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

Percentage Accurate: 68.8% → 90.4%

Time: 18.3s

Alternatives: 25

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: 68.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-283} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- z t) (- x y)) (- a t)))))
   (if (or (<= t_1 -1e-283) (not (<= t_1 0.0)))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (* (/ (- y x) t) (- a z))))))

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 <= -1e-283) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((y - x) / t) * (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((z - t) * (x - y)) / (a - t))
    if ((t_1 <= (-1d-283)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + (((y - x) / t) * (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((z - t) * (x - y)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-283) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((y - x) / t) * (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((z - t) * (x - y)) / (a - t))
	tmp = 0
	if (t_1 <= -1e-283) or not (t_1 <= 0.0):
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + (((y - x) / t) * (a - z))
	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 <= -1e-283) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	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 <= -1e-283) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + (((y - x) / t) * (a - z));
	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, -1e-283], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.99999999999999947e-284 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 73.5%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   if -9.99999999999999947e-284 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

      1. associate-/l* 4.7%

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

   3. Simplified 4.7%

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

      1. div-inv 4.7%

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

   5. Applied egg-rr 4.7%

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

   6. Taylor expanded in t around inf 95.1%

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

      1. +-commutative 95.1%

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

      2. *-commutative 95.1%

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

      3. associate--l+ 95.1%

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

      4. associate-*r/ 95.1%

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

      5. associate-*r/ 95.1%

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

      6. div-sub 95.0%

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

      7. distribute-lft-out-- 95.0%

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

      8. *-commutative 95.0%

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

      9. distribute-rgt-out-- 95.2%

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

      10. associate-*r/ 95.2%

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

      11. +-commutative 95.2%

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

      12. fma-def 95.2%

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

      13. associate-/l* 100.0%

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

   8. Simplified 99.9%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t} \leq -1 \cdot 10^{-283} \lor \neg \left(x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]

Alternative 2: 66.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+109}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{t}}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-22}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{+107}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.8e+109)
   (- x (/ y (/ (- a t) t)))
   (if (<= a -1.2e-57)
     (* y (/ (- z t) (- a t)))
     (if (<= a -2.55e-99)
       (+ x (/ (* (- y x) z) (- a t)))
       (if (<= a 3.1e-22)
         (- y (/ z (/ t (- y x))))
         (if (<= a 5.5e+91)
           (* z (/ (- y x) (- a t)))
           (if (<= a 9.1e+107)
             (- y (/ y (/ t z)))
             (+ x (/ (- y x) (/ a z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e+109) {
		tmp = x - (y / ((a - t) / t));
	} else if (a <= -1.2e-57) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= -2.55e-99) {
		tmp = x + (((y - x) * z) / (a - t));
	} else if (a <= 3.1e-22) {
		tmp = y - (z / (t / (y - x)));
	} else if (a <= 5.5e+91) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 9.1e+107) {
		tmp = y - (y / (t / z));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.8d+109)) then
        tmp = x - (y / ((a - t) / t))
    else if (a <= (-1.2d-57)) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= (-2.55d-99)) then
        tmp = x + (((y - x) * z) / (a - t))
    else if (a <= 3.1d-22) then
        tmp = y - (z / (t / (y - x)))
    else if (a <= 5.5d+91) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 9.1d+107) then
        tmp = y - (y / (t / z))
    else
        tmp = x + ((y - x) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e+109) {
		tmp = x - (y / ((a - t) / t));
	} else if (a <= -1.2e-57) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= -2.55e-99) {
		tmp = x + (((y - x) * z) / (a - t));
	} else if (a <= 3.1e-22) {
		tmp = y - (z / (t / (y - x)));
	} else if (a <= 5.5e+91) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 9.1e+107) {
		tmp = y - (y / (t / z));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.8e+109:
		tmp = x - (y / ((a - t) / t))
	elif a <= -1.2e-57:
		tmp = y * ((z - t) / (a - t))
	elif a <= -2.55e-99:
		tmp = x + (((y - x) * z) / (a - t))
	elif a <= 3.1e-22:
		tmp = y - (z / (t / (y - x)))
	elif a <= 5.5e+91:
		tmp = z * ((y - x) / (a - t))
	elif a <= 9.1e+107:
		tmp = y - (y / (t / z))
	else:
		tmp = x + ((y - x) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.8e+109)
		tmp = Float64(x - Float64(y / Float64(Float64(a - t) / t)));
	elseif (a <= -1.2e-57)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= -2.55e-99)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / Float64(a - t)));
	elseif (a <= 3.1e-22)
		tmp = Float64(y - Float64(z / Float64(t / Float64(y - x))));
	elseif (a <= 5.5e+91)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 9.1e+107)
		tmp = Float64(y - Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.8e+109)
		tmp = x - (y / ((a - t) / t));
	elseif (a <= -1.2e-57)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= -2.55e-99)
		tmp = x + (((y - x) * z) / (a - t));
	elseif (a <= 3.1e-22)
		tmp = y - (z / (t / (y - x)));
	elseif (a <= 5.5e+91)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 9.1e+107)
		tmp = y - (y / (t / z));
	else
		tmp = x + ((y - x) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.8e+109], N[(x - N[(y / N[(N[(a - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.2e-57], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.55e-99], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e-22], N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e+91], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.1e+107], N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -2.8000000000000002e109

   1. Initial program 66.8%

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

   2. Taylor expanded in y around inf 66.7%

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

      1. *-commutative 66.7%

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

      2. associate-/l* 85.6%

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

   4. Simplified 85.6%

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

   5. Taylor expanded in z around 0 73.4%

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

      1. +-commutative 73.4%

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

      2. mul-1-neg 73.4%

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

      3. unsub-neg 73.4%

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

      4. associate-/l* 76.6%

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

   7. Simplified 76.6%

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

   if -2.8000000000000002e109 < a < -1.20000000000000003e-57

   1. Initial program 73.5%

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

      1. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

      1. div-inv 81.6%

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

   5. Applied egg-rr 81.6%

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

   6. Taylor expanded in y around inf 70.2%

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

      1. *-commutative 70.2%

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

      2. div-sub 70.2%

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

   8. Simplified 70.2%

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

   if -1.20000000000000003e-57 < a < -2.5499999999999999e-99

   1. Initial program 85.6%

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

   2. Taylor expanded in z around inf 72.7%

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

   if -2.5499999999999999e-99 < a < 3.10000000000000013e-22

   1. Initial program 68.5%

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

   2. Taylor expanded in t around -inf 94.5%

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

      1. mul-1-neg 94.5%

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

      2. unsub-neg 94.5%

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

      3. div-sub 94.5%

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

      4. *-commutative 94.5%

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

      5. div-sub 94.5%

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

      6. distribute-rgt-out-- 94.6%

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

   4. Simplified 94.6%

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

   5. Taylor expanded in z around inf 91.0%

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

      1. associate-/l* 88.1%

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

   7. Simplified 88.1%

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

   if 3.10000000000000013e-22 < a < 5.4999999999999998e91

   1. Initial program 59.6%

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

      1. associate-/l* 84.3%

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

   3. Simplified 84.3%

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

      1. div-inv 84.3%

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

   5. Applied egg-rr 84.3%

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

   6. Taylor expanded in z around inf 79.8%

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

      1. div-sub 79.8%

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

   8. Simplified 79.8%

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

   if 5.4999999999999998e91 < a < 9.10000000000000007e107

   1. Initial program 42.9%

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

   2. Taylor expanded in t around -inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

      3. div-sub 80.0%

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

      4. *-commutative 80.0%

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

      5. div-sub 80.0%

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

      6. distribute-rgt-out-- 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 100.0%

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

      1. associate-/l* 100.0%

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

   10. Simplified 100.0%

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

   if 9.10000000000000007e107 < a

   1. Initial program 65.2%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around 0 87.4%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+109}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{t}}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-22}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{+107}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 3: 71.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{if}\;a \leq -2.55 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-21}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{+107}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+150}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z t) (/ (- a t) y)))))
   (if (<= a -2.55e-99)
     t_1
     (if (<= a 3.1e-21)
       (- y (/ z (/ t (- y x))))
       (if (<= a 6e+91)
         (* z (/ (- y x) (- a t)))
         (if (<= a 9.1e+107)
           (- y (/ y (/ t z)))
           (if (<= a 8e+150) (+ x (/ z (/ a (- y x)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) / ((a - t) / y));
	double tmp;
	if (a <= -2.55e-99) {
		tmp = t_1;
	} else if (a <= 3.1e-21) {
		tmp = y - (z / (t / (y - x)));
	} else if (a <= 6e+91) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 9.1e+107) {
		tmp = y - (y / (t / z));
	} else if (a <= 8e+150) {
		tmp = x + (z / (a / (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 + ((z - t) / ((a - t) / y))
    if (a <= (-2.55d-99)) then
        tmp = t_1
    else if (a <= 3.1d-21) then
        tmp = y - (z / (t / (y - x)))
    else if (a <= 6d+91) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 9.1d+107) then
        tmp = y - (y / (t / z))
    else if (a <= 8d+150) then
        tmp = x + (z / (a / (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 + ((z - t) / ((a - t) / y));
	double tmp;
	if (a <= -2.55e-99) {
		tmp = t_1;
	} else if (a <= 3.1e-21) {
		tmp = y - (z / (t / (y - x)));
	} else if (a <= 6e+91) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 9.1e+107) {
		tmp = y - (y / (t / z));
	} else if (a <= 8e+150) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) / ((a - t) / y))
	tmp = 0
	if a <= -2.55e-99:
		tmp = t_1
	elif a <= 3.1e-21:
		tmp = y - (z / (t / (y - x)))
	elif a <= 6e+91:
		tmp = z * ((y - x) / (a - t))
	elif a <= 9.1e+107:
		tmp = y - (y / (t / z))
	elif a <= 8e+150:
		tmp = x + (z / (a / (y - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / y)))
	tmp = 0.0
	if (a <= -2.55e-99)
		tmp = t_1;
	elseif (a <= 3.1e-21)
		tmp = Float64(y - Float64(z / Float64(t / Float64(y - x))));
	elseif (a <= 6e+91)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 9.1e+107)
		tmp = Float64(y - Float64(y / Float64(t / z)));
	elseif (a <= 8e+150)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) / ((a - t) / y));
	tmp = 0.0;
	if (a <= -2.55e-99)
		tmp = t_1;
	elseif (a <= 3.1e-21)
		tmp = y - (z / (t / (y - x)));
	elseif (a <= 6e+91)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 9.1e+107)
		tmp = y - (y / (t / z));
	elseif (a <= 8e+150)
		tmp = x + (z / (a / (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[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.55e-99], t$95$1, If[LessEqual[a, 3.1e-21], N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+91], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.1e+107], N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+150], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.5499999999999999e-99 or 7.99999999999999985e150 < a

   1. Initial program 70.7%

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

   2. Taylor expanded in y around inf 70.0%

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

      1. *-commutative 70.0%

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

      2. associate-/l* 80.5%

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

   4. Simplified 80.5%

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

   if -2.5499999999999999e-99 < a < 3.0999999999999998e-21

   1. Initial program 68.5%

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

   2. Taylor expanded in t around -inf 94.5%

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

      1. mul-1-neg 94.5%

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

      2. unsub-neg 94.5%

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

      3. div-sub 94.5%

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

      4. *-commutative 94.5%

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

      5. div-sub 94.5%

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

      6. distribute-rgt-out-- 94.6%

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

   4. Simplified 94.6%

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

   5. Taylor expanded in z around inf 91.0%

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

      1. associate-/l* 88.1%

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

   7. Simplified 88.1%

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

   if 3.0999999999999998e-21 < a < 6.00000000000000012e91

   1. Initial program 59.6%

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

      1. associate-/l* 84.3%

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

   3. Simplified 84.3%

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

      1. div-inv 84.3%

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

   5. Applied egg-rr 84.3%

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

   6. Taylor expanded in z around inf 79.8%

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

      1. div-sub 79.8%

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

   8. Simplified 79.8%

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

   if 6.00000000000000012e91 < a < 9.10000000000000007e107

   1. Initial program 42.9%

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

   2. Taylor expanded in t around -inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

      3. div-sub 80.0%

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

      4. *-commutative 80.0%

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

      5. div-sub 80.0%

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

      6. distribute-rgt-out-- 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 100.0%

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

      1. associate-/l* 100.0%

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

   10. Simplified 100.0%

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

   if 9.10000000000000007e107 < a < 7.99999999999999985e150

   1. Initial program 60.4%

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

   2. Taylor expanded in t around 0 60.3%

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

      1. associate-/l* 86.0%

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

   4. Simplified 86.0%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-21}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{+107}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+150}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 4: 52.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3600000:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+32} \lor \neg \left(t \leq 4 \cdot 10^{+53}\right) \land t \leq 2.2 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))))
   (if (<= t -7.2e+29)
     y
     (if (<= t 1.35e-9)
       t_1
       (if (<= t 3600000.0)
         (* (- z a) (/ x t))
         (if (or (<= t 3.5e+32) (and (not (<= t 4e+53)) (<= t 2.2e+64)))
           t_1
           y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (t <= -7.2e+29) {
		tmp = y;
	} else if (t <= 1.35e-9) {
		tmp = t_1;
	} else if (t <= 3600000.0) {
		tmp = (z - a) * (x / t);
	} else if ((t <= 3.5e+32) || (!(t <= 4e+53) && (t <= 2.2e+64))) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    if (t <= (-7.2d+29)) then
        tmp = y
    else if (t <= 1.35d-9) then
        tmp = t_1
    else if (t <= 3600000.0d0) then
        tmp = (z - a) * (x / t)
    else if ((t <= 3.5d+32) .or. (.not. (t <= 4d+53)) .and. (t <= 2.2d+64)) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (t <= -7.2e+29) {
		tmp = y;
	} else if (t <= 1.35e-9) {
		tmp = t_1;
	} else if (t <= 3600000.0) {
		tmp = (z - a) * (x / t);
	} else if ((t <= 3.5e+32) || (!(t <= 4e+53) && (t <= 2.2e+64))) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	tmp = 0
	if t <= -7.2e+29:
		tmp = y
	elif t <= 1.35e-9:
		tmp = t_1
	elif t <= 3600000.0:
		tmp = (z - a) * (x / t)
	elif (t <= 3.5e+32) or (not (t <= 4e+53) and (t <= 2.2e+64)):
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (t <= -7.2e+29)
		tmp = y;
	elseif (t <= 1.35e-9)
		tmp = t_1;
	elseif (t <= 3600000.0)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif ((t <= 3.5e+32) || (!(t <= 4e+53) && (t <= 2.2e+64)))
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	tmp = 0.0;
	if (t <= -7.2e+29)
		tmp = y;
	elseif (t <= 1.35e-9)
		tmp = t_1;
	elseif (t <= 3600000.0)
		tmp = (z - a) * (x / t);
	elseif ((t <= 3.5e+32) || (~((t <= 4e+53)) && (t <= 2.2e+64)))
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+29], y, If[LessEqual[t, 1.35e-9], t$95$1, If[LessEqual[t, 3600000.0], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 3.5e+32], And[N[Not[LessEqual[t, 4e+53]], $MachinePrecision], LessEqual[t, 2.2e+64]]], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.19999999999999952e29 or 3.5000000000000001e32 < t < 4e53 or 2.20000000000000002e64 < t

   1. Initial program 45.4%

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

   2. Taylor expanded in t around inf 60.2%

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

   if -7.19999999999999952e29 < t < 1.3500000000000001e-9 or 3.6e6 < t < 3.5000000000000001e32 or 4e53 < t < 2.20000000000000002e64

   1. Initial program 83.6%

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

   2. Taylor expanded in t around 0 61.8%

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

   3. Taylor expanded in y around inf 53.2%

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

      1. associate-/l* 59.0%

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

   5. Simplified 59.0%

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

   if 1.3500000000000001e-9 < t < 3.6e6

   1. Initial program 75.7%

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

   2. Taylor expanded in t around -inf 99.3%

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

      1. mul-1-neg 99.3%

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

      2. unsub-neg 99.3%

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

      3. div-sub 99.3%

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

      4. *-commutative 99.3%

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

      5. div-sub 99.3%

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

      6. distribute-rgt-out-- 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in y around 0 89.3%

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

   6. Taylor expanded in z around 0 89.3%

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

      1. associate-/l* 89.3%

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

      2. mul-1-neg 89.3%

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

      3. associate-/l* 89.5%

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

      4. sub-neg 89.5%

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

      5. div-sub 89.5%

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

      6. associate-/r/ 89.3%

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

      7. *-commutative 89.3%

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

      8. associate-*r/ 89.3%

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

      9. *-commutative 89.3%

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

      10. associate-*r/ 89.7%

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

   8. Simplified 89.7%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3600000:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+32} \lor \neg \left(t \leq 4 \cdot 10^{+53}\right) \land t \leq 2.2 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5: 48.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+54}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -9.5e+29)
     y
     (if (<= t 4.6e-10)
       t_1
       (if (<= t 1.6e+21)
         (* x (/ z t))
         (if (<= t 2.8e+32)
           (* y (/ (- z t) a))
           (if (<= t 9e+54) y (if (<= t 1.9e+68) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -9.5e+29) {
		tmp = y;
	} else if (t <= 4.6e-10) {
		tmp = t_1;
	} else if (t <= 1.6e+21) {
		tmp = x * (z / t);
	} else if (t <= 2.8e+32) {
		tmp = y * ((z - t) / a);
	} else if (t <= 9e+54) {
		tmp = y;
	} else if (t <= 1.9e+68) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-9.5d+29)) then
        tmp = y
    else if (t <= 4.6d-10) then
        tmp = t_1
    else if (t <= 1.6d+21) then
        tmp = x * (z / t)
    else if (t <= 2.8d+32) then
        tmp = y * ((z - t) / a)
    else if (t <= 9d+54) then
        tmp = y
    else if (t <= 1.9d+68) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -9.5e+29) {
		tmp = y;
	} else if (t <= 4.6e-10) {
		tmp = t_1;
	} else if (t <= 1.6e+21) {
		tmp = x * (z / t);
	} else if (t <= 2.8e+32) {
		tmp = y * ((z - t) / a);
	} else if (t <= 9e+54) {
		tmp = y;
	} else if (t <= 1.9e+68) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -9.5e+29:
		tmp = y
	elif t <= 4.6e-10:
		tmp = t_1
	elif t <= 1.6e+21:
		tmp = x * (z / t)
	elif t <= 2.8e+32:
		tmp = y * ((z - t) / a)
	elif t <= 9e+54:
		tmp = y
	elif t <= 1.9e+68:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -9.5e+29)
		tmp = y;
	elseif (t <= 4.6e-10)
		tmp = t_1;
	elseif (t <= 1.6e+21)
		tmp = Float64(x * Float64(z / t));
	elseif (t <= 2.8e+32)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 9e+54)
		tmp = y;
	elseif (t <= 1.9e+68)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -9.5e+29)
		tmp = y;
	elseif (t <= 4.6e-10)
		tmp = t_1;
	elseif (t <= 1.6e+21)
		tmp = x * (z / t);
	elseif (t <= 2.8e+32)
		tmp = y * ((z - t) / a);
	elseif (t <= 9e+54)
		tmp = y;
	elseif (t <= 1.9e+68)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+29], y, If[LessEqual[t, 4.6e-10], t$95$1, If[LessEqual[t, 1.6e+21], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+32], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+54], y, If[LessEqual[t, 1.9e+68], t$95$1, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.5000000000000003e29 or 2.8e32 < t < 8.99999999999999968e54 or 1.9e68 < t

   1. Initial program 44.9%

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

   2. Taylor expanded in t around inf 60.8%

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

   if -9.5000000000000003e29 < t < 4.60000000000000014e-10 or 8.99999999999999968e54 < t < 1.9e68

   1. Initial program 83.7%

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

   2. Taylor expanded in t around 0 62.3%

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

   3. Taylor expanded in x around inf 55.6%

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

      1. *-commutative 55.6%

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

      2. mul-1-neg 55.6%

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

      3. unsub-neg 55.6%

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

   5. Simplified 55.6%

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

   if 4.60000000000000014e-10 < t < 1.6e21

   1. Initial program 70.8%

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

   2. Taylor expanded in t around -inf 89.5%

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

      1. mul-1-neg 89.5%

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

      2. unsub-neg 89.5%

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

      3. div-sub 89.5%

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

      4. *-commutative 89.5%

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

      5. div-sub 89.5%

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

      6. distribute-rgt-out-- 89.5%

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

   4. Simplified 89.5%

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

   5. Taylor expanded in y around 0 72.3%

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

   6. Taylor expanded in z around inf 63.1%

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

      1. associate-/l* 63.1%

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

      2. associate-/r/ 63.1%

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

   8. Simplified 63.1%

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

   if 1.6e21 < t < 2.8e32

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. div-inv 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 75.3%

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

      1. *-commutative 75.3%

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

      2. div-sub 75.3%

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

   8. Simplified 75.3%

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

   9. Taylor expanded in a around inf 75.3%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+54}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6: 68.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-22}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{+107}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.8e+69)
   (+ x (/ z (/ a (- y x))))
   (if (<= a -2.6e-99)
     (+ x (/ (* y (- z t)) (- a t)))
     (if (<= a 3.4e-22)
       (- y (/ z (/ t (- y x))))
       (if (<= a 4.7e+91)
         (* z (/ (- y x) (- a t)))
         (if (<= a 9.1e+107)
           (- y (/ y (/ t z)))
           (+ x (/ (- y x) (/ a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.8e+69) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= -2.6e-99) {
		tmp = x + ((y * (z - t)) / (a - t));
	} else if (a <= 3.4e-22) {
		tmp = y - (z / (t / (y - x)));
	} else if (a <= 4.7e+91) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 9.1e+107) {
		tmp = y - (y / (t / z));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.8d+69)) then
        tmp = x + (z / (a / (y - x)))
    else if (a <= (-2.6d-99)) then
        tmp = x + ((y * (z - t)) / (a - t))
    else if (a <= 3.4d-22) then
        tmp = y - (z / (t / (y - x)))
    else if (a <= 4.7d+91) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 9.1d+107) then
        tmp = y - (y / (t / z))
    else
        tmp = x + ((y - x) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.8e+69) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= -2.6e-99) {
		tmp = x + ((y * (z - t)) / (a - t));
	} else if (a <= 3.4e-22) {
		tmp = y - (z / (t / (y - x)));
	} else if (a <= 4.7e+91) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 9.1e+107) {
		tmp = y - (y / (t / z));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.8e+69:
		tmp = x + (z / (a / (y - x)))
	elif a <= -2.6e-99:
		tmp = x + ((y * (z - t)) / (a - t))
	elif a <= 3.4e-22:
		tmp = y - (z / (t / (y - x)))
	elif a <= 4.7e+91:
		tmp = z * ((y - x) / (a - t))
	elif a <= 9.1e+107:
		tmp = y - (y / (t / z))
	else:
		tmp = x + ((y - x) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.8e+69)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (a <= -2.6e-99)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t)));
	elseif (a <= 3.4e-22)
		tmp = Float64(y - Float64(z / Float64(t / Float64(y - x))));
	elseif (a <= 4.7e+91)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 9.1e+107)
		tmp = Float64(y - Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.8e+69)
		tmp = x + (z / (a / (y - x)));
	elseif (a <= -2.6e-99)
		tmp = x + ((y * (z - t)) / (a - t));
	elseif (a <= 3.4e-22)
		tmp = y - (z / (t / (y - x)));
	elseif (a <= 4.7e+91)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 9.1e+107)
		tmp = y - (y / (t / z));
	else
		tmp = x + ((y - x) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.8e+69], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.6e-99], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-22], N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.7e+91], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.1e+107], N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -8.8000000000000006e69

   1. Initial program 67.1%

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

   2. Taylor expanded in t around 0 61.9%

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

      1. associate-/l* 75.1%

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

   4. Simplified 75.1%

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

   if -8.8000000000000006e69 < a < -2.60000000000000005e-99

   1. Initial program 78.3%

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

   2. Taylor expanded in x around 0 67.3%

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

   if -2.60000000000000005e-99 < a < 3.3999999999999998e-22

   1. Initial program 68.5%

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

   2. Taylor expanded in t around -inf 94.5%

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

      1. mul-1-neg 94.5%

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

      2. unsub-neg 94.5%

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

      3. div-sub 94.5%

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

      4. *-commutative 94.5%

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

      5. div-sub 94.5%

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

      6. distribute-rgt-out-- 94.6%

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

   4. Simplified 94.6%

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

   5. Taylor expanded in z around inf 91.0%

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

      1. associate-/l* 88.1%

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

   7. Simplified 88.1%

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

   if 3.3999999999999998e-22 < a < 4.6999999999999997e91

   1. Initial program 59.6%

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

      1. associate-/l* 84.3%

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

   3. Simplified 84.3%

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

      1. div-inv 84.3%

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

   5. Applied egg-rr 84.3%

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

   6. Taylor expanded in z around inf 79.8%

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

      1. div-sub 79.8%

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

   8. Simplified 79.8%

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

   if 4.6999999999999997e91 < a < 9.10000000000000007e107

   1. Initial program 42.9%

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

   2. Taylor expanded in t around -inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

      3. div-sub 80.0%

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

      4. *-commutative 80.0%

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

      5. div-sub 80.0%

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

      6. distribute-rgt-out-- 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 100.0%

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

      1. associate-/l* 100.0%

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

   10. Simplified 100.0%

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

   if 9.10000000000000007e107 < a

   1. Initial program 65.2%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around 0 87.4%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-22}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{+107}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 7: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-99}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-21}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z t) (/ (- a t) y)))))
   (if (<= a -2.6e+143)
     t_1
     (if (<= a -1.65e-99)
       (- x (/ (* (- z t) (- x y)) (- a t)))
       (if (<= a 2.8e-21)
         (- y (/ (* (- y x) (- z a)) t))
         (if (<= a 6.2e+91) (* z (/ (- y x) (- a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) / ((a - t) / y));
	double tmp;
	if (a <= -2.6e+143) {
		tmp = t_1;
	} else if (a <= -1.65e-99) {
		tmp = x - (((z - t) * (x - y)) / (a - t));
	} else if (a <= 2.8e-21) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else if (a <= 6.2e+91) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - t) / ((a - t) / y))
    if (a <= (-2.6d+143)) then
        tmp = t_1
    else if (a <= (-1.65d-99)) then
        tmp = x - (((z - t) * (x - y)) / (a - t))
    else if (a <= 2.8d-21) then
        tmp = y - (((y - x) * (z - a)) / t)
    else if (a <= 6.2d+91) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) / ((a - t) / y));
	double tmp;
	if (a <= -2.6e+143) {
		tmp = t_1;
	} else if (a <= -1.65e-99) {
		tmp = x - (((z - t) * (x - y)) / (a - t));
	} else if (a <= 2.8e-21) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else if (a <= 6.2e+91) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) / ((a - t) / y))
	tmp = 0
	if a <= -2.6e+143:
		tmp = t_1
	elif a <= -1.65e-99:
		tmp = x - (((z - t) * (x - y)) / (a - t))
	elif a <= 2.8e-21:
		tmp = y - (((y - x) * (z - a)) / t)
	elif a <= 6.2e+91:
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / y)))
	tmp = 0.0
	if (a <= -2.6e+143)
		tmp = t_1;
	elseif (a <= -1.65e-99)
		tmp = Float64(x - Float64(Float64(Float64(z - t) * Float64(x - y)) / Float64(a - t)));
	elseif (a <= 2.8e-21)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * Float64(z - a)) / t));
	elseif (a <= 6.2e+91)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) / ((a - t) / y));
	tmp = 0.0;
	if (a <= -2.6e+143)
		tmp = t_1;
	elseif (a <= -1.65e-99)
		tmp = x - (((z - t) * (x - y)) / (a - t));
	elseif (a <= 2.8e-21)
		tmp = y - (((y - x) * (z - a)) / t);
	elseif (a <= 6.2e+91)
		tmp = z * ((y - x) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e+143], t$95$1, If[LessEqual[a, -1.65e-99], N[(x - N[(N[(N[(z - t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-21], N[(y - N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e+91], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.5999999999999999e143 or 6.19999999999999995e91 < a

   1. Initial program 62.7%

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

   2. Taylor expanded in y around inf 71.1%

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

      1. *-commutative 71.1%

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

      2. associate-/l* 91.6%

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

   4. Simplified 91.6%

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

   if -2.5999999999999999e143 < a < -1.64999999999999993e-99

   1. Initial program 78.9%

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

   if -1.64999999999999993e-99 < a < 2.80000000000000004e-21

   1. Initial program 68.5%

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

   2. Taylor expanded in t around -inf 94.5%

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

      1. mul-1-neg 94.5%

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

      2. unsub-neg 94.5%

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

      3. div-sub 94.5%

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

      4. *-commutative 94.5%

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

      5. div-sub 94.5%

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

      6. distribute-rgt-out-- 94.6%

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

   4. Simplified 94.6%

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

   if 2.80000000000000004e-21 < a < 6.19999999999999995e91

   1. Initial program 56.8%

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

      1. associate-/l* 80.3%

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

   3. Simplified 80.3%

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

      1. div-inv 80.3%

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

   5. Applied egg-rr 80.3%

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

   6. Taylor expanded in z around inf 76.2%

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

      1. div-sub 76.2%

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

   8. Simplified 76.2%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+143}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-99}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-21}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 8: 54.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-88}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-105}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-176}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+107}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))))
   (if (<= a -3.1e+50)
     t_1
     (if (<= a -6e-88)
       (- y (/ z (/ t y)))
       (if (<= a -1.15e-105)
         (/ (* y (- z t)) a)
         (if (<= a -4.4e-176)
           (* (- z a) (/ x t))
           (if (<= a 9.5e+107) (- y (/ y (/ t z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (a <= -3.1e+50) {
		tmp = t_1;
	} else if (a <= -6e-88) {
		tmp = y - (z / (t / y));
	} else if (a <= -1.15e-105) {
		tmp = (y * (z - t)) / a;
	} else if (a <= -4.4e-176) {
		tmp = (z - a) * (x / t);
	} else if (a <= 9.5e+107) {
		tmp = y - (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    if (a <= (-3.1d+50)) then
        tmp = t_1
    else if (a <= (-6d-88)) then
        tmp = y - (z / (t / y))
    else if (a <= (-1.15d-105)) then
        tmp = (y * (z - t)) / a
    else if (a <= (-4.4d-176)) then
        tmp = (z - a) * (x / t)
    else if (a <= 9.5d+107) then
        tmp = y - (y / (t / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (a <= -3.1e+50) {
		tmp = t_1;
	} else if (a <= -6e-88) {
		tmp = y - (z / (t / y));
	} else if (a <= -1.15e-105) {
		tmp = (y * (z - t)) / a;
	} else if (a <= -4.4e-176) {
		tmp = (z - a) * (x / t);
	} else if (a <= 9.5e+107) {
		tmp = y - (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	tmp = 0
	if a <= -3.1e+50:
		tmp = t_1
	elif a <= -6e-88:
		tmp = y - (z / (t / y))
	elif a <= -1.15e-105:
		tmp = (y * (z - t)) / a
	elif a <= -4.4e-176:
		tmp = (z - a) * (x / t)
	elif a <= 9.5e+107:
		tmp = y - (y / (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -3.1e+50)
		tmp = t_1;
	elseif (a <= -6e-88)
		tmp = Float64(y - Float64(z / Float64(t / y)));
	elseif (a <= -1.15e-105)
		tmp = Float64(Float64(y * Float64(z - t)) / a);
	elseif (a <= -4.4e-176)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif (a <= 9.5e+107)
		tmp = Float64(y - Float64(y / Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -3.1e+50)
		tmp = t_1;
	elseif (a <= -6e-88)
		tmp = y - (z / (t / y));
	elseif (a <= -1.15e-105)
		tmp = (y * (z - t)) / a;
	elseif (a <= -4.4e-176)
		tmp = (z - a) * (x / t);
	elseif (a <= 9.5e+107)
		tmp = y - (y / (t / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.1e+50], t$95$1, If[LessEqual[a, -6e-88], N[(y - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.15e-105], N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -4.4e-176], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+107], N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.10000000000000003e50 or 9.50000000000000019e107 < a

   1. Initial program 66.3%

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

   2. Taylor expanded in t around 0 60.3%

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

   3. Taylor expanded in y around inf 62.1%

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

      1. associate-/l* 74.7%

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

   5. Simplified 74.7%

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

   if -3.10000000000000003e50 < a < -5.9999999999999999e-88

   1. Initial program 75.3%

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

   2. Taylor expanded in t around -inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. unsub-neg 69.7%

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

      3. div-sub 66.6%

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

      4. *-commutative 66.6%

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

      5. div-sub 69.7%

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

      6. distribute-rgt-out-- 69.7%

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

   4. Simplified 69.7%

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

   5. Taylor expanded in z around inf 59.9%

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

      1. associate-/l* 62.4%

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

   7. Simplified 62.4%

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

   8. Taylor expanded in y around inf 53.2%

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

   if -5.9999999999999999e-88 < a < -1.15e-105

   1. Initial program 86.3%

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

      1. associate-/l* 86.8%

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

   3. Simplified 86.8%

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

      1. div-inv 86.6%

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

   5. Applied egg-rr 86.6%

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

   6. Taylor expanded in y around inf 59.0%

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

      1. *-commutative 59.0%

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

      2. div-sub 59.0%

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

   8. Simplified 59.0%

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

   9. Taylor expanded in a around inf 57.4%

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

   if -1.15e-105 < a < -4.3999999999999997e-176

   1. Initial program 68.4%

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

   2. Taylor expanded in t around -inf 93.2%

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

      1. mul-1-neg 93.2%

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

      2. unsub-neg 93.2%

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

      3. div-sub 93.2%

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

      4. *-commutative 93.2%

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

      5. div-sub 93.2%

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

      6. distribute-rgt-out-- 93.2%

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

   4. Simplified 93.2%

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

   5. Taylor expanded in y around 0 54.7%

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

   6. Taylor expanded in z around 0 54.7%

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

      1. associate-/l* 54.9%

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

      2. mul-1-neg 54.9%

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

      3. associate-/l* 54.9%

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

      4. sub-neg 54.9%

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

      5. div-sub 54.9%

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

      6. associate-/r/ 54.9%

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

      7. *-commutative 54.9%

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

      8. associate-*r/ 54.7%

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

      9. *-commutative 54.7%

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

      10. associate-*r/ 54.8%

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

   8. Simplified 54.8%

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

   if -4.3999999999999997e-176 < a < 9.50000000000000019e107

   1. Initial program 66.4%

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

   2. Taylor expanded in t around -inf 85.0%

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

      1. mul-1-neg 85.0%

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

      2. unsub-neg 85.0%

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

      3. div-sub 83.1%

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

      4. *-commutative 83.1%

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

      5. div-sub 85.0%

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

      6. distribute-rgt-out-- 85.0%

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

   4. Simplified 85.0%

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

   5. Taylor expanded in z around inf 82.5%

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

      1. associate-/l* 83.1%

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

   7. Simplified 83.1%

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

   8. Taylor expanded in y around inf 67.0%

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

      1. associate-/l* 70.0%

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

   10. Simplified 70.0%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-88}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-105}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-176}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+107}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 9: 54.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-88}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-101}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-171}:\\ \;\;\;\;\frac{z - a}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 3.95 \cdot 10^{+108}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))))
   (if (<= a -2.6e+49)
     t_1
     (if (<= a -6e-88)
       (- y (/ z (/ t y)))
       (if (<= a -2.7e-101)
         (/ (* y (- z t)) a)
         (if (<= a -2.55e-171)
           (/ (- z a) (/ t x))
           (if (<= a 3.95e+108) (- y (/ y (/ t z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (a <= -2.6e+49) {
		tmp = t_1;
	} else if (a <= -6e-88) {
		tmp = y - (z / (t / y));
	} else if (a <= -2.7e-101) {
		tmp = (y * (z - t)) / a;
	} else if (a <= -2.55e-171) {
		tmp = (z - a) / (t / x);
	} else if (a <= 3.95e+108) {
		tmp = y - (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    if (a <= (-2.6d+49)) then
        tmp = t_1
    else if (a <= (-6d-88)) then
        tmp = y - (z / (t / y))
    else if (a <= (-2.7d-101)) then
        tmp = (y * (z - t)) / a
    else if (a <= (-2.55d-171)) then
        tmp = (z - a) / (t / x)
    else if (a <= 3.95d+108) then
        tmp = y - (y / (t / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (a <= -2.6e+49) {
		tmp = t_1;
	} else if (a <= -6e-88) {
		tmp = y - (z / (t / y));
	} else if (a <= -2.7e-101) {
		tmp = (y * (z - t)) / a;
	} else if (a <= -2.55e-171) {
		tmp = (z - a) / (t / x);
	} else if (a <= 3.95e+108) {
		tmp = y - (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	tmp = 0
	if a <= -2.6e+49:
		tmp = t_1
	elif a <= -6e-88:
		tmp = y - (z / (t / y))
	elif a <= -2.7e-101:
		tmp = (y * (z - t)) / a
	elif a <= -2.55e-171:
		tmp = (z - a) / (t / x)
	elif a <= 3.95e+108:
		tmp = y - (y / (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -2.6e+49)
		tmp = t_1;
	elseif (a <= -6e-88)
		tmp = Float64(y - Float64(z / Float64(t / y)));
	elseif (a <= -2.7e-101)
		tmp = Float64(Float64(y * Float64(z - t)) / a);
	elseif (a <= -2.55e-171)
		tmp = Float64(Float64(z - a) / Float64(t / x));
	elseif (a <= 3.95e+108)
		tmp = Float64(y - Float64(y / Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -2.6e+49)
		tmp = t_1;
	elseif (a <= -6e-88)
		tmp = y - (z / (t / y));
	elseif (a <= -2.7e-101)
		tmp = (y * (z - t)) / a;
	elseif (a <= -2.55e-171)
		tmp = (z - a) / (t / x);
	elseif (a <= 3.95e+108)
		tmp = y - (y / (t / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e+49], t$95$1, If[LessEqual[a, -6e-88], N[(y - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.7e-101], N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -2.55e-171], N[(N[(z - a), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.95e+108], N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.59999999999999989e49 or 3.9500000000000003e108 < a

   1. Initial program 66.3%

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

   2. Taylor expanded in t around 0 60.3%

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

   3. Taylor expanded in y around inf 62.1%

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

      1. associate-/l* 74.7%

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

   5. Simplified 74.7%

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

   if -2.59999999999999989e49 < a < -5.9999999999999999e-88

   1. Initial program 75.3%

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

   2. Taylor expanded in t around -inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. unsub-neg 69.7%

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

      3. div-sub 66.6%

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

      4. *-commutative 66.6%

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

      5. div-sub 69.7%

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

      6. distribute-rgt-out-- 69.7%

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

   4. Simplified 69.7%

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

   5. Taylor expanded in z around inf 59.9%

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

      1. associate-/l* 62.4%

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

   7. Simplified 62.4%

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

   8. Taylor expanded in y around inf 53.2%

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

   if -5.9999999999999999e-88 < a < -2.7000000000000002e-101

   1. Initial program 86.3%

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

      1. associate-/l* 86.8%

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

   3. Simplified 86.8%

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

      1. div-inv 86.6%

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

   5. Applied egg-rr 86.6%

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

   6. Taylor expanded in y around inf 59.0%

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

      1. *-commutative 59.0%

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

      2. div-sub 59.0%

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

   8. Simplified 59.0%

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

   9. Taylor expanded in a around inf 57.4%

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

   if -2.7000000000000002e-101 < a < -2.55e-171

   1. Initial program 68.4%

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

   2. Taylor expanded in t around -inf 93.2%

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

      1. mul-1-neg 93.2%

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

      2. unsub-neg 93.2%

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

      3. div-sub 93.2%

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

      4. *-commutative 93.2%

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

      5. div-sub 93.2%

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

      6. distribute-rgt-out-- 93.2%

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

   4. Simplified 93.2%

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

   5. Taylor expanded in y around 0 54.7%

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

      1. associate-/l* 54.9%

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

   7. Simplified 54.9%

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

   if -2.55e-171 < a < 3.9500000000000003e108

   1. Initial program 66.4%

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

   2. Taylor expanded in t around -inf 85.0%

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

      1. mul-1-neg 85.0%

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

      2. unsub-neg 85.0%

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

      3. div-sub 83.1%

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

      4. *-commutative 83.1%

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

      5. div-sub 85.0%

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

      6. distribute-rgt-out-- 85.0%

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

   4. Simplified 85.0%

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

   5. Taylor expanded in z around inf 82.5%

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

      1. associate-/l* 83.1%

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

   7. Simplified 83.1%

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

   8. Taylor expanded in y around inf 67.0%

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

      1. associate-/l* 70.0%

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

   10. Simplified 70.0%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-88}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-101}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-171}:\\ \;\;\;\;\frac{z - a}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 3.95 \cdot 10^{+108}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 10: 54.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -8 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-88}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-99}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;a \leq -1.58 \cdot 10^{-173}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+108}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))))
   (if (<= a -8e+49)
     t_1
     (if (<= a -6e-88)
       (- y (/ z (/ t y)))
       (if (<= a -1.55e-99)
         (/ (* y (- z t)) a)
         (if (<= a -1.58e-173)
           (* x (/ (- z a) t))
           (if (<= a 4.2e+108) (- y (/ y (/ t z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (a <= -8e+49) {
		tmp = t_1;
	} else if (a <= -6e-88) {
		tmp = y - (z / (t / y));
	} else if (a <= -1.55e-99) {
		tmp = (y * (z - t)) / a;
	} else if (a <= -1.58e-173) {
		tmp = x * ((z - a) / t);
	} else if (a <= 4.2e+108) {
		tmp = y - (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    if (a <= (-8d+49)) then
        tmp = t_1
    else if (a <= (-6d-88)) then
        tmp = y - (z / (t / y))
    else if (a <= (-1.55d-99)) then
        tmp = (y * (z - t)) / a
    else if (a <= (-1.58d-173)) then
        tmp = x * ((z - a) / t)
    else if (a <= 4.2d+108) then
        tmp = y - (y / (t / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (a <= -8e+49) {
		tmp = t_1;
	} else if (a <= -6e-88) {
		tmp = y - (z / (t / y));
	} else if (a <= -1.55e-99) {
		tmp = (y * (z - t)) / a;
	} else if (a <= -1.58e-173) {
		tmp = x * ((z - a) / t);
	} else if (a <= 4.2e+108) {
		tmp = y - (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	tmp = 0
	if a <= -8e+49:
		tmp = t_1
	elif a <= -6e-88:
		tmp = y - (z / (t / y))
	elif a <= -1.55e-99:
		tmp = (y * (z - t)) / a
	elif a <= -1.58e-173:
		tmp = x * ((z - a) / t)
	elif a <= 4.2e+108:
		tmp = y - (y / (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -8e+49)
		tmp = t_1;
	elseif (a <= -6e-88)
		tmp = Float64(y - Float64(z / Float64(t / y)));
	elseif (a <= -1.55e-99)
		tmp = Float64(Float64(y * Float64(z - t)) / a);
	elseif (a <= -1.58e-173)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (a <= 4.2e+108)
		tmp = Float64(y - Float64(y / Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -8e+49)
		tmp = t_1;
	elseif (a <= -6e-88)
		tmp = y - (z / (t / y));
	elseif (a <= -1.55e-99)
		tmp = (y * (z - t)) / a;
	elseif (a <= -1.58e-173)
		tmp = x * ((z - a) / t);
	elseif (a <= 4.2e+108)
		tmp = y - (y / (t / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e+49], t$95$1, If[LessEqual[a, -6e-88], N[(y - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.55e-99], N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -1.58e-173], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e+108], N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.99999999999999957e49 or 4.20000000000000019e108 < a

   1. Initial program 66.3%

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

   2. Taylor expanded in t around 0 60.3%

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

   3. Taylor expanded in y around inf 62.1%

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

      1. associate-/l* 74.7%

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

   5. Simplified 74.7%

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

   if -7.99999999999999957e49 < a < -5.9999999999999999e-88

   1. Initial program 75.3%

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

   2. Taylor expanded in t around -inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. unsub-neg 69.7%

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

      3. div-sub 66.6%

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

      4. *-commutative 66.6%

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

      5. div-sub 69.7%

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

      6. distribute-rgt-out-- 69.7%

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

   4. Simplified 69.7%

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

   5. Taylor expanded in z around inf 59.9%

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

      1. associate-/l* 62.4%

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

   7. Simplified 62.4%

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

   8. Taylor expanded in y around inf 53.2%

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

   if -5.9999999999999999e-88 < a < -1.5499999999999999e-99

   1. Initial program 86.3%

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

      1. associate-/l* 86.8%

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

   3. Simplified 86.8%

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

      1. div-inv 86.6%

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

   5. Applied egg-rr 86.6%

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

   6. Taylor expanded in y around inf 59.0%

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

      1. *-commutative 59.0%

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

      2. div-sub 59.0%

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

   8. Simplified 59.0%

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

   9. Taylor expanded in a around inf 57.4%

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

   if -1.5499999999999999e-99 < a < -1.57999999999999997e-173

   1. Initial program 68.4%

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

   2. Taylor expanded in t around -inf 93.2%

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

      1. mul-1-neg 93.2%

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

      2. unsub-neg 93.2%

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

      3. div-sub 93.2%

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

      4. *-commutative 93.2%

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

      5. div-sub 93.2%

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

      6. distribute-rgt-out-- 93.2%

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

   4. Simplified 93.2%

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

   5. Taylor expanded in x around -inf 54.9%

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

      1. mul-1-neg 54.9%

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

      2. div-sub 54.9%

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

   7. Simplified 54.9%

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

   if -1.57999999999999997e-173 < a < 4.20000000000000019e108

   1. Initial program 66.4%

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

   2. Taylor expanded in t around -inf 85.0%

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

      1. mul-1-neg 85.0%

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

      2. unsub-neg 85.0%

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

      3. div-sub 83.1%

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

      4. *-commutative 83.1%

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

      5. div-sub 85.0%

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

      6. distribute-rgt-out-- 85.0%

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

   4. Simplified 85.0%

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

   5. Taylor expanded in z around inf 82.5%

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

      1. associate-/l* 83.1%

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

   7. Simplified 83.1%

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

   8. Taylor expanded in y around inf 67.0%

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

      1. associate-/l* 70.0%

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

   10. Simplified 70.0%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-88}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-99}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;a \leq -1.58 \cdot 10^{-173}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+108}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 11: 54.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-88}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-99}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-194}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{+107}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))))
   (if (<= a -4.8e+51)
     t_1
     (if (<= a -6e-88)
       (- y (/ z (/ t y)))
       (if (<= a -1.6e-99)
         (/ (* y (- z t)) a)
         (if (<= a -1.85e-194)
           (* (/ z t) (- x y))
           (if (<= a 9.1e+107) (- y (/ y (/ t z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (a <= -4.8e+51) {
		tmp = t_1;
	} else if (a <= -6e-88) {
		tmp = y - (z / (t / y));
	} else if (a <= -1.6e-99) {
		tmp = (y * (z - t)) / a;
	} else if (a <= -1.85e-194) {
		tmp = (z / t) * (x - y);
	} else if (a <= 9.1e+107) {
		tmp = y - (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    if (a <= (-4.8d+51)) then
        tmp = t_1
    else if (a <= (-6d-88)) then
        tmp = y - (z / (t / y))
    else if (a <= (-1.6d-99)) then
        tmp = (y * (z - t)) / a
    else if (a <= (-1.85d-194)) then
        tmp = (z / t) * (x - y)
    else if (a <= 9.1d+107) then
        tmp = y - (y / (t / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (a <= -4.8e+51) {
		tmp = t_1;
	} else if (a <= -6e-88) {
		tmp = y - (z / (t / y));
	} else if (a <= -1.6e-99) {
		tmp = (y * (z - t)) / a;
	} else if (a <= -1.85e-194) {
		tmp = (z / t) * (x - y);
	} else if (a <= 9.1e+107) {
		tmp = y - (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	tmp = 0
	if a <= -4.8e+51:
		tmp = t_1
	elif a <= -6e-88:
		tmp = y - (z / (t / y))
	elif a <= -1.6e-99:
		tmp = (y * (z - t)) / a
	elif a <= -1.85e-194:
		tmp = (z / t) * (x - y)
	elif a <= 9.1e+107:
		tmp = y - (y / (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -4.8e+51)
		tmp = t_1;
	elseif (a <= -6e-88)
		tmp = Float64(y - Float64(z / Float64(t / y)));
	elseif (a <= -1.6e-99)
		tmp = Float64(Float64(y * Float64(z - t)) / a);
	elseif (a <= -1.85e-194)
		tmp = Float64(Float64(z / t) * Float64(x - y));
	elseif (a <= 9.1e+107)
		tmp = Float64(y - Float64(y / Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -4.8e+51)
		tmp = t_1;
	elseif (a <= -6e-88)
		tmp = y - (z / (t / y));
	elseif (a <= -1.6e-99)
		tmp = (y * (z - t)) / a;
	elseif (a <= -1.85e-194)
		tmp = (z / t) * (x - y);
	elseif (a <= 9.1e+107)
		tmp = y - (y / (t / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+51], t$95$1, If[LessEqual[a, -6e-88], N[(y - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.6e-99], N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -1.85e-194], N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.1e+107], N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.7999999999999997e51 or 9.10000000000000007e107 < a

   1. Initial program 66.3%

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

   2. Taylor expanded in t around 0 60.3%

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

   3. Taylor expanded in y around inf 62.1%

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

      1. associate-/l* 74.7%

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

   5. Simplified 74.7%

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

   if -4.7999999999999997e51 < a < -5.9999999999999999e-88

   1. Initial program 75.3%

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

   2. Taylor expanded in t around -inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. unsub-neg 69.7%

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

      3. div-sub 66.6%

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

      4. *-commutative 66.6%

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

      5. div-sub 69.7%

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

      6. distribute-rgt-out-- 69.7%

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

   4. Simplified 69.7%

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

   5. Taylor expanded in z around inf 59.9%

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

      1. associate-/l* 62.4%

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

   7. Simplified 62.4%

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

   8. Taylor expanded in y around inf 53.2%

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

   if -5.9999999999999999e-88 < a < -1.6e-99

   1. Initial program 86.3%

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

      1. associate-/l* 86.8%

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

   3. Simplified 86.8%

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

      1. div-inv 86.6%

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

   5. Applied egg-rr 86.6%

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

   6. Taylor expanded in y around inf 59.0%

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

      1. *-commutative 59.0%

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

      2. div-sub 59.0%

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

   8. Simplified 59.0%

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

   9. Taylor expanded in a around inf 57.4%

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

   if -1.6e-99 < a < -1.85000000000000004e-194

   1. Initial program 73.6%

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

   2. Taylor expanded in t around -inf 94.3%

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

      1. mul-1-neg 94.3%

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

      2. unsub-neg 94.3%

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

      3. div-sub 94.3%

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

      4. *-commutative 94.3%

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

      5. div-sub 94.3%

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

      6. distribute-rgt-out-- 94.3%

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

   4. Simplified 94.3%

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

   5. Taylor expanded in z around inf 89.4%

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

      1. associate-/l* 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in z around -inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. associate-*r/ 57.4%

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

      3. *-commutative 57.4%

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

      4. distribute-rgt-neg-in 57.4%

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

   10. Simplified 57.4%

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

   if -1.85000000000000004e-194 < a < 9.10000000000000007e107

   1. Initial program 65.5%

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

   2. Taylor expanded in t around -inf 84.6%

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

      1. mul-1-neg 84.6%

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

      2. unsub-neg 84.6%

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

      3. div-sub 82.7%

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

      4. *-commutative 82.7%

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

      5. div-sub 84.6%

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

      6. distribute-rgt-out-- 84.6%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in z around inf 82.1%

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

      1. associate-/l* 82.7%

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

   7. Simplified 82.7%

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

   8. Taylor expanded in y around inf 67.0%

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

      1. associate-/l* 70.1%

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

   10. Simplified 70.1%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-88}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-99}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-194}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{+107}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 12: 60.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a - t}\right)\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -7 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-299}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z (- a t))))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -7e-62)
     t_2
     (if (<= t -1.95e-113)
       t_1
       (if (<= t -5.2e-299)
         (+ x (/ y (/ a z)))
         (if (<= t 8.2e+14) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / (a - t)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -7e-62) {
		tmp = t_2;
	} else if (t <= -1.95e-113) {
		tmp = t_1;
	} else if (t <= -5.2e-299) {
		tmp = x + (y / (a / z));
	} else if (t <= 8.2e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / (a - t)))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-7d-62)) then
        tmp = t_2
    else if (t <= (-1.95d-113)) then
        tmp = t_1
    else if (t <= (-5.2d-299)) then
        tmp = x + (y / (a / z))
    else if (t <= 8.2d+14) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / (a - t)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -7e-62) {
		tmp = t_2;
	} else if (t <= -1.95e-113) {
		tmp = t_1;
	} else if (t <= -5.2e-299) {
		tmp = x + (y / (a / z));
	} else if (t <= 8.2e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / (a - t)))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -7e-62:
		tmp = t_2
	elif t <= -1.95e-113:
		tmp = t_1
	elif t <= -5.2e-299:
		tmp = x + (y / (a / z))
	elif t <= 8.2e+14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / Float64(a - t))))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -7e-62)
		tmp = t_2;
	elseif (t <= -1.95e-113)
		tmp = t_1;
	elseif (t <= -5.2e-299)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 8.2e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / (a - t)));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -7e-62)
		tmp = t_2;
	elseif (t <= -1.95e-113)
		tmp = t_1;
	elseif (t <= -5.2e-299)
		tmp = x + (y / (a / z));
	elseif (t <= 8.2e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e-62], t$95$2, If[LessEqual[t, -1.95e-113], t$95$1, If[LessEqual[t, -5.2e-299], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e+14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.0000000000000003e-62 or 8.2e14 < t

   1. Initial program 54.1%

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

      1. associate-/l* 76.6%

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

   3. Simplified 76.6%

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

      1. div-inv 76.5%

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

   5. Applied egg-rr 76.5%

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

   6. Taylor expanded in y around inf 68.5%

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

      1. *-commutative 68.5%

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

      2. div-sub 68.5%

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

   8. Simplified 68.5%

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

   if -7.0000000000000003e-62 < t < -1.9499999999999999e-113 or -5.1999999999999998e-299 < t < 8.2e14

   1. Initial program 87.2%

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

   2. Taylor expanded in z around inf 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-/l* 82.9%

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

   4. Simplified 82.9%

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

   5. Taylor expanded in x around inf 68.2%

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

      1. *-commutative 68.2%

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

      2. mul-1-neg 68.2%

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

      3. unsub-neg 68.2%

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

   7. Simplified 68.2%

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

   if -1.9499999999999999e-113 < t < -5.1999999999999998e-299

   1. Initial program 78.0%

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

   2. Taylor expanded in t around 0 69.8%

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

   3. Taylor expanded in y around inf 64.4%

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

      1. associate-/l* 78.0%

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

   5. Simplified 78.0%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a - t}\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-299}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 13: 60.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-137}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-297}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 19500000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.6e-12)
     t_1
     (if (<= t -1.3e-137)
       (* z (/ (- y x) (- a t)))
       (if (<= t -1.9e-297)
         (+ x (/ y (/ a z)))
         (if (<= t 19500000.0) (* x (- 1.0 (/ z (- a t)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.6e-12) {
		tmp = t_1;
	} else if (t <= -1.3e-137) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -1.9e-297) {
		tmp = x + (y / (a / z));
	} else if (t <= 19500000.0) {
		tmp = x * (1.0 - (z / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-1.6d-12)) then
        tmp = t_1
    else if (t <= (-1.3d-137)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= (-1.9d-297)) then
        tmp = x + (y / (a / z))
    else if (t <= 19500000.0d0) then
        tmp = x * (1.0d0 - (z / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.6e-12) {
		tmp = t_1;
	} else if (t <= -1.3e-137) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -1.9e-297) {
		tmp = x + (y / (a / z));
	} else if (t <= 19500000.0) {
		tmp = x * (1.0 - (z / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -1.6e-12:
		tmp = t_1
	elif t <= -1.3e-137:
		tmp = z * ((y - x) / (a - t))
	elif t <= -1.9e-297:
		tmp = x + (y / (a / z))
	elif t <= 19500000.0:
		tmp = x * (1.0 - (z / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.6e-12)
		tmp = t_1;
	elseif (t <= -1.3e-137)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= -1.9e-297)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 19500000.0)
		tmp = Float64(x * Float64(1.0 - Float64(z / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -1.6e-12)
		tmp = t_1;
	elseif (t <= -1.3e-137)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= -1.9e-297)
		tmp = x + (y / (a / z));
	elseif (t <= 19500000.0)
		tmp = x * (1.0 - (z / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e-12], t$95$1, If[LessEqual[t, -1.3e-137], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.9e-297], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 19500000.0], N[(x * N[(1.0 - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.6e-12 or 1.95e7 < t

   1. Initial program 49.4%

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

      1. associate-/l* 74.2%

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

   3. Simplified 74.2%

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

      1. div-inv 74.1%

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

   5. Applied egg-rr 74.1%

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

   6. Taylor expanded in y around inf 70.0%

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

      1. *-commutative 70.0%

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

      2. div-sub 70.0%

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

   8. Simplified 70.0%

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

   if -1.6e-12 < t < -1.3e-137

   1. Initial program 87.5%

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

      1. div-inv 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in z around inf 62.8%

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

      1. div-sub 62.8%

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

   8. Simplified 62.8%

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

   if -1.3e-137 < t < -1.90000000000000002e-297

   1. Initial program 79.6%

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

   2. Taylor expanded in t around 0 73.7%

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

   3. Taylor expanded in y around inf 67.9%

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

      1. associate-/l* 79.5%

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

   5. Simplified 79.5%

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

   if -1.90000000000000002e-297 < t < 1.95e7

   1. Initial program 88.5%

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

   2. Taylor expanded in z around inf 82.2%

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

      1. *-commutative 82.2%

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

      2. associate-/l* 83.6%

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

   4. Simplified 83.6%

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

   5. Taylor expanded in x around inf 68.3%

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

      1. *-commutative 68.3%

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

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

   7. Simplified 68.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a - t}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-12}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-137}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-297}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 19500000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 14: 68.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-21}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{+107}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2e+52)
   (+ x (/ z (/ a (- y x))))
   (if (<= a 2.9e-21)
     (- y (/ z (/ t (- y x))))
     (if (<= a 5.1e+91)
       (* z (/ (- y x) (- a t)))
       (if (<= a 9.1e+107) (- y (/ y (/ t z))) (+ x (/ (- y x) (/ a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e+52) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= 2.9e-21) {
		tmp = y - (z / (t / (y - x)));
	} else if (a <= 5.1e+91) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 9.1e+107) {
		tmp = y - (y / (t / z));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2d+52)) then
        tmp = x + (z / (a / (y - x)))
    else if (a <= 2.9d-21) then
        tmp = y - (z / (t / (y - x)))
    else if (a <= 5.1d+91) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 9.1d+107) then
        tmp = y - (y / (t / z))
    else
        tmp = x + ((y - x) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e+52) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= 2.9e-21) {
		tmp = y - (z / (t / (y - x)));
	} else if (a <= 5.1e+91) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 9.1e+107) {
		tmp = y - (y / (t / z));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2e+52:
		tmp = x + (z / (a / (y - x)))
	elif a <= 2.9e-21:
		tmp = y - (z / (t / (y - x)))
	elif a <= 5.1e+91:
		tmp = z * ((y - x) / (a - t))
	elif a <= 9.1e+107:
		tmp = y - (y / (t / z))
	else:
		tmp = x + ((y - x) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2e+52)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (a <= 2.9e-21)
		tmp = Float64(y - Float64(z / Float64(t / Float64(y - x))));
	elseif (a <= 5.1e+91)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 9.1e+107)
		tmp = Float64(y - Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2e+52)
		tmp = x + (z / (a / (y - x)));
	elseif (a <= 2.9e-21)
		tmp = y - (z / (t / (y - x)));
	elseif (a <= 5.1e+91)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 9.1e+107)
		tmp = y - (y / (t / z));
	else
		tmp = x + ((y - x) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2e+52], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-21], N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.1e+91], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.1e+107], N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2e52

   1. Initial program 67.1%

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

   2. Taylor expanded in t around 0 60.4%

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

      1. associate-/l* 72.9%

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

   4. Simplified 72.9%

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

   if -2e52 < a < 2.9e-21

   1. Initial program 71.3%

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

   2. Taylor expanded in t around -inf 85.3%

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

      1. mul-1-neg 85.3%

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

      2. unsub-neg 85.3%

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

      3. div-sub 84.6%

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

      4. *-commutative 84.6%

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

      5. div-sub 85.3%

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

      6. distribute-rgt-out-- 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in z around inf 80.6%

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

      1. associate-/l* 79.0%

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

   7. Simplified 79.0%

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

   if 2.9e-21 < a < 5.10000000000000013e91

   1. Initial program 59.6%

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

      1. associate-/l* 84.3%

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

   3. Simplified 84.3%

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

      1. div-inv 84.3%

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

   5. Applied egg-rr 84.3%

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

   6. Taylor expanded in z around inf 79.8%

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

      1. div-sub 79.8%

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

   8. Simplified 79.8%

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

   if 5.10000000000000013e91 < a < 9.10000000000000007e107

   1. Initial program 42.9%

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

   2. Taylor expanded in t around -inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

      3. div-sub 80.0%

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

      4. *-commutative 80.0%

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

      5. div-sub 80.0%

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

      6. distribute-rgt-out-- 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 100.0%

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

      1. associate-/l* 100.0%

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

   10. Simplified 100.0%

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

   if 9.10000000000000007e107 < a

   1. Initial program 65.2%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around 0 87.4%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-21}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{+107}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 15: 58.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{z}{\frac{-t}{x}}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{-271}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ z (/ (- t) x)))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -2.3e-18)
     t_2
     (if (<= a -5.5e-254)
       t_1
       (if (<= a 9.4e-271)
         (- y (/ y (/ t z)))
         (if (<= a 9.1e+107) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z / (-t / x));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -2.3e-18) {
		tmp = t_2;
	} else if (a <= -5.5e-254) {
		tmp = t_1;
	} else if (a <= 9.4e-271) {
		tmp = y - (y / (t / z));
	} else if (a <= 9.1e+107) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y - (z / (-t / x))
    t_2 = x + (y / (a / z))
    if (a <= (-2.3d-18)) then
        tmp = t_2
    else if (a <= (-5.5d-254)) then
        tmp = t_1
    else if (a <= 9.4d-271) then
        tmp = y - (y / (t / z))
    else if (a <= 9.1d+107) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z / (-t / x));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -2.3e-18) {
		tmp = t_2;
	} else if (a <= -5.5e-254) {
		tmp = t_1;
	} else if (a <= 9.4e-271) {
		tmp = y - (y / (t / z));
	} else if (a <= 9.1e+107) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z / (-t / x))
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -2.3e-18:
		tmp = t_2
	elif a <= -5.5e-254:
		tmp = t_1
	elif a <= 9.4e-271:
		tmp = y - (y / (t / z))
	elif a <= 9.1e+107:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(z / Float64(Float64(-t) / x)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -2.3e-18)
		tmp = t_2;
	elseif (a <= -5.5e-254)
		tmp = t_1;
	elseif (a <= 9.4e-271)
		tmp = Float64(y - Float64(y / Float64(t / z)));
	elseif (a <= 9.1e+107)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (z / (-t / x));
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -2.3e-18)
		tmp = t_2;
	elseif (a <= -5.5e-254)
		tmp = t_1;
	elseif (a <= 9.4e-271)
		tmp = y - (y / (t / z));
	elseif (a <= 9.1e+107)
		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[(z / N[((-t) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e-18], t$95$2, If[LessEqual[a, -5.5e-254], t$95$1, If[LessEqual[a, 9.4e-271], N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.1e+107], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.3000000000000001e-18 or 9.10000000000000007e107 < a

   1. Initial program 65.3%

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

   2. Taylor expanded in t around 0 58.6%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. associate-/l* 71.5%

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

   5. Simplified 71.5%

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

   if -2.3000000000000001e-18 < a < -5.4999999999999999e-254 or 9.4000000000000001e-271 < a < 9.10000000000000007e107

   1. Initial program 69.6%

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

   2. Taylor expanded in t around -inf 79.9%

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

      1. mul-1-neg 79.9%

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

      2. unsub-neg 79.9%

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

      3. div-sub 77.5%

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

      4. *-commutative 77.5%

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

      5. div-sub 79.9%

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

      6. distribute-rgt-out-- 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in z around inf 76.3%

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

      1. associate-/l* 77.9%

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

   7. Simplified 77.9%

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

   8. Taylor expanded in y around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. distribute-neg-frac 67.7%

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

   10. Simplified 67.7%

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

   if -5.4999999999999999e-254 < a < 9.4000000000000001e-271

   1. Initial program 72.3%

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

   2. Taylor expanded in t around -inf 94.0%

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

      1. mul-1-neg 94.0%

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

      2. unsub-neg 94.0%

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

      3. div-sub 94.0%

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

      4. *-commutative 94.0%

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

      5. div-sub 94.0%

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

      6. distribute-rgt-out-- 94.0%

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

   4. Simplified 94.0%

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

   5. Taylor expanded in z around inf 94.0%

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

      1. associate-/l* 86.2%

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

   7. Simplified 86.2%

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

   8. Taylor expanded in y around inf 85.0%

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

      1. associate-/l* 85.0%

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

   10. Simplified 85.0%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-254}:\\ \;\;\;\;y - \frac{z}{\frac{-t}{x}}\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{-271}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{+107}:\\ \;\;\;\;y - \frac{z}{\frac{-t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 16: 65.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 6600000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -1e-65)
     t_1
     (if (<= t 8.5e-101)
       (+ x (/ z (/ a (- y x))))
       (if (<= t 6600000000000.0) (* x (- 1.0 (/ z (- a t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1e-65) {
		tmp = t_1;
	} else if (t <= 8.5e-101) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 6600000000000.0) {
		tmp = x * (1.0 - (z / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-1d-65)) then
        tmp = t_1
    else if (t <= 8.5d-101) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= 6600000000000.0d0) then
        tmp = x * (1.0d0 - (z / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1e-65) {
		tmp = t_1;
	} else if (t <= 8.5e-101) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 6600000000000.0) {
		tmp = x * (1.0 - (z / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -1e-65:
		tmp = t_1
	elif t <= 8.5e-101:
		tmp = x + (z / (a / (y - x)))
	elif t <= 6600000000000.0:
		tmp = x * (1.0 - (z / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -1e-65)
		tmp = t_1;
	elseif (t <= 8.5e-101)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= 6600000000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(z / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -1e-65)
		tmp = t_1;
	elseif (t <= 8.5e-101)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= 6600000000000.0)
		tmp = x * (1.0 - (z / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e-65], t$95$1, If[LessEqual[t, 8.5e-101], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6600000000000.0], N[(x * N[(1.0 - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.99999999999999923e-66 or 6.6e12 < t

   1. Initial program 54.1%

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

      1. associate-/l* 76.6%

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

   3. Simplified 76.6%

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

      1. div-inv 76.5%

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

   5. Applied egg-rr 76.5%

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

   6. Taylor expanded in y around inf 68.5%

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

      1. *-commutative 68.5%

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

      2. div-sub 68.5%

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

   8. Simplified 68.5%

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

   if -9.99999999999999923e-66 < t < 8.49999999999999941e-101

   1. Initial program 87.0%

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

   2. Taylor expanded in t around 0 73.0%

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

      1. associate-/l* 83.6%

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

   4. Simplified 83.6%

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

   if 8.49999999999999941e-101 < t < 6.6e12

   1. Initial program 76.9%

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

   2. Taylor expanded in z around inf 65.5%

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

      1. *-commutative 65.5%

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

      2. associate-/l* 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in x around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. mul-1-neg 63.4%

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

      3. unsub-neg 63.4%

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

   7. Simplified 63.4%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 6600000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 17: 65.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 3300000000:\\ \;\;\;\;x - z \cdot \frac{x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.1e-61)
     t_1
     (if (<= t 6e-101)
       (+ x (/ z (/ a (- y x))))
       (if (<= t 3300000000.0) (- x (* z (/ x (- a t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.1e-61) {
		tmp = t_1;
	} else if (t <= 6e-101) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 3300000000.0) {
		tmp = x - (z * (x / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-2.1d-61)) then
        tmp = t_1
    else if (t <= 6d-101) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= 3300000000.0d0) then
        tmp = x - (z * (x / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.1e-61) {
		tmp = t_1;
	} else if (t <= 6e-101) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 3300000000.0) {
		tmp = x - (z * (x / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -2.1e-61:
		tmp = t_1
	elif t <= 6e-101:
		tmp = x + (z / (a / (y - x)))
	elif t <= 3300000000.0:
		tmp = x - (z * (x / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.1e-61)
		tmp = t_1;
	elseif (t <= 6e-101)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= 3300000000.0)
		tmp = Float64(x - Float64(z * Float64(x / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -2.1e-61)
		tmp = t_1;
	elseif (t <= 6e-101)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= 3300000000.0)
		tmp = x - (z * (x / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e-61], t$95$1, If[LessEqual[t, 6e-101], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3300000000.0], N[(x - N[(z * N[(x / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0999999999999999e-61 or 3.3e9 < t

   1. Initial program 54.1%

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

      1. associate-/l* 76.6%

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

   3. Simplified 76.6%

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

      1. div-inv 76.5%

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

   5. Applied egg-rr 76.5%

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

   6. Taylor expanded in y around inf 68.5%

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

      1. *-commutative 68.5%

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

      2. div-sub 68.5%

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

   8. Simplified 68.5%

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

   if -2.0999999999999999e-61 < t < 6.0000000000000006e-101

   1. Initial program 87.0%

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

   2. Taylor expanded in t around 0 73.0%

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

      1. associate-/l* 83.6%

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

   4. Simplified 83.6%

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

   if 6.0000000000000006e-101 < t < 3.3e9

   1. Initial program 76.9%

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

      1. associate-/l* 83.3%

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

   3. Simplified 83.3%

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

      1. div-inv 83.4%

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

   5. Applied egg-rr 83.4%

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

   6. Taylor expanded in z around inf 71.8%

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

   7. Taylor expanded in x around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. neg-mul-1 63.4%

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

      3. distribute-rgt-in 63.4%

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

      4. *-lft-identity 63.4%

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

      5. distribute-lft-neg-in 63.4%

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

      6. *-commutative 63.4%

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

      7. associate-*r/ 60.3%

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

      8. *-commutative 60.3%

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

      9. unsub-neg 60.3%

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

      10. *-lft-identity 60.3%

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

      11. times-frac 63.5%

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

      12. /-rgt-identity 63.5%

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

   9. Simplified 63.5%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-61}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 3300000000:\\ \;\;\;\;x - z \cdot \frac{x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 18: 77.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+29} \lor \neg \left(t \leq 2.3 \cdot 10^{+32}\right):\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.1e+29) (not (<= t 2.3e+32)))
   (- y (/ z (/ t (- y x))))
   (- x (/ (- x y) (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.1e+29) || !(t <= 2.3e+32)) {
		tmp = y - (z / (t / (y - x)));
	} else {
		tmp = x - ((x - y) / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.1d+29)) .or. (.not. (t <= 2.3d+32))) then
        tmp = y - (z / (t / (y - x)))
    else
        tmp = x - ((x - y) / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.1e+29) || !(t <= 2.3e+32)) {
		tmp = y - (z / (t / (y - x)));
	} else {
		tmp = x - ((x - y) / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.1e+29) or not (t <= 2.3e+32):
		tmp = y - (z / (t / (y - x)))
	else:
		tmp = x - ((x - y) / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.1e+29) || !(t <= 2.3e+32))
		tmp = Float64(y - Float64(z / Float64(t / Float64(y - x))));
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.1e+29) || ~((t <= 2.3e+32)))
		tmp = y - (z / (t / (y - x)));
	else
		tmp = x - ((x - y) / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.1e+29], N[Not[LessEqual[t, 2.3e+32]], $MachinePrecision]], N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.0999999999999999e29 or 2.3e32 < t

   1. Initial program 45.4%

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

   2. Taylor expanded in t around -inf 71.8%

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

      1. mul-1-neg 71.8%

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

      2. unsub-neg 71.8%

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

      3. div-sub 71.8%

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

      4. *-commutative 71.8%

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

      5. div-sub 71.8%

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

      6. distribute-rgt-out-- 72.1%

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

   4. Simplified 72.1%

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

   5. Taylor expanded in z around inf 69.7%

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

      1. associate-/l* 76.5%

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

   7. Simplified 76.5%

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

   if -3.0999999999999999e29 < t < 2.3e32

   1. Initial program 85.0%

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

   2. Taylor expanded in z around inf 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-/l* 83.3%

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

   4. Simplified 83.3%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+29} \lor \neg \left(t \leq 2.3 \cdot 10^{+32}\right):\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 19: 80.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+29} \lor \neg \left(t \leq 1.35 \cdot 10^{-9}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.2e+29) (not (<= t 1.35e-9)))
   (+ y (* (/ (- y x) t) (- a z)))
   (- x (/ (- x y) (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.2e+29) || !(t <= 1.35e-9)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = x - ((x - y) / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7.2d+29)) .or. (.not. (t <= 1.35d-9))) then
        tmp = y + (((y - x) / t) * (a - z))
    else
        tmp = x - ((x - y) / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.2e+29) || !(t <= 1.35e-9)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = x - ((x - y) / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.2e+29) or not (t <= 1.35e-9):
		tmp = y + (((y - x) / t) * (a - z))
	else:
		tmp = x - ((x - y) / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.2e+29) || !(t <= 1.35e-9))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.2e+29) || ~((t <= 1.35e-9)))
		tmp = y + (((y - x) / t) * (a - z));
	else
		tmp = x - ((x - y) / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.2e+29], N[Not[LessEqual[t, 1.35e-9]], $MachinePrecision]], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.19999999999999952e29 or 1.3500000000000001e-9 < t

   1. Initial program 49.2%

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

      1. associate-/l* 73.7%

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

   3. Simplified 73.7%

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

      1. div-inv 73.6%

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

   5. Applied egg-rr 73.6%

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

   6. Taylor expanded in t around inf 71.8%

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

      1. +-commutative 71.8%

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

      2. *-commutative 71.8%

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

      3. associate--l+ 71.8%

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

      4. associate-*r/ 71.8%

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

      5. associate-*r/ 71.8%

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

      6. div-sub 71.8%

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

      7. distribute-lft-out-- 71.8%

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

      8. *-commutative 71.8%

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

      9. distribute-rgt-out-- 72.0%

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

      10. associate-*r/ 72.0%

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

      11. +-commutative 72.0%

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

      12. fma-def 72.0%

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

      13. associate-/l* 82.7%

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

   8. Simplified 82.7%

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

   if -7.19999999999999952e29 < t < 1.3500000000000001e-9

   1. Initial program 85.6%

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

   2. Taylor expanded in z around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-/l* 85.0%

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

   4. Simplified 85.0%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+29} \lor \neg \left(t \leq 1.35 \cdot 10^{-9}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 20: 48.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+30}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5000000:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+30)
   y
   (if (<= t 6.8e-10)
     (* x (- 1.0 (/ z a)))
     (if (<= t 5000000.0) (* (- z a) (/ x t)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+30) {
		tmp = y;
	} else if (t <= 6.8e-10) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 5000000.0) {
		tmp = (z - a) * (x / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.8d+30)) then
        tmp = y
    else if (t <= 6.8d-10) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 5000000.0d0) then
        tmp = (z - a) * (x / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+30) {
		tmp = y;
	} else if (t <= 6.8e-10) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 5000000.0) {
		tmp = (z - a) * (x / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+30:
		tmp = y
	elif t <= 6.8e-10:
		tmp = x * (1.0 - (z / a))
	elif t <= 5000000.0:
		tmp = (z - a) * (x / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+30)
		tmp = y;
	elseif (t <= 6.8e-10)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 5000000.0)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+30)
		tmp = y;
	elseif (t <= 6.8e-10)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 5000000.0)
		tmp = (z - a) * (x / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+30], y, If[LessEqual[t, 6.8e-10], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5000000.0], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.79999999999999983e30 or 5e6 < t

   1. Initial program 47.4%

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

   2. Taylor expanded in t around inf 55.4%

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

   if -2.79999999999999983e30 < t < 6.8000000000000003e-10

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0 64.4%

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

   3. Taylor expanded in x around inf 55.9%

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

      1. *-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

   5. Simplified 55.9%

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

   if 6.8000000000000003e-10 < t < 5e6

   1. Initial program 75.7%

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

   2. Taylor expanded in t around -inf 99.3%

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

      1. mul-1-neg 99.3%

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

      2. unsub-neg 99.3%

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

      3. div-sub 99.3%

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

      4. *-commutative 99.3%

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

      5. div-sub 99.3%

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

      6. distribute-rgt-out-- 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in y around 0 89.3%

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

   6. Taylor expanded in z around 0 89.3%

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

      1. associate-/l* 89.3%

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

      2. mul-1-neg 89.3%

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

      3. associate-/l* 89.5%

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

      4. sub-neg 89.5%

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

      5. div-sub 89.5%

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

      6. associate-/r/ 89.3%

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

      7. *-commutative 89.3%

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

      8. associate-*r/ 89.3%

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

      9. *-commutative 89.3%

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

      10. associate-*r/ 89.7%

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

   8. Simplified 89.7%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+30}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5000000:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 21: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4300000:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4e+29)
   y
   (if (<= t 1.2e-47) x (if (<= t 4300000.0) (* x (/ z t)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+29) {
		tmp = y;
	} else if (t <= 1.2e-47) {
		tmp = x;
	} else if (t <= 4300000.0) {
		tmp = x * (z / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4d+29)) then
        tmp = y
    else if (t <= 1.2d-47) then
        tmp = x
    else if (t <= 4300000.0d0) then
        tmp = x * (z / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+29) {
		tmp = y;
	} else if (t <= 1.2e-47) {
		tmp = x;
	} else if (t <= 4300000.0) {
		tmp = x * (z / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4e+29:
		tmp = y
	elif t <= 1.2e-47:
		tmp = x
	elif t <= 4300000.0:
		tmp = x * (z / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4e+29)
		tmp = y;
	elseif (t <= 1.2e-47)
		tmp = x;
	elseif (t <= 4300000.0)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4e+29)
		tmp = y;
	elseif (t <= 1.2e-47)
		tmp = x;
	elseif (t <= 4300000.0)
		tmp = x * (z / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4e+29], y, If[LessEqual[t, 1.2e-47], x, If[LessEqual[t, 4300000.0], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.99999999999999966e29 or 4.3e6 < t

   1. Initial program 47.4%

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

   2. Taylor expanded in t around inf 55.4%

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

   if -3.99999999999999966e29 < t < 1.2e-47

   1. Initial program 86.8%

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

   2. Taylor expanded in a around inf 41.3%

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

   if 1.2e-47 < t < 4.3e6

   1. Initial program 73.1%

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

   2. Taylor expanded in t around -inf 72.5%

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

      1. mul-1-neg 72.5%

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

      2. unsub-neg 72.5%

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

      3. div-sub 72.5%

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

      4. *-commutative 72.5%

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

      5. div-sub 72.5%

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

      6. distribute-rgt-out-- 72.5%

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

   4. Simplified 72.5%

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

   5. Taylor expanded in y around 0 52.1%

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

   6. Taylor expanded in z around inf 48.3%

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

      1. associate-/l* 48.3%

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

      2. associate-/r/ 48.4%

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

   8. Simplified 48.4%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4300000:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 22: 48.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5200000:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.1e+29)
   y
   (if (<= t 2.2e-9)
     (* x (- 1.0 (/ z a)))
     (if (<= t 5200000.0) (* x (/ z t)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.1e+29) {
		tmp = y;
	} else if (t <= 2.2e-9) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 5200000.0) {
		tmp = x * (z / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.1d+29)) then
        tmp = y
    else if (t <= 2.2d-9) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 5200000.0d0) then
        tmp = x * (z / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.1e+29) {
		tmp = y;
	} else if (t <= 2.2e-9) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 5200000.0) {
		tmp = x * (z / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.1e+29:
		tmp = y
	elif t <= 2.2e-9:
		tmp = x * (1.0 - (z / a))
	elif t <= 5200000.0:
		tmp = x * (z / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.1e+29)
		tmp = y;
	elseif (t <= 2.2e-9)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 5200000.0)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.1e+29)
		tmp = y;
	elseif (t <= 2.2e-9)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 5200000.0)
		tmp = x * (z / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.1e+29], y, If[LessEqual[t, 2.2e-9], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5200000.0], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1000000000000001e29 or 5.2e6 < t

   1. Initial program 47.4%

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

   2. Taylor expanded in t around inf 55.4%

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

   if -1.1000000000000001e29 < t < 2.1999999999999998e-9

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0 64.4%

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

   3. Taylor expanded in x around inf 55.9%

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

      1. *-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

   5. Simplified 55.9%

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

   if 2.1999999999999998e-9 < t < 5.2e6

   1. Initial program 75.7%

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

   2. Taylor expanded in t around -inf 99.3%

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

      1. mul-1-neg 99.3%

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

      2. unsub-neg 99.3%

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

      3. div-sub 99.3%

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

      4. *-commutative 99.3%

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

      5. div-sub 99.3%

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

      6. distribute-rgt-out-- 99.3%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   4. Simplified 99.3%

      \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   5. Taylor expanded in y around 0 89.3%

      \[\leadsto \color{blue}{\frac{\left(z - a\right) \cdot x}{t}} \]

   6. Taylor expanded in z around inf 77.7%

      \[\leadsto \color{blue}{\frac{z \cdot x}{t}} \]
   7. Step-by-step derivation

      1. associate-/l* 77.7%

         \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

      2. associate-/r/ 77.7%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot x} \]

   8. Simplified 77.7%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5200000:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 23: 55.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+49} \lor \neg \left(a \leq 9.1 \cdot 10^{+107}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4e+49) (not (<= a 9.1e+107)))
   (+ x (/ y (/ a z)))
   (- y (/ y (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4e+49) || !(a <= 9.1e+107)) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y - (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4d+49)) .or. (.not. (a <= 9.1d+107))) then
        tmp = x + (y / (a / z))
    else
        tmp = y - (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4e+49) || !(a <= 9.1e+107)) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y - (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4e+49) or not (a <= 9.1e+107):
		tmp = x + (y / (a / z))
	else:
		tmp = y - (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4e+49) || !(a <= 9.1e+107))
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(y - Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4e+49) || ~((a <= 9.1e+107)))
		tmp = x + (y / (a / z));
	else
		tmp = y - (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4e+49], N[Not[LessEqual[a, 9.1e+107]], $MachinePrecision]], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.99999999999999979e49 or 9.10000000000000007e107 < a

   1. Initial program 66.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in t around 0 60.3%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a} + x} \]

   3. Taylor expanded in y around inf 62.1%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} + x \]
   4. Step-by-step derivation

      1. associate-/l* 74.7%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} + x \]

   5. Simplified 74.7%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} + x \]

   if -3.99999999999999979e49 < a < 9.10000000000000007e107

   1. Initial program 69.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in t around -inf 80.1%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]
   3. Step-by-step derivation

      1. mul-1-neg 80.1%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

      2. unsub-neg 80.1%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      3. div-sub 78.3%

         \[\leadsto y - \color{blue}{\left(\frac{\left(y - x\right) \cdot z}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      4. *-commutative 78.3%

         \[\leadsto y - \left(\frac{\color{blue}{z \cdot \left(y - x\right)}}{t} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      5. div-sub 80.1%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. distribute-rgt-out-- 80.1%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   4. Simplified 80.1%

      \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   5. Taylor expanded in z around inf 76.1%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* 77.0%

         \[\leadsto y - \color{blue}{\frac{z}{\frac{t}{y - x}}} \]

   7. Simplified 77.0%

      \[\leadsto y - \color{blue}{\frac{z}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around inf 59.6%

      \[\leadsto y - \color{blue}{\frac{y \cdot z}{t}} \]
   9. Step-by-step derivation

      1. associate-/l* 61.5%

         \[\leadsto y - \color{blue}{\frac{y}{\frac{t}{z}}} \]

   10. Simplified 61.5%

       \[\leadsto y - \color{blue}{\frac{y}{\frac{t}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+49} \lor \neg \left(a \leq 9.1 \cdot 10^{+107}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 24: 39.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+28}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.9e+28) y (if (<= t 1.15e+14) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.9e+28) {
		tmp = y;
	} else if (t <= 1.15e+14) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.9d+28)) then
        tmp = y
    else if (t <= 1.15d+14) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.9e+28) {
		tmp = y;
	} else if (t <= 1.15e+14) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.9e+28:
		tmp = y
	elif t <= 1.15e+14:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.9e+28)
		tmp = y;
	elseif (t <= 1.15e+14)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.9e+28)
		tmp = y;
	elseif (t <= 1.15e+14)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.9e+28], y, If[LessEqual[t, 1.15e+14], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -3.8999999999999999e28 or 1.15e14 < t

   1. Initial program 46.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in t around inf 55.9%

      \[\leadsto \color{blue}{y} \]

   if -3.8999999999999999e28 < t < 1.15e14

   1. Initial program 85.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in a around inf 38.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+28}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 25: 25.7% 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 68.1%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

2. Taylor expanded in a around inf 27.1%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 27.1%

   \[\leadsto x \]

Developer target: 87.0% 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 2023200 
(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))))