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

Percentage Accurate: 68.7% → 90.8%

Time: 17.6s

Alternatives: 18

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-300}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- z t) (- x y)) (- a t)))))
   (if (<= t_1 -5e-300)
     (+ x (* (- y x) (* (- z t) (/ 1.0 (- a t)))))
     (if (<= t_1 0.0)
       (+ y (/ (* (- z a) (- x y)) t))
       (+ x (* (- y x) (/ (- z t) (- a t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((z - t) * (x - y)) / (a - t));
	double tmp;
	if (t_1 <= -5e-300) {
		tmp = x + ((y - x) * ((z - t) * (1.0 / (a - t))));
	} else if (t_1 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else {
		tmp = x + ((y - x) * ((z - t) / (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) :: t_1
    real(8) :: tmp
    t_1 = x - (((z - t) * (x - y)) / (a - t))
    if (t_1 <= (-5d-300)) then
        tmp = x + ((y - x) * ((z - t) * (1.0d0 / (a - t))))
    else if (t_1 <= 0.0d0) then
        tmp = y + (((z - a) * (x - y)) / t)
    else
        tmp = x + ((y - x) * ((z - t) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((z - t) * (x - y)) / (a - t));
	double tmp;
	if (t_1 <= -5e-300) {
		tmp = x + ((y - x) * ((z - t) * (1.0 / (a - t))));
	} else if (t_1 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((z - t) * (x - y)) / (a - t))
	tmp = 0
	if t_1 <= -5e-300:
		tmp = x + ((y - x) * ((z - t) * (1.0 / (a - t))))
	elif t_1 <= 0.0:
		tmp = y + (((z - a) * (x - y)) / t)
	else:
		tmp = x + ((y - x) * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(z - t) * Float64(x - y)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -5e-300)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) * Float64(1.0 / Float64(a - t)))));
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((z - t) * (x - y)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -5e-300)
		tmp = x + ((y - x) * ((z - t) * (1.0 / (a - t))));
	elseif (t_1 <= 0.0)
		tmp = y + (((z - a) * (x - y)) / t);
	else
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(z - t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-300], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.99999999999999996e-300

   1. Initial program 75.6%

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

      1. associate-/l* 91.6%

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

      2. clear-num 91.5%

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

      3. associate-/r/ 91.6%

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

      4. clear-num 92.0%

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

   3. Applied egg-rr 92.0%

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

      1. div-inv 92.1%

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

   5. Applied egg-rr 92.1%

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

   if -4.99999999999999996e-300 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.6%

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

      1. associate-*l/ 4.5%

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

   3. Simplified 4.5%

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

   4. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. div-sub 99.9%

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

      5. distribute-lft-out-- 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-neg-frac 99.9%

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

      8. unsub-neg 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   6. Simplified 99.9%

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

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

   1. Initial program 63.9%

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

      1. associate-/l* 90.5%

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

      2. clear-num 90.4%

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

      3. associate-/r/ 90.5%

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

      4. clear-num 90.5%

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

   3. Applied egg-rr 90.5%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t} \leq -5 \cdot 10^{-300}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \mathbf{elif}\;x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 2: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-300} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- z t) (- x y)) (- a t)))))
   (if (or (<= t_1 -5e-300) (not (<= t_1 0.0)))
     (+ x (* (- y x) (/ (- z t) (- a t))))
     (+ y (/ (* (- z a) (- x y)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((z - t) * (x - y)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-300) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else {
		tmp = y + (((z - a) * (x - y)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((z - t) * (x - y)) / (a - t))
    if ((t_1 <= (-5d-300)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) * ((z - t) / (a - t)))
    else
        tmp = y + (((z - a) * (x - y)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((z - t) * (x - y)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-300) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else {
		tmp = y + (((z - a) * (x - y)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((z - t) * (x - y)) / (a - t))
	tmp = 0
	if (t_1 <= -5e-300) or not (t_1 <= 0.0):
		tmp = x + ((y - x) * ((z - t) / (a - t)))
	else:
		tmp = y + (((z - a) * (x - y)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(z - t) * Float64(x - y)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -5e-300) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((z - t) * (x - y)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -5e-300) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	else
		tmp = y + (((z - a) * (x - y)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(z - t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-300], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.99999999999999996e-300 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 69.6%

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

      1. associate-/l* 91.0%

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

      2. clear-num 90.9%

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

      3. associate-/r/ 91.0%

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

      4. clear-num 91.2%

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

   3. Applied egg-rr 91.2%

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

   if -4.99999999999999996e-300 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.6%

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

      1. associate-*l/ 4.5%

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

   3. Simplified 4.5%

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

   4. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. div-sub 99.9%

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

      5. distribute-lft-out-- 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-neg-frac 99.9%

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

      8. unsub-neg 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t} \leq -5 \cdot 10^{-300} \lor \neg \left(x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \end{array} \]

Alternative 3: 40.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{t - a}\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-253}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-237}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.45 \cdot 10^{-7}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 10^{+35}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t (- t a)))))
   (if (<= t -7.2e+78)
     t_1
     (if (<= t 8.5e-253)
       x
       (if (<= t 1.15e-237)
         (/ y (/ a z))
         (if (<= t 5.5e-94)
           x
           (if (<= t 4.45e-7)
             (* (- z t) (/ y a))
             (if (<= t 1e+35) (* z (/ x t)) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (t - a));
	double tmp;
	if (t <= -7.2e+78) {
		tmp = t_1;
	} else if (t <= 8.5e-253) {
		tmp = x;
	} else if (t <= 1.15e-237) {
		tmp = y / (a / z);
	} else if (t <= 5.5e-94) {
		tmp = x;
	} else if (t <= 4.45e-7) {
		tmp = (z - t) * (y / a);
	} else if (t <= 1e+35) {
		tmp = z * (x / 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 = y * (t / (t - a))
    if (t <= (-7.2d+78)) then
        tmp = t_1
    else if (t <= 8.5d-253) then
        tmp = x
    else if (t <= 1.15d-237) then
        tmp = y / (a / z)
    else if (t <= 5.5d-94) then
        tmp = x
    else if (t <= 4.45d-7) then
        tmp = (z - t) * (y / a)
    else if (t <= 1d+35) then
        tmp = z * (x / 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 = y * (t / (t - a));
	double tmp;
	if (t <= -7.2e+78) {
		tmp = t_1;
	} else if (t <= 8.5e-253) {
		tmp = x;
	} else if (t <= 1.15e-237) {
		tmp = y / (a / z);
	} else if (t <= 5.5e-94) {
		tmp = x;
	} else if (t <= 4.45e-7) {
		tmp = (z - t) * (y / a);
	} else if (t <= 1e+35) {
		tmp = z * (x / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / (t - a))
	tmp = 0
	if t <= -7.2e+78:
		tmp = t_1
	elif t <= 8.5e-253:
		tmp = x
	elif t <= 1.15e-237:
		tmp = y / (a / z)
	elif t <= 5.5e-94:
		tmp = x
	elif t <= 4.45e-7:
		tmp = (z - t) * (y / a)
	elif t <= 1e+35:
		tmp = z * (x / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / Float64(t - a)))
	tmp = 0.0
	if (t <= -7.2e+78)
		tmp = t_1;
	elseif (t <= 8.5e-253)
		tmp = x;
	elseif (t <= 1.15e-237)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 5.5e-94)
		tmp = x;
	elseif (t <= 4.45e-7)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	elseif (t <= 1e+35)
		tmp = Float64(z * Float64(x / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / (t - a));
	tmp = 0.0;
	if (t <= -7.2e+78)
		tmp = t_1;
	elseif (t <= 8.5e-253)
		tmp = x;
	elseif (t <= 1.15e-237)
		tmp = y / (a / z);
	elseif (t <= 5.5e-94)
		tmp = x;
	elseif (t <= 4.45e-7)
		tmp = (z - t) * (y / a);
	elseif (t <= 1e+35)
		tmp = z * (x / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+78], t$95$1, If[LessEqual[t, 8.5e-253], x, If[LessEqual[t, 1.15e-237], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-94], x, If[LessEqual[t, 4.45e-7], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+35], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.20000000000000039e78 or 9.9999999999999997e34 < t

   1. Initial program 34.5%

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

      1. associate-/l* 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in z around 0 59.2%

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

      1. associate-*r/ 59.2%

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

      2. neg-mul-1 59.2%

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

   6. Simplified 59.2%

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

   7. Taylor expanded in x around 0 41.5%

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

      1. associate-/l* 57.9%

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

   9. Simplified 57.9%

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

       1. associate-/r/ 69.9%

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

   11. Applied egg-rr 69.9%

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

   if -7.20000000000000039e78 < t < 8.4999999999999999e-253 or 1.15000000000000006e-237 < t < 5.49999999999999989e-94

   1. Initial program 84.8%

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

      1. associate-*l/ 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 a around inf 42.6%

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

   if 8.4999999999999999e-253 < t < 1.15000000000000006e-237

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 81.5%

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

   5. Taylor expanded in a around inf 81.5%

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

   6. Taylor expanded in z around inf 81.5%

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

      1. associate-/l* 100.0%

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

   8. Simplified 100.0%

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

   if 5.49999999999999989e-94 < t < 4.45e-7

   1. Initial program 70.2%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in x around 0 41.1%

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

   5. Taylor expanded in a around inf 35.1%

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

      1. expm1-log1p-u 21.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)} \]

      2. expm1-udef 10.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a}\right)} - 1} \]

      3. *-commutative 10.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\left(z - t\right) \cdot y}}{a}\right)} - 1 \]

   7. Applied egg-rr 10.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\left(z - t\right) \cdot y}{a}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 21.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\left(z - t\right) \cdot y}{a}\right)\right)} \]

      2. expm1-log1p 35.1%

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

      3. associate-*r/ 47.0%

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

   9. Simplified 47.0%

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

   if 4.45e-7 < t < 9.9999999999999997e34

   1. Initial program 87.1%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around -inf 51.3%

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

   5. Taylor expanded in a around 0 40.8%

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

      1. associate-*r/ 40.8%

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

      2. neg-mul-1 40.8%

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

      3. *-commutative 40.8%

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

      4. distribute-rgt-neg-in 40.8%

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

   7. Simplified 40.8%

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

   8. Taylor expanded in y around 0 40.0%

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

      1. associate-/l* 40.2%

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

      2. associate-/r/ 40.2%

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

   10. Simplified 40.2%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+78}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-253}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-237}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.45 \cdot 10^{-7}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 10^{+35}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \end{array} \]

Alternative 4: 41.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a}\\ t_2 := y \cdot \frac{t}{t - a}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-161}:\\ \;\;\;\;x + \frac{t}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 6.75 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ y a))) (t_2 (* y (/ t (- t a)))))
   (if (<= t -2.9e+77)
     t_2
     (if (<= t 2.05e-161)
       (+ x (/ t (/ a x)))
       (if (<= t 6.75e-122)
         t_1
         (if (<= t 3.8e-94)
           x
           (if (<= t 1.7e-6) t_1 (if (<= t 4e+32) (* z (/ x t)) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / a);
	double t_2 = y * (t / (t - a));
	double tmp;
	if (t <= -2.9e+77) {
		tmp = t_2;
	} else if (t <= 2.05e-161) {
		tmp = x + (t / (a / x));
	} else if (t <= 6.75e-122) {
		tmp = t_1;
	} else if (t <= 3.8e-94) {
		tmp = x;
	} else if (t <= 1.7e-6) {
		tmp = t_1;
	} else if (t <= 4e+32) {
		tmp = z * (x / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z - t) * (y / a)
    t_2 = y * (t / (t - a))
    if (t <= (-2.9d+77)) then
        tmp = t_2
    else if (t <= 2.05d-161) then
        tmp = x + (t / (a / x))
    else if (t <= 6.75d-122) then
        tmp = t_1
    else if (t <= 3.8d-94) then
        tmp = x
    else if (t <= 1.7d-6) then
        tmp = t_1
    else if (t <= 4d+32) then
        tmp = z * (x / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / a);
	double t_2 = y * (t / (t - a));
	double tmp;
	if (t <= -2.9e+77) {
		tmp = t_2;
	} else if (t <= 2.05e-161) {
		tmp = x + (t / (a / x));
	} else if (t <= 6.75e-122) {
		tmp = t_1;
	} else if (t <= 3.8e-94) {
		tmp = x;
	} else if (t <= 1.7e-6) {
		tmp = t_1;
	} else if (t <= 4e+32) {
		tmp = z * (x / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * (y / a)
	t_2 = y * (t / (t - a))
	tmp = 0
	if t <= -2.9e+77:
		tmp = t_2
	elif t <= 2.05e-161:
		tmp = x + (t / (a / x))
	elif t <= 6.75e-122:
		tmp = t_1
	elif t <= 3.8e-94:
		tmp = x
	elif t <= 1.7e-6:
		tmp = t_1
	elif t <= 4e+32:
		tmp = z * (x / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * Float64(y / a))
	t_2 = Float64(y * Float64(t / Float64(t - a)))
	tmp = 0.0
	if (t <= -2.9e+77)
		tmp = t_2;
	elseif (t <= 2.05e-161)
		tmp = Float64(x + Float64(t / Float64(a / x)));
	elseif (t <= 6.75e-122)
		tmp = t_1;
	elseif (t <= 3.8e-94)
		tmp = x;
	elseif (t <= 1.7e-6)
		tmp = t_1;
	elseif (t <= 4e+32)
		tmp = Float64(z * Float64(x / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * (y / a);
	t_2 = y * (t / (t - a));
	tmp = 0.0;
	if (t <= -2.9e+77)
		tmp = t_2;
	elseif (t <= 2.05e-161)
		tmp = x + (t / (a / x));
	elseif (t <= 6.75e-122)
		tmp = t_1;
	elseif (t <= 3.8e-94)
		tmp = x;
	elseif (t <= 1.7e-6)
		tmp = t_1;
	elseif (t <= 4e+32)
		tmp = z * (x / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+77], t$95$2, If[LessEqual[t, 2.05e-161], N[(x + N[(t / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.75e-122], t$95$1, If[LessEqual[t, 3.8e-94], x, If[LessEqual[t, 1.7e-6], t$95$1, If[LessEqual[t, 4e+32], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.9000000000000002e77 or 4.00000000000000021e32 < t

   1. Initial program 34.5%

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

      1. associate-/l* 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in z around 0 59.2%

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

      1. associate-*r/ 59.2%

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

      2. neg-mul-1 59.2%

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

   6. Simplified 59.2%

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

   7. Taylor expanded in x around 0 41.5%

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

      1. associate-/l* 57.9%

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

   9. Simplified 57.9%

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

       1. associate-/r/ 69.9%

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

   11. Applied egg-rr 69.9%

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

   if -2.9000000000000002e77 < t < 2.0499999999999999e-161

   1. Initial program 86.0%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in z around 0 46.2%

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

      1. associate-*r/ 46.2%

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

      2. neg-mul-1 46.2%

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

   6. Simplified 46.2%

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

   7. Taylor expanded in a around inf 44.6%

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

      1. mul-1-neg 44.6%

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

      2. unsub-neg 44.6%

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

      3. associate-/l* 50.2%

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

   9. Simplified 50.2%

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

   10. Taylor expanded in y around 0 40.6%

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

       1. sub-neg 40.6%

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

       2. mul-1-neg 40.6%

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

       3. remove-double-neg 40.6%

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

       4. associate-/l* 44.7%

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

   12. Simplified 44.7%

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

   if 2.0499999999999999e-161 < t < 6.7500000000000005e-122 or 3.79999999999999999e-94 < t < 1.70000000000000003e-6

   1. Initial program 77.0%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in x around 0 50.6%

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

   5. Taylor expanded in a around inf 39.0%

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

      1. expm1-log1p-u 25.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)} \]

      2. expm1-udef 14.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a}\right)} - 1} \]

      3. *-commutative 14.1%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\left(z - t\right) \cdot y}}{a}\right)} - 1 \]

   7. Applied egg-rr 14.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\left(z - t\right) \cdot y}{a}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 25.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\left(z - t\right) \cdot y}{a}\right)\right)} \]

      2. expm1-log1p 39.0%

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

      3. associate-*r/ 50.4%

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

   9. Simplified 50.4%

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

   if 6.7500000000000005e-122 < t < 3.79999999999999999e-94

   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/ 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in a around inf 84.0%

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

   if 1.70000000000000003e-6 < t < 4.00000000000000021e32

   1. Initial program 87.1%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around -inf 51.3%

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

   5. Taylor expanded in a around 0 40.8%

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

      1. associate-*r/ 40.8%

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

      2. neg-mul-1 40.8%

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

      3. *-commutative 40.8%

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

      4. distribute-rgt-neg-in 40.8%

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

   7. Simplified 40.8%

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

   8. Taylor expanded in y around 0 40.0%

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

      1. associate-/l* 40.2%

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

      2. associate-/r/ 40.2%

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

   10. Simplified 40.2%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-161}:\\ \;\;\;\;x + \frac{t}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 6.75 \cdot 10^{-122}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-6}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \end{array} \]

Alternative 5: 80.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+152}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{+38}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.25e+152)
   (/ y (/ (- a t) (- z t)))
   (if (<= t 1.56e+38)
     (+ x (* (- z t) (/ (- y x) (- a t))))
     (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e+152) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 1.56e+38) {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.25d+152)) then
        tmp = y / ((a - t) / (z - t))
    else if (t <= 1.56d+38) then
        tmp = x + ((z - t) * ((y - x) / (a - t)))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e+152) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 1.56e+38) {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.25e+152:
		tmp = y / ((a - t) / (z - t))
	elif t <= 1.56e+38:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.25e+152)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (t <= 1.56e+38)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.25e+152)
		tmp = y / ((a - t) / (z - t));
	elseif (t <= 1.56e+38)
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.25e+152], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.56e+38], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25e152

   1. Initial program 22.3%

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

      1. associate-/l* 56.2%

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

      2. clear-num 56.1%

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

      3. associate-/r/ 56.2%

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

      4. clear-num 56.1%

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

   3. Applied egg-rr 56.1%

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

   4. Taylor expanded in x around 0 46.5%

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

      1. associate-/l* 76.2%

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

   6. Simplified 76.2%

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

   if -1.25e152 < t < 1.5599999999999999e38

   1. Initial program 80.7%

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

      1. associate-*l/ 90.1%

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

   3. Simplified 90.1%

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

   if 1.5599999999999999e38 < t

   1. Initial program 33.5%

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

      1. associate-/l* 70.6%

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

      2. clear-num 70.3%

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

      3. associate-/r/ 70.6%

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

      4. clear-num 70.6%

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

   3. Applied egg-rr 70.6%

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

   4. Taylor expanded in y around inf 80.7%

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

      1. div-sub 80.7%

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

   6. Simplified 80.7%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+152}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{+38}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 6: 38.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+97}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+233}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+241}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e+65)
   x
   (if (<= a 1.12e+97)
     y
     (if (<= a 7.5e+233) x (if (<= a 6e+241) (* (- z t) (/ y a)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+65) {
		tmp = x;
	} else if (a <= 1.12e+97) {
		tmp = y;
	} else if (a <= 7.5e+233) {
		tmp = x;
	} else if (a <= 6e+241) {
		tmp = (z - t) * (y / a);
	} 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 <= (-1.2d+65)) then
        tmp = x
    else if (a <= 1.12d+97) then
        tmp = y
    else if (a <= 7.5d+233) then
        tmp = x
    else if (a <= 6d+241) then
        tmp = (z - t) * (y / a)
    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 <= -1.2e+65) {
		tmp = x;
	} else if (a <= 1.12e+97) {
		tmp = y;
	} else if (a <= 7.5e+233) {
		tmp = x;
	} else if (a <= 6e+241) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e+65:
		tmp = x
	elif a <= 1.12e+97:
		tmp = y
	elif a <= 7.5e+233:
		tmp = x
	elif a <= 6e+241:
		tmp = (z - t) * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e+65)
		tmp = x;
	elseif (a <= 1.12e+97)
		tmp = y;
	elseif (a <= 7.5e+233)
		tmp = x;
	elseif (a <= 6e+241)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.2e+65)
		tmp = x;
	elseif (a <= 1.12e+97)
		tmp = y;
	elseif (a <= 7.5e+233)
		tmp = x;
	elseif (a <= 6e+241)
		tmp = (z - t) * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e+65], x, If[LessEqual[a, 1.12e+97], y, If[LessEqual[a, 7.5e+233], x, If[LessEqual[a, 6e+241], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2000000000000001e65 or 1.12e97 < a < 7.4999999999999997e233 or 6.00000000000000031e241 < a

   1. Initial program 64.7%

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

      1. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in a around inf 60.6%

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

   if -1.2000000000000001e65 < a < 1.12e97

   1. Initial program 64.9%

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

      1. associate-*l/ 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in t around inf 41.8%

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

   if 7.4999999999999997e233 < a < 6.00000000000000031e241

   1. Initial program 23.9%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around 0 23.9%

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

   5. Taylor expanded in a around inf 23.9%

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

      1. expm1-log1p-u 2.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)} \]

      2. expm1-udef 2.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a}\right)} - 1} \]

      3. *-commutative 2.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\left(z - t\right) \cdot y}}{a}\right)} - 1 \]

   7. Applied egg-rr 2.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\left(z - t\right) \cdot y}{a}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 2.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\left(z - t\right) \cdot y}{a}\right)\right)} \]

      2. expm1-log1p 23.9%

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

      3. associate-*r/ 98.4%

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

   9. Simplified 98.4%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+97}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+233}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+241}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 43.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 10^{-166}:\\ \;\;\;\;y + y \cdot \frac{a}{t}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-153}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+44}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ t (/ a y)))))
   (if (<= a -9.5e+58)
     t_1
     (if (<= a 1e-166)
       (+ y (* y (/ a t)))
       (if (<= a 2.4e-153)
         (/ y (/ (- a t) z))
         (if (<= a 6e+44) (+ y (/ a (/ t y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / (a / y));
	double tmp;
	if (a <= -9.5e+58) {
		tmp = t_1;
	} else if (a <= 1e-166) {
		tmp = y + (y * (a / t));
	} else if (a <= 2.4e-153) {
		tmp = y / ((a - t) / z);
	} else if (a <= 6e+44) {
		tmp = y + (a / (t / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (t / (a / y))
    if (a <= (-9.5d+58)) then
        tmp = t_1
    else if (a <= 1d-166) then
        tmp = y + (y * (a / t))
    else if (a <= 2.4d-153) then
        tmp = y / ((a - t) / z)
    else if (a <= 6d+44) then
        tmp = y + (a / (t / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / (a / y));
	double tmp;
	if (a <= -9.5e+58) {
		tmp = t_1;
	} else if (a <= 1e-166) {
		tmp = y + (y * (a / t));
	} else if (a <= 2.4e-153) {
		tmp = y / ((a - t) / z);
	} else if (a <= 6e+44) {
		tmp = y + (a / (t / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t / (a / y))
	tmp = 0
	if a <= -9.5e+58:
		tmp = t_1
	elif a <= 1e-166:
		tmp = y + (y * (a / t))
	elif a <= 2.4e-153:
		tmp = y / ((a - t) / z)
	elif a <= 6e+44:
		tmp = y + (a / (t / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t / Float64(a / y)))
	tmp = 0.0
	if (a <= -9.5e+58)
		tmp = t_1;
	elseif (a <= 1e-166)
		tmp = Float64(y + Float64(y * Float64(a / t)));
	elseif (a <= 2.4e-153)
		tmp = Float64(y / Float64(Float64(a - t) / z));
	elseif (a <= 6e+44)
		tmp = Float64(y + Float64(a / Float64(t / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t / (a / y));
	tmp = 0.0;
	if (a <= -9.5e+58)
		tmp = t_1;
	elseif (a <= 1e-166)
		tmp = y + (y * (a / t));
	elseif (a <= 2.4e-153)
		tmp = y / ((a - t) / z);
	elseif (a <= 6e+44)
		tmp = y + (a / (t / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.5e+58], t$95$1, If[LessEqual[a, 1e-166], N[(y + N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e-153], N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+44], N[(y + N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.5000000000000002e58 or 5.99999999999999974e44 < a

   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* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around 0 74.0%

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

      1. associate-*r/ 74.0%

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

      2. neg-mul-1 74.0%

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

   6. Simplified 74.0%

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

   7. Taylor expanded in a around inf 55.5%

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

      1. mul-1-neg 55.5%

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

      2. unsub-neg 55.5%

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

      3. associate-/l* 65.7%

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

   9. Simplified 65.7%

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

   10. Taylor expanded in y around inf 58.9%

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

       1. associate-/l* 65.6%

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

   12. Simplified 65.6%

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

   if -9.5000000000000002e58 < a < 1.00000000000000004e-166

   1. Initial program 60.3%

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

      1. associate-/l* 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in z around 0 31.5%

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

      1. associate-*r/ 31.5%

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

      2. neg-mul-1 31.5%

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

   6. Simplified 31.5%

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

   7. Taylor expanded in a around 0 51.3%

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

      1. associate-/l* 51.0%

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

   9. Simplified 51.0%

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

   10. Taylor expanded in y around inf 46.0%

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

       1. distribute-lft-in 46.0%

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

       2. *-rgt-identity 46.0%

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

   12. Simplified 46.0%

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

   if 1.00000000000000004e-166 < a < 2.4000000000000002e-153

   1. Initial program 99.7%

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

      1. associate-*l/ 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in x around 0 81.2%

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

   5. Taylor expanded in z around inf 66.7%

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

      1. associate-/l* 84.8%

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

   7. Simplified 84.8%

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

   if 2.4000000000000002e-153 < a < 5.99999999999999974e44

   1. Initial program 68.9%

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

      1. associate-/l* 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in z around 0 45.0%

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

      1. associate-*r/ 45.0%

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

      2. neg-mul-1 45.0%

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

   6. Simplified 45.0%

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

   7. Taylor expanded in x around 0 25.6%

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

      1. associate-/l* 46.9%

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

   9. Simplified 46.9%

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

   10. Taylor expanded in t around inf 47.4%

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

       1. associate-/l* 52.4%

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

   12. Simplified 52.4%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+58}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 10^{-166}:\\ \;\;\;\;y + y \cdot \frac{a}{t}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-153}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+44}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 45.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{a}{\frac{t}{x}}\\ t_2 := x - \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ a (/ t x)))) (t_2 (- x (/ t (/ a y)))))
   (if (<= a -9.5e+58)
     t_2
     (if (<= a 4.5e-166)
       t_1
       (if (<= a 2.1e-156)
         (/ y (/ (- a t) z))
         (if (<= a 5.8e+134) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (a / (t / x));
	double t_2 = x - (t / (a / y));
	double tmp;
	if (a <= -9.5e+58) {
		tmp = t_2;
	} else if (a <= 4.5e-166) {
		tmp = t_1;
	} else if (a <= 2.1e-156) {
		tmp = y / ((a - t) / z);
	} else if (a <= 5.8e+134) {
		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 - (a / (t / x))
    t_2 = x - (t / (a / y))
    if (a <= (-9.5d+58)) then
        tmp = t_2
    else if (a <= 4.5d-166) then
        tmp = t_1
    else if (a <= 2.1d-156) then
        tmp = y / ((a - t) / z)
    else if (a <= 5.8d+134) 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 - (a / (t / x));
	double t_2 = x - (t / (a / y));
	double tmp;
	if (a <= -9.5e+58) {
		tmp = t_2;
	} else if (a <= 4.5e-166) {
		tmp = t_1;
	} else if (a <= 2.1e-156) {
		tmp = y / ((a - t) / z);
	} else if (a <= 5.8e+134) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (a / (t / x))
	t_2 = x - (t / (a / y))
	tmp = 0
	if a <= -9.5e+58:
		tmp = t_2
	elif a <= 4.5e-166:
		tmp = t_1
	elif a <= 2.1e-156:
		tmp = y / ((a - t) / z)
	elif a <= 5.8e+134:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(a / Float64(t / x)))
	t_2 = Float64(x - Float64(t / Float64(a / y)))
	tmp = 0.0
	if (a <= -9.5e+58)
		tmp = t_2;
	elseif (a <= 4.5e-166)
		tmp = t_1;
	elseif (a <= 2.1e-156)
		tmp = Float64(y / Float64(Float64(a - t) / z));
	elseif (a <= 5.8e+134)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (a / (t / x));
	t_2 = x - (t / (a / y));
	tmp = 0.0;
	if (a <= -9.5e+58)
		tmp = t_2;
	elseif (a <= 4.5e-166)
		tmp = t_1;
	elseif (a <= 2.1e-156)
		tmp = y / ((a - t) / z);
	elseif (a <= 5.8e+134)
		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[(a / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.5e+58], t$95$2, If[LessEqual[a, 4.5e-166], t$95$1, If[LessEqual[a, 2.1e-156], N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e+134], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.5000000000000002e58 or 5.80000000000000023e134 < a

   1. Initial program 63.6%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in z around 0 79.3%

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

      1. associate-*r/ 79.3%

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

      2. neg-mul-1 79.3%

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

   6. Simplified 79.3%

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

   7. Taylor expanded in a around inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. unsub-neg 62.0%

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

      3. associate-/l* 73.6%

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

   9. Simplified 73.6%

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

   10. Taylor expanded in y around inf 66.2%

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

       1. associate-/l* 73.5%

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

   12. Simplified 73.5%

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

   if -9.5000000000000002e58 < a < 4.4999999999999998e-166 or 2.10000000000000012e-156 < a < 5.80000000000000023e134

   1. Initial program 63.1%

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

      1. associate-/l* 78.2%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in z around 0 37.7%

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

      1. associate-*r/ 37.7%

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

      2. neg-mul-1 37.7%

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

   6. Simplified 37.7%

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

   7. Taylor expanded in a around 0 47.0%

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

      1. associate-/l* 49.8%

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

   9. Simplified 49.8%

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

   10. Taylor expanded in y around 0 47.4%

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

       1. mul-1-neg 47.4%

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

       2. associate-/l* 48.0%

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

       3. distribute-neg-frac 48.0%

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

   12. Simplified 48.0%

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

   if 4.4999999999999998e-166 < a < 2.10000000000000012e-156

   1. Initial program 99.7%

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

      1. associate-*l/ 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in x around 0 81.2%

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

   5. Taylor expanded in z around inf 66.7%

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

      1. associate-/l* 84.8%

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

   7. Simplified 84.8%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+58}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-166}:\\ \;\;\;\;y - \frac{a}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+134}:\\ \;\;\;\;y - \frac{a}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 9: 69.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-24} \lor \neg \left(a \leq 8.8 \cdot 10^{-38}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.9e-24) (not (<= a 8.8e-38)))
   (+ x (* (- z t) (/ y (- a t))))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.9e-24) || !(a <= 8.8e-38)) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.9d-24)) .or. (.not. (a <= 8.8d-38))) then
        tmp = x + ((z - t) * (y / (a - t)))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.9e-24) || !(a <= 8.8e-38)) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.9e-24) or not (a <= 8.8e-38):
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.9e-24) || !(a <= 8.8e-38))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.9e-24) || ~((a <= 8.8e-38)))
		tmp = x + ((z - t) * (y / (a - t)));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.9e-24], N[Not[LessEqual[a, 8.8e-38]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8999999999999999e-24 or 8.80000000000000029e-38 < a

   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/ 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. Taylor expanded in y around inf 84.7%

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

   if -2.8999999999999999e-24 < a < 8.80000000000000029e-38

   1. Initial program 62.5%

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

      1. associate-/l* 72.9%

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

      2. clear-num 72.7%

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

      3. associate-/r/ 72.9%

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

      4. clear-num 72.9%

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

   3. Applied egg-rr 72.9%

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

   4. Taylor expanded in y around inf 74.2%

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

      1. div-sub 74.2%

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

   6. Simplified 74.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-24} \lor \neg \left(a \leq 8.8 \cdot 10^{-38}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 10: 74.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e+79)
   (/ y (/ (- a t) (- z t)))
   (if (<= t 1.5e+38)
     (+ x (/ (- y x) (/ (- a t) z)))
     (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+79) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 1.5e+38) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.7d+79)) then
        tmp = y / ((a - t) / (z - t))
    else if (t <= 1.5d+38) then
        tmp = x + ((y - x) / ((a - t) / z))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+79) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 1.5e+38) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e+79:
		tmp = y / ((a - t) / (z - t))
	elif t <= 1.5e+38:
		tmp = x + ((y - x) / ((a - t) / z))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e+79)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (t <= 1.5e+38)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / z)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7e+79)
		tmp = y / ((a - t) / (z - t));
	elseif (t <= 1.5e+38)
		tmp = x + ((y - x) / ((a - t) / z));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e+79], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+38], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7e79

   1. Initial program 35.7%

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

      1. associate-/l* 67.8%

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

      2. clear-num 67.7%

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

      3. associate-/r/ 67.8%

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

      4. clear-num 67.8%

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

   3. Applied egg-rr 67.8%

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

   4. Taylor expanded in x around 0 47.3%

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

      1. associate-/l* 74.9%

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

   6. Simplified 74.9%

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

   if -2.7e79 < t < 1.5000000000000001e38

   1. Initial program 83.9%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around inf 83.8%

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

   if 1.5000000000000001e38 < t

   1. Initial program 33.5%

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

      1. associate-/l* 70.6%

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

      2. clear-num 70.3%

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

      3. associate-/r/ 70.6%

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

      4. clear-num 70.6%

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

   3. Applied egg-rr 70.6%

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

   4. Taylor expanded in y around inf 80.7%

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

      1. div-sub 80.7%

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

   6. Simplified 80.7%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 11: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+107} \lor \neg \left(a \leq 1.05 \cdot 10^{+156}\right):\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.5e+107) (not (<= a 1.05e+156)))
   (- x (/ t (/ a y)))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.5e+107) || !(a <= 1.05e+156)) {
		tmp = x - (t / (a / y));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.5d+107)) .or. (.not. (a <= 1.05d+156))) then
        tmp = x - (t / (a / y))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.5e+107) || !(a <= 1.05e+156)) {
		tmp = x - (t / (a / y));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.5e+107) or not (a <= 1.05e+156):
		tmp = x - (t / (a / y))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.5e+107) || !(a <= 1.05e+156))
		tmp = Float64(x - Float64(t / Float64(a / y)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.5e+107) || ~((a <= 1.05e+156)))
		tmp = x - (t / (a / y));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.5e+107], N[Not[LessEqual[a, 1.05e+156]], $MachinePrecision]], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.5e107 or 1.04999999999999991e156 < a

   1. Initial program 63.6%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in z around 0 81.8%

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

      1. associate-*r/ 81.8%

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

      2. neg-mul-1 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in a around inf 63.1%

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

      1. mul-1-neg 63.1%

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

      2. unsub-neg 63.1%

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

      3. associate-/l* 75.9%

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

   9. Simplified 75.9%

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

   10. Taylor expanded in y around inf 67.8%

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

       1. associate-/l* 75.8%

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

   12. Simplified 75.8%

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

   if -4.5e107 < a < 1.04999999999999991e156

   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* 78.8%

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

      2. clear-num 78.7%

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

      3. associate-/r/ 78.8%

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

      4. clear-num 78.8%

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

   3. Applied egg-rr 78.8%

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

   4. Taylor expanded in y around inf 69.1%

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

      1. div-sub 69.1%

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

   6. Simplified 69.1%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+107} \lor \neg \left(a \leq 1.05 \cdot 10^{+156}\right):\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 12: 66.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+30} \lor \neg \left(t \leq 3.2 \cdot 10^{+34}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.9e+30) (not (<= t 3.2e+34)))
   (* y (/ (- z t) (- a t)))
   (+ x (/ z (/ a (- y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.9e+30) || !(t <= 3.2e+34)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.9d+30)) .or. (.not. (t <= 3.2d+34))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (z / (a / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.9e+30) || !(t <= 3.2e+34)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.9e+30) or not (t <= 3.2e+34):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (z / (a / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.9e+30) || !(t <= 3.2e+34))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.9e+30) || ~((t <= 3.2e+34)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (z / (a / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.9e+30], N[Not[LessEqual[t, 3.2e+34]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8999999999999998e30 or 3.1999999999999998e34 < t

   1. Initial program 37.7%

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

      1. associate-/l* 70.3%

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

      2. clear-num 70.1%

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

      3. associate-/r/ 70.3%

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

      4. clear-num 70.3%

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

   3. Applied egg-rr 70.3%

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

   4. Taylor expanded in y around inf 76.7%

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

      1. div-sub 76.7%

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

   6. Simplified 76.7%

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

   if -2.8999999999999998e30 < t < 3.1999999999999998e34

   1. Initial program 84.8%

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

      1. associate-/l* 94.1%

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

      2. clear-num 94.1%

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

      3. associate-/r/ 94.1%

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

      4. clear-num 94.4%

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

   3. Applied egg-rr 94.4%

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

   4. Taylor expanded in t around 0 65.2%

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

      1. associate-/l* 73.7%

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

   6. Simplified 73.7%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+30} \lor \neg \left(t \leq 3.2 \cdot 10^{+34}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]

Alternative 13: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+28} \lor \neg \left(t \leq 9.2 \cdot 10^{+30}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.5e+28) (not (<= t 9.2e+30)))
   (* 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 ((t <= -9.5e+28) || !(t <= 9.2e+30)) {
		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 ((t <= (-9.5d+28)) .or. (.not. (t <= 9.2d+30))) 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 ((t <= -9.5e+28) || !(t <= 9.2e+30)) {
		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 (t <= -9.5e+28) or not (t <= 9.2e+30):
		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 ((t <= -9.5e+28) || !(t <= 9.2e+30))
		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 ((t <= -9.5e+28) || ~((t <= 9.2e+30)))
		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[Or[LessEqual[t, -9.5e+28], N[Not[LessEqual[t, 9.2e+30]], $MachinePrecision]], 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 2 regimes

2. if t < -9.49999999999999927e28 or 9.2e30 < t

   1. Initial program 37.7%

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

      1. associate-/l* 70.3%

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

      2. clear-num 70.1%

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

      3. associate-/r/ 70.3%

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

      4. clear-num 70.3%

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

   3. Applied egg-rr 70.3%

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

   4. Taylor expanded in y around inf 76.7%

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

      1. div-sub 76.7%

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

   6. Simplified 76.7%

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

   if -9.49999999999999927e28 < t < 9.2e30

   1. Initial program 84.8%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in t around 0 74.5%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+28} \lor \neg \left(t \leq 9.2 \cdot 10^{+30}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 14: 67.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.8e+29)
   (* y (/ (- z t) (- a t)))
   (if (<= t 5.5e-18) (+ x (/ (- y x) (/ a z))) (/ y (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+29) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 5.5e-18) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = y / ((a - t) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.8d+29)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= 5.5d-18) then
        tmp = x + ((y - x) / (a / z))
    else
        tmp = y / ((a - t) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+29) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 5.5e-18) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = y / ((a - t) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.8e+29:
		tmp = y * ((z - t) / (a - t))
	elif t <= 5.5e-18:
		tmp = x + ((y - x) / (a / z))
	else:
		tmp = y / ((a - t) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.8e+29)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= 5.5e-18)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	else
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.8e+29)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= 5.5e-18)
		tmp = x + ((y - x) / (a / z));
	else
		tmp = y / ((a - t) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.8e+29], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-18], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.79999999999999971e29

   1. Initial program 41.9%

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

      1. associate-/l* 70.1%

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

      2. clear-num 70.0%

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

      3. associate-/r/ 70.0%

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

      4. clear-num 70.1%

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

   3. Applied egg-rr 70.1%

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

   4. Taylor expanded in y around inf 72.7%

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

      1. div-sub 72.7%

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

   6. Simplified 72.7%

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

   if -3.79999999999999971e29 < t < 5.5e-18

   1. Initial program 84.5%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in t around 0 77.2%

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

   if 5.5e-18 < t

   1. Initial program 41.1%

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

      1. associate-/l* 74.6%

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

      2. clear-num 74.4%

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

      3. associate-/r/ 74.7%

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

      4. clear-num 74.6%

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

   3. Applied egg-rr 74.6%

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

   4. Taylor expanded in x around 0 41.6%

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

      1. associate-/l* 74.4%

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

   6. Simplified 74.4%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 15: 52.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+58} \lor \neg \left(a \leq 9.5 \cdot 10^{+105}\right):\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -9.6e+58) (not (<= a 9.5e+105)))
   (- x (/ t (/ a y)))
   (/ (- y) (/ t (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9.6e+58) || !(a <= 9.5e+105)) {
		tmp = x - (t / (a / y));
	} else {
		tmp = -y / (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 ((a <= (-9.6d+58)) .or. (.not. (a <= 9.5d+105))) then
        tmp = x - (t / (a / y))
    else
        tmp = -y / (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 ((a <= -9.6e+58) || !(a <= 9.5e+105)) {
		tmp = x - (t / (a / y));
	} else {
		tmp = -y / (t / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -9.6e+58) or not (a <= 9.5e+105):
		tmp = x - (t / (a / y))
	else:
		tmp = -y / (t / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -9.6e+58) || !(a <= 9.5e+105))
		tmp = Float64(x - Float64(t / Float64(a / y)));
	else
		tmp = Float64(Float64(-y) / Float64(t / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -9.6e+58) || ~((a <= 9.5e+105)))
		tmp = x - (t / (a / y));
	else
		tmp = -y / (t / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -9.6e+58], N[Not[LessEqual[a, 9.5e+105]], $MachinePrecision]], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-y) / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.5999999999999999e58 or 9.4999999999999995e105 < a

   1. Initial program 62.9%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in z around 0 77.5%

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

      1. associate-*r/ 77.5%

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

      2. neg-mul-1 77.5%

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

   6. Simplified 77.5%

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

   7. Taylor expanded in a around inf 59.3%

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

      1. mul-1-neg 59.3%

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

      2. unsub-neg 59.3%

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

      3. associate-/l* 71.1%

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

   9. Simplified 71.1%

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

   10. Taylor expanded in y around inf 63.3%

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

       1. associate-/l* 71.1%

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

   12. Simplified 71.1%

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

   if -9.5999999999999999e58 < a < 9.4999999999999995e105

   1. Initial program 64.7%

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

      1. associate-*l/ 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in x around 0 52.6%

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

   5. Taylor expanded in a around 0 40.9%

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

      1. mul-1-neg 40.9%

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

      2. associate-/l* 57.0%

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

      3. distribute-neg-frac 57.0%

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

   7. Simplified 57.0%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+58} \lor \neg \left(a \leq 9.5 \cdot 10^{+105}\right):\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \end{array} \]

Alternative 16: 44.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+59} \lor \neg \left(a \leq 7 \cdot 10^{+46}\right):\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.05e+59) (not (<= a 7e+46)))
   (- x (/ t (/ a y)))
   (+ y (/ a (/ t y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.05e+59) || !(a <= 7e+46)) {
		tmp = x - (t / (a / y));
	} else {
		tmp = y + (a / (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.05d+59)) .or. (.not. (a <= 7d+46))) then
        tmp = x - (t / (a / y))
    else
        tmp = y + (a / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.05e+59) || !(a <= 7e+46)) {
		tmp = x - (t / (a / y));
	} else {
		tmp = y + (a / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.05e+59) or not (a <= 7e+46):
		tmp = x - (t / (a / y))
	else:
		tmp = y + (a / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.05e+59) || !(a <= 7e+46))
		tmp = Float64(x - Float64(t / Float64(a / y)));
	else
		tmp = Float64(y + Float64(a / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.05e+59) || ~((a <= 7e+46)))
		tmp = x - (t / (a / y));
	else
		tmp = y + (a / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.05e+59], N[Not[LessEqual[a, 7e+46]], $MachinePrecision]], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.04999999999999992e59 or 6.9999999999999997e46 < a

   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* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around 0 74.0%

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

      1. associate-*r/ 74.0%

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

      2. neg-mul-1 74.0%

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

   6. Simplified 74.0%

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

   7. Taylor expanded in a around inf 55.5%

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

      1. mul-1-neg 55.5%

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

      2. unsub-neg 55.5%

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

      3. associate-/l* 65.7%

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

   9. Simplified 65.7%

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

   10. Taylor expanded in y around inf 58.9%

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

       1. associate-/l* 65.6%

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

   12. Simplified 65.6%

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

   if -1.04999999999999992e59 < a < 6.9999999999999997e46

   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* 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in z around 0 34.4%

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

      1. associate-*r/ 34.4%

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

      2. neg-mul-1 34.4%

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

   6. Simplified 34.4%

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

   7. Taylor expanded in x around 0 31.0%

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

      1. associate-/l* 38.7%

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

   9. Simplified 38.7%

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

   10. Taylor expanded in t around inf 45.5%

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

       1. associate-/l* 46.0%

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

   12. Simplified 46.0%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+59} \lor \neg \left(a \leq 7 \cdot 10^{+46}\right):\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y}}\\ \end{array} \]

Alternative 17: 38.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+96}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.7e+63) x (if (<= a 5.8e+96) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.7e+63) {
		tmp = x;
	} else if (a <= 5.8e+96) {
		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 <= (-5.7d+63)) then
        tmp = x
    else if (a <= 5.8d+96) 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 <= -5.7e+63) {
		tmp = x;
	} else if (a <= 5.8e+96) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.7e+63:
		tmp = x
	elif a <= 5.8e+96:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.7e+63)
		tmp = x;
	elseif (a <= 5.8e+96)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.7e+63)
		tmp = x;
	elseif (a <= 5.8e+96)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.7e+63], x, If[LessEqual[a, 5.8e+96], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.7000000000000002e63 or 5.79999999999999955e96 < a

   1. Initial program 62.6%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in a around inf 57.6%

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

   if -5.7000000000000002e63 < a < 5.79999999999999955e96

   1. Initial program 64.9%

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

      1. associate-*l/ 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in t around inf 41.8%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+96}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 25.1% 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 64.0%

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

   1. associate-*l/ 79.6%

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

3. Simplified 79.6%

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

4. Taylor expanded in a around inf 28.1%

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

5. Final simplification 28.1%

   \[\leadsto x \]

Developer target: 87.1% 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 2023290 
(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))))