= -6.1e-31)
		tmp = t_1;
	elseif (a <= -4.2e-50)
		tmp = t_3;
	elseif (a <= -5e-123)
		tmp = t_1;
	elseif (a <= -2.8e-156)
		tmp = t_3;
	elseif (a <= 8.8e-281)
		tmp = t_1;
	elseif (a <= 1.25e-275)
		tmp = z / (t / x);
	elseif (a <= 9.5e+47)
		tmp = y - (y / (t / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(z / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[((-z) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.1e+65], t$95$2, If[LessEqual[a, -6.1e-31], t$95$1, If[LessEqual[a, -4.2e-50], t$95$3, If[LessEqual[a, -5e-123], t$95$1, If[LessEqual[a, -2.8e-156], t$95$3, If[LessEqual[a, 8.8e-281], t$95$1, If[LessEqual[a, 1.25e-275], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+47], N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.1000000000000001e65 or 9.50000000000000001e47 < a

   1. Initial program 68.2%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in t around 0 57.0%

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

      1. +-commutative 57.0%

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

      2. *-commutative 57.0%

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

      3. associate-/l* 74.0%

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

   6. Simplified 74.0%

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

   7. Taylor expanded in y around 0 53.4%

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

      1. +-commutative 53.4%

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

      2. mul-1-neg 53.4%

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

      3. unsub-neg 53.4%

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

      4. associate-/l* 61.5%

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

   9. Simplified 61.5%

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

   if -4.1000000000000001e65 < a < -6.0999999999999998e-31 or -4.2000000000000002e-50 < a < -5.0000000000000003e-123 or -2.8000000000000002e-156 < a < 8.80000000000000016e-281

   1. Initial program 69.2%

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

      1. associate-/l* 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in t around -inf 76.4%

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

      1. mul-1-neg 76.4%

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

      2. unsub-neg 76.4%

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

      3. div-sub 76.4%

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

      4. *-commutative 76.4%

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

      5. div-sub 76.4%

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

      6. distribute-rgt-out-- 76.4%

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

   6. Simplified 76.4%

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

   7. Taylor expanded in a around 0 72.0%

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

   8. Taylor expanded in y around inf 62.3%

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

   if -6.0999999999999998e-31 < a < -4.2000000000000002e-50 or -5.0000000000000003e-123 < a < -2.8000000000000002e-156

   1. Initial program 71.1%

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

      1. associate-/l* 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in z around inf 80.6%

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

      1. div-sub 80.6%

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

      2. associate-*r/ 71.7%

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

   6. Simplified 71.7%

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

   7. Taylor expanded in y around 0 71.7%

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

      1. associate-*r/ 71.7%

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

      2. associate-*r* 71.7%

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

      3. *-rgt-identity 71.7%

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

      4. times-frac 80.7%

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

      5. mul-1-neg 80.7%

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

      6. /-rgt-identity 80.7%

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

   9. Simplified 80.7%

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

   if 8.80000000000000016e-281 < a < 1.24999999999999996e-275

   1. Initial program 42.3%

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

      1. associate-/l* 74.7%

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

   3. Simplified 74.7%

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

   4. Taylor expanded in z around inf 100.0%

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

      1. div-sub 100.0%

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

      2. associate-*r/ 62.1%

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

   6. Simplified 62.1%

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

   7. Taylor expanded in y around 0 62.1%

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

      1. associate-*r/ 62.1%

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

      2. associate-*r* 62.1%

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

      3. *-rgt-identity 62.1%

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

      4. times-frac 80.9%

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

      5. mul-1-neg 80.9%

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

      6. /-rgt-identity 80.9%

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

   9. Simplified 80.9%

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

   10. Taylor expanded in a around 0 62.1%

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

       1. associate-/l* 99.4%

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

   12. Simplified 99.4%

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

   if 1.24999999999999996e-275 < a < 9.50000000000000001e47

   1. Initial program 73.6%

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

      1. associate-/l* 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in t around -inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

      3. div-sub 70.9%

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

      4. *-commutative 70.9%

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

      5. div-sub 72.2%

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

      6. distribute-rgt-out-- 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in a around 0 71.8%

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

   8. Taylor expanded in y around inf 50.7%

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

      1. associate-/l* 53.3%

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

   10. Simplified 53.3%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+65}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-123}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-156}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-281}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-275}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+47}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \end{array} \]

Alternative 9: 52.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ t_2 := x - t \cdot \frac{y}{a}\\ t_3 := x \cdot \frac{-z}{a - t}\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-172}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-275}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+46}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t))))
        (t_2 (- x (* t (/ y a))))
        (t_3 (* x (/ (- z) (- a t)))))
   (if (<= a -3.2e+65)
     t_2
     (if (<= a -3.8e-31)
       t_1
       (if (<= a -3.9e-50)
         t_3
         (if (<= a -4.6e-123)
           t_1
           (if (<= a -2.3e-172)
             t_3
             (if (<= a 2.6e-280)
               t_1
               (if (<= a 1.25e-275)
                 (/ z (/ t x))
                 (if (<= a 1.8e+46) (- y (/ y (/ t z))) t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double t_2 = x - (t * (y / a));
	double t_3 = x * (-z / (a - t));
	double tmp;
	if (a <= -3.2e+65) {
		tmp = t_2;
	} else if (a <= -3.8e-31) {
		tmp = t_1;
	} else if (a <= -3.9e-50) {
		tmp = t_3;
	} else if (a <= -4.6e-123) {
		tmp = t_1;
	} else if (a <= -2.3e-172) {
		tmp = t_3;
	} else if (a <= 2.6e-280) {
		tmp = t_1;
	} else if (a <= 1.25e-275) {
		tmp = z / (t / x);
	} else if (a <= 1.8e+46) {
		tmp = y - (y / (t / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (1.0d0 - (z / t))
    t_2 = x - (t * (y / a))
    t_3 = x * (-z / (a - t))
    if (a <= (-3.2d+65)) then
        tmp = t_2
    else if (a <= (-3.8d-31)) then
        tmp = t_1
    else if (a <= (-3.9d-50)) then
        tmp = t_3
    else if (a <= (-4.6d-123)) then
        tmp = t_1
    else if (a <= (-2.3d-172)) then
        tmp = t_3
    else if (a <= 2.6d-280) then
        tmp = t_1
    else if (a <= 1.25d-275) then
        tmp = z / (t / x)
    else if (a <= 1.8d+46) then
        tmp = y - (y / (t / z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double t_2 = x - (t * (y / a));
	double t_3 = x * (-z / (a - t));
	double tmp;
	if (a <= -3.2e+65) {
		tmp = t_2;
	} else if (a <= -3.8e-31) {
		tmp = t_1;
	} else if (a <= -3.9e-50) {
		tmp = t_3;
	} else if (a <= -4.6e-123) {
		tmp = t_1;
	} else if (a <= -2.3e-172) {
		tmp = t_3;
	} else if (a <= 2.6e-280) {
		tmp = t_1;
	} else if (a <= 1.25e-275) {
		tmp = z / (t / x);
	} else if (a <= 1.8e+46) {
		tmp = y - (y / (t / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / t))
	t_2 = x - (t * (y / a))
	t_3 = x * (-z / (a - t))
	tmp = 0
	if a <= -3.2e+65:
		tmp = t_2
	elif a <= -3.8e-31:
		tmp = t_1
	elif a <= -3.9e-50:
		tmp = t_3
	elif a <= -4.6e-123:
		tmp = t_1
	elif a <= -2.3e-172:
		tmp = t_3
	elif a <= 2.6e-280:
		tmp = t_1
	elif a <= 1.25e-275:
		tmp = z / (t / x)
	elif a <= 1.8e+46:
		tmp = y - (y / (t / z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	t_2 = Float64(x - Float64(t * Float64(y / a)))
	t_3 = Float64(x * Float64(Float64(-z) / Float64(a - t)))
	tmp = 0.0
	if (a <= -3.2e+65)
		tmp = t_2;
	elseif (a <= -3.8e-31)
		tmp = t_1;
	elseif (a <= -3.9e-50)
		tmp = t_3;
	elseif (a <= -4.6e-123)
		tmp = t_1;
	elseif (a <= -2.3e-172)
		tmp = t_3;
	elseif (a <= 2.6e-280)
		tmp = t_1;
	elseif (a <= 1.25e-275)
		tmp = Float64(z / Float64(t / x));
	elseif (a <= 1.8e+46)
		tmp = Float64(y - Float64(y / Float64(t / z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / t));
	t_2 = x - (t * (y / a));
	t_3 = x * (-z / (a - t));
	tmp = 0.0;
	if (a <= -3.2e+65)
		tmp = t_2;
	elseif (a <= -3.8e-31)
		tmp = t_1;
	elseif (a <= -3.9e-50)
		tmp = t_3;
	elseif (a <= -4.6e-123)
		tmp = t_1;
	elseif (a <= -2.3e-172)
		tmp = t_3;
	elseif (a <= 2.6e-280)
		tmp = t_1;
	elseif (a <= 1.25e-275)
		tmp = z / (t / x);
	elseif (a <= 1.8e+46)
		tmp = y - (y / (t / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[((-z) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e+65], t$95$2, If[LessEqual[a, -3.8e-31], t$95$1, If[LessEqual[a, -3.9e-50], t$95$3, If[LessEqual[a, -4.6e-123], t$95$1, If[LessEqual[a, -2.3e-172], t$95$3, If[LessEqual[a, 2.6e-280], t$95$1, If[LessEqual[a, 1.25e-275], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+46], N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.20000000000000007e65 or 1.7999999999999999e46 < a

   1. Initial program 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around inf 84.3%

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

   5. Taylor expanded in a around inf 75.4%

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

   6. Taylor expanded in z around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. *-commutative 61.7%

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

      3. associate-*r/ 62.7%

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

      4. distribute-rgt-neg-in 62.7%

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

      5. distribute-neg-frac 62.7%

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

   8. Simplified 62.7%

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

   if -3.20000000000000007e65 < a < -3.8e-31 or -3.90000000000000021e-50 < a < -4.59999999999999973e-123 or -2.29999999999999995e-172 < a < 2.6e-280

   1. Initial program 69.2%

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

      1. associate-/l* 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in t around -inf 76.4%

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

      1. mul-1-neg 76.4%

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

      2. unsub-neg 76.4%

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

      3. div-sub 76.4%

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

      4. *-commutative 76.4%

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

      5. div-sub 76.4%

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

      6. distribute-rgt-out-- 76.4%

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

   6. Simplified 76.4%

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

   7. Taylor expanded in a around 0 72.0%

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

   8. Taylor expanded in y around inf 62.3%

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

   if -3.8e-31 < a < -3.90000000000000021e-50 or -4.59999999999999973e-123 < a < -2.29999999999999995e-172

   1. Initial program 71.1%

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

      1. associate-/l* 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in z around inf 80.6%

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

      1. div-sub 80.6%

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

      2. associate-*r/ 71.7%

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

   6. Simplified 71.7%

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

   7. Taylor expanded in y around 0 71.7%

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

      1. associate-*r/ 71.7%

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

      2. associate-*r* 71.7%

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

      3. *-rgt-identity 71.7%

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

      4. times-frac 80.7%

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

      5. mul-1-neg 80.7%

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

      6. /-rgt-identity 80.7%

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

   9. Simplified 80.7%

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

   if 2.6e-280 < a < 1.24999999999999996e-275

   1. Initial program 42.3%

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

      1. associate-/l* 74.7%

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

   3. Simplified 74.7%

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

   4. Taylor expanded in z around inf 100.0%

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

      1. div-sub 100.0%

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

      2. associate-*r/ 62.1%

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

   6. Simplified 62.1%

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

   7. Taylor expanded in y around 0 62.1%

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

      1. associate-*r/ 62.1%

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

      2. associate-*r* 62.1%

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

      3. *-rgt-identity 62.1%

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

      4. times-frac 80.9%

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

      5. mul-1-neg 80.9%

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

      6. /-rgt-identity 80.9%

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

   9. Simplified 80.9%

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

   10. Taylor expanded in a around 0 62.1%

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

       1. associate-/l* 99.4%

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

   12. Simplified 99.4%

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

   if 1.24999999999999996e-275 < a < 1.7999999999999999e46

   1. Initial program 73.6%

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

      1. associate-/l* 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in t around -inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

      3. div-sub 70.9%

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

      4. *-commutative 70.9%

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

      5. div-sub 72.2%

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

      6. distribute-rgt-out-- 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in a around 0 71.8%

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

   8. Taylor expanded in y around inf 50.7%

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

      1. associate-/l* 53.3%

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

   10. Simplified 53.3%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+65}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-123}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-280}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-275}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+46}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10: 57.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z}{\frac{a}{x}}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-307}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-188} \lor \neg \left(y \leq 1.25 \cdot 10^{-108}\right) \land y \leq 1.85 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ z (/ a x)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= y -5.6e-9)
     t_2
     (if (<= y -1.3e-159)
       t_1
       (if (<= y -3.25e-307)
         (+ y (* x (/ z t)))
         (if (or (<= y 2e-188) (and (not (<= y 1.25e-108)) (<= y 1.85e+50)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z / (a / x));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -5.6e-9) {
		tmp = t_2;
	} else if (y <= -1.3e-159) {
		tmp = t_1;
	} else if (y <= -3.25e-307) {
		tmp = y + (x * (z / t));
	} else if ((y <= 2e-188) || (!(y <= 1.25e-108) && (y <= 1.85e+50))) {
		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 / (a / x))
    t_2 = y * ((z - t) / (a - t))
    if (y <= (-5.6d-9)) then
        tmp = t_2
    else if (y <= (-1.3d-159)) then
        tmp = t_1
    else if (y <= (-3.25d-307)) then
        tmp = y + (x * (z / t))
    else if ((y <= 2d-188) .or. (.not. (y <= 1.25d-108)) .and. (y <= 1.85d+50)) 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 / (a / x));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -5.6e-9) {
		tmp = t_2;
	} else if (y <= -1.3e-159) {
		tmp = t_1;
	} else if (y <= -3.25e-307) {
		tmp = y + (x * (z / t));
	} else if ((y <= 2e-188) || (!(y <= 1.25e-108) && (y <= 1.85e+50))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (z / (a / x))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if y <= -5.6e-9:
		tmp = t_2
	elif y <= -1.3e-159:
		tmp = t_1
	elif y <= -3.25e-307:
		tmp = y + (x * (z / t))
	elif (y <= 2e-188) or (not (y <= 1.25e-108) and (y <= 1.85e+50)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(z / Float64(a / x)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (y <= -5.6e-9)
		tmp = t_2;
	elseif (y <= -1.3e-159)
		tmp = t_1;
	elseif (y <= -3.25e-307)
		tmp = Float64(y + Float64(x * Float64(z / t)));
	elseif ((y <= 2e-188) || (!(y <= 1.25e-108) && (y <= 1.85e+50)))
		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 / (a / x));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (y <= -5.6e-9)
		tmp = t_2;
	elseif (y <= -1.3e-159)
		tmp = t_1;
	elseif (y <= -3.25e-307)
		tmp = y + (x * (z / t));
	elseif ((y <= 2e-188) || (~((y <= 1.25e-108)) && (y <= 1.85e+50)))
		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[(z / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e-9], t$95$2, If[LessEqual[y, -1.3e-159], t$95$1, If[LessEqual[y, -3.25e-307], N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2e-188], And[N[Not[LessEqual[y, 1.25e-108]], $MachinePrecision], LessEqual[y, 1.85e+50]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.59999999999999969e-9 or 1.9999999999999999e-188 < y < 1.25e-108 or 1.85e50 < y

   1. Initial program 66.5%

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

      1. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in x around 0 52.7%

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

      1. associate-*r/ 73.6%

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

   6. Simplified 73.6%

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

   if -5.59999999999999969e-9 < y < -1.2999999999999999e-159 or -3.2500000000000001e-307 < y < 1.9999999999999999e-188 or 1.25e-108 < y < 1.85e50

   1. Initial program 75.5%

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

      1. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in t around 0 56.2%

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

      1. +-commutative 56.2%

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

      2. *-commutative 56.2%

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

      3. associate-/l* 61.4%

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

   6. Simplified 61.4%

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

   7. Taylor expanded in y around 0 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. associate-/l* 59.4%

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

   9. Simplified 59.4%

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

   if -1.2999999999999999e-159 < y < -3.2500000000000001e-307

   1. Initial program 66.3%

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

      1. associate-/l* 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in t around -inf 72.9%

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

      1. mul-1-neg 72.9%

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

      2. unsub-neg 72.9%

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

      3. div-sub 72.9%

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

      4. *-commutative 72.9%

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

      5. div-sub 72.9%

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

      6. distribute-rgt-out-- 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in a around 0 62.9%

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

   8. Taylor expanded in z around 0 62.9%

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

      1. *-commutative 62.9%

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

      2. associate-*r/ 60.3%

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

   10. Simplified 60.3%

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

   11. Taylor expanded in y around 0 59.4%

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

       1. mul-1-neg 59.4%

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

       2. associate-*l/ 56.4%

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

       3. distribute-rgt-neg-out 56.4%

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

   13. Simplified 56.4%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-159}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-307}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-188} \lor \neg \left(y \leq 1.25 \cdot 10^{-108}\right) \land y \leq 1.85 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 11: 69.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+40}:\\ \;\;\;\;x - \frac{t - z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (/ z t) (- x y)))))
   (if (<= t -1.5e+73)
     t_1
     (if (<= t -4.2e+28)
       (+ x (/ z (/ a (- y x))))
       (if (<= t -3.8e-18)
         t_1
         (if (<= t 1.35e-125)
           (+ x (/ (- y x) (/ a z)))
           (if (<= t 2.5e-17)
             (* z (/ (- y x) (- a t)))
             (if (<= t 2.9e+40) (- x (/ (- t z) (/ a y))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z / t) * (x - y));
	double tmp;
	if (t <= -1.5e+73) {
		tmp = t_1;
	} else if (t <= -4.2e+28) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= -3.8e-18) {
		tmp = t_1;
	} else if (t <= 1.35e-125) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 2.5e-17) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 2.9e+40) {
		tmp = x - ((t - z) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + ((z / t) * (x - y))
    if (t <= (-1.5d+73)) then
        tmp = t_1
    else if (t <= (-4.2d+28)) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= (-3.8d-18)) then
        tmp = t_1
    else if (t <= 1.35d-125) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 2.5d-17) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 2.9d+40) then
        tmp = x - ((t - z) / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z / t) * (x - y));
	double tmp;
	if (t <= -1.5e+73) {
		tmp = t_1;
	} else if (t <= -4.2e+28) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= -3.8e-18) {
		tmp = t_1;
	} else if (t <= 1.35e-125) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 2.5e-17) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 2.9e+40) {
		tmp = x - ((t - z) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((z / t) * (x - y))
	tmp = 0
	if t <= -1.5e+73:
		tmp = t_1
	elif t <= -4.2e+28:
		tmp = x + (z / (a / (y - x)))
	elif t <= -3.8e-18:
		tmp = t_1
	elif t <= 1.35e-125:
		tmp = x + ((y - x) / (a / z))
	elif t <= 2.5e-17:
		tmp = z * ((y - x) / (a - t))
	elif t <= 2.9e+40:
		tmp = x - ((t - z) / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(z / t) * Float64(x - y)))
	tmp = 0.0
	if (t <= -1.5e+73)
		tmp = t_1;
	elseif (t <= -4.2e+28)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= -3.8e-18)
		tmp = t_1;
	elseif (t <= 1.35e-125)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 2.5e-17)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 2.9e+40)
		tmp = Float64(x - Float64(Float64(t - z) / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((z / t) * (x - y));
	tmp = 0.0;
	if (t <= -1.5e+73)
		tmp = t_1;
	elseif (t <= -4.2e+28)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= -3.8e-18)
		tmp = t_1;
	elseif (t <= 1.35e-125)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 2.5e-17)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 2.9e+40)
		tmp = x - ((t - z) / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e+73], t$95$1, If[LessEqual[t, -4.2e+28], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e-18], t$95$1, If[LessEqual[t, 1.35e-125], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e-17], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+40], N[(x - N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.50000000000000005e73 or -4.19999999999999978e28 < t < -3.7999999999999998e-18 or 2.90000000000000017e40 < t

   1. Initial program 53.4%

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

      1. associate-/l* 77.1%

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

   3. Simplified 77.1%

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

   4. Taylor expanded in t around -inf 64.0%

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

      1. mul-1-neg 64.0%

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

      2. unsub-neg 64.0%

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

      3. div-sub 64.0%

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

      4. *-commutative 64.0%

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

      5. div-sub 64.0%

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

      6. distribute-rgt-out-- 64.2%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in a around 0 64.1%

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

   8. Taylor expanded in z around 0 64.1%

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

      1. *-commutative 64.1%

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

      2. associate-*r/ 76.0%

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

   10. Simplified 76.0%

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

   if -1.50000000000000005e73 < t < -4.19999999999999978e28

   1. Initial program 57.3%

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

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

   4. Taylor expanded in t around 0 47.3%

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

      1. +-commutative 47.3%

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

      2. *-commutative 47.3%

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

      3. associate-/l* 79.1%

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

   6. Simplified 79.1%

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

   if -3.7999999999999998e-18 < t < 1.3499999999999999e-125

   1. Initial program 84.8%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in t around 0 80.5%

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

   if 1.3499999999999999e-125 < t < 2.4999999999999999e-17

   1. Initial program 91.8%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 88.4%

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

      1. div-sub 88.4%

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

   6. Simplified 88.4%

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

   if 2.4999999999999999e-17 < t < 2.90000000000000017e40

   1. Initial program 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in a around inf 92.7%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+73}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-18}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+40}:\\ \;\;\;\;x - \frac{t - z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 12: 69.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-19}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+31}:\\ \;\;\;\;x - \frac{t - z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (/ z t) (- x y)))))
   (if (<= t -2.6e+74)
     t_1
     (if (<= t -7.2e+28)
       (+ x (/ z (/ a (- y x))))
       (if (<= t -4.2e-19)
         (- y (/ (* (- y x) z) t))
         (if (<= t 1.18e-125)
           (+ x (/ (- y x) (/ a z)))
           (if (<= t 3.5e-17)
             (* z (/ (- y x) (- a t)))
             (if (<= t 5.2e+31) (- x (/ (- t z) (/ a y))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z / t) * (x - y));
	double tmp;
	if (t <= -2.6e+74) {
		tmp = t_1;
	} else if (t <= -7.2e+28) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= -4.2e-19) {
		tmp = y - (((y - x) * z) / t);
	} else if (t <= 1.18e-125) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 3.5e-17) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 5.2e+31) {
		tmp = x - ((t - z) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + ((z / t) * (x - y))
    if (t <= (-2.6d+74)) then
        tmp = t_1
    else if (t <= (-7.2d+28)) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= (-4.2d-19)) then
        tmp = y - (((y - x) * z) / t)
    else if (t <= 1.18d-125) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 3.5d-17) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 5.2d+31) then
        tmp = x - ((t - z) / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z / t) * (x - y));
	double tmp;
	if (t <= -2.6e+74) {
		tmp = t_1;
	} else if (t <= -7.2e+28) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= -4.2e-19) {
		tmp = y - (((y - x) * z) / t);
	} else if (t <= 1.18e-125) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 3.5e-17) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 5.2e+31) {
		tmp = x - ((t - z) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((z / t) * (x - y))
	tmp = 0
	if t <= -2.6e+74:
		tmp = t_1
	elif t <= -7.2e+28:
		tmp = x + (z / (a / (y - x)))
	elif t <= -4.2e-19:
		tmp = y - (((y - x) * z) / t)
	elif t <= 1.18e-125:
		tmp = x + ((y - x) / (a / z))
	elif t <= 3.5e-17:
		tmp = z * ((y - x) / (a - t))
	elif t <= 5.2e+31:
		tmp = x - ((t - z) / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(z / t) * Float64(x - y)))
	tmp = 0.0
	if (t <= -2.6e+74)
		tmp = t_1;
	elseif (t <= -7.2e+28)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= -4.2e-19)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * z) / t));
	elseif (t <= 1.18e-125)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 3.5e-17)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 5.2e+31)
		tmp = Float64(x - Float64(Float64(t - z) / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((z / t) * (x - y));
	tmp = 0.0;
	if (t <= -2.6e+74)
		tmp = t_1;
	elseif (t <= -7.2e+28)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= -4.2e-19)
		tmp = y - (((y - x) * z) / t);
	elseif (t <= 1.18e-125)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 3.5e-17)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 5.2e+31)
		tmp = x - ((t - z) / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e+74], t$95$1, If[LessEqual[t, -7.2e+28], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.2e-19], N[(y - N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.18e-125], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-17], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+31], N[(x - N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.6000000000000001e74 or 5.2e31 < t

   1. Initial program 49.0%

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

      1. associate-/l* 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in t around -inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. unsub-neg 62.8%

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

      3. div-sub 62.8%

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

      4. *-commutative 62.8%

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

      5. div-sub 62.8%

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

      6. distribute-rgt-out-- 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in a around 0 63.7%

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

   8. Taylor expanded in z around 0 63.7%

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

      1. *-commutative 63.7%

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

      2. associate-*r/ 77.5%

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

   10. Simplified 77.5%

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

   if -2.6000000000000001e74 < t < -7.1999999999999999e28

   1. Initial program 57.3%

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

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

   4. Taylor expanded in t around 0 47.3%

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

      1. +-commutative 47.3%

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

      2. *-commutative 47.3%

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

      3. associate-/l* 79.1%

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

   6. Simplified 79.1%

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

   if -7.1999999999999999e28 < t < -4.1999999999999998e-19

   1. Initial program 82.0%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in t around -inf 72.0%

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

      1. mul-1-neg 72.0%

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

      2. unsub-neg 72.0%

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

      3. div-sub 72.0%

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

      4. *-commutative 72.0%

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

      5. div-sub 72.0%

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

      6. distribute-rgt-out-- 72.0%

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

   6. Simplified 72.0%

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

   7. Taylor expanded in a around 0 66.4%

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

   if -4.1999999999999998e-19 < t < 1.17999999999999994e-125

   1. Initial program 84.8%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in t around 0 80.5%

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

   if 1.17999999999999994e-125 < t < 3.5000000000000002e-17

   1. Initial program 91.8%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 88.4%

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

      1. div-sub 88.4%

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

   6. Simplified 88.4%

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

   if 3.5000000000000002e-17 < t < 5.2e31

   1. Initial program 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in a around inf 92.7%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+74}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-19}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+31}:\\ \;\;\;\;x - \frac{t - z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 13: 52.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ t_2 := x - \frac{z}{\frac{a}{x}}\\ \mathbf{if}\;a \leq -3.05 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.3 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-147}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-274}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+47}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))) (t_2 (- x (/ z (/ a x)))))
   (if (<= a -3.05e+65)
     t_2
     (if (<= a -6.3e-121)
       t_1
       (if (<= a -1.05e-147)
         (/ (* x (- z a)) t)
         (if (<= a 8.8e-281)
           t_1
           (if (<= a 4.7e-274)
             (/ z (/ t x))
             (if (<= a 3.6e+47) (- y (/ y (/ t z))) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double t_2 = x - (z / (a / x));
	double tmp;
	if (a <= -3.05e+65) {
		tmp = t_2;
	} else if (a <= -6.3e-121) {
		tmp = t_1;
	} else if (a <= -1.05e-147) {
		tmp = (x * (z - a)) / t;
	} else if (a <= 8.8e-281) {
		tmp = t_1;
	} else if (a <= 4.7e-274) {
		tmp = z / (t / x);
	} else if (a <= 3.6e+47) {
		tmp = y - (y / (t / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (1.0d0 - (z / t))
    t_2 = x - (z / (a / x))
    if (a <= (-3.05d+65)) then
        tmp = t_2
    else if (a <= (-6.3d-121)) then
        tmp = t_1
    else if (a <= (-1.05d-147)) then
        tmp = (x * (z - a)) / t
    else if (a <= 8.8d-281) then
        tmp = t_1
    else if (a <= 4.7d-274) then
        tmp = z / (t / x)
    else if (a <= 3.6d+47) then
        tmp = y - (y / (t / z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double t_2 = x - (z / (a / x));
	double tmp;
	if (a <= -3.05e+65) {
		tmp = t_2;
	} else if (a <= -6.3e-121) {
		tmp = t_1;
	} else if (a <= -1.05e-147) {
		tmp = (x * (z - a)) / t;
	} else if (a <= 8.8e-281) {
		tmp = t_1;
	} else if (a <= 4.7e-274) {
		tmp = z / (t / x);
	} else if (a <= 3.6e+47) {
		tmp = y - (y / (t / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / t))
	t_2 = x - (z / (a / x))
	tmp = 0
	if a <= -3.05e+65:
		tmp = t_2
	elif a <= -6.3e-121:
		tmp = t_1
	elif a <= -1.05e-147:
		tmp = (x * (z - a)) / t
	elif a <= 8.8e-281:
		tmp = t_1
	elif a <= 4.7e-274:
		tmp = z / (t / x)
	elif a <= 3.6e+47:
		tmp = y - (y / (t / z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	t_2 = Float64(x - Float64(z / Float64(a / x)))
	tmp = 0.0
	if (a <= -3.05e+65)
		tmp = t_2;
	elseif (a <= -6.3e-121)
		tmp = t_1;
	elseif (a <= -1.05e-147)
		tmp = Float64(Float64(x * Float64(z - a)) / t);
	elseif (a <= 8.8e-281)
		tmp = t_1;
	elseif (a <= 4.7e-274)
		tmp = Float64(z / Float64(t / x));
	elseif (a <= 3.6e+47)
		tmp = Float64(y - Float64(y / Float64(t / z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / t));
	t_2 = x - (z / (a / x));
	tmp = 0.0;
	if (a <= -3.05e+65)
		tmp = t_2;
	elseif (a <= -6.3e-121)
		tmp = t_1;
	elseif (a <= -1.05e-147)
		tmp = (x * (z - a)) / t;
	elseif (a <= 8.8e-281)
		tmp = t_1;
	elseif (a <= 4.7e-274)
		tmp = z / (t / x);
	elseif (a <= 3.6e+47)
		tmp = y - (y / (t / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(z / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.05e+65], t$95$2, If[LessEqual[a, -6.3e-121], t$95$1, If[LessEqual[a, -1.05e-147], N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 8.8e-281], t$95$1, If[LessEqual[a, 4.7e-274], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e+47], N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.04999999999999982e65 or 3.60000000000000008e47 < a

   1. Initial program 68.2%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in t around 0 57.0%

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

      1. +-commutative 57.0%

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

      2. *-commutative 57.0%

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

      3. associate-/l* 74.0%

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

   6. Simplified 74.0%

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

   7. Taylor expanded in y around 0 53.4%

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

      1. +-commutative 53.4%

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

      2. mul-1-neg 53.4%

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

      3. unsub-neg 53.4%

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

      4. associate-/l* 61.5%

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

   9. Simplified 61.5%

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

   if -3.04999999999999982e65 < a < -6.29999999999999961e-121 or -1.05e-147 < a < 8.80000000000000016e-281

   1. Initial program 70.0%

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

      1. associate-/l* 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in t around -inf 69.3%

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

      1. mul-1-neg 69.3%

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

      2. unsub-neg 69.3%

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

      3. div-sub 69.3%

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

      4. *-commutative 69.3%

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

      5. div-sub 69.3%

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

      6. distribute-rgt-out-- 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in a around 0 66.9%

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

   8. Taylor expanded in y around inf 58.6%

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

   if -6.29999999999999961e-121 < a < -1.05e-147

   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* 65.6%

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

   3. Simplified 65.6%

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

   4. Taylor expanded in t around -inf 72.1%

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

      1. mul-1-neg 72.1%

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

      2. unsub-neg 72.1%

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

      3. div-sub 57.8%

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

      4. *-commutative 57.8%

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

      5. div-sub 72.1%

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

      6. distribute-rgt-out-- 72.1%

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

   6. Simplified 72.1%

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

   7. Taylor expanded in y around 0 72.1%

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

   if 8.80000000000000016e-281 < a < 4.7000000000000004e-274

   1. Initial program 42.3%

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

      1. associate-/l* 74.7%

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

   3. Simplified 74.7%

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

   4. Taylor expanded in z around inf 100.0%

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

      1. div-sub 100.0%

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

      2. associate-*r/ 62.1%

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

   6. Simplified 62.1%

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

   7. Taylor expanded in y around 0 62.1%

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

      1. associate-*r/ 62.1%

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

      2. associate-*r* 62.1%

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

      3. *-rgt-identity 62.1%

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

      4. times-frac 80.9%

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

      5. mul-1-neg 80.9%

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

      6. /-rgt-identity 80.9%

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

   9. Simplified 80.9%

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

   10. Taylor expanded in a around 0 62.1%

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

       1. associate-/l* 99.4%

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

   12. Simplified 99.4%

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

   if 4.7000000000000004e-274 < a < 3.60000000000000008e47

   1. Initial program 73.6%

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

      1. associate-/l* 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in t around -inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

      3. div-sub 70.9%

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

      4. *-commutative 70.9%

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

      5. div-sub 72.2%

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

      6. distribute-rgt-out-- 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in a around 0 71.8%

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

   8. Taylor expanded in y around inf 50.7%

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

      1. associate-/l* 53.3%

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

   10. Simplified 53.3%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.05 \cdot 10^{+65}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;a \leq -6.3 \cdot 10^{-121}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-147}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-281}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-274}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+47}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \end{array} \]

Alternative 14: 52.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \frac{y}{a}\\ t_2 := y + x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-193}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-165}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (/ y a)))) (t_2 (+ y (* x (/ z t)))))
   (if (<= t -8.6e-18)
     t_2
     (if (<= t -3e-137)
       t_1
       (if (<= t -1.3e-193)
         (* z (/ (- y x) a))
         (if (<= t 2.7e-165)
           (- x (/ z (/ a x)))
           (if (<= t 2.2e-36)
             (/ y (/ (- a t) z))
             (if (<= t 2e+32) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (y / a));
	double t_2 = y + (x * (z / t));
	double tmp;
	if (t <= -8.6e-18) {
		tmp = t_2;
	} else if (t <= -3e-137) {
		tmp = t_1;
	} else if (t <= -1.3e-193) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.7e-165) {
		tmp = x - (z / (a / x));
	} else if (t <= 2.2e-36) {
		tmp = y / ((a - t) / z);
	} else if (t <= 2e+32) {
		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 - (t * (y / a))
    t_2 = y + (x * (z / t))
    if (t <= (-8.6d-18)) then
        tmp = t_2
    else if (t <= (-3d-137)) then
        tmp = t_1
    else if (t <= (-1.3d-193)) then
        tmp = z * ((y - x) / a)
    else if (t <= 2.7d-165) then
        tmp = x - (z / (a / x))
    else if (t <= 2.2d-36) then
        tmp = y / ((a - t) / z)
    else if (t <= 2d+32) 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 - (t * (y / a));
	double t_2 = y + (x * (z / t));
	double tmp;
	if (t <= -8.6e-18) {
		tmp = t_2;
	} else if (t <= -3e-137) {
		tmp = t_1;
	} else if (t <= -1.3e-193) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.7e-165) {
		tmp = x - (z / (a / x));
	} else if (t <= 2.2e-36) {
		tmp = y / ((a - t) / z);
	} else if (t <= 2e+32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * (y / a))
	t_2 = y + (x * (z / t))
	tmp = 0
	if t <= -8.6e-18:
		tmp = t_2
	elif t <= -3e-137:
		tmp = t_1
	elif t <= -1.3e-193:
		tmp = z * ((y - x) / a)
	elif t <= 2.7e-165:
		tmp = x - (z / (a / x))
	elif t <= 2.2e-36:
		tmp = y / ((a - t) / z)
	elif t <= 2e+32:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t * Float64(y / a)))
	t_2 = Float64(y + Float64(x * Float64(z / t)))
	tmp = 0.0
	if (t <= -8.6e-18)
		tmp = t_2;
	elseif (t <= -3e-137)
		tmp = t_1;
	elseif (t <= -1.3e-193)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 2.7e-165)
		tmp = Float64(x - Float64(z / Float64(a / x)));
	elseif (t <= 2.2e-36)
		tmp = Float64(y / Float64(Float64(a - t) / z));
	elseif (t <= 2e+32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t * (y / a));
	t_2 = y + (x * (z / t));
	tmp = 0.0;
	if (t <= -8.6e-18)
		tmp = t_2;
	elseif (t <= -3e-137)
		tmp = t_1;
	elseif (t <= -1.3e-193)
		tmp = z * ((y - x) / a);
	elseif (t <= 2.7e-165)
		tmp = x - (z / (a / x));
	elseif (t <= 2.2e-36)
		tmp = y / ((a - t) / z);
	elseif (t <= 2e+32)
		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[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.6e-18], t$95$2, If[LessEqual[t, -3e-137], t$95$1, If[LessEqual[t, -1.3e-193], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e-165], N[(x - N[(z / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e-36], N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+32], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.6000000000000005e-18 or 2.00000000000000011e32 < t

   1. Initial program 53.7%

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

      1. associate-/l* 77.9%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in t around -inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. unsub-neg 62.0%

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

      3. div-sub 62.0%

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

      4. *-commutative 62.0%

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

      5. div-sub 62.0%

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

      6. distribute-rgt-out-- 62.1%

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

   6. Simplified 62.1%

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

   7. Taylor expanded in a around 0 62.0%

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

   8. Taylor expanded in z around 0 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-*r/ 73.1%

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

   10. Simplified 73.1%

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

   11. Taylor expanded in y around 0 54.9%

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

       1. mul-1-neg 54.9%

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

       2. associate-*l/ 61.4%

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

       3. distribute-rgt-neg-out 61.4%

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

   13. Simplified 61.4%

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

   if -8.6000000000000005e-18 < t < -2.9999999999999998e-137 or 2.1999999999999999e-36 < t < 2.00000000000000011e32

   1. Initial program 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-/l* 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in y around inf 75.7%

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

   5. Taylor expanded in a around inf 66.2%

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

   6. Taylor expanded in z around 0 54.1%

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

      1. mul-1-neg 54.1%

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

      2. *-commutative 54.1%

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

      3. associate-*r/ 56.3%

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

      4. distribute-rgt-neg-in 56.3%

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

      5. distribute-neg-frac 56.3%

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

   8. Simplified 56.3%

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

   if -2.9999999999999998e-137 < t < -1.30000000000000004e-193

   1. Initial program 91.1%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around 0 69.6%

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

      1. +-commutative 69.6%

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

      2. *-commutative 69.6%

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

      3. associate-/l* 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in z around inf 69.1%

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

      1. div-sub 69.1%

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

   9. Simplified 69.1%

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

   if -1.30000000000000004e-193 < t < 2.6999999999999998e-165

   1. Initial program 91.6%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around 0 84.5%

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

      1. +-commutative 84.5%

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

      2. *-commutative 84.5%

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

      3. associate-/l* 90.1%

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

   6. Simplified 90.1%

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

   7. Taylor expanded in y around 0 69.1%

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

      1. +-commutative 69.1%

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

      2. mul-1-neg 69.1%

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

      3. unsub-neg 69.1%

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

      4. associate-/l* 73.1%

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

   9. Simplified 73.1%

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

   if 2.6999999999999998e-165 < t < 2.1999999999999999e-36

   1. Initial program 78.6%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in z around inf 71.4%

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

      1. div-sub 71.4%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. associate-*r/ 61.9%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Simplified 61.9%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   7. Taylor expanded in y around inf 37.4%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a - t}} \]
   8. Step-by-step derivation

      1. associate-/l* 47.1%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - t}{z}}} \]

   9. Simplified 47.1%

      \[\leadsto \color{blue}{\frac{y}{\frac{a - t}{z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-18}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-137}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-193}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-165}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+32}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 15: 57.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z}{\frac{a}{x}}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-300}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+111}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ z (/ a x)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= y -7.6e-8)
     t_2
     (if (<= y -1.2e-159)
       t_1
       (if (<= y -1.12e-300)
         (+ y (* x (/ z t)))
         (if (<= y 2.05e-200)
           t_1
           (if (<= y 7e+111) (* z (/ (- y x) (- a t))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z / (a / x));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -7.6e-8) {
		tmp = t_2;
	} else if (y <= -1.2e-159) {
		tmp = t_1;
	} else if (y <= -1.12e-300) {
		tmp = y + (x * (z / t));
	} else if (y <= 2.05e-200) {
		tmp = t_1;
	} else if (y <= 7e+111) {
		tmp = z * ((y - x) / (a - t));
	} 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 / (a / x))
    t_2 = y * ((z - t) / (a - t))
    if (y <= (-7.6d-8)) then
        tmp = t_2
    else if (y <= (-1.2d-159)) then
        tmp = t_1
    else if (y <= (-1.12d-300)) then
        tmp = y + (x * (z / t))
    else if (y <= 2.05d-200) then
        tmp = t_1
    else if (y <= 7d+111) then
        tmp = z * ((y - x) / (a - t))
    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 / (a / x));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -7.6e-8) {
		tmp = t_2;
	} else if (y <= -1.2e-159) {
		tmp = t_1;
	} else if (y <= -1.12e-300) {
		tmp = y + (x * (z / t));
	} else if (y <= 2.05e-200) {
		tmp = t_1;
	} else if (y <= 7e+111) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (z / (a / x))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if y <= -7.6e-8:
		tmp = t_2
	elif y <= -1.2e-159:
		tmp = t_1
	elif y <= -1.12e-300:
		tmp = y + (x * (z / t))
	elif y <= 2.05e-200:
		tmp = t_1
	elif y <= 7e+111:
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(z / Float64(a / x)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (y <= -7.6e-8)
		tmp = t_2;
	elseif (y <= -1.2e-159)
		tmp = t_1;
	elseif (y <= -1.12e-300)
		tmp = Float64(y + Float64(x * Float64(z / t)));
	elseif (y <= 2.05e-200)
		tmp = t_1;
	elseif (y <= 7e+111)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (z / (a / x));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (y <= -7.6e-8)
		tmp = t_2;
	elseif (y <= -1.2e-159)
		tmp = t_1;
	elseif (y <= -1.12e-300)
		tmp = y + (x * (z / t));
	elseif (y <= 2.05e-200)
		tmp = t_1;
	elseif (y <= 7e+111)
		tmp = z * ((y - x) / (a - t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(z / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.6e-8], t$95$2, If[LessEqual[y, -1.2e-159], t$95$1, If[LessEqual[y, -1.12e-300], N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e-200], t$95$1, If[LessEqual[y, 7e+111], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.60000000000000056e-8 or 7.0000000000000004e111 < y

   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* 91.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in x around 0 54.3%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 79.7%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Simplified 79.7%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -7.60000000000000056e-8 < y < -1.19999999999999999e-159 or -1.12e-300 < y < 2.04999999999999993e-200

   1. Initial program 73.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 82.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 82.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around 0 58.0%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 58.0%

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot z}{a}} \]

      2. *-commutative 58.0%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(y - x\right)}}{a} \]

      3. associate-/l* 63.7%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   6. Simplified 63.7%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   7. Taylor expanded in y around 0 58.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{a} + x} \]
   8. Step-by-step derivation

      1. +-commutative 58.0%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{z \cdot x}{a}} \]

      2. mul-1-neg 58.0%

         \[\leadsto x + \color{blue}{\left(-\frac{z \cdot x}{a}\right)} \]

      3. unsub-neg 58.0%

         \[\leadsto \color{blue}{x - \frac{z \cdot x}{a}} \]

      4. associate-/l* 63.7%

         \[\leadsto x - \color{blue}{\frac{z}{\frac{a}{x}}} \]

   9. Simplified 63.7%

      \[\leadsto \color{blue}{x - \frac{z}{\frac{a}{x}}} \]

   if -1.19999999999999999e-159 < y < -1.12e-300

   1. Initial program 66.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 75.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 75.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around -inf 72.9%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. mul-1-neg 72.9%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

      2. unsub-neg 72.9%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      3. div-sub 72.9%

         \[\leadsto y - \color{blue}{\left(\frac{\left(y - x\right) \cdot z}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      4. *-commutative 72.9%

         \[\leadsto y - \left(\frac{\color{blue}{z \cdot \left(y - x\right)}}{t} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      5. div-sub 72.9%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. distribute-rgt-out-- 72.9%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   6. Simplified 72.9%

      \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in a around 0 62.9%

      \[\leadsto y - \color{blue}{\frac{\left(y - x\right) \cdot z}{t}} \]

   8. Taylor expanded in z around 0 62.9%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   9. Step-by-step derivation

      1. *-commutative 62.9%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} \]

      2. associate-*r/ 60.3%

         \[\leadsto y - \color{blue}{\left(y - x\right) \cdot \frac{z}{t}} \]

   10. Simplified 60.3%

       \[\leadsto y - \color{blue}{\left(y - x\right) \cdot \frac{z}{t}} \]

   11. Taylor expanded in y around 0 59.4%

       \[\leadsto y - \color{blue}{-1 \cdot \frac{z \cdot x}{t}} \]
   12. Step-by-step derivation

       1. mul-1-neg 59.4%

          \[\leadsto y - \color{blue}{\left(-\frac{z \cdot x}{t}\right)} \]

       2. associate-*l/ 56.4%

          \[\leadsto y - \left(-\color{blue}{\frac{z}{t} \cdot x}\right) \]

       3. distribute-rgt-neg-out 56.4%

          \[\leadsto y - \color{blue}{\frac{z}{t} \cdot \left(-x\right)} \]

   13. Simplified 56.4%

       \[\leadsto y - \color{blue}{\frac{z}{t} \cdot \left(-x\right)} \]

   if 2.04999999999999993e-200 < y < 7.0000000000000004e111

   1. Initial program 76.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 86.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 56.9%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 56.9%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   6. Simplified 56.9%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-159}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-300}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-200}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+111}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 16: 43.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+21}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+153}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) a))))
   (if (<= t -6.2e+21)
     y
     (if (<= t -1.8e-130)
       x
       (if (<= t 7.4e-221)
         t_1
         (if (<= t 2.35e-166)
           x
           (if (<= t 2.3e-17) t_1 (if (<= t 1.05e+153) (+ x y) y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / a);
	double tmp;
	if (t <= -6.2e+21) {
		tmp = y;
	} else if (t <= -1.8e-130) {
		tmp = x;
	} else if (t <= 7.4e-221) {
		tmp = t_1;
	} else if (t <= 2.35e-166) {
		tmp = x;
	} else if (t <= 2.3e-17) {
		tmp = t_1;
	} else if (t <= 1.05e+153) {
		tmp = x + y;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((y - x) / a)
    if (t <= (-6.2d+21)) then
        tmp = y
    else if (t <= (-1.8d-130)) then
        tmp = x
    else if (t <= 7.4d-221) then
        tmp = t_1
    else if (t <= 2.35d-166) then
        tmp = x
    else if (t <= 2.3d-17) then
        tmp = t_1
    else if (t <= 1.05d+153) then
        tmp = x + y
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / a);
	double tmp;
	if (t <= -6.2e+21) {
		tmp = y;
	} else if (t <= -1.8e-130) {
		tmp = x;
	} else if (t <= 7.4e-221) {
		tmp = t_1;
	} else if (t <= 2.35e-166) {
		tmp = x;
	} else if (t <= 2.3e-17) {
		tmp = t_1;
	} else if (t <= 1.05e+153) {
		tmp = x + y;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / a)
	tmp = 0
	if t <= -6.2e+21:
		tmp = y
	elif t <= -1.8e-130:
		tmp = x
	elif t <= 7.4e-221:
		tmp = t_1
	elif t <= 2.35e-166:
		tmp = x
	elif t <= 2.3e-17:
		tmp = t_1
	elif t <= 1.05e+153:
		tmp = x + y
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / a))
	tmp = 0.0
	if (t <= -6.2e+21)
		tmp = y;
	elseif (t <= -1.8e-130)
		tmp = x;
	elseif (t <= 7.4e-221)
		tmp = t_1;
	elseif (t <= 2.35e-166)
		tmp = x;
	elseif (t <= 2.3e-17)
		tmp = t_1;
	elseif (t <= 1.05e+153)
		tmp = Float64(x + y);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / a);
	tmp = 0.0;
	if (t <= -6.2e+21)
		tmp = y;
	elseif (t <= -1.8e-130)
		tmp = x;
	elseif (t <= 7.4e-221)
		tmp = t_1;
	elseif (t <= 2.35e-166)
		tmp = x;
	elseif (t <= 2.3e-17)
		tmp = t_1;
	elseif (t <= 1.05e+153)
		tmp = x + y;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+21], y, If[LessEqual[t, -1.8e-130], x, If[LessEqual[t, 7.4e-221], t$95$1, If[LessEqual[t, 2.35e-166], x, If[LessEqual[t, 2.3e-17], t$95$1, If[LessEqual[t, 1.05e+153], N[(x + y), $MachinePrecision], y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.2e21 or 1.05000000000000008e153 < t

   1. Initial program 47.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 74.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 74.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around inf 49.5%

      \[\leadsto \color{blue}{y} \]

   if -6.2e21 < t < -1.8000000000000001e-130 or 7.39999999999999971e-221 < t < 2.35000000000000007e-166

   1. Initial program 80.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 92.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 92.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in a around inf 44.5%

      \[\leadsto \color{blue}{x} \]

   if -1.8000000000000001e-130 < t < 7.39999999999999971e-221 or 2.35000000000000007e-166 < t < 2.30000000000000009e-17

   1. Initial program 89.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 96.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around 0 73.0%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 73.0%

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot z}{a}} \]

      2. *-commutative 73.0%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(y - x\right)}}{a} \]

      3. associate-/l* 78.0%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   6. Simplified 78.0%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   7. Taylor expanded in z around inf 53.6%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a} - \frac{x}{a}\right)} \]
   8. Step-by-step derivation

      1. div-sub 56.2%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a}} \]

   9. Simplified 56.2%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a}} \]

   if 2.30000000000000009e-17 < t < 1.05000000000000008e153

   1. Initial program 70.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. *-commutative 70.3%

         \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot \left(y - x\right)}}{a - t} \]

      2. associate-/l* 88.0%

         \[\leadsto x + \color{blue}{\frac{z - t}{\frac{a - t}{y - x}}} \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{x + \frac{z - t}{\frac{a - t}{y - x}}} \]

   4. Taylor expanded in y around inf 73.4%

      \[\leadsto x + \frac{z - t}{\color{blue}{\frac{a - t}{y}}} \]

   5. Taylor expanded in t around inf 41.1%

      \[\leadsto x + \color{blue}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+21}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-221}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+153}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 17: 36.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-283}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-273}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-213}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-76}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.5e+65)
   x
   (if (<= a 3.7e-283)
     y
     (if (<= a 1.2e-273)
       (/ z (/ t x))
       (if (<= a 2.9e-213) y (if (<= a 5.6e-76) (* z (/ (- y) t)) (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+65) {
		tmp = x;
	} else if (a <= 3.7e-283) {
		tmp = y;
	} else if (a <= 1.2e-273) {
		tmp = z / (t / x);
	} else if (a <= 2.9e-213) {
		tmp = y;
	} else if (a <= 5.6e-76) {
		tmp = z * (-y / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.5d+65)) then
        tmp = x
    else if (a <= 3.7d-283) then
        tmp = y
    else if (a <= 1.2d-273) then
        tmp = z / (t / x)
    else if (a <= 2.9d-213) then
        tmp = y
    else if (a <= 5.6d-76) then
        tmp = z * (-y / t)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+65) {
		tmp = x;
	} else if (a <= 3.7e-283) {
		tmp = y;
	} else if (a <= 1.2e-273) {
		tmp = z / (t / x);
	} else if (a <= 2.9e-213) {
		tmp = y;
	} else if (a <= 5.6e-76) {
		tmp = z * (-y / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.5e+65:
		tmp = x
	elif a <= 3.7e-283:
		tmp = y
	elif a <= 1.2e-273:
		tmp = z / (t / x)
	elif a <= 2.9e-213:
		tmp = y
	elif a <= 5.6e-76:
		tmp = z * (-y / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.5e+65)
		tmp = x;
	elseif (a <= 3.7e-283)
		tmp = y;
	elseif (a <= 1.2e-273)
		tmp = Float64(z / Float64(t / x));
	elseif (a <= 2.9e-213)
		tmp = y;
	elseif (a <= 5.6e-76)
		tmp = Float64(z * Float64(Float64(-y) / t));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.5e+65)
		tmp = x;
	elseif (a <= 3.7e-283)
		tmp = y;
	elseif (a <= 1.2e-273)
		tmp = z / (t / x);
	elseif (a <= 2.9e-213)
		tmp = y;
	elseif (a <= 5.6e-76)
		tmp = z * (-y / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.5e+65], x, If[LessEqual[a, 3.7e-283], y, If[LessEqual[a, 1.2e-273], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-213], y, If[LessEqual[a, 5.6e-76], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.5000000000000001e65

   1. Initial program 65.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 96.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 96.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in a around inf 57.3%

      \[\leadsto \color{blue}{x} \]

   if -3.5000000000000001e65 < a < 3.7e-283 or 1.19999999999999991e-273 < a < 2.8999999999999999e-213

   1. Initial program 68.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 78.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 78.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around inf 37.8%

      \[\leadsto \color{blue}{y} \]

   if 3.7e-283 < a < 1.19999999999999991e-273

   1. Initial program 42.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 74.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 74.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 100.0%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. associate-*r/ 62.1%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Simplified 62.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   7. Taylor expanded in y around 0 62.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{a - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 62.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(z \cdot x\right)}{a - t}} \]

      2. associate-*r* 62.1%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot z\right) \cdot x}}{a - t} \]

      3. *-rgt-identity 62.1%

         \[\leadsto \frac{\left(-1 \cdot z\right) \cdot x}{\color{blue}{\left(a - t\right) \cdot 1}} \]

      4. times-frac 80.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot z}{a - t} \cdot \frac{x}{1}} \]

      5. mul-1-neg 80.9%

         \[\leadsto \frac{\color{blue}{-z}}{a - t} \cdot \frac{x}{1} \]

      6. /-rgt-identity 80.9%

         \[\leadsto \frac{-z}{a - t} \cdot \color{blue}{x} \]

   9. Simplified 80.9%

      \[\leadsto \color{blue}{\frac{-z}{a - t} \cdot x} \]

   10. Taylor expanded in a around 0 62.1%

       \[\leadsto \color{blue}{\frac{z \cdot x}{t}} \]
   11. Step-by-step derivation

       1. associate-/l* 99.4%

          \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   12. Simplified 99.4%

       \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   if 2.8999999999999999e-213 < a < 5.6000000000000002e-76

   1. Initial program 77.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 82.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 72.2%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 72.2%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. associate-*r/ 69.8%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Simplified 69.8%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   7. Taylor expanded in y around inf 39.2%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a - t}} \]

   8. Taylor expanded in a around 0 33.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 33.4%

         \[\leadsto \color{blue}{-\frac{y \cdot z}{t}} \]

      2. associate-/l* 36.0%

         \[\leadsto -\color{blue}{\frac{y}{\frac{t}{z}}} \]

      3. associate-/r/ 35.8%

         \[\leadsto -\color{blue}{\frac{y}{t} \cdot z} \]

      4. distribute-rgt-neg-in 35.8%

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \left(-z\right)} \]

   10. Simplified 35.8%

       \[\leadsto \color{blue}{\frac{y}{t} \cdot \left(-z\right)} \]

   if 5.6000000000000002e-76 < a

   1. Initial program 72.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. *-commutative 72.6%

         \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot \left(y - x\right)}}{a - t} \]

      2. associate-/l* 88.9%

         \[\leadsto x + \color{blue}{\frac{z - t}{\frac{a - t}{y - x}}} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{x + \frac{z - t}{\frac{a - t}{y - x}}} \]

   4. Taylor expanded in y around inf 73.3%

      \[\leadsto x + \frac{z - t}{\color{blue}{\frac{a - t}{y}}} \]

   5. Taylor expanded in t around inf 44.7%

      \[\leadsto x + \color{blue}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-283}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-273}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-213}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-76}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 18: 36.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-281}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-271}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-213}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-75}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.9e+65)
   x
   (if (<= a 1.05e-281)
     y
     (if (<= a 1.12e-271)
       (/ z (/ t x))
       (if (<= a 3.5e-213) y (if (<= a 1.1e-75) (* (/ z t) (- y)) (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.9e+65) {
		tmp = x;
	} else if (a <= 1.05e-281) {
		tmp = y;
	} else if (a <= 1.12e-271) {
		tmp = z / (t / x);
	} else if (a <= 3.5e-213) {
		tmp = y;
	} else if (a <= 1.1e-75) {
		tmp = (z / t) * -y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.9d+65)) then
        tmp = x
    else if (a <= 1.05d-281) then
        tmp = y
    else if (a <= 1.12d-271) then
        tmp = z / (t / x)
    else if (a <= 3.5d-213) then
        tmp = y
    else if (a <= 1.1d-75) then
        tmp = (z / t) * -y
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.9e+65) {
		tmp = x;
	} else if (a <= 1.05e-281) {
		tmp = y;
	} else if (a <= 1.12e-271) {
		tmp = z / (t / x);
	} else if (a <= 3.5e-213) {
		tmp = y;
	} else if (a <= 1.1e-75) {
		tmp = (z / t) * -y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.9e+65:
		tmp = x
	elif a <= 1.05e-281:
		tmp = y
	elif a <= 1.12e-271:
		tmp = z / (t / x)
	elif a <= 3.5e-213:
		tmp = y
	elif a <= 1.1e-75:
		tmp = (z / t) * -y
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.9e+65)
		tmp = x;
	elseif (a <= 1.05e-281)
		tmp = y;
	elseif (a <= 1.12e-271)
		tmp = Float64(z / Float64(t / x));
	elseif (a <= 3.5e-213)
		tmp = y;
	elseif (a <= 1.1e-75)
		tmp = Float64(Float64(z / t) * Float64(-y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.9e+65)
		tmp = x;
	elseif (a <= 1.05e-281)
		tmp = y;
	elseif (a <= 1.12e-271)
		tmp = z / (t / x);
	elseif (a <= 3.5e-213)
		tmp = y;
	elseif (a <= 1.1e-75)
		tmp = (z / t) * -y;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.9e+65], x, If[LessEqual[a, 1.05e-281], y, If[LessEqual[a, 1.12e-271], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-213], y, If[LessEqual[a, 1.1e-75], N[(N[(z / t), $MachinePrecision] * (-y)), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.9e65

   1. Initial program 65.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 96.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 96.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in a around inf 57.3%

      \[\leadsto \color{blue}{x} \]

   if -2.9e65 < a < 1.0499999999999999e-281 or 1.11999999999999997e-271 < a < 3.50000000000000017e-213

   1. Initial program 68.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 78.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 78.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around inf 37.8%

      \[\leadsto \color{blue}{y} \]

   if 1.0499999999999999e-281 < a < 1.11999999999999997e-271

   1. Initial program 42.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 74.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 74.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 100.0%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. associate-*r/ 62.1%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Simplified 62.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   7. Taylor expanded in y around 0 62.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{a - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 62.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(z \cdot x\right)}{a - t}} \]

      2. associate-*r* 62.1%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot z\right) \cdot x}}{a - t} \]

      3. *-rgt-identity 62.1%

         \[\leadsto \frac{\left(-1 \cdot z\right) \cdot x}{\color{blue}{\left(a - t\right) \cdot 1}} \]

      4. times-frac 80.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot z}{a - t} \cdot \frac{x}{1}} \]

      5. mul-1-neg 80.9%

         \[\leadsto \frac{\color{blue}{-z}}{a - t} \cdot \frac{x}{1} \]

      6. /-rgt-identity 80.9%

         \[\leadsto \frac{-z}{a - t} \cdot \color{blue}{x} \]

   9. Simplified 80.9%

      \[\leadsto \color{blue}{\frac{-z}{a - t} \cdot x} \]

   10. Taylor expanded in a around 0 62.1%

       \[\leadsto \color{blue}{\frac{z \cdot x}{t}} \]
   11. Step-by-step derivation

       1. associate-/l* 99.4%

          \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   12. Simplified 99.4%

       \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   if 3.50000000000000017e-213 < a < 1.10000000000000003e-75

   1. Initial program 77.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 82.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 72.2%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 72.2%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. associate-*r/ 69.8%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Simplified 69.8%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   7. Taylor expanded in y around inf 39.2%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a - t}} \]

   8. Taylor expanded in a around 0 33.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 33.4%

         \[\leadsto \color{blue}{-\frac{y \cdot z}{t}} \]

      2. associate-/l* 36.0%

         \[\leadsto -\color{blue}{\frac{y}{\frac{t}{z}}} \]

      3. associate-/r/ 35.8%

         \[\leadsto -\color{blue}{\frac{y}{t} \cdot z} \]

      4. distribute-rgt-neg-in 35.8%

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \left(-z\right)} \]

   10. Simplified 35.8%

       \[\leadsto \color{blue}{\frac{y}{t} \cdot \left(-z\right)} \]

   11. Taylor expanded in y around 0 33.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t}} \]
   12. Step-by-step derivation

       1. mul-1-neg 33.4%

          \[\leadsto \color{blue}{-\frac{y \cdot z}{t}} \]

       2. associate-*r/ 35.9%

          \[\leadsto -\color{blue}{y \cdot \frac{z}{t}} \]

       3. *-commutative 35.9%

          \[\leadsto -\color{blue}{\frac{z}{t} \cdot y} \]

       4. distribute-rgt-neg-in 35.9%

          \[\leadsto \color{blue}{\frac{z}{t} \cdot \left(-y\right)} \]

   13. Simplified 35.9%

       \[\leadsto \color{blue}{\frac{z}{t} \cdot \left(-y\right)} \]

   if 1.10000000000000003e-75 < a

   1. Initial program 72.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. *-commutative 72.6%

         \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot \left(y - x\right)}}{a - t} \]

      2. associate-/l* 88.9%

         \[\leadsto x + \color{blue}{\frac{z - t}{\frac{a - t}{y - x}}} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{x + \frac{z - t}{\frac{a - t}{y - x}}} \]

   4. Taylor expanded in y around inf 73.3%

      \[\leadsto x + \frac{z - t}{\color{blue}{\frac{a - t}{y}}} \]

   5. Taylor expanded in t around inf 44.7%

      \[\leadsto x + \color{blue}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-281}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-271}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-213}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-75}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 19: 38.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-282}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-271}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-216}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+212}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.2e+65)
   x
   (if (<= a 1.9e-282)
     y
     (if (<= a 4e-271)
       (/ z (/ t x))
       (if (<= a 1.4e-216)
         y
         (if (<= a 3.35e-102)
           (* x (/ z t))
           (if (<= a 4.6e+212) (+ x y) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.2e+65) {
		tmp = x;
	} else if (a <= 1.9e-282) {
		tmp = y;
	} else if (a <= 4e-271) {
		tmp = z / (t / x);
	} else if (a <= 1.4e-216) {
		tmp = y;
	} else if (a <= 3.35e-102) {
		tmp = x * (z / t);
	} else if (a <= 4.6e+212) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.2d+65)) then
        tmp = x
    else if (a <= 1.9d-282) then
        tmp = y
    else if (a <= 4d-271) then
        tmp = z / (t / x)
    else if (a <= 1.4d-216) then
        tmp = y
    else if (a <= 3.35d-102) then
        tmp = x * (z / t)
    else if (a <= 4.6d+212) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.2e+65) {
		tmp = x;
	} else if (a <= 1.9e-282) {
		tmp = y;
	} else if (a <= 4e-271) {
		tmp = z / (t / x);
	} else if (a <= 1.4e-216) {
		tmp = y;
	} else if (a <= 3.35e-102) {
		tmp = x * (z / t);
	} else if (a <= 4.6e+212) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.2e+65:
		tmp = x
	elif a <= 1.9e-282:
		tmp = y
	elif a <= 4e-271:
		tmp = z / (t / x)
	elif a <= 1.4e-216:
		tmp = y
	elif a <= 3.35e-102:
		tmp = x * (z / t)
	elif a <= 4.6e+212:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.2e+65)
		tmp = x;
	elseif (a <= 1.9e-282)
		tmp = y;
	elseif (a <= 4e-271)
		tmp = Float64(z / Float64(t / x));
	elseif (a <= 1.4e-216)
		tmp = y;
	elseif (a <= 3.35e-102)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 4.6e+212)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.2e+65)
		tmp = x;
	elseif (a <= 1.9e-282)
		tmp = y;
	elseif (a <= 4e-271)
		tmp = z / (t / x);
	elseif (a <= 1.4e-216)
		tmp = y;
	elseif (a <= 3.35e-102)
		tmp = x * (z / t);
	elseif (a <= 4.6e+212)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.2e+65], x, If[LessEqual[a, 1.9e-282], y, If[LessEqual[a, 4e-271], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e-216], y, If[LessEqual[a, 3.35e-102], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e+212], N[(x + y), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.20000000000000005e65 or 4.5999999999999997e212 < a

   1. Initial program 65.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 97.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 97.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in a around inf 58.2%

      \[\leadsto \color{blue}{x} \]

   if -5.20000000000000005e65 < a < 1.89999999999999996e-282 or 3.99999999999999985e-271 < a < 1.4e-216

   1. Initial program 69.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 79.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around inf 38.4%

      \[\leadsto \color{blue}{y} \]

   if 1.89999999999999996e-282 < a < 3.99999999999999985e-271

   1. Initial program 42.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 74.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 74.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 100.0%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. associate-*r/ 62.1%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Simplified 62.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   7. Taylor expanded in y around 0 62.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{a - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 62.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(z \cdot x\right)}{a - t}} \]

      2. associate-*r* 62.1%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot z\right) \cdot x}}{a - t} \]

      3. *-rgt-identity 62.1%

         \[\leadsto \frac{\left(-1 \cdot z\right) \cdot x}{\color{blue}{\left(a - t\right) \cdot 1}} \]

      4. times-frac 80.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot z}{a - t} \cdot \frac{x}{1}} \]

      5. mul-1-neg 80.9%

         \[\leadsto \frac{\color{blue}{-z}}{a - t} \cdot \frac{x}{1} \]

      6. /-rgt-identity 80.9%

         \[\leadsto \frac{-z}{a - t} \cdot \color{blue}{x} \]

   9. Simplified 80.9%

      \[\leadsto \color{blue}{\frac{-z}{a - t} \cdot x} \]

   10. Taylor expanded in a around 0 62.1%

       \[\leadsto \color{blue}{\frac{z \cdot x}{t}} \]
   11. Step-by-step derivation

       1. associate-/l* 99.4%

          \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   12. Simplified 99.4%

       \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   if 1.4e-216 < a < 3.35e-102

   1. Initial program 72.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 79.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 79.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 74.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 74.0%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. associate-*r/ 71.1%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Simplified 71.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   7. Taylor expanded in y around 0 44.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{a - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 44.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(z \cdot x\right)}{a - t}} \]

      2. associate-*r* 44.9%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot z\right) \cdot x}}{a - t} \]

      3. *-rgt-identity 44.9%

         \[\leadsto \frac{\left(-1 \cdot z\right) \cdot x}{\color{blue}{\left(a - t\right) \cdot 1}} \]

      4. times-frac 45.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot z}{a - t} \cdot \frac{x}{1}} \]

      5. mul-1-neg 45.0%

         \[\leadsto \frac{\color{blue}{-z}}{a - t} \cdot \frac{x}{1} \]

      6. /-rgt-identity 45.0%

         \[\leadsto \frac{-z}{a - t} \cdot \color{blue}{x} \]

   9. Simplified 45.0%

      \[\leadsto \color{blue}{\frac{-z}{a - t} \cdot x} \]

   10. Taylor expanded in a around 0 35.5%

       \[\leadsto \color{blue}{\frac{z}{t}} \cdot x \]

   if 3.35e-102 < a < 4.5999999999999997e212

   1. Initial program 76.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. *-commutative 76.0%

         \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot \left(y - x\right)}}{a - t} \]

      2. associate-/l* 87.0%

         \[\leadsto x + \color{blue}{\frac{z - t}{\frac{a - t}{y - x}}} \]

   3. Simplified 87.0%

      \[\leadsto \color{blue}{x + \frac{z - t}{\frac{a - t}{y - x}}} \]

   4. Taylor expanded in y around inf 68.6%

      \[\leadsto x + \frac{z - t}{\color{blue}{\frac{a - t}{y}}} \]

   5. Taylor expanded in t around inf 41.4%

      \[\leadsto x + \color{blue}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-282}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-271}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-216}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+212}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 50.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-275}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))))
   (if (<= a -6.2e+65)
     x
     (if (<= a 5.5e-281)
       t_1
       (if (<= a 1.25e-275) (/ z (/ t x)) (if (<= a 4e+49) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double tmp;
	if (a <= -6.2e+65) {
		tmp = x;
	} else if (a <= 5.5e-281) {
		tmp = t_1;
	} else if (a <= 1.25e-275) {
		tmp = z / (t / x);
	} else if (a <= 4e+49) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (1.0d0 - (z / t))
    if (a <= (-6.2d+65)) then
        tmp = x
    else if (a <= 5.5d-281) then
        tmp = t_1
    else if (a <= 1.25d-275) then
        tmp = z / (t / x)
    else if (a <= 4d+49) then
        tmp = t_1
    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 t_1 = y * (1.0 - (z / t));
	double tmp;
	if (a <= -6.2e+65) {
		tmp = x;
	} else if (a <= 5.5e-281) {
		tmp = t_1;
	} else if (a <= 1.25e-275) {
		tmp = z / (t / x);
	} else if (a <= 4e+49) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / t))
	tmp = 0
	if a <= -6.2e+65:
		tmp = x
	elif a <= 5.5e-281:
		tmp = t_1
	elif a <= 1.25e-275:
		tmp = z / (t / x)
	elif a <= 4e+49:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (a <= -6.2e+65)
		tmp = x;
	elseif (a <= 5.5e-281)
		tmp = t_1;
	elseif (a <= 1.25e-275)
		tmp = Float64(z / Float64(t / x));
	elseif (a <= 4e+49)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / t));
	tmp = 0.0;
	if (a <= -6.2e+65)
		tmp = x;
	elseif (a <= 5.5e-281)
		tmp = t_1;
	elseif (a <= 1.25e-275)
		tmp = z / (t / x);
	elseif (a <= 4e+49)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e+65], x, If[LessEqual[a, 5.5e-281], t$95$1, If[LessEqual[a, 1.25e-275], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+49], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.19999999999999981e65 or 3.99999999999999979e49 < a

   1. Initial program 68.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 96.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in a around inf 54.8%

      \[\leadsto \color{blue}{x} \]

   if -6.19999999999999981e65 < a < 5.5000000000000003e-281 or 1.24999999999999996e-275 < a < 3.99999999999999979e49

   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* 80.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 80.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around -inf 70.9%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. mul-1-neg 70.9%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

      2. unsub-neg 70.9%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      3. div-sub 69.6%

         \[\leadsto y - \color{blue}{\left(\frac{\left(y - x\right) \cdot z}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      4. *-commutative 69.6%

         \[\leadsto y - \left(\frac{\color{blue}{z \cdot \left(y - x\right)}}{t} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      5. div-sub 70.9%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. distribute-rgt-out-- 70.9%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   6. Simplified 70.9%

      \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in a around 0 68.3%

      \[\leadsto y - \color{blue}{\frac{\left(y - x\right) \cdot z}{t}} \]

   8. Taylor expanded in y around inf 53.4%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot y} \]

   if 5.5000000000000003e-281 < a < 1.24999999999999996e-275

   1. Initial program 42.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 74.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 74.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 100.0%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. associate-*r/ 62.1%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Simplified 62.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   7. Taylor expanded in y around 0 62.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{a - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 62.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(z \cdot x\right)}{a - t}} \]

      2. associate-*r* 62.1%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot z\right) \cdot x}}{a - t} \]

      3. *-rgt-identity 62.1%

         \[\leadsto \frac{\left(-1 \cdot z\right) \cdot x}{\color{blue}{\left(a - t\right) \cdot 1}} \]

      4. times-frac 80.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot z}{a - t} \cdot \frac{x}{1}} \]

      5. mul-1-neg 80.9%

         \[\leadsto \frac{\color{blue}{-z}}{a - t} \cdot \frac{x}{1} \]

      6. /-rgt-identity 80.9%

         \[\leadsto \frac{-z}{a - t} \cdot \color{blue}{x} \]

   9. Simplified 80.9%

      \[\leadsto \color{blue}{\frac{-z}{a - t} \cdot x} \]

   10. Taylor expanded in a around 0 62.1%

       \[\leadsto \color{blue}{\frac{z \cdot x}{t}} \]
   11. Step-by-step derivation

       1. associate-/l* 99.4%

          \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   12. Simplified 99.4%

       \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-281}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-275}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 52.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ t_2 := x - \frac{z}{\frac{a}{x}}\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-275}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))) (t_2 (- x (/ z (/ a x)))))
   (if (<= a -3.9e+65)
     t_2
     (if (<= a 1.08e-280)
       t_1
       (if (<= a 1.25e-275) (/ z (/ t x)) (if (<= a 1.4e+46) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double t_2 = x - (z / (a / x));
	double tmp;
	if (a <= -3.9e+65) {
		tmp = t_2;
	} else if (a <= 1.08e-280) {
		tmp = t_1;
	} else if (a <= 1.25e-275) {
		tmp = z / (t / x);
	} else if (a <= 1.4e+46) {
		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 * (1.0d0 - (z / t))
    t_2 = x - (z / (a / x))
    if (a <= (-3.9d+65)) then
        tmp = t_2
    else if (a <= 1.08d-280) then
        tmp = t_1
    else if (a <= 1.25d-275) then
        tmp = z / (t / x)
    else if (a <= 1.4d+46) 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 * (1.0 - (z / t));
	double t_2 = x - (z / (a / x));
	double tmp;
	if (a <= -3.9e+65) {
		tmp = t_2;
	} else if (a <= 1.08e-280) {
		tmp = t_1;
	} else if (a <= 1.25e-275) {
		tmp = z / (t / x);
	} else if (a <= 1.4e+46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / t))
	t_2 = x - (z / (a / x))
	tmp = 0
	if a <= -3.9e+65:
		tmp = t_2
	elif a <= 1.08e-280:
		tmp = t_1
	elif a <= 1.25e-275:
		tmp = z / (t / x)
	elif a <= 1.4e+46:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	t_2 = Float64(x - Float64(z / Float64(a / x)))
	tmp = 0.0
	if (a <= -3.9e+65)
		tmp = t_2;
	elseif (a <= 1.08e-280)
		tmp = t_1;
	elseif (a <= 1.25e-275)
		tmp = Float64(z / Float64(t / x));
	elseif (a <= 1.4e+46)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / t));
	t_2 = x - (z / (a / x));
	tmp = 0.0;
	if (a <= -3.9e+65)
		tmp = t_2;
	elseif (a <= 1.08e-280)
		tmp = t_1;
	elseif (a <= 1.25e-275)
		tmp = z / (t / x);
	elseif (a <= 1.4e+46)
		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[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(z / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.9e+65], t$95$2, If[LessEqual[a, 1.08e-280], t$95$1, If[LessEqual[a, 1.25e-275], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+46], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.8999999999999998e65 or 1.40000000000000009e46 < a

   1. Initial program 68.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 96.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around 0 57.0%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 57.0%

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot z}{a}} \]

      2. *-commutative 57.0%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(y - x\right)}}{a} \]

      3. associate-/l* 74.0%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   6. Simplified 74.0%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   7. Taylor expanded in y around 0 53.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{a} + x} \]
   8. Step-by-step derivation

      1. +-commutative 53.4%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{z \cdot x}{a}} \]

      2. mul-1-neg 53.4%

         \[\leadsto x + \color{blue}{\left(-\frac{z \cdot x}{a}\right)} \]

      3. unsub-neg 53.4%

         \[\leadsto \color{blue}{x - \frac{z \cdot x}{a}} \]

      4. associate-/l* 61.5%

         \[\leadsto x - \color{blue}{\frac{z}{\frac{a}{x}}} \]

   9. Simplified 61.5%

      \[\leadsto \color{blue}{x - \frac{z}{\frac{a}{x}}} \]

   if -3.8999999999999998e65 < a < 1.07999999999999996e-280 or 1.24999999999999996e-275 < a < 1.40000000000000009e46

   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* 80.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 80.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around -inf 70.9%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. mul-1-neg 70.9%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

      2. unsub-neg 70.9%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      3. div-sub 69.6%

         \[\leadsto y - \color{blue}{\left(\frac{\left(y - x\right) \cdot z}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      4. *-commutative 69.6%

         \[\leadsto y - \left(\frac{\color{blue}{z \cdot \left(y - x\right)}}{t} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      5. div-sub 70.9%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. distribute-rgt-out-- 70.9%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   6. Simplified 70.9%

      \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in a around 0 68.3%

      \[\leadsto y - \color{blue}{\frac{\left(y - x\right) \cdot z}{t}} \]

   8. Taylor expanded in y around inf 53.4%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot y} \]

   if 1.07999999999999996e-280 < a < 1.24999999999999996e-275

   1. Initial program 42.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 74.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 74.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 100.0%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. associate-*r/ 62.1%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Simplified 62.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   7. Taylor expanded in y around 0 62.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{a - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 62.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(z \cdot x\right)}{a - t}} \]

      2. associate-*r* 62.1%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot z\right) \cdot x}}{a - t} \]

      3. *-rgt-identity 62.1%

         \[\leadsto \frac{\left(-1 \cdot z\right) \cdot x}{\color{blue}{\left(a - t\right) \cdot 1}} \]

      4. times-frac 80.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot z}{a - t} \cdot \frac{x}{1}} \]

      5. mul-1-neg 80.9%

         \[\leadsto \frac{\color{blue}{-z}}{a - t} \cdot \frac{x}{1} \]

      6. /-rgt-identity 80.9%

         \[\leadsto \frac{-z}{a - t} \cdot \color{blue}{x} \]

   9. Simplified 80.9%

      \[\leadsto \color{blue}{\frac{-z}{a - t} \cdot x} \]

   10. Taylor expanded in a around 0 62.1%

       \[\leadsto \color{blue}{\frac{z \cdot x}{t}} \]
   11. Step-by-step derivation

       1. associate-/l* 99.4%

          \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   12. Simplified 99.4%

       \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+65}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-280}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-275}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \end{array} \]

Alternative 22: 52.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z}{\frac{a}{x}}\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-275}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+48}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ z (/ a x)))))
   (if (<= a -3.5e+65)
     t_1
     (if (<= a 2.4e-282)
       (* y (- 1.0 (/ z t)))
       (if (<= a 9.8e-275)
         (/ z (/ t x))
         (if (<= a 6e+48) (- y (/ y (/ t z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z / (a / x));
	double tmp;
	if (a <= -3.5e+65) {
		tmp = t_1;
	} else if (a <= 2.4e-282) {
		tmp = y * (1.0 - (z / t));
	} else if (a <= 9.8e-275) {
		tmp = z / (t / x);
	} else if (a <= 6e+48) {
		tmp = y - (y / (t / z));
	} 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 - (z / (a / x))
    if (a <= (-3.5d+65)) then
        tmp = t_1
    else if (a <= 2.4d-282) then
        tmp = y * (1.0d0 - (z / t))
    else if (a <= 9.8d-275) then
        tmp = z / (t / x)
    else if (a <= 6d+48) then
        tmp = y - (y / (t / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z / (a / x));
	double tmp;
	if (a <= -3.5e+65) {
		tmp = t_1;
	} else if (a <= 2.4e-282) {
		tmp = y * (1.0 - (z / t));
	} else if (a <= 9.8e-275) {
		tmp = z / (t / x);
	} else if (a <= 6e+48) {
		tmp = y - (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (z / (a / x))
	tmp = 0
	if a <= -3.5e+65:
		tmp = t_1
	elif a <= 2.4e-282:
		tmp = y * (1.0 - (z / t))
	elif a <= 9.8e-275:
		tmp = z / (t / x)
	elif a <= 6e+48:
		tmp = y - (y / (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(z / Float64(a / x)))
	tmp = 0.0
	if (a <= -3.5e+65)
		tmp = t_1;
	elseif (a <= 2.4e-282)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (a <= 9.8e-275)
		tmp = Float64(z / Float64(t / x));
	elseif (a <= 6e+48)
		tmp = Float64(y - Float64(y / Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (z / (a / x));
	tmp = 0.0;
	if (a <= -3.5e+65)
		tmp = t_1;
	elseif (a <= 2.4e-282)
		tmp = y * (1.0 - (z / t));
	elseif (a <= 9.8e-275)
		tmp = z / (t / x);
	elseif (a <= 6e+48)
		tmp = y - (y / (t / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(z / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+65], t$95$1, If[LessEqual[a, 2.4e-282], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.8e-275], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+48], N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.5000000000000001e65 or 5.9999999999999999e48 < a

   1. Initial program 68.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 96.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around 0 57.0%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 57.0%

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot z}{a}} \]

      2. *-commutative 57.0%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(y - x\right)}}{a} \]

      3. associate-/l* 74.0%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   6. Simplified 74.0%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   7. Taylor expanded in y around 0 53.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{a} + x} \]
   8. Step-by-step derivation

      1. +-commutative 53.4%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{z \cdot x}{a}} \]

      2. mul-1-neg 53.4%

         \[\leadsto x + \color{blue}{\left(-\frac{z \cdot x}{a}\right)} \]

      3. unsub-neg 53.4%

         \[\leadsto \color{blue}{x - \frac{z \cdot x}{a}} \]

      4. associate-/l* 61.5%

         \[\leadsto x - \color{blue}{\frac{z}{\frac{a}{x}}} \]

   9. Simplified 61.5%

      \[\leadsto \color{blue}{x - \frac{z}{\frac{a}{x}}} \]

   if -3.5000000000000001e65 < a < 2.39999999999999997e-282

   1. Initial program 69.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 79.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 79.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around -inf 69.6%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. mul-1-neg 69.6%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

      2. unsub-neg 69.6%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      3. div-sub 68.3%

         \[\leadsto y - \color{blue}{\left(\frac{\left(y - x\right) \cdot z}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      4. *-commutative 68.3%

         \[\leadsto y - \left(\frac{\color{blue}{z \cdot \left(y - x\right)}}{t} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      5. div-sub 69.6%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. distribute-rgt-out-- 69.6%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   6. Simplified 69.6%

      \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in a around 0 64.8%

      \[\leadsto y - \color{blue}{\frac{\left(y - x\right) \cdot z}{t}} \]

   8. Taylor expanded in y around inf 53.5%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot y} \]

   if 2.39999999999999997e-282 < a < 9.79999999999999964e-275

   1. Initial program 42.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 74.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 74.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 100.0%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. associate-*r/ 62.1%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Simplified 62.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   7. Taylor expanded in y around 0 62.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{a - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 62.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(z \cdot x\right)}{a - t}} \]

      2. associate-*r* 62.1%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot z\right) \cdot x}}{a - t} \]

      3. *-rgt-identity 62.1%

         \[\leadsto \frac{\left(-1 \cdot z\right) \cdot x}{\color{blue}{\left(a - t\right) \cdot 1}} \]

      4. times-frac 80.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot z}{a - t} \cdot \frac{x}{1}} \]

      5. mul-1-neg 80.9%

         \[\leadsto \frac{\color{blue}{-z}}{a - t} \cdot \frac{x}{1} \]

      6. /-rgt-identity 80.9%

         \[\leadsto \frac{-z}{a - t} \cdot \color{blue}{x} \]

   9. Simplified 80.9%

      \[\leadsto \color{blue}{\frac{-z}{a - t} \cdot x} \]

   10. Taylor expanded in a around 0 62.1%

       \[\leadsto \color{blue}{\frac{z \cdot x}{t}} \]
   11. Step-by-step derivation

       1. associate-/l* 99.4%

          \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   12. Simplified 99.4%

       \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   if 9.79999999999999964e-275 < a < 5.9999999999999999e48

   1. Initial program 73.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 82.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around -inf 72.2%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. mul-1-neg 72.2%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

      2. unsub-neg 72.2%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      3. div-sub 70.9%

         \[\leadsto y - \color{blue}{\left(\frac{\left(y - x\right) \cdot z}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      4. *-commutative 70.9%

         \[\leadsto y - \left(\frac{\color{blue}{z \cdot \left(y - x\right)}}{t} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      5. div-sub 72.2%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. distribute-rgt-out-- 72.2%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   6. Simplified 72.2%

      \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in a around 0 71.8%

      \[\leadsto y - \color{blue}{\frac{\left(y - x\right) \cdot z}{t}} \]

   8. Taylor expanded in y around inf 50.7%

      \[\leadsto y - \color{blue}{\frac{y \cdot z}{t}} \]
   9. Step-by-step derivation

      1. associate-/l* 53.3%

         \[\leadsto y - \color{blue}{\frac{y}{\frac{t}{z}}} \]

   10. Simplified 53.3%

       \[\leadsto y - \color{blue}{\frac{y}{\frac{t}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+65}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-275}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+48}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \end{array} \]

Alternative 23: 76.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-21} \lor \neg \left(a \leq 7.6 \cdot 10^{+52}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.6e-21) (not (<= a 7.6e+52)))
   (+ x (/ (- z t) (/ (- a t) y)))
   (+ y (* (/ z t) (- x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.6e-21) || !(a <= 7.6e+52)) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else {
		tmp = y + ((z / t) * (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5.6d-21)) .or. (.not. (a <= 7.6d+52))) then
        tmp = x + ((z - t) / ((a - t) / y))
    else
        tmp = y + ((z / t) * (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.6e-21) || !(a <= 7.6e+52)) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else {
		tmp = y + ((z / t) * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.6e-21) or not (a <= 7.6e+52):
		tmp = x + ((z - t) / ((a - t) / y))
	else:
		tmp = y + ((z / t) * (x - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.6e-21) || !(a <= 7.6e+52))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / y)));
	else
		tmp = Float64(y + Float64(Float64(z / t) * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.6e-21) || ~((a <= 7.6e+52)))
		tmp = x + ((z - t) / ((a - t) / y));
	else
		tmp = y + ((z / t) * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.6e-21], N[Not[LessEqual[a, 7.6e+52]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.60000000000000008e-21 or 7.5999999999999999e52 < a

   1. Initial program 68.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. *-commutative 68.2%

         \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot \left(y - x\right)}}{a - t} \]

      2. associate-/l* 91.3%

         \[\leadsto x + \color{blue}{\frac{z - t}{\frac{a - t}{y - x}}} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{x + \frac{z - t}{\frac{a - t}{y - x}}} \]

   4. Taylor expanded in y around inf 83.9%

      \[\leadsto x + \frac{z - t}{\color{blue}{\frac{a - t}{y}}} \]

   if -5.60000000000000008e-21 < a < 7.5999999999999999e52

   1. Initial program 70.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 79.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 79.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around -inf 72.4%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. mul-1-neg 72.4%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

      2. unsub-neg 72.4%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      3. div-sub 71.0%

         \[\leadsto y - \color{blue}{\left(\frac{\left(y - x\right) \cdot z}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      4. *-commutative 71.0%

         \[\leadsto y - \left(\frac{\color{blue}{z \cdot \left(y - x\right)}}{t} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      5. div-sub 72.4%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. distribute-rgt-out-- 72.4%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   6. Simplified 72.4%

      \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in a around 0 70.2%

      \[\leadsto y - \color{blue}{\frac{\left(y - x\right) \cdot z}{t}} \]

   8. Taylor expanded in z around 0 70.2%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   9. Step-by-step derivation

      1. *-commutative 70.2%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} \]

      2. associate-*r/ 76.7%

         \[\leadsto y - \color{blue}{\left(y - x\right) \cdot \frac{z}{t}} \]

   10. Simplified 76.7%

       \[\leadsto y - \color{blue}{\left(y - x\right) \cdot \frac{z}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-21} \lor \neg \left(a \leq 7.6 \cdot 10^{+52}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 24: 77.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-24} \lor \neg \left(a \leq 1.65 \cdot 10^{+52}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.8e-24) (not (<= a 1.65e+52)))
   (+ x (/ (- z t) (/ (- a t) y)))
   (+ y (* (- y x) (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e-24) || !(a <= 1.65e+52)) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.8d-24)) .or. (.not. (a <= 1.65d+52))) then
        tmp = x + ((z - t) / ((a - t) / y))
    else
        tmp = y + ((y - x) * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e-24) || !(a <= 1.65e+52)) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.8e-24) or not (a <= 1.65e+52):
		tmp = x + ((z - t) / ((a - t) / y))
	else:
		tmp = y + ((y - x) * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.8e-24) || !(a <= 1.65e+52))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / y)));
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.8e-24) || ~((a <= 1.65e+52)))
		tmp = x + ((z - t) / ((a - t) / y));
	else
		tmp = y + ((y - x) * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.8e-24], N[Not[LessEqual[a, 1.65e+52]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8000000000000002e-24 or 1.65e52 < a

   1. Initial program 68.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. *-commutative 68.2%

         \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot \left(y - x\right)}}{a - t} \]

      2. associate-/l* 91.3%

         \[\leadsto x + \color{blue}{\frac{z - t}{\frac{a - t}{y - x}}} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{x + \frac{z - t}{\frac{a - t}{y - x}}} \]

   4. Taylor expanded in y around inf 83.9%

      \[\leadsto x + \frac{z - t}{\color{blue}{\frac{a - t}{y}}} \]

   if -2.8000000000000002e-24 < a < 1.65e52

   1. Initial program 70.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 79.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 79.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]
   4. Step-by-step derivation

      1. div-inv 79.8%

         \[\leadsto x + \frac{y - x}{\color{blue}{\left(a - t\right) \cdot \frac{1}{z - t}}} \]

   5. Applied egg-rr 79.8%

      \[\leadsto x + \frac{y - x}{\color{blue}{\left(a - t\right) \cdot \frac{1}{z - t}}} \]

   6. Taylor expanded in t around inf 71.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + y\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. +-commutative 71.0%

         \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right)} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      2. *-commutative 71.0%

         \[\leadsto \left(y + -1 \cdot \frac{\color{blue}{\left(y - x\right) \cdot z}}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      3. associate--l+ 71.0%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{\left(y - x\right) \cdot z}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      4. associate-*r/ 71.0%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(\left(y - x\right) \cdot z\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      5. associate-*r/ 71.0%

         \[\leadsto y + \left(\frac{-1 \cdot \left(\left(y - x\right) \cdot z\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      6. div-sub 72.4%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      7. distribute-lft-out-- 72.4%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z - a \cdot \left(y - x\right)\right)}}{t} \]

      8. *-commutative 72.4%

         \[\leadsto y + \frac{-1 \cdot \left(\color{blue}{z \cdot \left(y - x\right)} - a \cdot \left(y - x\right)\right)}{t} \]

      9. distribute-rgt-out-- 72.4%

         \[\leadsto y + \frac{-1 \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - a\right)\right)}}{t} \]

      10. associate-*r/ 72.4%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

      11. +-commutative 72.4%

          \[\leadsto \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t} + y} \]

      12. fma-def 72.4%

          \[\leadsto \color{blue}{\mathsf{fma}\left(-1, \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}, y\right)} \]

      13. associate-/l* 80.0%

          \[\leadsto \mathsf{fma}\left(-1, \color{blue}{\frac{y - x}{\frac{t}{z - a}}}, y\right) \]

   8. Simplified 79.5%

      \[\leadsto \color{blue}{y - \left(y - x\right) \cdot \frac{z - a}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-24} \lor \neg \left(a \leq 1.65 \cdot 10^{+52}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]

Alternative 25: 39.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-217}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+212}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.3e+65)
   x
   (if (<= a 6.5e-217)
     y
     (if (<= a 5.8e-102) (* x (/ z t)) (if (<= a 3.6e+212) (+ x y) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.3e+65) {
		tmp = x;
	} else if (a <= 6.5e-217) {
		tmp = y;
	} else if (a <= 5.8e-102) {
		tmp = x * (z / t);
	} else if (a <= 3.6e+212) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.3d+65)) then
        tmp = x
    else if (a <= 6.5d-217) then
        tmp = y
    else if (a <= 5.8d-102) then
        tmp = x * (z / t)
    else if (a <= 3.6d+212) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.3e+65) {
		tmp = x;
	} else if (a <= 6.5e-217) {
		tmp = y;
	} else if (a <= 5.8e-102) {
		tmp = x * (z / t);
	} else if (a <= 3.6e+212) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.3e+65:
		tmp = x
	elif a <= 6.5e-217:
		tmp = y
	elif a <= 5.8e-102:
		tmp = x * (z / t)
	elif a <= 3.6e+212:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.3e+65)
		tmp = x;
	elseif (a <= 6.5e-217)
		tmp = y;
	elseif (a <= 5.8e-102)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 3.6e+212)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.3e+65)
		tmp = x;
	elseif (a <= 6.5e-217)
		tmp = y;
	elseif (a <= 5.8e-102)
		tmp = x * (z / t);
	elseif (a <= 3.6e+212)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.3e+65], x, If[LessEqual[a, 6.5e-217], y, If[LessEqual[a, 5.8e-102], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e+212], N[(x + y), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.30000000000000046e65 or 3.6e212 < a

   1. Initial program 65.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 97.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 97.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in a around inf 58.2%

      \[\leadsto \color{blue}{x} \]

   if -4.30000000000000046e65 < a < 6.4999999999999996e-217

   1. Initial program 67.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 78.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around inf 36.6%

      \[\leadsto \color{blue}{y} \]

   if 6.4999999999999996e-217 < a < 5.79999999999999973e-102

   1. Initial program 72.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 79.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 79.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 74.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 74.0%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. associate-*r/ 71.1%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Simplified 71.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   7. Taylor expanded in y around 0 44.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{a - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 44.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(z \cdot x\right)}{a - t}} \]

      2. associate-*r* 44.9%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot z\right) \cdot x}}{a - t} \]

      3. *-rgt-identity 44.9%

         \[\leadsto \frac{\left(-1 \cdot z\right) \cdot x}{\color{blue}{\left(a - t\right) \cdot 1}} \]

      4. times-frac 45.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot z}{a - t} \cdot \frac{x}{1}} \]

      5. mul-1-neg 45.0%

         \[\leadsto \frac{\color{blue}{-z}}{a - t} \cdot \frac{x}{1} \]

      6. /-rgt-identity 45.0%

         \[\leadsto \frac{-z}{a - t} \cdot \color{blue}{x} \]

   9. Simplified 45.0%

      \[\leadsto \color{blue}{\frac{-z}{a - t} \cdot x} \]

   10. Taylor expanded in a around 0 35.5%

       \[\leadsto \color{blue}{\frac{z}{t}} \cdot x \]

   if 5.79999999999999973e-102 < a < 3.6e212

   1. Initial program 76.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. *-commutative 76.0%

         \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot \left(y - x\right)}}{a - t} \]

      2. associate-/l* 87.0%

         \[\leadsto x + \color{blue}{\frac{z - t}{\frac{a - t}{y - x}}} \]

   3. Simplified 87.0%

      \[\leadsto \color{blue}{x + \frac{z - t}{\frac{a - t}{y - x}}} \]

   4. Taylor expanded in y around inf 68.6%

      \[\leadsto x + \frac{z - t}{\color{blue}{\frac{a - t}{y}}} \]

   5. Taylor expanded in t around inf 41.4%

      \[\leadsto x + \color{blue}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-217}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+212}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 26: 39.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{+45}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.4e+65) x (if (<= a 2.75e+45) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.4e+65) {
		tmp = x;
	} else if (a <= 2.75e+45) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.4d+65)) then
        tmp = x
    else if (a <= 2.75d+45) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.4e+65) {
		tmp = x;
	} else if (a <= 2.75e+45) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.4e+65:
		tmp = x
	elif a <= 2.75e+45:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.4e+65)
		tmp = x;
	elseif (a <= 2.75e+45)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.4e+65)
		tmp = x;
	elseif (a <= 2.75e+45)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.4e+65], x, If[LessEqual[a, 2.75e+45], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.40000000000000038e65 or 2.75e45 < a

   1. Initial program 68.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 96.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 96.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in a around inf 54.3%

      \[\leadsto \color{blue}{x} \]

   if -5.40000000000000038e65 < a < 2.75e45

   1. Initial program 70.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 80.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 80.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around inf 32.3%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{+45}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 27: 25.0% 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 69.7%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-/l* 86.6%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

3. Simplified 86.6%

   \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

4. Taylor expanded in a around inf 25.4%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 25.4%

   \[\leadsto x \]

Developer target: 87.2% 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 2023221 
(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))))