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

Percentage Accurate: 68.8% → 88.9%

Time: 24.8s

Alternatives: 24

Speedup: 1.0×

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: 68.8% 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: 88.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{y - x}\\ \mathbf{if}\;t \leq -3.25 \cdot 10^{+171} \lor \neg \left(t \leq 4.5 \cdot 10^{+108}\right):\\ \;\;\;\;y + \mathsf{fma}\left(-1, \frac{z}{t_1}, \frac{a}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{z - t}{a - t}}{\frac{1}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (- y x))))
   (if (or (<= t -3.25e+171) (not (<= t 4.5e+108)))
     (+ y (fma -1.0 (/ z t_1) (/ a t_1)))
     (+ x (/ (/ (- z t) (- a t)) (/ 1.0 (- y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (y - x);
	double tmp;
	if ((t <= -3.25e+171) || !(t <= 4.5e+108)) {
		tmp = y + fma(-1.0, (z / t_1), (a / t_1));
	} else {
		tmp = x + (((z - t) / (a - t)) / (1.0 / (y - x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(y - x))
	tmp = 0.0
	if ((t <= -3.25e+171) || !(t <= 4.5e+108))
		tmp = Float64(y + fma(-1.0, Float64(z / t_1), Float64(a / t_1)));
	else
		tmp = Float64(x + Float64(Float64(Float64(z - t) / Float64(a - t)) / Float64(1.0 / Float64(y - x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -3.25e+171], N[Not[LessEqual[t, 4.5e+108]], $MachinePrecision]], N[(y + N[(-1.0 * N[(z / t$95$1), $MachinePrecision] + N[(a / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.25e171 or 4.5e108 < t

   1. Initial program 32.3%

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

      1. +-commutative 32.3%

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

      2. associate-*l/ 58.2%

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

      3. fma-def 58.3%

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

   3. Simplified 58.3%

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

   4. Taylor expanded in t around inf 64.5%

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

      1. fma-def 64.5%

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

      2. associate-/l* 78.4%

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

      3. associate-/l* 92.9%

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

   6. Simplified 92.9%

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

   if -3.25e171 < t < 4.5e108

   1. Initial program 82.7%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

      1. *-commutative 90.6%

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

      2. clear-num 90.5%

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

      3. un-div-inv 90.6%

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

      4. div-inv 90.6%

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

      5. associate-/r* 93.9%

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

   5. Applied egg-rr 93.9%

      \[\leadsto x + \color{blue}{\frac{\frac{z - t}{a - t}}{\frac{1}{y - x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.25 \cdot 10^{+171} \lor \neg \left(t \leq 4.5 \cdot 10^{+108}\right):\\ \;\;\;\;y + \mathsf{fma}\left(-1, \frac{z}{\frac{t}{y - x}}, \frac{a}{\frac{t}{y - x}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{z - t}{a - t}}{\frac{1}{y - x}}\\ \end{array} \]

Alternative 2: 89.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-292}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) (- a t)))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -1e+307)
     t_1
     (if (<= t_2 -5e-292)
       t_2
       (if (<= t_2 0.0) (+ y (/ (* (- y x) (- a z)) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -1e+307) {
		tmp = t_1;
	} else if (t_2 <= -5e-292) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z - t) * ((y - x) / (a - t)))
    t_2 = x + (((y - x) * (z - t)) / (a - t))
    if (t_2 <= (-1d+307)) then
        tmp = t_1
    else if (t_2 <= (-5d-292)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = y + (((y - x) * (a - z)) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -1e+307) {
		tmp = t_1;
	} else if (t_2 <= -5e-292) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) / (a - t)))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -1e+307:
		tmp = t_1
	elif t_2 <= -5e-292:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + (((y - x) * (a - z)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -1e+307)
		tmp = t_1;
	elseif (t_2 <= -5e-292)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) / (a - t)));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -1e+307)
		tmp = t_1;
	elseif (t_2 <= -5e-292)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + (((y - x) * (a - z)) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+307], t$95$1, If[LessEqual[t$95$2, -5e-292], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.99999999999999986e306 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 63.3%

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

      1. associate-*l/ 87.8%

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

   3. Simplified 87.8%

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

   if -9.99999999999999986e306 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.99999999999999981e-292

   1. Initial program 97.4%

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

   if -4.99999999999999981e-292 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.2%

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

      1. associate-*l/ 3.8%

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

   3. Simplified 3.8%

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

      1. associate-/r/ 4.2%

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

   5. Applied egg-rr 4.2%

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

   6. Taylor expanded in t around -inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. distribute-rgt-out-- 99.6%

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

   8. Simplified 99.6%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{+307}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-292}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 3: 91.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-292} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y - \left(\frac{a \cdot \left(x - y\right)}{t} + \left(y - x\right) \cdot \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -5e-292) (not (<= t_1 0.0)))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (- y (+ (/ (* a (- x y)) t) (* (- y x) (/ z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-292) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y - (((a * (x - y)) / t) + ((y - x) * (z / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * (z - t)) / (a - t))
    if ((t_1 <= (-5d-292)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y - (((a * (x - y)) / t) + ((y - x) * (z / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-292) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y - (((a * (x - y)) / t) + ((y - x) * (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if (t_1 <= -5e-292) or not (t_1 <= 0.0):
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y - (((a * (x - y)) / t) + ((y - x) * (z / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -5e-292) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y - Float64(Float64(Float64(a * Float64(x - y)) / t) + Float64(Float64(y - x) * Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -5e-292) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y - (((a * (x - y)) / t) + ((y - x) * (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-292], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(N[(a * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.99999999999999981e-292 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 73.7%

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

      1. associate-*l/ 87.4%

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

   3. Simplified 87.4%

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

      1. associate-/r/ 91.8%

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

   5. Applied egg-rr 91.8%

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

   if -4.99999999999999981e-292 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.2%

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

      1. associate-*l/ 3.8%

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

   3. Simplified 3.8%

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

      1. clear-num 4.0%

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

      2. inv-pow 4.0%

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

      3. metadata-eval 4.0%

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

      4. sqr-pow 2.2%

         \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right)} \cdot \left(z - t\right) \]

      5. metadata-eval 2.2%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      6. metadata-eval 2.2%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      7. metadata-eval 2.2%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)}\right) \cdot \left(z - t\right) \]

      8. metadata-eval 2.2%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}}\right) \cdot \left(z - t\right) \]

   5. Applied egg-rr 2.2%

      \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{-0.5}\right)} \cdot \left(z - t\right) \]
   6. Step-by-step derivation

      1. pow-sqr 4.0%

         \[\leadsto x + \color{blue}{{\left(\frac{a - t}{y - x}\right)}^{\left(2 \cdot -0.5\right)}} \cdot \left(z - t\right) \]

      2. metadata-eval 4.0%

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

      3. unpow-1 4.0%

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

   7. Simplified 4.0%

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

      1. clear-num 3.8%

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

      2. associate-/r/ 4.2%

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

      3. clear-num 4.5%

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

   9. Applied egg-rr 4.5%

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

       1. div-inv 4.5%

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

   11. Applied egg-rr 4.5%

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

   12. Taylor expanded in t around inf 99.7%

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

       1. associate--l+ 99.7%

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

       2. mul-1-neg 99.7%

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

       3. associate-/l* 99.7%

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

       4. distribute-frac-neg 99.7%

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

       5. associate-/r/ 99.8%

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

       6. *-commutative 99.8%

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

       7. associate-*r/ 99.8%

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

       8. associate-*r* 99.8%

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

       9. neg-mul-1 99.8%

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

   14. Simplified 99.8%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-292} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y - \left(\frac{a \cdot \left(x - y\right)}{t} + \left(y - x\right) \cdot \frac{z}{t}\right)\\ \end{array} \]

Alternative 4: 91.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-292} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -5e-292) (not (<= t_1 0.0)))
     (+ x (/ (- y x) (/ (- 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) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-292) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((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) * (z - t)) / (a - t))
    if ((t_1 <= (-5d-292)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) / ((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) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-292) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((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) * (z - t)) / (a - t))
	tmp = 0
	if (t_1 <= -5e-292) or not (t_1 <= 0.0):
		tmp = x + ((y - x) / ((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(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -5e-292) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) / 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) * (z - t)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -5e-292) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) / ((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[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-292], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(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))) < -4.99999999999999981e-292 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 73.7%

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

      1. associate-*l/ 87.4%

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

   3. Simplified 87.4%

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

      1. associate-/r/ 91.8%

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

   5. Applied egg-rr 91.8%

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

   if -4.99999999999999981e-292 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.2%

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

      1. associate-*l/ 3.8%

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

   3. Simplified 3.8%

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

      1. associate-/r/ 4.2%

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

   5. Applied egg-rr 4.2%

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

   6. Taylor expanded in t around -inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. distribute-rgt-out-- 99.6%

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

   8. Simplified 99.6%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-292} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]

Alternative 5: 92.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{\frac{z - t}{a - t}}{\frac{1}{y - x}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.05e+48)
   (+ x (/ (/ (- z t) (- a t)) (/ 1.0 (- y x))))
   (if (<= y 6.6e+28)
     (+
      (* x (- (+ 1.0 (/ t (- a t))) (/ z (- a t))))
      (/ (* y (- z t)) (- a t)))
     (+ x (/ (- y x) (/ (- a t) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.05e+48) {
		tmp = x + (((z - t) / (a - t)) / (1.0 / (y - x)));
	} else if (y <= 6.6e+28) {
		tmp = (x * ((1.0 + (t / (a - t))) - (z / (a - t)))) + ((y * (z - t)) / (a - t));
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.05d+48)) then
        tmp = x + (((z - t) / (a - t)) / (1.0d0 / (y - x)))
    else if (y <= 6.6d+28) then
        tmp = (x * ((1.0d0 + (t / (a - t))) - (z / (a - t)))) + ((y * (z - t)) / (a - t))
    else
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.05e+48) {
		tmp = x + (((z - t) / (a - t)) / (1.0 / (y - x)));
	} else if (y <= 6.6e+28) {
		tmp = (x * ((1.0 + (t / (a - t))) - (z / (a - t)))) + ((y * (z - t)) / (a - t));
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.05e+48:
		tmp = x + (((z - t) / (a - t)) / (1.0 / (y - x)))
	elif y <= 6.6e+28:
		tmp = (x * ((1.0 + (t / (a - t))) - (z / (a - t)))) + ((y * (z - t)) / (a - t))
	else:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.05e+48)
		tmp = Float64(x + Float64(Float64(Float64(z - t) / Float64(a - t)) / Float64(1.0 / Float64(y - x))));
	elseif (y <= 6.6e+28)
		tmp = Float64(Float64(x * Float64(Float64(1.0 + Float64(t / Float64(a - t))) - Float64(z / Float64(a - t)))) + Float64(Float64(y * Float64(z - t)) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.05e+48)
		tmp = x + (((z - t) / (a - t)) / (1.0 / (y - x)));
	elseif (y <= 6.6e+28)
		tmp = (x * ((1.0 + (t / (a - t))) - (z / (a - t)))) + ((y * (z - t)) / (a - t));
	else
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.05e+48], N[(x + N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+28], N[(N[(x * N[(N[(1.0 + N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0500000000000001e48

   1. Initial program 58.7%

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

      1. associate-*l/ 89.8%

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

   3. Simplified 89.8%

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

      1. *-commutative 89.8%

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

      2. clear-num 89.7%

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

      3. un-div-inv 89.7%

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

      4. div-inv 89.8%

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

      5. associate-/r* 92.6%

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

   5. Applied egg-rr 92.6%

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

   if -2.0500000000000001e48 < y < 6.6e28

   1. Initial program 75.3%

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

      1. associate-*l/ 74.0%

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

   3. Simplified 74.0%

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

   4. Taylor expanded in x around -inf 93.1%

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

   if 6.6e28 < y

   1. Initial program 64.2%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

      1. associate-/r/ 93.4%

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

   5. Applied egg-rr 93.4%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{\frac{z - t}{a - t}}{\frac{1}{y - x}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 6: 56.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x - \frac{x}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -9 \cdot 10^{+212}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -22000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-118}:\\ \;\;\;\;\frac{x}{\frac{t - a}{z}}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-259}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (- x (/ x (/ a z)))))
   (if (<= a -9e+212)
     t_2
     (if (<= a -1.75e+92)
       t_1
       (if (<= a -22000000000000.0)
         t_2
         (if (<= a -9.2e-107)
           t_1
           (if (<= a -2.1e-118)
             (/ x (/ (- t a) z))
             (if (<= a -9e-205)
               t_1
               (if (<= a -5.4e-259)
                 (* (/ z t) (- x y))
                 (if (<= a 8.8e+122) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x - (x / (a / z));
	double tmp;
	if (a <= -9e+212) {
		tmp = t_2;
	} else if (a <= -1.75e+92) {
		tmp = t_1;
	} else if (a <= -22000000000000.0) {
		tmp = t_2;
	} else if (a <= -9.2e-107) {
		tmp = t_1;
	} else if (a <= -2.1e-118) {
		tmp = x / ((t - a) / z);
	} else if (a <= -9e-205) {
		tmp = t_1;
	} else if (a <= -5.4e-259) {
		tmp = (z / t) * (x - y);
	} else if (a <= 8.8e+122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x - (x / (a / z))
    if (a <= (-9d+212)) then
        tmp = t_2
    else if (a <= (-1.75d+92)) then
        tmp = t_1
    else if (a <= (-22000000000000.0d0)) then
        tmp = t_2
    else if (a <= (-9.2d-107)) then
        tmp = t_1
    else if (a <= (-2.1d-118)) then
        tmp = x / ((t - a) / z)
    else if (a <= (-9d-205)) then
        tmp = t_1
    else if (a <= (-5.4d-259)) then
        tmp = (z / t) * (x - y)
    else if (a <= 8.8d+122) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x - (x / (a / z));
	double tmp;
	if (a <= -9e+212) {
		tmp = t_2;
	} else if (a <= -1.75e+92) {
		tmp = t_1;
	} else if (a <= -22000000000000.0) {
		tmp = t_2;
	} else if (a <= -9.2e-107) {
		tmp = t_1;
	} else if (a <= -2.1e-118) {
		tmp = x / ((t - a) / z);
	} else if (a <= -9e-205) {
		tmp = t_1;
	} else if (a <= -5.4e-259) {
		tmp = (z / t) * (x - y);
	} else if (a <= 8.8e+122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x - (x / (a / z))
	tmp = 0
	if a <= -9e+212:
		tmp = t_2
	elif a <= -1.75e+92:
		tmp = t_1
	elif a <= -22000000000000.0:
		tmp = t_2
	elif a <= -9.2e-107:
		tmp = t_1
	elif a <= -2.1e-118:
		tmp = x / ((t - a) / z)
	elif a <= -9e-205:
		tmp = t_1
	elif a <= -5.4e-259:
		tmp = (z / t) * (x - y)
	elif a <= 8.8e+122:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x - Float64(x / Float64(a / z)))
	tmp = 0.0
	if (a <= -9e+212)
		tmp = t_2;
	elseif (a <= -1.75e+92)
		tmp = t_1;
	elseif (a <= -22000000000000.0)
		tmp = t_2;
	elseif (a <= -9.2e-107)
		tmp = t_1;
	elseif (a <= -2.1e-118)
		tmp = Float64(x / Float64(Float64(t - a) / z));
	elseif (a <= -9e-205)
		tmp = t_1;
	elseif (a <= -5.4e-259)
		tmp = Float64(Float64(z / t) * Float64(x - y));
	elseif (a <= 8.8e+122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x - (x / (a / z));
	tmp = 0.0;
	if (a <= -9e+212)
		tmp = t_2;
	elseif (a <= -1.75e+92)
		tmp = t_1;
	elseif (a <= -22000000000000.0)
		tmp = t_2;
	elseif (a <= -9.2e-107)
		tmp = t_1;
	elseif (a <= -2.1e-118)
		tmp = x / ((t - a) / z);
	elseif (a <= -9e-205)
		tmp = t_1;
	elseif (a <= -5.4e-259)
		tmp = (z / t) * (x - y);
	elseif (a <= 8.8e+122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e+212], t$95$2, If[LessEqual[a, -1.75e+92], t$95$1, If[LessEqual[a, -22000000000000.0], t$95$2, If[LessEqual[a, -9.2e-107], t$95$1, If[LessEqual[a, -2.1e-118], N[(x / N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9e-205], t$95$1, If[LessEqual[a, -5.4e-259], N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e+122], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.0000000000000003e212 or -1.74999999999999993e92 < a < -2.2e13 or 8.7999999999999997e122 < a

   1. Initial program 72.8%

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

      1. associate-*l/ 88.0%

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

   3. Simplified 88.0%

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

      1. clear-num 88.0%

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

      2. inv-pow 88.0%

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

      3. metadata-eval 88.0%

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

      4. sqr-pow 44.9%

         \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right)} \cdot \left(z - t\right) \]

      5. metadata-eval 44.9%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      6. metadata-eval 44.9%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      7. metadata-eval 44.9%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)}\right) \cdot \left(z - t\right) \]

      8. metadata-eval 44.9%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}}\right) \cdot \left(z - t\right) \]

   5. Applied egg-rr 44.9%

      \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{-0.5}\right)} \cdot \left(z - t\right) \]
   6. Step-by-step derivation

      1. pow-sqr 88.0%

         \[\leadsto x + \color{blue}{{\left(\frac{a - t}{y - x}\right)}^{\left(2 \cdot -0.5\right)}} \cdot \left(z - t\right) \]

      2. metadata-eval 88.0%

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

      3. unpow-1 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in y around 0 72.3%

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

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

   10. Simplified 72.3%

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

   11. Taylor expanded in t around 0 57.6%

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

       1. mul-1-neg 57.6%

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

       2. associate-/l* 68.7%

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

   13. Simplified 68.7%

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

   if -9.0000000000000003e212 < a < -1.74999999999999993e92 or -2.2e13 < a < -9.20000000000000014e-107 or -2.1e-118 < a < -8.99999999999999912e-205 or -5.39999999999999968e-259 < a < 8.7999999999999997e122

   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/ 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in x around 0 51.7%

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

      1. associate-*r/ 69.3%

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

   6. Simplified 69.3%

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

   if -9.20000000000000014e-107 < a < -2.1e-118

   1. Initial program 61.5%

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

      1. associate-*l/ 42.8%

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

   3. Simplified 42.8%

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

      1. clear-num 42.8%

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

      2. inv-pow 42.8%

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

      3. metadata-eval 42.8%

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

      4. sqr-pow 21.7%

         \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right)} \cdot \left(z - t\right) \]

      5. metadata-eval 21.7%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      6. metadata-eval 21.7%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      7. metadata-eval 21.7%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)}\right) \cdot \left(z - t\right) \]

      8. metadata-eval 21.7%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}}\right) \cdot \left(z - t\right) \]

   5. Applied egg-rr 21.7%

      \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{-0.5}\right)} \cdot \left(z - t\right) \]
   6. Step-by-step derivation

      1. pow-sqr 42.8%

         \[\leadsto x + \color{blue}{{\left(\frac{a - t}{y - x}\right)}^{\left(2 \cdot -0.5\right)}} \cdot \left(z - t\right) \]

      2. metadata-eval 42.8%

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

      3. unpow-1 42.8%

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

   7. Simplified 42.8%

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

   8. Taylor expanded in y around 0 42.8%

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

      1. associate-*r/ 42.8%

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

      2. neg-mul-1 42.8%

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

   10. Simplified 42.8%

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

   11. Taylor expanded in z around inf 88.7%

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

       1. associate-/l* 88.8%

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

   13. Simplified 88.8%

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

   if -8.99999999999999912e-205 < a < -5.39999999999999968e-259

   1. Initial program 68.4%

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

      1. associate-*l/ 58.3%

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

   3. Simplified 58.3%

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

   4. Taylor expanded in z around -inf 86.1%

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

      1. associate-/l* 88.5%

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

      2. associate-/r/ 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 92.6%

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

      1. associate-*r/ 92.6%

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

      2. mul-1-neg 92.6%

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

   9. Simplified 92.6%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+212}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -22000000000000:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-107}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-118}:\\ \;\;\;\;\frac{x}{\frac{t - a}{z}}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-205}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-259}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \end{array} \]

Alternative 7: 39.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-204}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{t - a}{z}}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+61}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z a))))
   (if (<= a -3.7e+165)
     x
     (if (<= a -5.3e+65)
       t_1
       (if (<= a -5500000000000.0)
         x
         (if (<= a -1.6e-146)
           t_1
           (if (<= a -4.6e-204)
             y
             (if (<= a -2.45e-291)
               (/ x (/ (- t a) z))
               (if (<= a 8.8e+61) y (if (<= a 4.4e+145) t_1 x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) * (z / a);
	double tmp;
	if (a <= -3.7e+165) {
		tmp = x;
	} else if (a <= -5.3e+65) {
		tmp = t_1;
	} else if (a <= -5500000000000.0) {
		tmp = x;
	} else if (a <= -1.6e-146) {
		tmp = t_1;
	} else if (a <= -4.6e-204) {
		tmp = y;
	} else if (a <= -2.45e-291) {
		tmp = x / ((t - a) / z);
	} else if (a <= 8.8e+61) {
		tmp = y;
	} else if (a <= 4.4e+145) {
		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 - x) * (z / a)
    if (a <= (-3.7d+165)) then
        tmp = x
    else if (a <= (-5.3d+65)) then
        tmp = t_1
    else if (a <= (-5500000000000.0d0)) then
        tmp = x
    else if (a <= (-1.6d-146)) then
        tmp = t_1
    else if (a <= (-4.6d-204)) then
        tmp = y
    else if (a <= (-2.45d-291)) then
        tmp = x / ((t - a) / z)
    else if (a <= 8.8d+61) then
        tmp = y
    else if (a <= 4.4d+145) 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 - x) * (z / a);
	double tmp;
	if (a <= -3.7e+165) {
		tmp = x;
	} else if (a <= -5.3e+65) {
		tmp = t_1;
	} else if (a <= -5500000000000.0) {
		tmp = x;
	} else if (a <= -1.6e-146) {
		tmp = t_1;
	} else if (a <= -4.6e-204) {
		tmp = y;
	} else if (a <= -2.45e-291) {
		tmp = x / ((t - a) / z);
	} else if (a <= 8.8e+61) {
		tmp = y;
	} else if (a <= 4.4e+145) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - x) * (z / a)
	tmp = 0
	if a <= -3.7e+165:
		tmp = x
	elif a <= -5.3e+65:
		tmp = t_1
	elif a <= -5500000000000.0:
		tmp = x
	elif a <= -1.6e-146:
		tmp = t_1
	elif a <= -4.6e-204:
		tmp = y
	elif a <= -2.45e-291:
		tmp = x / ((t - a) / z)
	elif a <= 8.8e+61:
		tmp = y
	elif a <= 4.4e+145:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - x) * Float64(z / a))
	tmp = 0.0
	if (a <= -3.7e+165)
		tmp = x;
	elseif (a <= -5.3e+65)
		tmp = t_1;
	elseif (a <= -5500000000000.0)
		tmp = x;
	elseif (a <= -1.6e-146)
		tmp = t_1;
	elseif (a <= -4.6e-204)
		tmp = y;
	elseif (a <= -2.45e-291)
		tmp = Float64(x / Float64(Float64(t - a) / z));
	elseif (a <= 8.8e+61)
		tmp = y;
	elseif (a <= 4.4e+145)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - x) * (z / a);
	tmp = 0.0;
	if (a <= -3.7e+165)
		tmp = x;
	elseif (a <= -5.3e+65)
		tmp = t_1;
	elseif (a <= -5500000000000.0)
		tmp = x;
	elseif (a <= -1.6e-146)
		tmp = t_1;
	elseif (a <= -4.6e-204)
		tmp = y;
	elseif (a <= -2.45e-291)
		tmp = x / ((t - a) / z);
	elseif (a <= 8.8e+61)
		tmp = y;
	elseif (a <= 4.4e+145)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.7e+165], x, If[LessEqual[a, -5.3e+65], t$95$1, If[LessEqual[a, -5500000000000.0], x, If[LessEqual[a, -1.6e-146], t$95$1, If[LessEqual[a, -4.6e-204], y, If[LessEqual[a, -2.45e-291], N[(x / N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e+61], y, If[LessEqual[a, 4.4e+145], t$95$1, x]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.70000000000000006e165 or -5.30000000000000022e65 < a < -5.5e12 or 4.40000000000000017e145 < 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/ 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in a around inf 60.5%

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

   if -3.70000000000000006e165 < a < -5.30000000000000022e65 or -5.5e12 < a < -1.6e-146 or 8.8000000000000001e61 < a < 4.40000000000000017e145

   1. Initial program 75.9%

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

      1. associate-*l/ 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in z around -inf 56.0%

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

      1. associate-/l* 60.9%

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

      2. associate-/r/ 63.5%

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

   6. Applied egg-rr 63.5%

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

      1. div-inv 63.5%

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

      2. *-commutative 63.5%

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

   8. Applied egg-rr 63.5%

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

   9. Taylor expanded in a around inf 51.1%

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

   if -1.6e-146 < a < -4.5999999999999998e-204 or -2.44999999999999997e-291 < a < 8.8000000000000001e61

   1. Initial program 64.2%

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

      1. associate-*l/ 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in t around inf 54.7%

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

   if -4.5999999999999998e-204 < a < -2.44999999999999997e-291

   1. Initial program 67.8%

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

      1. associate-*l/ 64.7%

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

   3. Simplified 64.7%

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

      1. clear-num 64.8%

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

      2. inv-pow 64.8%

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

      3. metadata-eval 64.8%

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

      4. sqr-pow 25.7%

         \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right)} \cdot \left(z - t\right) \]

      5. metadata-eval 25.7%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      6. metadata-eval 25.7%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      7. metadata-eval 25.7%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)}\right) \cdot \left(z - t\right) \]

      8. metadata-eval 25.7%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}}\right) \cdot \left(z - t\right) \]

   5. Applied egg-rr 25.7%

      \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{-0.5}\right)} \cdot \left(z - t\right) \]
   6. Step-by-step derivation

      1. pow-sqr 64.8%

         \[\leadsto x + \color{blue}{{\left(\frac{a - t}{y - x}\right)}^{\left(2 \cdot -0.5\right)}} \cdot \left(z - t\right) \]

      2. metadata-eval 64.8%

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

      3. unpow-1 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in y around 0 31.4%

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

      1. associate-*r/ 31.4%

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

      2. neg-mul-1 31.4%

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

   10. Simplified 31.4%

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

   11. Taylor expanded in z around inf 57.2%

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

       1. associate-/l* 68.0%

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

   13. Simplified 68.0%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{+65}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -5500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-146}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-204}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{t - a}{z}}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+61}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+145}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 39.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{+168}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -15000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z a))))
   (if (<= a -1.45e+168)
     x
     (if (<= a -6.8e+65)
       t_1
       (if (<= a -15000000000000.0)
         x
         (if (<= a -5.2e-144)
           t_1
           (if (<= a -1e-291)
             (/ x (/ t z))
             (if (<= a 3.6e+51) y (if (<= a 2.7e+149) t_1 x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) * (z / a);
	double tmp;
	if (a <= -1.45e+168) {
		tmp = x;
	} else if (a <= -6.8e+65) {
		tmp = t_1;
	} else if (a <= -15000000000000.0) {
		tmp = x;
	} else if (a <= -5.2e-144) {
		tmp = t_1;
	} else if (a <= -1e-291) {
		tmp = x / (t / z);
	} else if (a <= 3.6e+51) {
		tmp = y;
	} else if (a <= 2.7e+149) {
		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 - x) * (z / a)
    if (a <= (-1.45d+168)) then
        tmp = x
    else if (a <= (-6.8d+65)) then
        tmp = t_1
    else if (a <= (-15000000000000.0d0)) then
        tmp = x
    else if (a <= (-5.2d-144)) then
        tmp = t_1
    else if (a <= (-1d-291)) then
        tmp = x / (t / z)
    else if (a <= 3.6d+51) then
        tmp = y
    else if (a <= 2.7d+149) 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 - x) * (z / a);
	double tmp;
	if (a <= -1.45e+168) {
		tmp = x;
	} else if (a <= -6.8e+65) {
		tmp = t_1;
	} else if (a <= -15000000000000.0) {
		tmp = x;
	} else if (a <= -5.2e-144) {
		tmp = t_1;
	} else if (a <= -1e-291) {
		tmp = x / (t / z);
	} else if (a <= 3.6e+51) {
		tmp = y;
	} else if (a <= 2.7e+149) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - x) * (z / a)
	tmp = 0
	if a <= -1.45e+168:
		tmp = x
	elif a <= -6.8e+65:
		tmp = t_1
	elif a <= -15000000000000.0:
		tmp = x
	elif a <= -5.2e-144:
		tmp = t_1
	elif a <= -1e-291:
		tmp = x / (t / z)
	elif a <= 3.6e+51:
		tmp = y
	elif a <= 2.7e+149:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - x) * Float64(z / a))
	tmp = 0.0
	if (a <= -1.45e+168)
		tmp = x;
	elseif (a <= -6.8e+65)
		tmp = t_1;
	elseif (a <= -15000000000000.0)
		tmp = x;
	elseif (a <= -5.2e-144)
		tmp = t_1;
	elseif (a <= -1e-291)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 3.6e+51)
		tmp = y;
	elseif (a <= 2.7e+149)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - x) * (z / a);
	tmp = 0.0;
	if (a <= -1.45e+168)
		tmp = x;
	elseif (a <= -6.8e+65)
		tmp = t_1;
	elseif (a <= -15000000000000.0)
		tmp = x;
	elseif (a <= -5.2e-144)
		tmp = t_1;
	elseif (a <= -1e-291)
		tmp = x / (t / z);
	elseif (a <= 3.6e+51)
		tmp = y;
	elseif (a <= 2.7e+149)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e+168], x, If[LessEqual[a, -6.8e+65], t$95$1, If[LessEqual[a, -15000000000000.0], x, If[LessEqual[a, -5.2e-144], t$95$1, If[LessEqual[a, -1e-291], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e+51], y, If[LessEqual[a, 2.7e+149], t$95$1, x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.45e168 or -6.7999999999999999e65 < a < -1.5e13 or 2.7000000000000001e149 < 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/ 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in a around inf 60.5%

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

   if -1.45e168 < a < -6.7999999999999999e65 or -1.5e13 < a < -5.2000000000000002e-144 or 3.60000000000000011e51 < a < 2.7000000000000001e149

   1. Initial program 75.9%

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

      1. associate-*l/ 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in z around -inf 56.0%

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

      1. associate-/l* 60.9%

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

      2. associate-/r/ 63.5%

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

   6. Applied egg-rr 63.5%

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

      1. div-inv 63.5%

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

      2. *-commutative 63.5%

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

   8. Applied egg-rr 63.5%

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

   9. Taylor expanded in a around inf 51.1%

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

   if -5.2000000000000002e-144 < a < -9.99999999999999962e-292

   1. Initial program 66.9%

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

      1. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in z around -inf 64.2%

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

      1. associate-/l* 70.6%

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

      2. associate-/r/ 72.5%

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

   6. Applied egg-rr 72.5%

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

   7. Taylor expanded in a around 0 64.1%

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

      1. associate-*r/ 64.1%

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

      2. mul-1-neg 64.1%

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

   9. Simplified 64.1%

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

   10. Taylor expanded in y around 0 41.3%

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

       1. associate-/l* 56.0%

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

   12. Simplified 56.0%

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

   if -9.99999999999999962e-292 < a < 3.60000000000000011e51

   1. Initial program 64.0%

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

      1. associate-*l/ 74.5%

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

   3. Simplified 74.5%

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

   4. Taylor expanded in t around inf 54.0%

      \[\leadsto \color{blue}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+168}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+65}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -15000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-144}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+149}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 41.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -3.65 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -100000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 10^{-261}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z a))))
   (if (<= a -3.65e+165)
     x
     (if (<= a -8e+65)
       t_1
       (if (<= a -100000000000.0)
         x
         (if (<= a -5.6e-144)
           t_1
           (if (<= a 1e-261)
             (* (/ z t) (- x y))
             (if (<= a 1.3e+51) y (if (<= a 2.1e+147) t_1 x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) * (z / a);
	double tmp;
	if (a <= -3.65e+165) {
		tmp = x;
	} else if (a <= -8e+65) {
		tmp = t_1;
	} else if (a <= -100000000000.0) {
		tmp = x;
	} else if (a <= -5.6e-144) {
		tmp = t_1;
	} else if (a <= 1e-261) {
		tmp = (z / t) * (x - y);
	} else if (a <= 1.3e+51) {
		tmp = y;
	} else if (a <= 2.1e+147) {
		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 - x) * (z / a)
    if (a <= (-3.65d+165)) then
        tmp = x
    else if (a <= (-8d+65)) then
        tmp = t_1
    else if (a <= (-100000000000.0d0)) then
        tmp = x
    else if (a <= (-5.6d-144)) then
        tmp = t_1
    else if (a <= 1d-261) then
        tmp = (z / t) * (x - y)
    else if (a <= 1.3d+51) then
        tmp = y
    else if (a <= 2.1d+147) 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 - x) * (z / a);
	double tmp;
	if (a <= -3.65e+165) {
		tmp = x;
	} else if (a <= -8e+65) {
		tmp = t_1;
	} else if (a <= -100000000000.0) {
		tmp = x;
	} else if (a <= -5.6e-144) {
		tmp = t_1;
	} else if (a <= 1e-261) {
		tmp = (z / t) * (x - y);
	} else if (a <= 1.3e+51) {
		tmp = y;
	} else if (a <= 2.1e+147) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - x) * (z / a)
	tmp = 0
	if a <= -3.65e+165:
		tmp = x
	elif a <= -8e+65:
		tmp = t_1
	elif a <= -100000000000.0:
		tmp = x
	elif a <= -5.6e-144:
		tmp = t_1
	elif a <= 1e-261:
		tmp = (z / t) * (x - y)
	elif a <= 1.3e+51:
		tmp = y
	elif a <= 2.1e+147:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - x) * Float64(z / a))
	tmp = 0.0
	if (a <= -3.65e+165)
		tmp = x;
	elseif (a <= -8e+65)
		tmp = t_1;
	elseif (a <= -100000000000.0)
		tmp = x;
	elseif (a <= -5.6e-144)
		tmp = t_1;
	elseif (a <= 1e-261)
		tmp = Float64(Float64(z / t) * Float64(x - y));
	elseif (a <= 1.3e+51)
		tmp = y;
	elseif (a <= 2.1e+147)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - x) * (z / a);
	tmp = 0.0;
	if (a <= -3.65e+165)
		tmp = x;
	elseif (a <= -8e+65)
		tmp = t_1;
	elseif (a <= -100000000000.0)
		tmp = x;
	elseif (a <= -5.6e-144)
		tmp = t_1;
	elseif (a <= 1e-261)
		tmp = (z / t) * (x - y);
	elseif (a <= 1.3e+51)
		tmp = y;
	elseif (a <= 2.1e+147)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.65e+165], x, If[LessEqual[a, -8e+65], t$95$1, If[LessEqual[a, -100000000000.0], x, If[LessEqual[a, -5.6e-144], t$95$1, If[LessEqual[a, 1e-261], N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+51], y, If[LessEqual[a, 2.1e+147], t$95$1, x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.6500000000000001e165 or -7.9999999999999999e65 < a < -1e11 or 2.10000000000000006e147 < 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/ 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in a around inf 60.5%

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

   if -3.6500000000000001e165 < a < -7.9999999999999999e65 or -1e11 < a < -5.59999999999999995e-144 or 1.3000000000000001e51 < a < 2.10000000000000006e147

   1. Initial program 75.9%

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

      1. associate-*l/ 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in z around -inf 56.0%

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

      1. associate-/l* 60.9%

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

      2. associate-/r/ 63.5%

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

   6. Applied egg-rr 63.5%

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

      1. div-inv 63.5%

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

      2. *-commutative 63.5%

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

   8. Applied egg-rr 63.5%

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

   9. Taylor expanded in a around inf 51.1%

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

   if -5.59999999999999995e-144 < a < 9.99999999999999984e-262

   1. Initial program 67.8%

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

      1. associate-*l/ 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in z around -inf 61.4%

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

      1. associate-/l* 66.5%

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

      2. associate-/r/ 70.0%

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

   6. Applied egg-rr 70.0%

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

   7. Taylor expanded in a around 0 63.4%

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

      1. associate-*r/ 63.4%

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

      2. mul-1-neg 63.4%

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

   9. Simplified 63.4%

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

   if 9.99999999999999984e-262 < a < 1.3000000000000001e51

   1. Initial program 62.8%

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

      1. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in t around inf 55.8%

      \[\leadsto \color{blue}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.65 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+65}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -100000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-144}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 10^{-261}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+147}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 55.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x - \frac{x}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -2 \cdot 10^{+214}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.45 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -22000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-291}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (- x (/ x (/ a z)))))
   (if (<= a -2e+214)
     t_2
     (if (<= a -3.45e+84)
       t_1
       (if (<= a -22000000000000.0)
         t_2
         (if (<= a -2.15e-291)
           (* z (/ (- y x) (- a t)))
           (if (<= a 7.6e+122) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x - (x / (a / z));
	double tmp;
	if (a <= -2e+214) {
		tmp = t_2;
	} else if (a <= -3.45e+84) {
		tmp = t_1;
	} else if (a <= -22000000000000.0) {
		tmp = t_2;
	} else if (a <= -2.15e-291) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 7.6e+122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x - (x / (a / z))
    if (a <= (-2d+214)) then
        tmp = t_2
    else if (a <= (-3.45d+84)) then
        tmp = t_1
    else if (a <= (-22000000000000.0d0)) then
        tmp = t_2
    else if (a <= (-2.15d-291)) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 7.6d+122) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x - (x / (a / z));
	double tmp;
	if (a <= -2e+214) {
		tmp = t_2;
	} else if (a <= -3.45e+84) {
		tmp = t_1;
	} else if (a <= -22000000000000.0) {
		tmp = t_2;
	} else if (a <= -2.15e-291) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 7.6e+122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x - (x / (a / z))
	tmp = 0
	if a <= -2e+214:
		tmp = t_2
	elif a <= -3.45e+84:
		tmp = t_1
	elif a <= -22000000000000.0:
		tmp = t_2
	elif a <= -2.15e-291:
		tmp = z * ((y - x) / (a - t))
	elif a <= 7.6e+122:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x - Float64(x / Float64(a / z)))
	tmp = 0.0
	if (a <= -2e+214)
		tmp = t_2;
	elseif (a <= -3.45e+84)
		tmp = t_1;
	elseif (a <= -22000000000000.0)
		tmp = t_2;
	elseif (a <= -2.15e-291)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 7.6e+122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x - (x / (a / z));
	tmp = 0.0;
	if (a <= -2e+214)
		tmp = t_2;
	elseif (a <= -3.45e+84)
		tmp = t_1;
	elseif (a <= -22000000000000.0)
		tmp = t_2;
	elseif (a <= -2.15e-291)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 7.6e+122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e+214], t$95$2, If[LessEqual[a, -3.45e+84], t$95$1, If[LessEqual[a, -22000000000000.0], t$95$2, If[LessEqual[a, -2.15e-291], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e+122], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9999999999999999e214 or -3.4499999999999998e84 < a < -2.2e13 or 7.5999999999999996e122 < a

   1. Initial program 72.8%

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

      1. associate-*l/ 88.0%

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

   3. Simplified 88.0%

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

      1. clear-num 88.0%

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

      2. inv-pow 88.0%

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

      3. metadata-eval 88.0%

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

      4. sqr-pow 44.9%

         \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right)} \cdot \left(z - t\right) \]

      5. metadata-eval 44.9%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      6. metadata-eval 44.9%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      7. metadata-eval 44.9%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)}\right) \cdot \left(z - t\right) \]

      8. metadata-eval 44.9%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}}\right) \cdot \left(z - t\right) \]

   5. Applied egg-rr 44.9%

      \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{-0.5}\right)} \cdot \left(z - t\right) \]
   6. Step-by-step derivation

      1. pow-sqr 88.0%

         \[\leadsto x + \color{blue}{{\left(\frac{a - t}{y - x}\right)}^{\left(2 \cdot -0.5\right)}} \cdot \left(z - t\right) \]

      2. metadata-eval 88.0%

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

      3. unpow-1 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in y around 0 72.3%

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

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

   10. Simplified 72.3%

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

   11. Taylor expanded in t around 0 57.6%

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

       1. mul-1-neg 57.6%

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

       2. associate-/l* 68.7%

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

   13. Simplified 68.7%

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

   if -1.9999999999999999e214 < a < -3.4499999999999998e84 or -2.15000000000000018e-291 < a < 7.5999999999999996e122

   1. Initial program 65.4%

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

      1. associate-*l/ 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in x around 0 49.4%

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

      1. associate-*r/ 69.3%

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

   6. Simplified 69.3%

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

   if -2.2e13 < a < -2.15000000000000018e-291

   1. Initial program 70.7%

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

      1. associate-*l/ 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in z around inf 70.3%

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

      1. div-sub 70.3%

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

   6. Simplified 70.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+214}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -3.45 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -22000000000000:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-291}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \end{array} \]

Alternative 11: 55.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x - \frac{x}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.28 \cdot 10^{+213}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -21000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-291}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (- x (/ x (/ a z)))))
   (if (<= a -1.28e+213)
     t_2
     (if (<= a -1.1e+89)
       t_1
       (if (<= a -21000000000000.0)
         t_2
         (if (<= a -2.8e-291)
           (* (- y x) (/ z (- a t)))
           (if (<= a 5.6e+122) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x - (x / (a / z));
	double tmp;
	if (a <= -1.28e+213) {
		tmp = t_2;
	} else if (a <= -1.1e+89) {
		tmp = t_1;
	} else if (a <= -21000000000000.0) {
		tmp = t_2;
	} else if (a <= -2.8e-291) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 5.6e+122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x - (x / (a / z))
    if (a <= (-1.28d+213)) then
        tmp = t_2
    else if (a <= (-1.1d+89)) then
        tmp = t_1
    else if (a <= (-21000000000000.0d0)) then
        tmp = t_2
    else if (a <= (-2.8d-291)) then
        tmp = (y - x) * (z / (a - t))
    else if (a <= 5.6d+122) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x - (x / (a / z));
	double tmp;
	if (a <= -1.28e+213) {
		tmp = t_2;
	} else if (a <= -1.1e+89) {
		tmp = t_1;
	} else if (a <= -21000000000000.0) {
		tmp = t_2;
	} else if (a <= -2.8e-291) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 5.6e+122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x - (x / (a / z))
	tmp = 0
	if a <= -1.28e+213:
		tmp = t_2
	elif a <= -1.1e+89:
		tmp = t_1
	elif a <= -21000000000000.0:
		tmp = t_2
	elif a <= -2.8e-291:
		tmp = (y - x) * (z / (a - t))
	elif a <= 5.6e+122:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x - Float64(x / Float64(a / z)))
	tmp = 0.0
	if (a <= -1.28e+213)
		tmp = t_2;
	elseif (a <= -1.1e+89)
		tmp = t_1;
	elseif (a <= -21000000000000.0)
		tmp = t_2;
	elseif (a <= -2.8e-291)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (a <= 5.6e+122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x - (x / (a / z));
	tmp = 0.0;
	if (a <= -1.28e+213)
		tmp = t_2;
	elseif (a <= -1.1e+89)
		tmp = t_1;
	elseif (a <= -21000000000000.0)
		tmp = t_2;
	elseif (a <= -2.8e-291)
		tmp = (y - x) * (z / (a - t));
	elseif (a <= 5.6e+122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.28e+213], t$95$2, If[LessEqual[a, -1.1e+89], t$95$1, If[LessEqual[a, -21000000000000.0], t$95$2, If[LessEqual[a, -2.8e-291], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e+122], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2799999999999999e213 or -1.1e89 < a < -2.1e13 or 5.5999999999999999e122 < a

   1. Initial program 72.8%

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

      1. associate-*l/ 88.0%

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

   3. Simplified 88.0%

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

      1. clear-num 88.0%

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

      2. inv-pow 88.0%

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

      3. metadata-eval 88.0%

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

      4. sqr-pow 44.9%

         \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right)} \cdot \left(z - t\right) \]

      5. metadata-eval 44.9%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      6. metadata-eval 44.9%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      7. metadata-eval 44.9%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)}\right) \cdot \left(z - t\right) \]

      8. metadata-eval 44.9%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}}\right) \cdot \left(z - t\right) \]

   5. Applied egg-rr 44.9%

      \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{-0.5}\right)} \cdot \left(z - t\right) \]
   6. Step-by-step derivation

      1. pow-sqr 88.0%

         \[\leadsto x + \color{blue}{{\left(\frac{a - t}{y - x}\right)}^{\left(2 \cdot -0.5\right)}} \cdot \left(z - t\right) \]

      2. metadata-eval 88.0%

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

      3. unpow-1 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in y around 0 72.3%

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

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

   10. Simplified 72.3%

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

   11. Taylor expanded in t around 0 57.6%

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

       1. mul-1-neg 57.6%

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

       2. associate-/l* 68.7%

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

   13. Simplified 68.7%

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

   if -1.2799999999999999e213 < a < -1.1e89 or -2.8e-291 < a < 5.5999999999999999e122

   1. Initial program 65.4%

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

      1. associate-*l/ 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in x around 0 49.4%

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

      1. associate-*r/ 69.3%

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

   6. Simplified 69.3%

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

   if -2.1e13 < a < -2.8e-291

   1. Initial program 70.7%

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

      1. associate-*l/ 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in z around -inf 67.4%

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

      1. associate-/l* 70.7%

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

      2. associate-/r/ 73.0%

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

   6. Applied egg-rr 73.0%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.28 \cdot 10^{+213}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -21000000000000:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-291}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \end{array} \]

Alternative 12: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.56 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+19}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.56e+157)
   (* y (/ (- z t) (- a t)))
   (if (<= t -8.5e+19)
     (+ x (* (- z t) (/ y (- a t))))
     (if (<= t 6.1e+26)
       (+ x (/ (- y x) (/ (- a t) z)))
       (+ y (/ (* (- y x) (- a z)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.56e+157) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -8.5e+19) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else if (t <= 6.1e+26) {
		tmp = x + ((y - x) / ((a - t) / z));
	} 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 (t <= (-2.56d+157)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= (-8.5d+19)) then
        tmp = x + ((z - t) * (y / (a - t)))
    else if (t <= 6.1d+26) then
        tmp = x + ((y - x) / ((a - t) / z))
    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 (t <= -2.56e+157) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -8.5e+19) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else if (t <= 6.1e+26) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.56e+157:
		tmp = y * ((z - t) / (a - t))
	elif t <= -8.5e+19:
		tmp = x + ((z - t) * (y / (a - t)))
	elif t <= 6.1e+26:
		tmp = x + ((y - x) / ((a - t) / z))
	else:
		tmp = y + (((y - x) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.56e+157)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= -8.5e+19)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	elseif (t <= 6.1e+26)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / z)));
	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)
	tmp = 0.0;
	if (t <= -2.56e+157)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= -8.5e+19)
		tmp = x + ((z - t) * (y / (a - t)));
	elseif (t <= 6.1e+26)
		tmp = x + ((y - x) / ((a - t) / z));
	else
		tmp = y + (((y - x) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.56e+157], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.5e+19], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.1e+26], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.56000000000000002e157

   1. Initial program 20.5%

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

      1. associate-*l/ 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in x around 0 37.1%

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

      1. associate-*r/ 74.0%

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

   6. Simplified 74.0%

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

   if -2.56000000000000002e157 < t < -8.5e19

   1. Initial program 65.3%

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

      1. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in y around inf 81.1%

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

   if -8.5e19 < t < 6.1000000000000003e26

   1. Initial program 89.9%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

      1. associate-/r/ 97.6%

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

   5. Applied egg-rr 97.6%

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

   6. Taylor expanded in z around inf 86.4%

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

   if 6.1000000000000003e26 < t

   1. Initial program 49.4%

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

      1. associate-*l/ 67.4%

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

   3. Simplified 67.4%

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

      1. associate-/r/ 73.2%

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

   5. Applied egg-rr 73.2%

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

   6. Taylor expanded in t around -inf 63.8%

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

      1. mul-1-neg 63.8%

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

      2. distribute-rgt-out-- 67.0%

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

   8. Simplified 67.0%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.56 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+19}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]

Alternative 13: 37.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{a - t}\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a t)))))
   (if (<= a -3.5e+165)
     x
     (if (<= a -6e+115)
       t_1
       (if (<= a -1500000000000.0)
         x
         (if (<= a -3.8e-154)
           t_1
           (if (<= a -1.12e-291) (/ x (/ t z)) (if (<= a 2.2e+75) y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (a - t));
	double tmp;
	if (a <= -3.5e+165) {
		tmp = x;
	} else if (a <= -6e+115) {
		tmp = t_1;
	} else if (a <= -1500000000000.0) {
		tmp = x;
	} else if (a <= -3.8e-154) {
		tmp = t_1;
	} else if (a <= -1.12e-291) {
		tmp = x / (t / z);
	} else if (a <= 2.2e+75) {
		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) :: t_1
    real(8) :: tmp
    t_1 = z * (y / (a - t))
    if (a <= (-3.5d+165)) then
        tmp = x
    else if (a <= (-6d+115)) then
        tmp = t_1
    else if (a <= (-1500000000000.0d0)) then
        tmp = x
    else if (a <= (-3.8d-154)) then
        tmp = t_1
    else if (a <= (-1.12d-291)) then
        tmp = x / (t / z)
    else if (a <= 2.2d+75) 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 t_1 = z * (y / (a - t));
	double tmp;
	if (a <= -3.5e+165) {
		tmp = x;
	} else if (a <= -6e+115) {
		tmp = t_1;
	} else if (a <= -1500000000000.0) {
		tmp = x;
	} else if (a <= -3.8e-154) {
		tmp = t_1;
	} else if (a <= -1.12e-291) {
		tmp = x / (t / z);
	} else if (a <= 2.2e+75) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / (a - t))
	tmp = 0
	if a <= -3.5e+165:
		tmp = x
	elif a <= -6e+115:
		tmp = t_1
	elif a <= -1500000000000.0:
		tmp = x
	elif a <= -3.8e-154:
		tmp = t_1
	elif a <= -1.12e-291:
		tmp = x / (t / z)
	elif a <= 2.2e+75:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (a <= -3.5e+165)
		tmp = x;
	elseif (a <= -6e+115)
		tmp = t_1;
	elseif (a <= -1500000000000.0)
		tmp = x;
	elseif (a <= -3.8e-154)
		tmp = t_1;
	elseif (a <= -1.12e-291)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 2.2e+75)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / (a - t));
	tmp = 0.0;
	if (a <= -3.5e+165)
		tmp = x;
	elseif (a <= -6e+115)
		tmp = t_1;
	elseif (a <= -1500000000000.0)
		tmp = x;
	elseif (a <= -3.8e-154)
		tmp = t_1;
	elseif (a <= -1.12e-291)
		tmp = x / (t / z);
	elseif (a <= 2.2e+75)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+165], x, If[LessEqual[a, -6e+115], t$95$1, If[LessEqual[a, -1500000000000.0], x, If[LessEqual[a, -3.8e-154], t$95$1, If[LessEqual[a, -1.12e-291], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e+75], y, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.49999999999999996e165 or -6.0000000000000001e115 < a < -1.5e12 or 2.20000000000000012e75 < a

   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/ 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in a around inf 54.0%

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

   if -3.49999999999999996e165 < a < -6.0000000000000001e115 or -1.5e12 < a < -3.8000000000000001e-154

   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/ 82.0%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in z around -inf 61.3%

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

   5. Taylor expanded in y around inf 33.8%

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

      1. associate-/l* 41.5%

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

      2. associate-/r/ 39.6%

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

   7. Simplified 39.6%

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

   if -3.8000000000000001e-154 < a < -1.1200000000000001e-291

   1. Initial program 70.8%

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

      1. associate-*l/ 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in z around -inf 67.7%

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

      1. associate-/l* 74.5%

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

      2. associate-/r/ 76.5%

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

   6. Applied egg-rr 76.5%

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

   7. Taylor expanded in a around 0 67.5%

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

      1. associate-*r/ 67.5%

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

      2. mul-1-neg 67.5%

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

   9. Simplified 67.5%

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

   10. Taylor expanded in y around 0 43.6%

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

       1. associate-/l* 59.1%

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

   12. Simplified 59.1%

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

   if -1.1200000000000001e-291 < a < 2.20000000000000012e75

   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/ 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in t around inf 51.3%

      \[\leadsto \color{blue}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -1500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-154}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 62.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{if}\;a \leq -2100000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-292}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a (- y x))))))
   (if (<= a -2100000000.0)
     t_1
     (if (<= a -7e-292)
       (* (- y x) (/ z (- a t)))
       (if (<= a 7.2e+56) (* y (/ (- z t) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double tmp;
	if (a <= -2100000000.0) {
		tmp = t_1;
	} else if (a <= -7e-292) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 7.2e+56) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / (a / (y - x)))
    if (a <= (-2100000000.0d0)) then
        tmp = t_1
    else if (a <= (-7d-292)) then
        tmp = (y - x) * (z / (a - t))
    else if (a <= 7.2d+56) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double tmp;
	if (a <= -2100000000.0) {
		tmp = t_1;
	} else if (a <= -7e-292) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 7.2e+56) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / (y - x)))
	tmp = 0
	if a <= -2100000000.0:
		tmp = t_1
	elif a <= -7e-292:
		tmp = (y - x) * (z / (a - t))
	elif a <= 7.2e+56:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	tmp = 0.0
	if (a <= -2100000000.0)
		tmp = t_1;
	elseif (a <= -7e-292)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (a <= 7.2e+56)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / (y - x)));
	tmp = 0.0;
	if (a <= -2100000000.0)
		tmp = t_1;
	elseif (a <= -7e-292)
		tmp = (y - x) * (z / (a - t));
	elseif (a <= 7.2e+56)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2100000000.0], t$95$1, If[LessEqual[a, -7e-292], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e+56], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1e9 or 7.19999999999999996e56 < a

   1. Initial program 71.3%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in t around 0 59.3%

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

      1. associate-/l* 70.2%

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

   6. Simplified 70.2%

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

   if -2.1e9 < a < -6.9999999999999999e-292

   1. Initial program 70.7%

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

      1. associate-*l/ 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in z around -inf 67.4%

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

      1. associate-/l* 70.7%

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

      2. associate-/r/ 73.0%

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

   6. Applied egg-rr 73.0%

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

   if -6.9999999999999999e-292 < a < 7.19999999999999996e56

   1. Initial program 64.0%

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

      1. associate-*l/ 74.5%

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

   3. Simplified 74.5%

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

   4. Taylor expanded in x around 0 52.6%

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

      1. associate-*r/ 68.8%

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

   6. Simplified 68.8%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2100000000:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-292}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]

Alternative 15: 62.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -20000000000000:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-291}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -20000000000000.0)
   (+ x (/ z (/ a (- y x))))
   (if (<= a -2e-291)
     (* (- y x) (/ z (- a t)))
     (if (<= a 2.9e+66) (* y (/ (- z t) (- a t))) (+ x (/ (- y x) (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -20000000000000.0) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= -2e-291) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 2.9e+66) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-20000000000000.0d0)) then
        tmp = x + (z / (a / (y - x)))
    else if (a <= (-2d-291)) then
        tmp = (y - x) * (z / (a - t))
    else if (a <= 2.9d+66) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + ((y - x) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -20000000000000.0) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= -2e-291) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 2.9e+66) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -20000000000000.0:
		tmp = x + (z / (a / (y - x)))
	elif a <= -2e-291:
		tmp = (y - x) * (z / (a - t))
	elif a <= 2.9e+66:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + ((y - x) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -20000000000000.0)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (a <= -2e-291)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (a <= 2.9e+66)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -20000000000000.0)
		tmp = x + (z / (a / (y - x)));
	elseif (a <= -2e-291)
		tmp = (y - x) * (z / (a - t));
	elseif (a <= 2.9e+66)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + ((y - x) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -20000000000000.0], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2e-291], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e+66], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2e13

   1. Initial program 68.8%

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

      1. associate-*l/ 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in t around 0 56.8%

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

      1. associate-/l* 67.6%

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

   6. Simplified 67.6%

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

   if -2e13 < a < -1.99999999999999992e-291

   1. Initial program 70.7%

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

      1. associate-*l/ 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in z around -inf 67.4%

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

      1. associate-/l* 70.7%

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

      2. associate-/r/ 73.0%

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

   6. Applied egg-rr 73.0%

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

   if -1.99999999999999992e-291 < a < 2.89999999999999986e66

   1. Initial program 64.4%

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

      1. associate-*l/ 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in x around 0 53.2%

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

      1. associate-*r/ 69.3%

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

   6. Simplified 69.3%

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

   if 2.89999999999999986e66 < a

   1. Initial program 73.7%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

      1. associate-/r/ 97.3%

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

   5. Applied egg-rr 97.3%

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

   6. Taylor expanded in t around 0 76.4%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -20000000000000:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-291}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 16: 69.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+102} \lor \neg \left(x \leq 1.1 \cdot 10^{+131}\right):\\ \;\;\;\;x \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.2e+102) (not (<= x 1.1e+131)))
   (* x (+ 1.0 (/ (- z t) (- t a))))
   (+ x (* (- z t) (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.2e+102) || !(x <= 1.1e+131)) {
		tmp = x * (1.0 + ((z - t) / (t - a)));
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-2.2d+102)) .or. (.not. (x <= 1.1d+131))) then
        tmp = x * (1.0d0 + ((z - t) / (t - a)))
    else
        tmp = x + ((z - t) * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.2e+102) || !(x <= 1.1e+131)) {
		tmp = x * (1.0 + ((z - t) / (t - a)));
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.2e+102) or not (x <= 1.1e+131):
		tmp = x * (1.0 + ((z - t) / (t - a)))
	else:
		tmp = x + ((z - t) * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.2e+102) || !(x <= 1.1e+131))
		tmp = Float64(x * Float64(1.0 + Float64(Float64(z - t) / Float64(t - a))));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.2e+102) || ~((x <= 1.1e+131)))
		tmp = x * (1.0 + ((z - t) / (t - a)));
	else
		tmp = x + ((z - t) * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.2e+102], N[Not[LessEqual[x, 1.1e+131]], $MachinePrecision]], N[(x * N[(1.0 + N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.20000000000000007e102 or 1.0999999999999999e131 < x

   1. Initial program 55.7%

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

      1. associate-*l/ 73.3%

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

   3. Simplified 73.3%

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

      1. clear-num 73.5%

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

      2. inv-pow 73.5%

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

      3. metadata-eval 73.5%

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

      4. sqr-pow 33.5%

         \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right)} \cdot \left(z - t\right) \]

      5. metadata-eval 33.5%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      6. metadata-eval 33.5%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      7. metadata-eval 33.5%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)}\right) \cdot \left(z - t\right) \]

      8. metadata-eval 33.5%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}}\right) \cdot \left(z - t\right) \]

   5. Applied egg-rr 33.5%

      \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{-0.5}\right)} \cdot \left(z - t\right) \]
   6. Step-by-step derivation

      1. pow-sqr 73.5%

         \[\leadsto x + \color{blue}{{\left(\frac{a - t}{y - x}\right)}^{\left(2 \cdot -0.5\right)}} \cdot \left(z - t\right) \]

      2. metadata-eval 73.5%

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

      3. unpow-1 73.5%

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

   7. Simplified 73.5%

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

   8. Taylor expanded in y around 0 66.7%

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

      1. associate-*r/ 66.7%

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

      2. neg-mul-1 66.7%

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

   10. Simplified 66.7%

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

   11. Taylor expanded in x around 0 71.1%

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

       1. associate--l+ 71.1%

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

       2. div-sub 71.1%

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

   13. Simplified 71.1%

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

   if -2.20000000000000007e102 < x < 1.0999999999999999e131

   1. Initial program 74.4%

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

      1. associate-*l/ 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in y around inf 77.3%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+102} \lor \neg \left(x \leq 1.1 \cdot 10^{+131}\right):\\ \;\;\;\;x \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 17: 70.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \mathbf{elif}\;x \leq 1250000:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.55e+105)
   (* x (+ 1.0 (/ (- z t) (- t a))))
   (if (<= x 1250000.0)
     (+ x (* (- z t) (/ y (- a t))))
     (+ x (/ (- y x) (/ (- a t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.55e+105) {
		tmp = x * (1.0 + ((z - t) / (t - a)));
	} else if (x <= 1250000.0) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = x + ((y - x) / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.55d+105)) then
        tmp = x * (1.0d0 + ((z - t) / (t - a)))
    else if (x <= 1250000.0d0) then
        tmp = x + ((z - t) * (y / (a - t)))
    else
        tmp = x + ((y - x) / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.55e+105) {
		tmp = x * (1.0 + ((z - t) / (t - a)));
	} else if (x <= 1250000.0) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = x + ((y - x) / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.55e+105:
		tmp = x * (1.0 + ((z - t) / (t - a)))
	elif x <= 1250000.0:
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = x + ((y - x) / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.55e+105)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(z - t) / Float64(t - a))));
	elseif (x <= 1250000.0)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.55e+105)
		tmp = x * (1.0 + ((z - t) / (t - a)));
	elseif (x <= 1250000.0)
		tmp = x + ((z - t) * (y / (a - t)));
	else
		tmp = x + ((y - x) / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.55e+105], N[(x * N[(1.0 + N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1250000.0], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55000000000000002e105

   1. Initial program 50.5%

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

      1. associate-*l/ 69.0%

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

   3. Simplified 69.0%

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

      1. clear-num 69.3%

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

      2. inv-pow 69.3%

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

      3. metadata-eval 69.3%

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

      4. sqr-pow 24.2%

         \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right)} \cdot \left(z - t\right) \]

      5. metadata-eval 24.2%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      6. metadata-eval 24.2%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      7. metadata-eval 24.2%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)}\right) \cdot \left(z - t\right) \]

      8. metadata-eval 24.2%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}}\right) \cdot \left(z - t\right) \]

   5. Applied egg-rr 24.2%

      \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{-0.5}\right)} \cdot \left(z - t\right) \]
   6. Step-by-step derivation

      1. pow-sqr 69.3%

         \[\leadsto x + \color{blue}{{\left(\frac{a - t}{y - x}\right)}^{\left(2 \cdot -0.5\right)}} \cdot \left(z - t\right) \]

      2. metadata-eval 69.3%

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

      3. unpow-1 69.3%

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

   7. Simplified 69.3%

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

   8. Taylor expanded in y around 0 66.6%

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

      1. associate-*r/ 66.6%

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

      2. neg-mul-1 66.6%

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

   10. Simplified 66.6%

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

   11. Taylor expanded in x around 0 72.9%

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

       1. associate--l+ 72.9%

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

       2. div-sub 72.9%

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

   13. Simplified 72.9%

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

   if -1.55000000000000002e105 < x < 1.25e6

   1. Initial program 76.0%

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

      1. associate-*l/ 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in y around inf 81.0%

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

   if 1.25e6 < x

   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/ 78.2%

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

   3. Simplified 78.2%

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

      1. associate-/r/ 80.8%

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

   5. Applied egg-rr 80.8%

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

   6. Taylor expanded in z around inf 69.2%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \mathbf{elif}\;x \leq 1250000:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 18: 37.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{+116}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.3e+165)
   x
   (if (<= a -1.12e+116)
     (* z (/ y a))
     (if (<= a -5.5e-16)
       x
       (if (<= a -2.15e-291) (/ x (/ t z)) (if (<= a 7e+75) y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.3e+165) {
		tmp = x;
	} else if (a <= -1.12e+116) {
		tmp = z * (y / a);
	} else if (a <= -5.5e-16) {
		tmp = x;
	} else if (a <= -2.15e-291) {
		tmp = x / (t / z);
	} else if (a <= 7e+75) {
		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 <= (-5.3d+165)) then
        tmp = x
    else if (a <= (-1.12d+116)) then
        tmp = z * (y / a)
    else if (a <= (-5.5d-16)) then
        tmp = x
    else if (a <= (-2.15d-291)) then
        tmp = x / (t / z)
    else if (a <= 7d+75) 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 <= -5.3e+165) {
		tmp = x;
	} else if (a <= -1.12e+116) {
		tmp = z * (y / a);
	} else if (a <= -5.5e-16) {
		tmp = x;
	} else if (a <= -2.15e-291) {
		tmp = x / (t / z);
	} else if (a <= 7e+75) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.3e+165:
		tmp = x
	elif a <= -1.12e+116:
		tmp = z * (y / a)
	elif a <= -5.5e-16:
		tmp = x
	elif a <= -2.15e-291:
		tmp = x / (t / z)
	elif a <= 7e+75:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.3e+165)
		tmp = x;
	elseif (a <= -1.12e+116)
		tmp = Float64(z * Float64(y / a));
	elseif (a <= -5.5e-16)
		tmp = x;
	elseif (a <= -2.15e-291)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 7e+75)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.3e+165)
		tmp = x;
	elseif (a <= -1.12e+116)
		tmp = z * (y / a);
	elseif (a <= -5.5e-16)
		tmp = x;
	elseif (a <= -2.15e-291)
		tmp = x / (t / z);
	elseif (a <= 7e+75)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.3e+165], x, If[LessEqual[a, -1.12e+116], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.5e-16], x, If[LessEqual[a, -2.15e-291], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e+75], y, x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.3000000000000001e165 or -1.12e116 < a < -5.49999999999999964e-16 or 6.9999999999999997e75 < a

   1. Initial program 70.1%

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

      1. associate-*l/ 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in a around inf 53.0%

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

   if -5.3000000000000001e165 < a < -1.12e116

   1. Initial program 76.3%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around -inf 43.7%

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

   5. Taylor expanded in y around inf 35.7%

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

      1. associate-/l* 50.9%

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

      2. associate-/r/ 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in a around inf 51.2%

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

   if -5.49999999999999964e-16 < a < -2.15000000000000018e-291

   1. Initial program 71.2%

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

      1. associate-*l/ 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in z around -inf 67.8%

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

      1. associate-/l* 71.2%

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

      2. associate-/r/ 73.6%

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

   6. Applied egg-rr 73.6%

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

   7. Taylor expanded in a around 0 52.5%

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

      1. associate-*r/ 52.5%

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

      2. mul-1-neg 52.5%

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

   9. Simplified 52.5%

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

   10. Taylor expanded in y around 0 34.6%

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

       1. associate-/l* 42.3%

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

   12. Simplified 42.3%

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

   if -2.15000000000000018e-291 < a < 6.9999999999999997e75

   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/ 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in t around inf 51.3%

      \[\leadsto \color{blue}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{+116}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 80.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.1%

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

   1. associate-*l/ 81.9%

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

3. Simplified 81.9%

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

4. Final simplification 81.9%

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

Alternative 20: 50.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.9 \cdot 10^{+99}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+89}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.9e+99) y (if (<= t 4.2e+89) (- x (/ x (/ a z))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.9e+99) {
		tmp = y;
	} else if (t <= 4.2e+89) {
		tmp = x - (x / (a / z));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.9d+99)) then
        tmp = y
    else if (t <= 4.2d+89) then
        tmp = x - (x / (a / z))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.9e+99) {
		tmp = y;
	} else if (t <= 4.2e+89) {
		tmp = x - (x / (a / z));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.9e+99:
		tmp = y
	elif t <= 4.2e+89:
		tmp = x - (x / (a / z))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.9e+99)
		tmp = y;
	elseif (t <= 4.2e+89)
		tmp = Float64(x - Float64(x / Float64(a / z)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.9e+99)
		tmp = y;
	elseif (t <= 4.2e+89)
		tmp = x - (x / (a / z));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.9e+99], y, If[LessEqual[t, 4.2e+89], N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -6.9000000000000001e99 or 4.19999999999999972e89 < t

   1. Initial program 36.5%

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

      1. associate-*l/ 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in t around inf 57.2%

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

   if -6.9000000000000001e99 < t < 4.19999999999999972e89

   1. Initial program 86.8%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

      1. clear-num 91.7%

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

      2. inv-pow 91.7%

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

      3. metadata-eval 91.7%

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

      4. sqr-pow 41.9%

         \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right)} \cdot \left(z - t\right) \]

      5. metadata-eval 41.9%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      6. metadata-eval 41.9%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

      7. metadata-eval 41.9%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)}\right) \cdot \left(z - t\right) \]

      8. metadata-eval 41.9%

         \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}}\right) \cdot \left(z - t\right) \]

   5. Applied egg-rr 41.9%

      \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{-0.5}\right)} \cdot \left(z - t\right) \]
   6. Step-by-step derivation

      1. pow-sqr 91.7%

         \[\leadsto x + \color{blue}{{\left(\frac{a - t}{y - x}\right)}^{\left(2 \cdot -0.5\right)}} \cdot \left(z - t\right) \]

      2. metadata-eval 91.7%

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

      3. unpow-1 91.7%

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

   7. Simplified 91.7%

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

   8. Taylor expanded in y around 0 56.1%

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

      1. associate-*r/ 56.1%

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

      2. neg-mul-1 56.1%

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

   10. Simplified 56.1%

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

   11. Taylor expanded in t around 0 43.7%

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

       1. mul-1-neg 43.7%

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

       2. associate-/l* 50.7%

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

   13. Simplified 50.7%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.9 \cdot 10^{+99}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+89}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 21: 39.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.32 \cdot 10^{+168}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -100000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.32e+168)
   x
   (if (<= a -7e+115)
     (* z (/ y a))
     (if (<= a -100000000000.0) x (if (<= a 2.7e+77) y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.32e+168) {
		tmp = x;
	} else if (a <= -7e+115) {
		tmp = z * (y / a);
	} else if (a <= -100000000000.0) {
		tmp = x;
	} else if (a <= 2.7e+77) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.32d+168)) then
        tmp = x
    else if (a <= (-7d+115)) then
        tmp = z * (y / a)
    else if (a <= (-100000000000.0d0)) then
        tmp = x
    else if (a <= 2.7d+77) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.32e+168) {
		tmp = x;
	} else if (a <= -7e+115) {
		tmp = z * (y / a);
	} else if (a <= -100000000000.0) {
		tmp = x;
	} else if (a <= 2.7e+77) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.32e+168:
		tmp = x
	elif a <= -7e+115:
		tmp = z * (y / a)
	elif a <= -100000000000.0:
		tmp = x
	elif a <= 2.7e+77:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.32e+168)
		tmp = x;
	elseif (a <= -7e+115)
		tmp = Float64(z * Float64(y / a));
	elseif (a <= -100000000000.0)
		tmp = x;
	elseif (a <= 2.7e+77)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.32e+168)
		tmp = x;
	elseif (a <= -7e+115)
		tmp = z * (y / a);
	elseif (a <= -100000000000.0)
		tmp = x;
	elseif (a <= 2.7e+77)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.32e+168], x, If[LessEqual[a, -7e+115], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -100000000000.0], x, If[LessEqual[a, 2.7e+77], y, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.32000000000000007e168 or -7.00000000000000011e115 < a < -1e11 or 2.6999999999999998e77 < a

   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/ 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in a around inf 54.0%

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

   if -1.32000000000000007e168 < a < -7.00000000000000011e115

   1. Initial program 76.3%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around -inf 43.7%

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

   5. Taylor expanded in y around inf 35.7%

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

      1. associate-/l* 50.9%

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

      2. associate-/r/ 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in a around inf 51.2%

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

   if -1e11 < a < 2.6999999999999998e77

   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/ 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in t around inf 37.8%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.32 \cdot 10^{+168}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -100000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22: 40.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -50000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -50000000000.0) x (if (<= a 6e+75) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -50000000000.0) {
		tmp = x;
	} else if (a <= 6e+75) {
		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 <= (-50000000000.0d0)) then
        tmp = x
    else if (a <= 6d+75) 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 <= -50000000000.0) {
		tmp = x;
	} else if (a <= 6e+75) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -50000000000.0:
		tmp = x
	elif a <= 6e+75:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -50000000000.0)
		tmp = x;
	elseif (a <= 6e+75)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -50000000000.0)
		tmp = x;
	elseif (a <= 6e+75)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -50000000000.0], x, If[LessEqual[a, 6e+75], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -5e10 or 6e75 < a

   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/ 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in a around inf 49.5%

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

   if -5e10 < a < 6e75

   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/ 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in t around inf 37.8%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -50000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 69.1%

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

   1. associate-*l/ 81.9%

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

3. Simplified 81.9%

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

   1. clear-num 81.8%

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

   2. inv-pow 81.8%

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

   3. metadata-eval 81.8%

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

   4. sqr-pow 38.6%

      \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right)} \cdot \left(z - t\right) \]

   5. metadata-eval 38.6%

      \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

   6. metadata-eval 38.6%

      \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{-1}{2}\right)}\right) \cdot \left(z - t\right) \]

   7. metadata-eval 38.6%

      \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)}\right) \cdot \left(z - t\right) \]

   8. metadata-eval 38.6%

      \[\leadsto x + \left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{\color{blue}{-0.5}}\right) \cdot \left(z - t\right) \]

5. Applied egg-rr 38.6%

   \[\leadsto x + \color{blue}{\left({\left(\frac{a - t}{y - x}\right)}^{-0.5} \cdot {\left(\frac{a - t}{y - x}\right)}^{-0.5}\right)} \cdot \left(z - t\right) \]
6. Step-by-step derivation

   1. pow-sqr 81.8%

      \[\leadsto x + \color{blue}{{\left(\frac{a - t}{y - x}\right)}^{\left(2 \cdot -0.5\right)}} \cdot \left(z - t\right) \]

   2. metadata-eval 81.8%

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

   3. unpow-1 81.8%

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

7. Simplified 81.8%

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

8. Taylor expanded in y around 0 42.1%

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

   1. associate-*r/ 42.1%

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

   2. neg-mul-1 42.1%

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

10. Simplified 42.1%

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

11. Taylor expanded in t around inf 2.8%

    \[\leadsto \color{blue}{x + -1 \cdot x} \]
12. Step-by-step derivation

    1. distribute-rgt1-in 2.8%

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

    2. metadata-eval 2.8%

       \[\leadsto \color{blue}{0} \cdot x \]

    3. div0 2.8%

       \[\leadsto \color{blue}{\frac{0}{a - t}} \cdot x \]

    4. associate-/r/ 2.7%

       \[\leadsto \color{blue}{\frac{0}{\frac{a - t}{x}}} \]

    5. div0 2.8%

       \[\leadsto \color{blue}{0} \]

13. Simplified 2.8%

    \[\leadsto \color{blue}{0} \]

14. Final simplification 2.8%

    \[\leadsto 0 \]

Alternative 24: 25.5% 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 69.1%

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

   1. associate-*l/ 81.9%

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

3. Simplified 81.9%

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

4. Taylor expanded in a around inf 25.1%

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

5. Final simplification 25.1%

   \[\leadsto x \]

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 2023297 
(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))))