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

Percentage Accurate: 67.7% → 85.9%

Time: 16.6s

Alternatives: 27

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 85.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.66 \cdot 10^{-116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-64}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(z - t\right)}{t - a}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) (- a t)))))
        (t_2 (+ y (* (- z a) (/ (- x y) t)))))
   (if (<= t -2.1e+113)
     t_2
     (if (<= t -1.66e-116)
       t_1
       (if (<= t 9e-64)
         (- x (/ (* (- y x) (- z t)) (- t a)))
         (if (<= t 1.5e+68) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double t_2 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -2.1e+113) {
		tmp = t_2;
	} else if (t <= -1.66e-116) {
		tmp = t_1;
	} else if (t <= 9e-64) {
		tmp = x - (((y - x) * (z - t)) / (t - a));
	} else if (t <= 1.5e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z - t) * ((y - x) / (a - t)))
    t_2 = y + ((z - a) * ((x - y) / t))
    if (t <= (-2.1d+113)) then
        tmp = t_2
    else if (t <= (-1.66d-116)) then
        tmp = t_1
    else if (t <= 9d-64) then
        tmp = x - (((y - x) * (z - t)) / (t - a))
    else if (t <= 1.5d+68) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double t_2 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -2.1e+113) {
		tmp = t_2;
	} else if (t <= -1.66e-116) {
		tmp = t_1;
	} else if (t <= 9e-64) {
		tmp = x - (((y - x) * (z - t)) / (t - a));
	} else if (t <= 1.5e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) / (a - t)))
	t_2 = y + ((z - a) * ((x - y) / t))
	tmp = 0
	if t <= -2.1e+113:
		tmp = t_2
	elif t <= -1.66e-116:
		tmp = t_1
	elif t <= 9e-64:
		tmp = x - (((y - x) * (z - t)) / (t - a))
	elif t <= 1.5e+68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))))
	t_2 = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (t <= -2.1e+113)
		tmp = t_2;
	elseif (t <= -1.66e-116)
		tmp = t_1;
	elseif (t <= 9e-64)
		tmp = Float64(x - Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(t - a)));
	elseif (t <= 1.5e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) / (a - t)));
	t_2 = y + ((z - a) * ((x - y) / t));
	tmp = 0.0;
	if (t <= -2.1e+113)
		tmp = t_2;
	elseif (t <= -1.66e-116)
		tmp = t_1;
	elseif (t <= 9e-64)
		tmp = x - (((y - x) * (z - t)) / (t - a));
	elseif (t <= 1.5e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+113], t$95$2, If[LessEqual[t, -1.66e-116], t$95$1, If[LessEqual[t, 9e-64], N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0999999999999999e113 or 1.5000000000000001e68 < t

   1. Initial program 28.3%

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

   3. Taylor expanded in t around inf 65.8%

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

      1. associate--l+ 65.8%

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

      2. distribute-lft-out-- 65.8%

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

      3. div-sub 65.8%

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

      4. mul-1-neg 65.8%

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

      5. unsub-neg 65.8%

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

      6. div-sub 65.8%

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

      7. associate-/l* 78.7%

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

      8. associate-/l* 86.8%

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

      9. distribute-rgt-out-- 86.8%

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

   5. Simplified 86.8%

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

   if -2.0999999999999999e113 < t < -1.65999999999999988e-116 or 9.00000000000000019e-64 < t < 1.5000000000000001e68

   1. Initial program 78.3%

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

   3. Taylor expanded in y around 0 81.6%

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

      1. +-commutative 81.6%

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

      2. div-sub 81.6%

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

      3. mul-1-neg 81.6%

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

      4. associate-/l* 91.2%

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

      5. distribute-lft-neg-in 91.2%

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

      6. distribute-rgt-in 92.4%

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

      7. sub-neg 92.4%

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

      8. associate-*l/ 78.3%

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

      9. associate-*r/ 91.3%

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

   5. Simplified 91.3%

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

   if -1.65999999999999988e-116 < t < 9.00000000000000019e-64

   1. Initial program 96.0%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+113}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -1.66 \cdot 10^{-116}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-64}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(z - t\right)}{t - a}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+68}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(z - t\right)}{t - a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-291} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- z t)) (- t a)))))
   (if (or (<= t_1 -4e-291) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (+ y (* x (/ (- z a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (z - t)) / (t - a));
	double tmp;
	if ((t_1 <= -4e-291) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + (x * ((z - a) / t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(t - a)))
	tmp = 0.0
	if ((t_1 <= -4e-291) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-291], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $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))) < -3.99999999999999985e-291 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 69.3%

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

      1. +-commutative 69.3%

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

      2. associate-/l* 88.5%

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

      3. fma-define 88.5%

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

   3. Simplified 88.5%

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

   if -3.99999999999999985e-291 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.3%

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

      1. +-commutative 3.3%

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

      2. associate-/l* 3.3%

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

      3. fma-define 3.3%

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

   3. Simplified 3.3%

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

      1. clear-num 3.3%

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

      2. inv-pow 3.3%

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

   6. Applied egg-rr 3.3%

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

      1. unpow-1 3.3%

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

   8. Simplified 3.3%

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

   9. Taylor expanded in t around inf 99.7%

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

       1. associate--l+ 99.7%

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

       2. associate-*r/ 99.7%

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

       3. associate-*r/ 99.7%

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

       4. mul-1-neg 99.7%

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

       5. div-sub 99.7%

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

       6. mul-1-neg 99.7%

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

       7. distribute-lft-out-- 99.7%

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

       8. associate-*r/ 99.7%

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

       9. mul-1-neg 99.7%

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

       10. unsub-neg 99.7%

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

       11. distribute-rgt-out-- 99.7%

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

   11. Simplified 99.7%

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

   12. Taylor expanded in y around 0 99.7%

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

       1. mul-1-neg 99.7%

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

       2. associate-/l* 99.8%

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

       3. distribute-rgt-neg-in 99.8%

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

       4. distribute-neg-frac2 99.8%

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

   14. Simplified 99.8%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(z - t\right)}{t - a} \leq -4 \cdot 10^{-291} \lor \neg \left(x - \frac{\left(y - x\right) \cdot \left(z - t\right)}{t - a} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - z\right) \cdot \frac{y}{t - a}\\ t_2 := y + x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+29}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-49}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-161}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t z) (/ y (- t a)))) (t_2 (+ y (* x (/ z t)))))
   (if (<= t -8.5e+111)
     t_2
     (if (<= t -8.2e+29)
       (- x (* y (/ (- t z) a)))
       (if (<= t -4.1e+23)
         (* x (/ (- z a) t))
         (if (<= t -6.8e-49)
           (+ x (* z (/ (- y x) a)))
           (if (<= t -1.8e-98)
             t_1
             (if (<= t -1.1e-161)
               (* z (/ (- y x) (- a t)))
               (if (<= t 2.8e-106)
                 (+ x (/ (* (- y x) z) a))
                 (if (<= t 1.7e+102) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) * (y / (t - a));
	double t_2 = y + (x * (z / t));
	double tmp;
	if (t <= -8.5e+111) {
		tmp = t_2;
	} else if (t <= -8.2e+29) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= -4.1e+23) {
		tmp = x * ((z - a) / t);
	} else if (t <= -6.8e-49) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= -1.8e-98) {
		tmp = t_1;
	} else if (t <= -1.1e-161) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 2.8e-106) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= 1.7e+102) {
		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 = (t - z) * (y / (t - a))
    t_2 = y + (x * (z / t))
    if (t <= (-8.5d+111)) then
        tmp = t_2
    else if (t <= (-8.2d+29)) then
        tmp = x - (y * ((t - z) / a))
    else if (t <= (-4.1d+23)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-6.8d-49)) then
        tmp = x + (z * ((y - x) / a))
    else if (t <= (-1.8d-98)) then
        tmp = t_1
    else if (t <= (-1.1d-161)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 2.8d-106) then
        tmp = x + (((y - x) * z) / a)
    else if (t <= 1.7d+102) 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 = (t - z) * (y / (t - a));
	double t_2 = y + (x * (z / t));
	double tmp;
	if (t <= -8.5e+111) {
		tmp = t_2;
	} else if (t <= -8.2e+29) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= -4.1e+23) {
		tmp = x * ((z - a) / t);
	} else if (t <= -6.8e-49) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= -1.8e-98) {
		tmp = t_1;
	} else if (t <= -1.1e-161) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 2.8e-106) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= 1.7e+102) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - z) * (y / (t - a))
	t_2 = y + (x * (z / t))
	tmp = 0
	if t <= -8.5e+111:
		tmp = t_2
	elif t <= -8.2e+29:
		tmp = x - (y * ((t - z) / a))
	elif t <= -4.1e+23:
		tmp = x * ((z - a) / t)
	elif t <= -6.8e-49:
		tmp = x + (z * ((y - x) / a))
	elif t <= -1.8e-98:
		tmp = t_1
	elif t <= -1.1e-161:
		tmp = z * ((y - x) / (a - t))
	elif t <= 2.8e-106:
		tmp = x + (((y - x) * z) / a)
	elif t <= 1.7e+102:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) * Float64(y / Float64(t - a)))
	t_2 = Float64(y + Float64(x * Float64(z / t)))
	tmp = 0.0
	if (t <= -8.5e+111)
		tmp = t_2;
	elseif (t <= -8.2e+29)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / a)));
	elseif (t <= -4.1e+23)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -6.8e-49)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (t <= -1.8e-98)
		tmp = t_1;
	elseif (t <= -1.1e-161)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 2.8e-106)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / a));
	elseif (t <= 1.7e+102)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - z) * (y / (t - a));
	t_2 = y + (x * (z / t));
	tmp = 0.0;
	if (t <= -8.5e+111)
		tmp = t_2;
	elseif (t <= -8.2e+29)
		tmp = x - (y * ((t - z) / a));
	elseif (t <= -4.1e+23)
		tmp = x * ((z - a) / t);
	elseif (t <= -6.8e-49)
		tmp = x + (z * ((y - x) / a));
	elseif (t <= -1.8e-98)
		tmp = t_1;
	elseif (t <= -1.1e-161)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 2.8e-106)
		tmp = x + (((y - x) * z) / a);
	elseif (t <= 1.7e+102)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+111], t$95$2, If[LessEqual[t, -8.2e+29], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.1e+23], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.8e-49], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.8e-98], t$95$1, If[LessEqual[t, -1.1e-161], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-106], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+102], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -8.49999999999999983e111 or 1.7e102 < t

   1. Initial program 27.6%

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

      1. +-commutative 27.6%

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

      2. associate-/l* 66.3%

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

      3. fma-define 66.3%

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

   3. Simplified 66.3%

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

      1. clear-num 66.3%

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

      2. inv-pow 66.3%

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

   6. Applied egg-rr 66.3%

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

      1. unpow-1 66.3%

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

   8. Simplified 66.3%

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

   9. Taylor expanded in t around inf 66.0%

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

       1. associate--l+ 66.0%

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

       2. associate-*r/ 66.0%

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

       3. associate-*r/ 66.0%

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

       4. mul-1-neg 66.0%

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

       5. div-sub 66.0%

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

       6. mul-1-neg 66.0%

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

       7. distribute-lft-out-- 66.0%

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

       8. associate-*r/ 66.0%

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

       9. mul-1-neg 66.0%

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

       10. unsub-neg 66.0%

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

       11. distribute-rgt-out-- 66.0%

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

   11. Simplified 66.0%

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

   12. Taylor expanded in y around 0 70.8%

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

       1. mul-1-neg 70.8%

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

       2. associate-/l* 83.5%

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

       3. distribute-rgt-neg-in 83.5%

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

       4. distribute-neg-frac2 83.5%

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

   14. Simplified 83.5%

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

   15. Taylor expanded in z around inf 64.8%

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

       1. mul-1-neg 64.8%

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

       2. associate-/l* 76.3%

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

       3. distribute-rgt-neg-in 76.3%

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

       4. mul-1-neg 76.3%

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

       5. associate-*r/ 76.3%

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

       6. neg-mul-1 76.3%

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

   17. Simplified 76.3%

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

   if -8.49999999999999983e111 < t < -8.2000000000000007e29

   1. Initial program 74.8%

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

   3. Taylor expanded in y around inf 83.3%

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

      1. *-commutative 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in a around inf 57.1%

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

      1. associate-/l* 65.9%

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

   8. Simplified 65.9%

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

   if -8.2000000000000007e29 < t < -4.09999999999999996e23

   1. Initial program 51.3%

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

      1. +-commutative 51.3%

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

      2. associate-/l* 51.3%

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

      3. fma-define 51.3%

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

   3. Simplified 51.3%

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

      1. clear-num 51.3%

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

      2. inv-pow 51.3%

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

   6. Applied egg-rr 51.3%

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

      1. unpow-1 51.3%

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

   8. Simplified 51.3%

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

   9. Taylor expanded in t around inf 75.0%

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

       1. associate--l+ 75.0%

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

       2. associate-*r/ 75.0%

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

       3. associate-*r/ 75.0%

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

       4. mul-1-neg 75.0%

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

       5. div-sub 75.0%

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

       6. mul-1-neg 75.0%

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

       7. distribute-lft-out-- 75.0%

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

       8. associate-*r/ 75.0%

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

       9. mul-1-neg 75.0%

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

       10. unsub-neg 75.0%

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

       11. distribute-rgt-out-- 75.0%

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

   11. Simplified 75.0%

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

   12. Taylor expanded in y around 0 100.0%

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

       1. associate-/l* 100.0%

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

   14. Simplified 100.0%

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

   if -4.09999999999999996e23 < t < -6.8000000000000001e-49

   1. Initial program 81.0%

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

   3. Taylor expanded in t around 0 60.6%

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

      1. associate-/l* 72.8%

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

   5. Simplified 72.8%

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

   if -6.8000000000000001e-49 < t < -1.8000000000000001e-98 or 2.79999999999999988e-106 < t < 1.7e102

   1. Initial program 79.1%

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

      1. +-commutative 79.1%

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

      2. associate-/l* 91.0%

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

      3. fma-define 91.0%

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

   3. Simplified 91.0%

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

      1. clear-num 91.0%

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

      2. inv-pow 91.0%

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

   6. Applied egg-rr 91.0%

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

      1. unpow-1 91.0%

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

   8. Simplified 91.0%

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

   9. Taylor expanded in y around inf 70.6%

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

       1. div-sub 70.6%

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

       2. associate-*r/ 62.1%

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

       3. associate-*l/ 67.2%

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

       4. *-commutative 67.2%

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

   11. Simplified 67.2%

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

   if -1.8000000000000001e-98 < t < -1.10000000000000001e-161

   1. Initial program 92.4%

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

      1. +-commutative 92.4%

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

      2. associate-/l* 85.2%

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

      3. fma-define 85.2%

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

   3. Simplified 85.2%

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

      1. clear-num 85.2%

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

      2. inv-pow 85.2%

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

   6. Applied egg-rr 85.2%

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

      1. unpow-1 85.2%

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

   8. Simplified 85.2%

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

   9. Taylor expanded in z around inf 77.3%

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

       1. div-sub 77.3%

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

   11. Simplified 77.3%

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

   if -1.10000000000000001e-161 < t < 2.79999999999999988e-106

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 0 89.9%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+111}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+29}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-49}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-98}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-161}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+102}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(z - t\right)}{t - a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-291} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- z t)) (- t a)))))
   (if (or (<= t_1 -4e-291) (not (<= t_1 0.0)))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (* x (/ (- z a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (z - t)) / (t - a));
	double tmp;
	if ((t_1 <= -4e-291) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (x * ((z - a) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - x) * (z - t)) / (t - a))
    if ((t_1 <= (-4d-291)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + (x * ((z - a) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (z - t)) / (t - a));
	double tmp;
	if ((t_1 <= -4e-291) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (x * ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - x) * (z - t)) / (t - a))
	tmp = 0
	if (t_1 <= -4e-291) or not (t_1 <= 0.0):
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + (x * ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(t - a)))
	tmp = 0.0
	if ((t_1 <= -4e-291) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - x) * (z - t)) / (t - a));
	tmp = 0.0;
	if ((t_1 <= -4e-291) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + (x * ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-291], 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[(x * N[(N[(z - a), $MachinePrecision] / t), $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))) < -3.99999999999999985e-291 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 69.3%

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

      1. div-inv 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-*l* 84.0%

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

   4. Applied egg-rr 84.0%

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

      1. *-commutative 84.0%

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

      2. associate-*r* 88.4%

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

      3. associate-/r/ 88.5%

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

      4. un-div-inv 88.5%

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

   6. Applied egg-rr 88.5%

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

   if -3.99999999999999985e-291 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.3%

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

      1. +-commutative 3.3%

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

      2. associate-/l* 3.3%

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

      3. fma-define 3.3%

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

   3. Simplified 3.3%

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

      1. clear-num 3.3%

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

      2. inv-pow 3.3%

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

   6. Applied egg-rr 3.3%

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

      1. unpow-1 3.3%

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

   8. Simplified 3.3%

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

   9. Taylor expanded in t around inf 99.7%

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

       1. associate--l+ 99.7%

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

       2. associate-*r/ 99.7%

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

       3. associate-*r/ 99.7%

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

       4. mul-1-neg 99.7%

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

       5. div-sub 99.7%

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

       6. mul-1-neg 99.7%

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

       7. distribute-lft-out-- 99.7%

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

       8. associate-*r/ 99.7%

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

       9. mul-1-neg 99.7%

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

       10. unsub-neg 99.7%

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

       11. distribute-rgt-out-- 99.7%

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

   11. Simplified 99.7%

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

   12. Taylor expanded in y around 0 99.7%

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

       1. mul-1-neg 99.7%

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

       2. associate-/l* 99.8%

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

       3. distribute-rgt-neg-in 99.8%

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

       4. distribute-neg-frac2 99.8%

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

   14. Simplified 99.8%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(z - t\right)}{t - a} \leq -4 \cdot 10^{-291} \lor \neg \left(x - \frac{\left(y - x\right) \cdot \left(z - t\right)}{t - a} \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+111}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-98}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -2.3e+111)
     y
     (if (<= t -8.4e-49)
       t_1
       (if (<= t -9e-98)
         (* y (/ (- z t) a))
         (if (<= t 2.2e-106)
           t_1
           (if (<= t 3.2e-16)
             (* y (/ z (- a t)))
             (if (<= t 6.6e+62)
               t_1
               (if (<= t 3e+115) (* x (/ (- z a) t)) 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 <= -2.3e+111) {
		tmp = y;
	} else if (t <= -8.4e-49) {
		tmp = t_1;
	} else if (t <= -9e-98) {
		tmp = y * ((z - t) / a);
	} else if (t <= 2.2e-106) {
		tmp = t_1;
	} else if (t <= 3.2e-16) {
		tmp = y * (z / (a - t));
	} else if (t <= 6.6e+62) {
		tmp = t_1;
	} else if (t <= 3e+115) {
		tmp = x * ((z - a) / 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-2.3d+111)) then
        tmp = y
    else if (t <= (-8.4d-49)) then
        tmp = t_1
    else if (t <= (-9d-98)) then
        tmp = y * ((z - t) / a)
    else if (t <= 2.2d-106) then
        tmp = t_1
    else if (t <= 3.2d-16) then
        tmp = y * (z / (a - t))
    else if (t <= 6.6d+62) then
        tmp = t_1
    else if (t <= 3d+115) then
        tmp = x * ((z - a) / 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 t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -2.3e+111) {
		tmp = y;
	} else if (t <= -8.4e-49) {
		tmp = t_1;
	} else if (t <= -9e-98) {
		tmp = y * ((z - t) / a);
	} else if (t <= 2.2e-106) {
		tmp = t_1;
	} else if (t <= 3.2e-16) {
		tmp = y * (z / (a - t));
	} else if (t <= 6.6e+62) {
		tmp = t_1;
	} else if (t <= 3e+115) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -2.3e+111:
		tmp = y
	elif t <= -8.4e-49:
		tmp = t_1
	elif t <= -9e-98:
		tmp = y * ((z - t) / a)
	elif t <= 2.2e-106:
		tmp = t_1
	elif t <= 3.2e-16:
		tmp = y * (z / (a - t))
	elif t <= 6.6e+62:
		tmp = t_1
	elif t <= 3e+115:
		tmp = x * ((z - a) / t)
	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 <= -2.3e+111)
		tmp = y;
	elseif (t <= -8.4e-49)
		tmp = t_1;
	elseif (t <= -9e-98)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 2.2e-106)
		tmp = t_1;
	elseif (t <= 3.2e-16)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 6.6e+62)
		tmp = t_1;
	elseif (t <= 3e+115)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	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 <= -2.3e+111)
		tmp = y;
	elseif (t <= -8.4e-49)
		tmp = t_1;
	elseif (t <= -9e-98)
		tmp = y * ((z - t) / a);
	elseif (t <= 2.2e-106)
		tmp = t_1;
	elseif (t <= 3.2e-16)
		tmp = y * (z / (a - t));
	elseif (t <= 6.6e+62)
		tmp = t_1;
	elseif (t <= 3e+115)
		tmp = x * ((z - a) / t);
	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, -2.3e+111], y, If[LessEqual[t, -8.4e-49], t$95$1, If[LessEqual[t, -9e-98], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e-106], t$95$1, If[LessEqual[t, 3.2e-16], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e+62], t$95$1, If[LessEqual[t, 3e+115], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.30000000000000002e111 or 3e115 < t

   1. Initial program 29.6%

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

   3. Taylor expanded in t around inf 65.0%

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

   if -2.30000000000000002e111 < t < -8.3999999999999995e-49 or -8.99999999999999994e-98 < t < 2.19999999999999994e-106 or 3.20000000000000023e-16 < t < 6.6e62

   1. Initial program 86.6%

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

   3. Taylor expanded in t around 0 70.4%

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

   4. Taylor expanded in x around inf 58.4%

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

      1. mul-1-neg 58.4%

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

      2. unsub-neg 58.4%

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

   6. Simplified 58.4%

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

   if -8.3999999999999995e-49 < t < -8.99999999999999994e-98

   1. Initial program 93.2%

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

      1. +-commutative 93.2%

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

      2. associate-/l* 93.3%

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

      3. fma-define 93.3%

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

   3. Simplified 93.3%

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

      1. clear-num 93.2%

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

      2. inv-pow 93.2%

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

   6. Applied egg-rr 93.2%

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

      1. unpow-1 93.2%

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

   8. Simplified 93.2%

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

   9. Taylor expanded in y around inf 82.9%

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

       1. div-sub 82.9%

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

       2. associate-*r/ 82.8%

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

       3. associate-*l/ 82.7%

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

       4. *-commutative 82.7%

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

   11. Simplified 82.7%

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

   12. Taylor expanded in a around inf 64.4%

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

       1. associate-/l* 64.5%

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

   14. Simplified 64.5%

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

   if 2.19999999999999994e-106 < t < 3.20000000000000023e-16

   1. Initial program 85.0%

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

      1. +-commutative 85.0%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. unpow-1 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in z around -inf 49.9%

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

   10. Taylor expanded in y around inf 44.8%

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

       1. associate-/l* 59.7%

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

   12. Simplified 59.7%

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

   if 6.6e62 < t < 3e115

   1. Initial program 30.9%

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

      1. +-commutative 30.9%

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

      2. associate-/l* 61.1%

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

      3. fma-define 61.1%

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

   3. Simplified 61.1%

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

      1. clear-num 61.2%

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

      2. inv-pow 61.2%

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

   6. Applied egg-rr 61.2%

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

      1. unpow-1 61.2%

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

   8. Simplified 61.2%

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

   9. Taylor expanded in t around inf 56.8%

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

       1. associate--l+ 56.8%

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

       2. associate-*r/ 56.8%

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

       3. associate-*r/ 56.8%

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

       4. mul-1-neg 56.8%

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

       5. div-sub 56.8%

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

       6. mul-1-neg 56.8%

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

       7. distribute-lft-out-- 56.8%

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

       8. associate-*r/ 56.8%

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

       9. mul-1-neg 56.8%

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

       10. unsub-neg 56.8%

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

       11. distribute-rgt-out-- 56.8%

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

   11. Simplified 56.8%

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

   12. Taylor expanded in y around 0 28.7%

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

       1. associate-/l* 58.8%

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

   14. Simplified 58.8%

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

Alternative 6: 46.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ t_2 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+111}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))) (t_2 (* x (- 1.0 (/ z a)))))
   (if (<= t -2.8e+111)
     y
     (if (<= t -8.5e-49)
       t_2
       (if (<= t -5.5e-79)
         t_1
         (if (<= t 1.25e-107)
           t_2
           (if (<= t 8e-12)
             t_1
             (if (<= t 3.2e+66)
               t_2
               (if (<= t 3.6e+115) (* x (/ (- z a) t)) y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -2.8e+111) {
		tmp = y;
	} else if (t <= -8.5e-49) {
		tmp = t_2;
	} else if (t <= -5.5e-79) {
		tmp = t_1;
	} else if (t <= 1.25e-107) {
		tmp = t_2;
	} else if (t <= 8e-12) {
		tmp = t_1;
	} else if (t <= 3.2e+66) {
		tmp = t_2;
	} else if (t <= 3.6e+115) {
		tmp = x * ((z - a) / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (z / (a - t))
    t_2 = x * (1.0d0 - (z / a))
    if (t <= (-2.8d+111)) then
        tmp = y
    else if (t <= (-8.5d-49)) then
        tmp = t_2
    else if (t <= (-5.5d-79)) then
        tmp = t_1
    else if (t <= 1.25d-107) then
        tmp = t_2
    else if (t <= 8d-12) then
        tmp = t_1
    else if (t <= 3.2d+66) then
        tmp = t_2
    else if (t <= 3.6d+115) then
        tmp = x * ((z - a) / 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 t_1 = y * (z / (a - t));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -2.8e+111) {
		tmp = y;
	} else if (t <= -8.5e-49) {
		tmp = t_2;
	} else if (t <= -5.5e-79) {
		tmp = t_1;
	} else if (t <= 1.25e-107) {
		tmp = t_2;
	} else if (t <= 8e-12) {
		tmp = t_1;
	} else if (t <= 3.2e+66) {
		tmp = t_2;
	} else if (t <= 3.6e+115) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	t_2 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -2.8e+111:
		tmp = y
	elif t <= -8.5e-49:
		tmp = t_2
	elif t <= -5.5e-79:
		tmp = t_1
	elif t <= 1.25e-107:
		tmp = t_2
	elif t <= 8e-12:
		tmp = t_1
	elif t <= 3.2e+66:
		tmp = t_2
	elif t <= 3.6e+115:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	t_2 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -2.8e+111)
		tmp = y;
	elseif (t <= -8.5e-49)
		tmp = t_2;
	elseif (t <= -5.5e-79)
		tmp = t_1;
	elseif (t <= 1.25e-107)
		tmp = t_2;
	elseif (t <= 8e-12)
		tmp = t_1;
	elseif (t <= 3.2e+66)
		tmp = t_2;
	elseif (t <= 3.6e+115)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	t_2 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -2.8e+111)
		tmp = y;
	elseif (t <= -8.5e-49)
		tmp = t_2;
	elseif (t <= -5.5e-79)
		tmp = t_1;
	elseif (t <= 1.25e-107)
		tmp = t_2;
	elseif (t <= 8e-12)
		tmp = t_1;
	elseif (t <= 3.2e+66)
		tmp = t_2;
	elseif (t <= 3.6e+115)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+111], y, If[LessEqual[t, -8.5e-49], t$95$2, If[LessEqual[t, -5.5e-79], t$95$1, If[LessEqual[t, 1.25e-107], t$95$2, If[LessEqual[t, 8e-12], t$95$1, If[LessEqual[t, 3.2e+66], t$95$2, If[LessEqual[t, 3.6e+115], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.7999999999999999e111 or 3.6000000000000001e115 < t

   1. Initial program 29.6%

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

   3. Taylor expanded in t around inf 65.0%

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

   if -2.7999999999999999e111 < t < -8.50000000000000069e-49 or -5.4999999999999997e-79 < t < 1.24999999999999993e-107 or 7.99999999999999984e-12 < t < 3.2e66

   1. Initial program 87.0%

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

   3. Taylor expanded in t around 0 69.9%

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

   4. Taylor expanded in x around inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. unsub-neg 57.5%

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

   6. Simplified 57.5%

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

   if -8.50000000000000069e-49 < t < -5.4999999999999997e-79 or 1.24999999999999993e-107 < t < 7.99999999999999984e-12

   1. Initial program 87.2%

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

      1. +-commutative 87.2%

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

      2. associate-/l* 96.5%

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

      3. fma-define 96.5%

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

   3. Simplified 96.5%

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

      1. clear-num 96.5%

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

      2. inv-pow 96.5%

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

   6. Applied egg-rr 96.5%

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

      1. unpow-1 96.5%

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

   8. Simplified 96.5%

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

   9. Taylor expanded in z around -inf 58.6%

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

   10. Taylor expanded in y around inf 52.1%

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

       1. associate-/l* 61.6%

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

   12. Simplified 61.6%

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

   if 3.2e66 < t < 3.6000000000000001e115

   1. Initial program 30.9%

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

      1. +-commutative 30.9%

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

      2. associate-/l* 61.1%

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

      3. fma-define 61.1%

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

   3. Simplified 61.1%

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

      1. clear-num 61.2%

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

      2. inv-pow 61.2%

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

   6. Applied egg-rr 61.2%

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

      1. unpow-1 61.2%

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

   8. Simplified 61.2%

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

   9. Taylor expanded in t around inf 56.8%

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

       1. associate--l+ 56.8%

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

       2. associate-*r/ 56.8%

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

       3. associate-*r/ 56.8%

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

       4. mul-1-neg 56.8%

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

       5. div-sub 56.8%

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

       6. mul-1-neg 56.8%

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

       7. distribute-lft-out-- 56.8%

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

       8. associate-*r/ 56.8%

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

       9. mul-1-neg 56.8%

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

       10. unsub-neg 56.8%

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

       11. distribute-rgt-out-- 56.8%

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

   11. Simplified 56.8%

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

   12. Taylor expanded in y around 0 28.7%

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

       1. associate-/l* 58.8%

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

   14. Simplified 58.8%

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

Alternative 7: 65.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{\frac{a}{z}}\\ t_2 := y + x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{+29}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-79}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (/ a z)))) (t_2 (+ y (* x (/ z t)))))
   (if (<= t -2.25e+111)
     t_2
     (if (<= t -1.16e+29)
       (- x (* y (/ (- t z) a)))
       (if (<= t -4.1e+23)
         (* x (/ (- z a) t))
         (if (<= t -9.2e-49)
           t_1
           (if (<= t -4.5e-79)
             (* (- t z) (/ y (- t a)))
             (if (<= t 1.45e+62) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / z));
	double t_2 = y + (x * (z / t));
	double tmp;
	if (t <= -2.25e+111) {
		tmp = t_2;
	} else if (t <= -1.16e+29) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= -4.1e+23) {
		tmp = x * ((z - a) / t);
	} else if (t <= -9.2e-49) {
		tmp = t_1;
	} else if (t <= -4.5e-79) {
		tmp = (t - z) * (y / (t - a));
	} else if (t <= 1.45e+62) {
		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 + ((y - x) / (a / z))
    t_2 = y + (x * (z / t))
    if (t <= (-2.25d+111)) then
        tmp = t_2
    else if (t <= (-1.16d+29)) then
        tmp = x - (y * ((t - z) / a))
    else if (t <= (-4.1d+23)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-9.2d-49)) then
        tmp = t_1
    else if (t <= (-4.5d-79)) then
        tmp = (t - z) * (y / (t - a))
    else if (t <= 1.45d+62) 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 + ((y - x) / (a / z));
	double t_2 = y + (x * (z / t));
	double tmp;
	if (t <= -2.25e+111) {
		tmp = t_2;
	} else if (t <= -1.16e+29) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= -4.1e+23) {
		tmp = x * ((z - a) / t);
	} else if (t <= -9.2e-49) {
		tmp = t_1;
	} else if (t <= -4.5e-79) {
		tmp = (t - z) * (y / (t - a));
	} else if (t <= 1.45e+62) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / (a / z))
	t_2 = y + (x * (z / t))
	tmp = 0
	if t <= -2.25e+111:
		tmp = t_2
	elif t <= -1.16e+29:
		tmp = x - (y * ((t - z) / a))
	elif t <= -4.1e+23:
		tmp = x * ((z - a) / t)
	elif t <= -9.2e-49:
		tmp = t_1
	elif t <= -4.5e-79:
		tmp = (t - z) * (y / (t - a))
	elif t <= 1.45e+62:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(a / z)))
	t_2 = Float64(y + Float64(x * Float64(z / t)))
	tmp = 0.0
	if (t <= -2.25e+111)
		tmp = t_2;
	elseif (t <= -1.16e+29)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / a)));
	elseif (t <= -4.1e+23)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -9.2e-49)
		tmp = t_1;
	elseif (t <= -4.5e-79)
		tmp = Float64(Float64(t - z) * Float64(y / Float64(t - a)));
	elseif (t <= 1.45e+62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) / (a / z));
	t_2 = y + (x * (z / t));
	tmp = 0.0;
	if (t <= -2.25e+111)
		tmp = t_2;
	elseif (t <= -1.16e+29)
		tmp = x - (y * ((t - z) / a));
	elseif (t <= -4.1e+23)
		tmp = x * ((z - a) / t);
	elseif (t <= -9.2e-49)
		tmp = t_1;
	elseif (t <= -4.5e-79)
		tmp = (t - z) * (y / (t - a));
	elseif (t <= 1.45e+62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.25e+111], t$95$2, If[LessEqual[t, -1.16e+29], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.1e+23], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.2e-49], t$95$1, If[LessEqual[t, -4.5e-79], N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+62], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.25e111 or 1.44999999999999992e62 < t

   1. Initial program 29.8%

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

      1. +-commutative 29.8%

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

      2. associate-/l* 66.7%

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

      3. fma-define 66.7%

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

   3. Simplified 66.7%

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

      1. clear-num 66.7%

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

      2. inv-pow 66.7%

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

   6. Applied egg-rr 66.7%

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

      1. unpow-1 66.7%

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

   8. Simplified 66.7%

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

   9. Taylor expanded in t around inf 65.5%

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

       1. associate--l+ 65.5%

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

       2. associate-*r/ 65.5%

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

       3. associate-*r/ 65.5%

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

       4. mul-1-neg 65.5%

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

       5. div-sub 65.5%

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

       6. mul-1-neg 65.5%

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

       7. distribute-lft-out-- 65.5%

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

       8. associate-*r/ 65.5%

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

       9. mul-1-neg 65.5%

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

       10. unsub-neg 65.5%

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

       11. distribute-rgt-out-- 65.6%

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

   11. Simplified 65.6%

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

   12. Taylor expanded in y around 0 68.1%

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

       1. mul-1-neg 68.1%

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

       2. associate-/l* 81.7%

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

       3. distribute-rgt-neg-in 81.7%

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

       4. distribute-neg-frac2 81.7%

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

   14. Simplified 81.7%

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

   15. Taylor expanded in z around inf 62.4%

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

       1. mul-1-neg 62.4%

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

       2. associate-/l* 74.0%

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

       3. distribute-rgt-neg-in 74.0%

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

       4. mul-1-neg 74.0%

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

       5. associate-*r/ 74.0%

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

       6. neg-mul-1 74.0%

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

   17. Simplified 74.0%

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

   if -2.25e111 < t < -1.16e29

   1. Initial program 74.8%

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

   3. Taylor expanded in y around inf 83.3%

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

      1. *-commutative 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in a around inf 57.1%

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

      1. associate-/l* 65.9%

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

   8. Simplified 65.9%

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

   if -1.16e29 < t < -4.09999999999999996e23

   1. Initial program 51.3%

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

      1. +-commutative 51.3%

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

      2. associate-/l* 51.3%

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

      3. fma-define 51.3%

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

   3. Simplified 51.3%

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

      1. clear-num 51.3%

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

      2. inv-pow 51.3%

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

   6. Applied egg-rr 51.3%

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

      1. unpow-1 51.3%

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

   8. Simplified 51.3%

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

   9. Taylor expanded in t around inf 75.0%

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

       1. associate--l+ 75.0%

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

       2. associate-*r/ 75.0%

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

       3. associate-*r/ 75.0%

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

       4. mul-1-neg 75.0%

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

       5. div-sub 75.0%

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

       6. mul-1-neg 75.0%

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

       7. distribute-lft-out-- 75.0%

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

       8. associate-*r/ 75.0%

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

       9. mul-1-neg 75.0%

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

       10. unsub-neg 75.0%

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

       11. distribute-rgt-out-- 75.0%

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

   11. Simplified 75.0%

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

   12. Taylor expanded in y around 0 100.0%

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

       1. associate-/l* 100.0%

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

   14. Simplified 100.0%

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

   if -4.09999999999999996e23 < t < -9.1999999999999996e-49 or -4.5000000000000003e-79 < t < 1.44999999999999992e62

   1. Initial program 88.8%

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

      1. div-inv 88.7%

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

      2. *-commutative 88.7%

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

      3. associate-*l* 90.3%

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

   4. Applied egg-rr 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*r* 93.7%

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

      3. associate-/r/ 93.8%

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

      4. un-div-inv 93.8%

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

   6. Applied egg-rr 93.8%

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

   7. Taylor expanded in t around 0 75.5%

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

   if -9.1999999999999996e-49 < t < -4.5000000000000003e-79

   1. Initial program 91.5%

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

      1. +-commutative 91.5%

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

      2. associate-/l* 91.6%

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

      3. fma-define 91.6%

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

   3. Simplified 91.6%

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

      1. clear-num 91.6%

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

      2. inv-pow 91.6%

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

   6. Applied egg-rr 91.6%

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

      1. unpow-1 91.6%

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

   8. Simplified 91.6%

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

   9. Taylor expanded in y around inf 86.7%

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

       1. div-sub 86.7%

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

       2. associate-*r/ 86.6%

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

       3. associate-*l/ 86.6%

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

       4. *-commutative 86.6%

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

   11. Simplified 86.6%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+111}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{+29}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-79}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+117}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+240}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) (- a t)))))
        (t_2 (+ y (* (- z a) (/ (- x y) t)))))
   (if (<= t -1.4e+113)
     t_2
     (if (<= t 1.55e+68)
       t_1
       (if (<= t 1.7e+117)
         t_2
         (if (<= t 1.9e+173)
           t_1
           (if (<= t 9e+240) (+ y (/ (* (- y x) (- a z)) t)) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double t_2 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -1.4e+113) {
		tmp = t_2;
	} else if (t <= 1.55e+68) {
		tmp = t_1;
	} else if (t <= 1.7e+117) {
		tmp = t_2;
	} else if (t <= 1.9e+173) {
		tmp = t_1;
	} else if (t <= 9e+240) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z - t) * ((y - x) / (a - t)))
    t_2 = y + ((z - a) * ((x - y) / t))
    if (t <= (-1.4d+113)) then
        tmp = t_2
    else if (t <= 1.55d+68) then
        tmp = t_1
    else if (t <= 1.7d+117) then
        tmp = t_2
    else if (t <= 1.9d+173) then
        tmp = t_1
    else if (t <= 9d+240) then
        tmp = y + (((y - x) * (a - z)) / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double t_2 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -1.4e+113) {
		tmp = t_2;
	} else if (t <= 1.55e+68) {
		tmp = t_1;
	} else if (t <= 1.7e+117) {
		tmp = t_2;
	} else if (t <= 1.9e+173) {
		tmp = t_1;
	} else if (t <= 9e+240) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) / (a - t)))
	t_2 = y + ((z - a) * ((x - y) / t))
	tmp = 0
	if t <= -1.4e+113:
		tmp = t_2
	elif t <= 1.55e+68:
		tmp = t_1
	elif t <= 1.7e+117:
		tmp = t_2
	elif t <= 1.9e+173:
		tmp = t_1
	elif t <= 9e+240:
		tmp = y + (((y - x) * (a - z)) / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))))
	t_2 = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (t <= -1.4e+113)
		tmp = t_2;
	elseif (t <= 1.55e+68)
		tmp = t_1;
	elseif (t <= 1.7e+117)
		tmp = t_2;
	elseif (t <= 1.9e+173)
		tmp = t_1;
	elseif (t <= 9e+240)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) / (a - t)));
	t_2 = y + ((z - a) * ((x - y) / t));
	tmp = 0.0;
	if (t <= -1.4e+113)
		tmp = t_2;
	elseif (t <= 1.55e+68)
		tmp = t_1;
	elseif (t <= 1.7e+117)
		tmp = t_2;
	elseif (t <= 1.9e+173)
		tmp = t_1;
	elseif (t <= 9e+240)
		tmp = y + (((y - x) * (a - z)) / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e+113], t$95$2, If[LessEqual[t, 1.55e+68], t$95$1, If[LessEqual[t, 1.7e+117], t$95$2, If[LessEqual[t, 1.9e+173], t$95$1, If[LessEqual[t, 9e+240], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.39999999999999999e113 or 1.5499999999999999e68 < t < 1.7e117 or 8.99999999999999957e240 < t

   1. Initial program 22.9%

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

   3. Taylor expanded in t around inf 67.6%

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

      1. associate--l+ 67.6%

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

      2. distribute-lft-out-- 67.6%

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

      3. div-sub 67.6%

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

      4. mul-1-neg 67.6%

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

      5. unsub-neg 67.6%

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

      6. div-sub 67.6%

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

      7. associate-/l* 83.0%

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

      8. associate-/l* 92.4%

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

      9. distribute-rgt-out-- 92.4%

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

   5. Simplified 92.4%

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

   if -1.39999999999999999e113 < t < 1.5499999999999999e68 or 1.7e117 < t < 1.90000000000000005e173

   1. Initial program 83.9%

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

   3. Taylor expanded in y around 0 81.2%

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

      1. +-commutative 81.2%

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

      2. div-sub 81.2%

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

      3. mul-1-neg 81.2%

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

      4. associate-/l* 87.2%

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

      5. distribute-lft-neg-in 87.2%

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

      6. distribute-rgt-in 92.4%

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

      7. sub-neg 92.4%

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

      8. associate-*l/ 83.9%

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

      9. associate-*r/ 89.8%

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

   5. Simplified 89.8%

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

   if 1.90000000000000005e173 < t < 8.99999999999999957e240

   1. Initial program 47.1%

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

      1. +-commutative 47.1%

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

      2. associate-/l* 56.0%

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

      3. fma-define 56.0%

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

   3. Simplified 56.0%

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

      1. clear-num 56.0%

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

      2. inv-pow 56.0%

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

   6. Applied egg-rr 56.0%

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

      1. unpow-1 56.0%

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

   8. Simplified 56.0%

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

   9. Taylor expanded in t around inf 92.1%

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

       1. associate--l+ 92.1%

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

       2. associate-*r/ 92.1%

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

       3. associate-*r/ 92.1%

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

       4. mul-1-neg 92.1%

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

       5. div-sub 92.1%

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

       6. mul-1-neg 92.1%

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

       7. distribute-lft-out-- 92.1%

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

       8. associate-*r/ 92.1%

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

       9. mul-1-neg 92.1%

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

       10. unsub-neg 92.1%

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

       11. distribute-rgt-out-- 92.1%

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

   11. Simplified 92.1%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+113}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+68}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+117}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+173}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+240}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-190}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-250}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* x (/ z t)))))
   (if (<= t -4.3e+14)
     t_1
     (if (<= t -1.7e-190)
       (* z (/ (- y x) (- a t)))
       (if (<= t -3.4e-227)
         (* x (- 1.0 (/ z a)))
         (if (<= t -6.5e-250)
           (* z (/ (- y x) a))
           (if (<= t 1.5e+59) (+ x (/ y (/ a z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x * (z / t));
	double tmp;
	if (t <= -4.3e+14) {
		tmp = t_1;
	} else if (t <= -1.7e-190) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -3.4e-227) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= -6.5e-250) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.5e+59) {
		tmp = x + (y / (a / 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 = y + (x * (z / t))
    if (t <= (-4.3d+14)) then
        tmp = t_1
    else if (t <= (-1.7d-190)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= (-3.4d-227)) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= (-6.5d-250)) then
        tmp = z * ((y - x) / a)
    else if (t <= 1.5d+59) then
        tmp = x + (y / (a / 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 = y + (x * (z / t));
	double tmp;
	if (t <= -4.3e+14) {
		tmp = t_1;
	} else if (t <= -1.7e-190) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -3.4e-227) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= -6.5e-250) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.5e+59) {
		tmp = x + (y / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (x * (z / t))
	tmp = 0
	if t <= -4.3e+14:
		tmp = t_1
	elif t <= -1.7e-190:
		tmp = z * ((y - x) / (a - t))
	elif t <= -3.4e-227:
		tmp = x * (1.0 - (z / a))
	elif t <= -6.5e-250:
		tmp = z * ((y - x) / a)
	elif t <= 1.5e+59:
		tmp = x + (y / (a / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(x * Float64(z / t)))
	tmp = 0.0
	if (t <= -4.3e+14)
		tmp = t_1;
	elseif (t <= -1.7e-190)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= -3.4e-227)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= -6.5e-250)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 1.5e+59)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (x * (z / t));
	tmp = 0.0;
	if (t <= -4.3e+14)
		tmp = t_1;
	elseif (t <= -1.7e-190)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= -3.4e-227)
		tmp = x * (1.0 - (z / a));
	elseif (t <= -6.5e-250)
		tmp = z * ((y - x) / a);
	elseif (t <= 1.5e+59)
		tmp = x + (y / (a / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.3e+14], t$95$1, If[LessEqual[t, -1.7e-190], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.4e-227], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e-250], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+59], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.3e14 or 1.5e59 < t

   1. Initial program 37.1%

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

      1. +-commutative 37.1%

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

      2. associate-/l* 70.4%

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

      3. fma-define 70.4%

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

   3. Simplified 70.4%

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

      1. clear-num 70.4%

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

      2. inv-pow 70.4%

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

   6. Applied egg-rr 70.4%

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

      1. unpow-1 70.4%

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

   8. Simplified 70.4%

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

   9. Taylor expanded in t around inf 61.0%

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

       1. associate--l+ 61.0%

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

       2. associate-*r/ 61.0%

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

       3. associate-*r/ 61.0%

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

       4. mul-1-neg 61.0%

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

       5. div-sub 61.0%

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

       6. mul-1-neg 61.0%

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

       7. distribute-lft-out-- 61.0%

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

       8. associate-*r/ 61.0%

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

       9. mul-1-neg 61.0%

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

       10. unsub-neg 61.0%

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

       11. distribute-rgt-out-- 61.2%

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

   11. Simplified 61.2%

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

   12. Taylor expanded in y around 0 63.3%

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

       1. mul-1-neg 63.3%

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

       2. associate-/l* 75.0%

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

       3. distribute-rgt-neg-in 75.0%

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

       4. distribute-neg-frac2 75.0%

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

   14. Simplified 75.0%

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

   15. Taylor expanded in z around inf 57.0%

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

       1. mul-1-neg 57.0%

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

       2. associate-/l* 67.0%

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

       3. distribute-rgt-neg-in 67.0%

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

       4. mul-1-neg 67.0%

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

       5. associate-*r/ 67.0%

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

       6. neg-mul-1 67.0%

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

   17. Simplified 67.0%

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

   if -4.3e14 < t < -1.69999999999999991e-190

   1. Initial program 88.4%

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

      1. +-commutative 88.4%

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

      2. associate-/l* 90.6%

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

      3. fma-define 90.6%

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

   3. Simplified 90.6%

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

      1. clear-num 90.5%

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

      2. inv-pow 90.5%

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

   6. Applied egg-rr 90.5%

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

      1. unpow-1 90.5%

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

   8. Simplified 90.5%

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

   9. Taylor expanded in z around inf 64.4%

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

       1. div-sub 64.4%

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

   11. Simplified 64.4%

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

   if -1.69999999999999991e-190 < t < -3.39999999999999979e-227

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 99.5%

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

   4. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   if -3.39999999999999979e-227 < t < -6.49999999999999942e-250

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

   4. Taylor expanded in z around inf 99.6%

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

      1. div-sub 99.6%

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

   6. Simplified 99.6%

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

   if -6.49999999999999942e-250 < t < 1.5e59

   1. Initial program 87.5%

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

   3. Taylor expanded in t around 0 71.1%

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

   4. Taylor expanded in y around inf 63.0%

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

      1. associate-/l* 66.3%

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

   6. Simplified 66.3%

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

      1. clear-num 66.3%

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

      2. un-div-inv 66.3%

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

   8. Applied egg-rr 66.3%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+14}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-190}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-250}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - x \cdot \frac{a}{t}\\ t_2 := z \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-107}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-180}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+56}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 10^{+105}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* x (/ a t)))) (t_2 (* z (/ (- x y) t))))
   (if (<= t -2.25e+111)
     t_1
     (if (<= t -1.15e-107)
       (+ x (* y (/ z a)))
       (if (<= t -3.9e-180)
         t_2
         (if (<= t 5.3e+56)
           (+ x (/ y (/ a z)))
           (if (<= t 1e+105) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x * (a / t));
	double t_2 = z * ((x - y) / t);
	double tmp;
	if (t <= -2.25e+111) {
		tmp = t_1;
	} else if (t <= -1.15e-107) {
		tmp = x + (y * (z / a));
	} else if (t <= -3.9e-180) {
		tmp = t_2;
	} else if (t <= 5.3e+56) {
		tmp = x + (y / (a / z));
	} else if (t <= 1e+105) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y - (x * (a / t))
    t_2 = z * ((x - y) / t)
    if (t <= (-2.25d+111)) then
        tmp = t_1
    else if (t <= (-1.15d-107)) then
        tmp = x + (y * (z / a))
    else if (t <= (-3.9d-180)) then
        tmp = t_2
    else if (t <= 5.3d+56) then
        tmp = x + (y / (a / z))
    else if (t <= 1d+105) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x * (a / t));
	double t_2 = z * ((x - y) / t);
	double tmp;
	if (t <= -2.25e+111) {
		tmp = t_1;
	} else if (t <= -1.15e-107) {
		tmp = x + (y * (z / a));
	} else if (t <= -3.9e-180) {
		tmp = t_2;
	} else if (t <= 5.3e+56) {
		tmp = x + (y / (a / z));
	} else if (t <= 1e+105) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x * (a / t))
	t_2 = z * ((x - y) / t)
	tmp = 0
	if t <= -2.25e+111:
		tmp = t_1
	elif t <= -1.15e-107:
		tmp = x + (y * (z / a))
	elif t <= -3.9e-180:
		tmp = t_2
	elif t <= 5.3e+56:
		tmp = x + (y / (a / z))
	elif t <= 1e+105:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x * Float64(a / t)))
	t_2 = Float64(z * Float64(Float64(x - y) / t))
	tmp = 0.0
	if (t <= -2.25e+111)
		tmp = t_1;
	elseif (t <= -1.15e-107)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= -3.9e-180)
		tmp = t_2;
	elseif (t <= 5.3e+56)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1e+105)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x * (a / t));
	t_2 = z * ((x - y) / t);
	tmp = 0.0;
	if (t <= -2.25e+111)
		tmp = t_1;
	elseif (t <= -1.15e-107)
		tmp = x + (y * (z / a));
	elseif (t <= -3.9e-180)
		tmp = t_2;
	elseif (t <= 5.3e+56)
		tmp = x + (y / (a / z));
	elseif (t <= 1e+105)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.25e+111], t$95$1, If[LessEqual[t, -1.15e-107], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.9e-180], t$95$2, If[LessEqual[t, 5.3e+56], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+105], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.25e111 or 9.9999999999999994e104 < t

   1. Initial program 28.0%

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

      1. +-commutative 28.0%

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

      2. associate-/l* 65.6%

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

      3. fma-define 65.6%

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

   3. Simplified 65.6%

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

      1. clear-num 65.6%

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

      2. inv-pow 65.6%

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

   6. Applied egg-rr 65.6%

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

      1. unpow-1 65.6%

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

   8. Simplified 65.6%

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

   9. Taylor expanded in t around inf 67.2%

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

       1. associate--l+ 67.2%

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

       2. associate-*r/ 67.2%

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

       3. associate-*r/ 67.2%

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

       4. mul-1-neg 67.2%

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

       5. div-sub 67.2%

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

       6. mul-1-neg 67.2%

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

       7. distribute-lft-out-- 67.2%

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

       8. associate-*r/ 67.2%

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

       9. mul-1-neg 67.2%

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

       10. unsub-neg 67.2%

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

       11. distribute-rgt-out-- 67.3%

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

   11. Simplified 67.3%

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

   12. Taylor expanded in y around 0 72.2%

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

       1. mul-1-neg 72.2%

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

       2. associate-/l* 83.2%

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

       3. distribute-rgt-neg-in 83.2%

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

       4. distribute-neg-frac2 83.2%

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

   14. Simplified 83.2%

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

   15. Taylor expanded in z around 0 69.4%

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

   if -2.25e111 < t < -1.15000000000000002e-107

   1. Initial program 79.8%

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

   3. Taylor expanded in t around 0 50.9%

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

   4. Taylor expanded in y around inf 46.3%

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

      1. associate-/l* 48.5%

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

   6. Simplified 48.5%

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

   if -1.15000000000000002e-107 < t < -3.9000000000000003e-180 or 5.3000000000000002e56 < t < 9.9999999999999994e104

   1. Initial program 74.3%

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

      1. +-commutative 74.3%

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

      2. associate-/l* 82.2%

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

      3. fma-define 82.2%

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

   3. Simplified 82.2%

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

      1. clear-num 82.3%

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

      2. inv-pow 82.3%

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

   6. Applied egg-rr 82.3%

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

      1. unpow-1 82.3%

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

   8. Simplified 82.3%

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

   9. Taylor expanded in z around -inf 61.1%

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

   10. Taylor expanded in a around 0 50.9%

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

       1. mul-1-neg 50.9%

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

       2. associate-/l* 67.4%

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

       3. distribute-rgt-neg-in 67.4%

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

       4. distribute-neg-frac2 67.4%

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

   12. Simplified 67.4%

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

   if -3.9000000000000003e-180 < t < 5.3000000000000002e56

   1. Initial program 89.8%

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

   3. Taylor expanded in t around 0 75.3%

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

   4. Taylor expanded in y around inf 62.2%

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

      1. associate-/l* 65.1%

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

   6. Simplified 65.1%

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

      1. clear-num 65.1%

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

      2. un-div-inv 65.2%

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

   8. Applied egg-rr 65.2%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+111}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-107}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-180}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+56}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 10^{+105}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z - t}{t - a}\\ t_2 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-128}:\\ \;\;\;\;x - \frac{y - x}{\frac{t - a}{z}}\\ \mathbf{elif}\;t \leq 7.7 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- z t) (- t a)))))
        (t_2 (+ y (* (- z a) (/ (- x y) t)))))
   (if (<= t -4.2e+111)
     t_2
     (if (<= t -5.2e+38)
       t_1
       (if (<= t 7e-128)
         (- x (/ (- y x) (/ (- t a) z)))
         (if (<= t 7.7e+56) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((z - t) / (t - a)));
	double t_2 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -4.2e+111) {
		tmp = t_2;
	} else if (t <= -5.2e+38) {
		tmp = t_1;
	} else if (t <= 7e-128) {
		tmp = x - ((y - x) / ((t - a) / z));
	} else if (t <= 7.7e+56) {
		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 - (y * ((z - t) / (t - a)))
    t_2 = y + ((z - a) * ((x - y) / t))
    if (t <= (-4.2d+111)) then
        tmp = t_2
    else if (t <= (-5.2d+38)) then
        tmp = t_1
    else if (t <= 7d-128) then
        tmp = x - ((y - x) / ((t - a) / z))
    else if (t <= 7.7d+56) 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 - (y * ((z - t) / (t - a)));
	double t_2 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -4.2e+111) {
		tmp = t_2;
	} else if (t <= -5.2e+38) {
		tmp = t_1;
	} else if (t <= 7e-128) {
		tmp = x - ((y - x) / ((t - a) / z));
	} else if (t <= 7.7e+56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((z - t) / (t - a)))
	t_2 = y + ((z - a) * ((x - y) / t))
	tmp = 0
	if t <= -4.2e+111:
		tmp = t_2
	elif t <= -5.2e+38:
		tmp = t_1
	elif t <= 7e-128:
		tmp = x - ((y - x) / ((t - a) / z))
	elif t <= 7.7e+56:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(z - t) / Float64(t - a))))
	t_2 = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (t <= -4.2e+111)
		tmp = t_2;
	elseif (t <= -5.2e+38)
		tmp = t_1;
	elseif (t <= 7e-128)
		tmp = Float64(x - Float64(Float64(y - x) / Float64(Float64(t - a) / z)));
	elseif (t <= 7.7e+56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((z - t) / (t - a)));
	t_2 = y + ((z - a) * ((x - y) / t));
	tmp = 0.0;
	if (t <= -4.2e+111)
		tmp = t_2;
	elseif (t <= -5.2e+38)
		tmp = t_1;
	elseif (t <= 7e-128)
		tmp = x - ((y - x) / ((t - a) / z));
	elseif (t <= 7.7e+56)
		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[(y * N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+111], t$95$2, If[LessEqual[t, -5.2e+38], t$95$1, If[LessEqual[t, 7e-128], N[(x - N[(N[(y - x), $MachinePrecision] / N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.7e+56], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.1999999999999999e111 or 7.6999999999999999e56 < t

   1. Initial program 29.6%

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

   3. Taylor expanded in t around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. distribute-lft-out-- 64.9%

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

      3. div-sub 64.9%

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

      4. mul-1-neg 64.9%

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

      5. unsub-neg 64.9%

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

      6. div-sub 64.9%

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

      7. associate-/l* 78.4%

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

      8. associate-/l* 86.3%

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

      9. distribute-rgt-out-- 86.3%

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

   5. Simplified 86.3%

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

   if -4.1999999999999999e111 < t < -5.1999999999999998e38 or 6.99999999999999999e-128 < t < 7.6999999999999999e56

   1. Initial program 81.3%

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

   3. Taylor expanded in y around inf 81.5%

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

      1. associate-/l* 90.4%

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

   5. Simplified 90.4%

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

   if -5.1999999999999998e38 < t < 6.99999999999999999e-128

   1. Initial program 90.7%

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

      1. div-inv 90.6%

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

      2. *-commutative 90.6%

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

      3. associate-*l* 89.7%

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

   4. Applied egg-rr 89.7%

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

      1. *-commutative 89.7%

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

      2. associate-*r* 91.5%

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

      3. associate-/r/ 91.6%

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

      4. un-div-inv 91.6%

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

   6. Applied egg-rr 91.6%

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

   7. Taylor expanded in z around inf 84.3%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+111}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+38}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-128}:\\ \;\;\;\;x - \frac{y - x}{\frac{t - a}{z}}\\ \mathbf{elif}\;t \leq 7.7 \cdot 10^{+56}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z - t}{t - a}\\ t_2 := y + x \cdot \frac{z - a}{t}\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+112}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-128}:\\ \;\;\;\;x - \frac{y - x}{\frac{t - a}{z}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- z t) (- t a))))) (t_2 (+ y (* x (/ (- z a) t)))))
   (if (<= t -3.4e+112)
     t_2
     (if (<= t -5.4e+35)
       t_1
       (if (<= t 6.6e-128)
         (- x (/ (- y x) (/ (- t a) z)))
         (if (<= t 2.8e+67) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((z - t) / (t - a)));
	double t_2 = y + (x * ((z - a) / t));
	double tmp;
	if (t <= -3.4e+112) {
		tmp = t_2;
	} else if (t <= -5.4e+35) {
		tmp = t_1;
	} else if (t <= 6.6e-128) {
		tmp = x - ((y - x) / ((t - a) / z));
	} else if (t <= 2.8e+67) {
		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 - (y * ((z - t) / (t - a)))
    t_2 = y + (x * ((z - a) / t))
    if (t <= (-3.4d+112)) then
        tmp = t_2
    else if (t <= (-5.4d+35)) then
        tmp = t_1
    else if (t <= 6.6d-128) then
        tmp = x - ((y - x) / ((t - a) / z))
    else if (t <= 2.8d+67) 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 - (y * ((z - t) / (t - a)));
	double t_2 = y + (x * ((z - a) / t));
	double tmp;
	if (t <= -3.4e+112) {
		tmp = t_2;
	} else if (t <= -5.4e+35) {
		tmp = t_1;
	} else if (t <= 6.6e-128) {
		tmp = x - ((y - x) / ((t - a) / z));
	} else if (t <= 2.8e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((z - t) / (t - a)))
	t_2 = y + (x * ((z - a) / t))
	tmp = 0
	if t <= -3.4e+112:
		tmp = t_2
	elif t <= -5.4e+35:
		tmp = t_1
	elif t <= 6.6e-128:
		tmp = x - ((y - x) / ((t - a) / z))
	elif t <= 2.8e+67:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(z - t) / Float64(t - a))))
	t_2 = Float64(y + Float64(x * Float64(Float64(z - a) / t)))
	tmp = 0.0
	if (t <= -3.4e+112)
		tmp = t_2;
	elseif (t <= -5.4e+35)
		tmp = t_1;
	elseif (t <= 6.6e-128)
		tmp = Float64(x - Float64(Float64(y - x) / Float64(Float64(t - a) / z)));
	elseif (t <= 2.8e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((z - t) / (t - a)));
	t_2 = y + (x * ((z - a) / t));
	tmp = 0.0;
	if (t <= -3.4e+112)
		tmp = t_2;
	elseif (t <= -5.4e+35)
		tmp = t_1;
	elseif (t <= 6.6e-128)
		tmp = x - ((y - x) / ((t - a) / z));
	elseif (t <= 2.8e+67)
		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[(y * N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+112], t$95$2, If[LessEqual[t, -5.4e+35], t$95$1, If[LessEqual[t, 6.6e-128], N[(x - N[(N[(y - x), $MachinePrecision] / N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+67], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.39999999999999993e112 or 2.7999999999999998e67 < t

   1. Initial program 29.8%

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

      1. +-commutative 29.8%

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

      2. associate-/l* 66.7%

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

      3. fma-define 66.7%

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

   3. Simplified 66.7%

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

      1. clear-num 66.7%

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

      2. inv-pow 66.7%

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

   6. Applied egg-rr 66.7%

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

      1. unpow-1 66.7%

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

   8. Simplified 66.7%

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

   9. Taylor expanded in t around inf 65.5%

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

       1. associate--l+ 65.5%

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

       2. associate-*r/ 65.5%

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

       3. associate-*r/ 65.5%

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

       4. mul-1-neg 65.5%

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

       5. div-sub 65.5%

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

       6. mul-1-neg 65.5%

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

       7. distribute-lft-out-- 65.5%

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

       8. associate-*r/ 65.5%

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

       9. mul-1-neg 65.5%

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

       10. unsub-neg 65.5%

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

       11. distribute-rgt-out-- 65.6%

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

   11. Simplified 65.6%

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

   12. Taylor expanded in y around 0 68.1%

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

       1. mul-1-neg 68.1%

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

       2. associate-/l* 81.7%

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

       3. distribute-rgt-neg-in 81.7%

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

       4. distribute-neg-frac2 81.7%

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

   14. Simplified 81.7%

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

   if -3.39999999999999993e112 < t < -5.40000000000000005e35 or 6.6e-128 < t < 2.7999999999999998e67

   1. Initial program 79.9%

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

   3. Taylor expanded in y around inf 80.1%

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

      1. associate-/l* 90.5%

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

   5. Simplified 90.5%

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

   if -5.40000000000000005e35 < t < 6.6e-128

   1. Initial program 90.7%

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

      1. div-inv 90.6%

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

      2. *-commutative 90.6%

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

      3. associate-*l* 89.7%

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

   4. Applied egg-rr 89.7%

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

      1. *-commutative 89.7%

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

      2. associate-*r* 91.5%

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

      3. associate-/r/ 91.6%

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

      4. un-div-inv 91.6%

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

   6. Applied egg-rr 91.6%

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

   7. Taylor expanded in z around inf 84.3%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+112}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{+35}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-128}:\\ \;\;\;\;x - \frac{y - x}{\frac{t - a}{z}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+67}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 77.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z - t}{t - a}\\ t_2 := y + x \cdot \frac{z - a}{t}\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-130}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- z t) (- t a))))) (t_2 (+ y (* x (/ (- z a) t)))))
   (if (<= t -2.4e+113)
     t_2
     (if (<= t -5.8e-95)
       t_1
       (if (<= t 2.2e-130)
         (+ x (/ (* (- y x) z) (- a t)))
         (if (<= t 8e+63) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((z - t) / (t - a)));
	double t_2 = y + (x * ((z - a) / t));
	double tmp;
	if (t <= -2.4e+113) {
		tmp = t_2;
	} else if (t <= -5.8e-95) {
		tmp = t_1;
	} else if (t <= 2.2e-130) {
		tmp = x + (((y - x) * z) / (a - t));
	} else if (t <= 8e+63) {
		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 - (y * ((z - t) / (t - a)))
    t_2 = y + (x * ((z - a) / t))
    if (t <= (-2.4d+113)) then
        tmp = t_2
    else if (t <= (-5.8d-95)) then
        tmp = t_1
    else if (t <= 2.2d-130) then
        tmp = x + (((y - x) * z) / (a - t))
    else if (t <= 8d+63) 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 - (y * ((z - t) / (t - a)));
	double t_2 = y + (x * ((z - a) / t));
	double tmp;
	if (t <= -2.4e+113) {
		tmp = t_2;
	} else if (t <= -5.8e-95) {
		tmp = t_1;
	} else if (t <= 2.2e-130) {
		tmp = x + (((y - x) * z) / (a - t));
	} else if (t <= 8e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((z - t) / (t - a)))
	t_2 = y + (x * ((z - a) / t))
	tmp = 0
	if t <= -2.4e+113:
		tmp = t_2
	elif t <= -5.8e-95:
		tmp = t_1
	elif t <= 2.2e-130:
		tmp = x + (((y - x) * z) / (a - t))
	elif t <= 8e+63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(z - t) / Float64(t - a))))
	t_2 = Float64(y + Float64(x * Float64(Float64(z - a) / t)))
	tmp = 0.0
	if (t <= -2.4e+113)
		tmp = t_2;
	elseif (t <= -5.8e-95)
		tmp = t_1;
	elseif (t <= 2.2e-130)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / Float64(a - t)));
	elseif (t <= 8e+63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((z - t) / (t - a)));
	t_2 = y + (x * ((z - a) / t));
	tmp = 0.0;
	if (t <= -2.4e+113)
		tmp = t_2;
	elseif (t <= -5.8e-95)
		tmp = t_1;
	elseif (t <= 2.2e-130)
		tmp = x + (((y - x) * z) / (a - t));
	elseif (t <= 8e+63)
		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[(y * N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e+113], t$95$2, If[LessEqual[t, -5.8e-95], t$95$1, If[LessEqual[t, 2.2e-130], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+63], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.39999999999999983e113 or 8.00000000000000046e63 < t

   1. Initial program 29.8%

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

      1. +-commutative 29.8%

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

      2. associate-/l* 66.7%

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

      3. fma-define 66.7%

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

   3. Simplified 66.7%

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

      1. clear-num 66.7%

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

      2. inv-pow 66.7%

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

   6. Applied egg-rr 66.7%

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

      1. unpow-1 66.7%

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

   8. Simplified 66.7%

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

   9. Taylor expanded in t around inf 65.5%

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

       1. associate--l+ 65.5%

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

       2. associate-*r/ 65.5%

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

       3. associate-*r/ 65.5%

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

       4. mul-1-neg 65.5%

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

       5. div-sub 65.5%

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

       6. mul-1-neg 65.5%

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

       7. distribute-lft-out-- 65.5%

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

       8. associate-*r/ 65.5%

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

       9. mul-1-neg 65.5%

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

       10. unsub-neg 65.5%

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

       11. distribute-rgt-out-- 65.6%

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

   11. Simplified 65.6%

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

   12. Taylor expanded in y around 0 68.1%

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

       1. mul-1-neg 68.1%

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

       2. associate-/l* 81.7%

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

       3. distribute-rgt-neg-in 81.7%

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

       4. distribute-neg-frac2 81.7%

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

   14. Simplified 81.7%

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

   if -2.39999999999999983e113 < t < -5.80000000000000004e-95 or 2.1999999999999999e-130 < t < 8.00000000000000046e63

   1. Initial program 81.3%

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

   3. Taylor expanded in y around inf 75.0%

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

      1. associate-/l* 81.3%

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

   5. Simplified 81.3%

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

   if -5.80000000000000004e-95 < t < 2.1999999999999999e-130

   1. Initial program 94.4%

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

   3. Taylor expanded in z around inf 91.6%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+113}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-95}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-130}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+63}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 76.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z - t}{t - a}\\ t_2 := y + x \cdot \frac{z - a}{t}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-132}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- z t) (- t a))))) (t_2 (+ y (* x (/ (- z a) t)))))
   (if (<= t -2.6e+113)
     t_2
     (if (<= t -3.6e-99)
       t_1
       (if (<= t 4.3e-132)
         (+ x (/ (- y x) (/ a z)))
         (if (<= t 1.2e+65) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((z - t) / (t - a)));
	double t_2 = y + (x * ((z - a) / t));
	double tmp;
	if (t <= -2.6e+113) {
		tmp = t_2;
	} else if (t <= -3.6e-99) {
		tmp = t_1;
	} else if (t <= 4.3e-132) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 1.2e+65) {
		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 - (y * ((z - t) / (t - a)))
    t_2 = y + (x * ((z - a) / t))
    if (t <= (-2.6d+113)) then
        tmp = t_2
    else if (t <= (-3.6d-99)) then
        tmp = t_1
    else if (t <= 4.3d-132) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 1.2d+65) 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 - (y * ((z - t) / (t - a)));
	double t_2 = y + (x * ((z - a) / t));
	double tmp;
	if (t <= -2.6e+113) {
		tmp = t_2;
	} else if (t <= -3.6e-99) {
		tmp = t_1;
	} else if (t <= 4.3e-132) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 1.2e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((z - t) / (t - a)))
	t_2 = y + (x * ((z - a) / t))
	tmp = 0
	if t <= -2.6e+113:
		tmp = t_2
	elif t <= -3.6e-99:
		tmp = t_1
	elif t <= 4.3e-132:
		tmp = x + ((y - x) / (a / z))
	elif t <= 1.2e+65:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(z - t) / Float64(t - a))))
	t_2 = Float64(y + Float64(x * Float64(Float64(z - a) / t)))
	tmp = 0.0
	if (t <= -2.6e+113)
		tmp = t_2;
	elseif (t <= -3.6e-99)
		tmp = t_1;
	elseif (t <= 4.3e-132)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 1.2e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((z - t) / (t - a)));
	t_2 = y + (x * ((z - a) / t));
	tmp = 0.0;
	if (t <= -2.6e+113)
		tmp = t_2;
	elseif (t <= -3.6e-99)
		tmp = t_1;
	elseif (t <= 4.3e-132)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 1.2e+65)
		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[(y * N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e+113], t$95$2, If[LessEqual[t, -3.6e-99], t$95$1, If[LessEqual[t, 4.3e-132], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+65], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5999999999999999e113 or 1.2000000000000001e65 < t

   1. Initial program 29.8%

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

      1. +-commutative 29.8%

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

      2. associate-/l* 66.7%

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

      3. fma-define 66.7%

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

   3. Simplified 66.7%

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

      1. clear-num 66.7%

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

      2. inv-pow 66.7%

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

   6. Applied egg-rr 66.7%

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

      1. unpow-1 66.7%

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

   8. Simplified 66.7%

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

   9. Taylor expanded in t around inf 65.5%

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

       1. associate--l+ 65.5%

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

       2. associate-*r/ 65.5%

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

       3. associate-*r/ 65.5%

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

       4. mul-1-neg 65.5%

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

       5. div-sub 65.5%

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

       6. mul-1-neg 65.5%

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

       7. distribute-lft-out-- 65.5%

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

       8. associate-*r/ 65.5%

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

       9. mul-1-neg 65.5%

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

       10. unsub-neg 65.5%

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

       11. distribute-rgt-out-- 65.6%

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

   11. Simplified 65.6%

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

   12. Taylor expanded in y around 0 68.1%

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

       1. mul-1-neg 68.1%

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

       2. associate-/l* 81.7%

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

       3. distribute-rgt-neg-in 81.7%

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

       4. distribute-neg-frac2 81.7%

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

   14. Simplified 81.7%

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

   if -2.5999999999999999e113 < t < -3.6000000000000001e-99 or 4.2999999999999997e-132 < t < 1.2000000000000001e65

   1. Initial program 81.3%

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

   3. Taylor expanded in y around inf 75.0%

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

      1. associate-/l* 81.3%

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

   5. Simplified 81.3%

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

   if -3.6000000000000001e-99 < t < 4.2999999999999997e-132

   1. Initial program 94.4%

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

      1. div-inv 94.3%

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

      2. *-commutative 94.3%

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

      3. associate-*l* 90.2%

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

   4. Applied egg-rr 90.2%

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

      1. *-commutative 90.2%

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

      2. associate-*r* 92.9%

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

      3. associate-/r/ 93.0%

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

      4. un-div-inv 93.1%

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

   6. Applied egg-rr 93.1%

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

   7. Taylor expanded in t around 0 84.8%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+113}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-99}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-132}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+65}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-72}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-172}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+83}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= a -4.6e+142)
     t_1
     (if (<= a -7.8e-72)
       (* (- t z) (/ y (- t a)))
       (if (<= a 2.8e-172)
         (+ y (* x (/ z t)))
         (if (<= a 1.55e+83) (* z (/ (- y x) (- a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (a <= -4.6e+142) {
		tmp = t_1;
	} else if (a <= -7.8e-72) {
		tmp = (t - z) * (y / (t - a));
	} else if (a <= 2.8e-172) {
		tmp = y + (x * (z / t));
	} else if (a <= 1.55e+83) {
		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 + (y * (z / a))
    if (a <= (-4.6d+142)) then
        tmp = t_1
    else if (a <= (-7.8d-72)) then
        tmp = (t - z) * (y / (t - a))
    else if (a <= 2.8d-172) then
        tmp = y + (x * (z / t))
    else if (a <= 1.55d+83) 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 + (y * (z / a));
	double tmp;
	if (a <= -4.6e+142) {
		tmp = t_1;
	} else if (a <= -7.8e-72) {
		tmp = (t - z) * (y / (t - a));
	} else if (a <= 2.8e-172) {
		tmp = y + (x * (z / t));
	} else if (a <= 1.55e+83) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if a <= -4.6e+142:
		tmp = t_1
	elif a <= -7.8e-72:
		tmp = (t - z) * (y / (t - a))
	elif a <= 2.8e-172:
		tmp = y + (x * (z / t))
	elif a <= 1.55e+83:
		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(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -4.6e+142)
		tmp = t_1;
	elseif (a <= -7.8e-72)
		tmp = Float64(Float64(t - z) * Float64(y / Float64(t - a)));
	elseif (a <= 2.8e-172)
		tmp = Float64(y + Float64(x * Float64(z / t)));
	elseif (a <= 1.55e+83)
		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 + (y * (z / a));
	tmp = 0.0;
	if (a <= -4.6e+142)
		tmp = t_1;
	elseif (a <= -7.8e-72)
		tmp = (t - z) * (y / (t - a));
	elseif (a <= 2.8e-172)
		tmp = y + (x * (z / t));
	elseif (a <= 1.55e+83)
		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[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.6e+142], t$95$1, If[LessEqual[a, -7.8e-72], N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-172], N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+83], 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 < -4.60000000000000004e142 or 1.54999999999999996e83 < a

   1. Initial program 71.0%

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

   3. Taylor expanded in t around 0 66.5%

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

   4. Taylor expanded in y around inf 65.2%

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

      1. associate-/l* 70.0%

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

   6. Simplified 70.0%

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

   if -4.60000000000000004e142 < a < -7.8e-72

   1. Initial program 63.8%

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

      1. +-commutative 63.8%

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

      2. associate-/l* 83.6%

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

      3. fma-define 83.6%

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

   3. Simplified 83.6%

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

      1. clear-num 83.6%

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

      2. inv-pow 83.6%

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

   6. Applied egg-rr 83.6%

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

      1. unpow-1 83.6%

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

   8. Simplified 83.6%

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

   9. Taylor expanded in y around inf 59.5%

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

       1. div-sub 59.5%

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

       2. associate-*r/ 42.0%

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

       3. associate-*l/ 54.9%

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

       4. *-commutative 54.9%

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

   11. Simplified 54.9%

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

   if -7.8e-72 < a < 2.80000000000000011e-172

   1. Initial program 58.2%

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

      1. +-commutative 58.2%

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

      2. associate-/l* 77.3%

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

      3. fma-define 77.4%

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

   3. Simplified 77.4%

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

      1. clear-num 77.5%

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

      2. inv-pow 77.5%

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

   6. Applied egg-rr 77.5%

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

      1. unpow-1 77.5%

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

   8. Simplified 77.5%

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

   9. Taylor expanded in t around inf 81.0%

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

       1. associate--l+ 81.0%

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

       2. associate-*r/ 81.0%

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

       3. associate-*r/ 81.0%

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

       4. mul-1-neg 81.0%

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

       5. div-sub 81.0%

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

       6. mul-1-neg 81.0%

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

       7. distribute-lft-out-- 81.0%

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

       8. associate-*r/ 81.0%

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

       9. mul-1-neg 81.0%

          \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

       10. unsub-neg 81.0%

           \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       11. distribute-rgt-out-- 81.0%

           \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   11. Simplified 81.0%

       \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   12. Taylor expanded in y around 0 68.2%

       \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   13. Step-by-step derivation

       1. mul-1-neg 68.2%

          \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

       2. associate-/l* 75.3%

          \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

       3. distribute-rgt-neg-in 75.3%

          \[\leadsto y - \color{blue}{x \cdot \left(-\frac{z - a}{t}\right)} \]

       4. distribute-neg-frac2 75.3%

          \[\leadsto y - x \cdot \color{blue}{\frac{z - a}{-t}} \]

   14. Simplified 75.3%

       \[\leadsto y - \color{blue}{x \cdot \frac{z - a}{-t}} \]

   15. Taylor expanded in z around inf 65.1%

       \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
   16. Step-by-step derivation

       1. mul-1-neg 65.1%

          \[\leadsto y - \color{blue}{\left(-\frac{x \cdot z}{t}\right)} \]

       2. associate-/l* 73.4%

          \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z}{t}}\right) \]

       3. distribute-rgt-neg-in 73.4%

          \[\leadsto y - \color{blue}{x \cdot \left(-\frac{z}{t}\right)} \]

       4. mul-1-neg 73.4%

          \[\leadsto y - x \cdot \color{blue}{\left(-1 \cdot \frac{z}{t}\right)} \]

       5. associate-*r/ 73.4%

          \[\leadsto y - x \cdot \color{blue}{\frac{-1 \cdot z}{t}} \]

       6. neg-mul-1 73.4%

          \[\leadsto y - x \cdot \frac{\color{blue}{-z}}{t} \]

   17. Simplified 73.4%

       \[\leadsto y - \color{blue}{x \cdot \frac{-z}{t}} \]

   if 2.80000000000000011e-172 < a < 1.54999999999999996e83

   1. Initial program 66.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 66.4%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 76.3%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 76.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 76.3%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

      2. inv-pow 76.3%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 76.3%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 76.3%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   8. Simplified 76.3%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   9. Taylor expanded in z around inf 59.4%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   10. Step-by-step derivation

       1. div-sub 61.2%

          \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   11. Simplified 61.2%

       \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+142}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-72}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-172}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+83}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 57.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-107}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-180}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* x (/ z t)))))
   (if (<= t -2.25e+111)
     t_1
     (if (<= t -1.12e-107)
       (+ x (* y (/ z a)))
       (if (<= t -4.5e-180)
         (* z (/ (- x y) t))
         (if (<= t 1.7e+63) (+ x (/ y (/ a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x * (z / t));
	double tmp;
	if (t <= -2.25e+111) {
		tmp = t_1;
	} else if (t <= -1.12e-107) {
		tmp = x + (y * (z / a));
	} else if (t <= -4.5e-180) {
		tmp = z * ((x - y) / t);
	} else if (t <= 1.7e+63) {
		tmp = x + (y / (a / 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 = y + (x * (z / t))
    if (t <= (-2.25d+111)) then
        tmp = t_1
    else if (t <= (-1.12d-107)) then
        tmp = x + (y * (z / a))
    else if (t <= (-4.5d-180)) then
        tmp = z * ((x - y) / t)
    else if (t <= 1.7d+63) then
        tmp = x + (y / (a / 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 = y + (x * (z / t));
	double tmp;
	if (t <= -2.25e+111) {
		tmp = t_1;
	} else if (t <= -1.12e-107) {
		tmp = x + (y * (z / a));
	} else if (t <= -4.5e-180) {
		tmp = z * ((x - y) / t);
	} else if (t <= 1.7e+63) {
		tmp = x + (y / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (x * (z / t))
	tmp = 0
	if t <= -2.25e+111:
		tmp = t_1
	elif t <= -1.12e-107:
		tmp = x + (y * (z / a))
	elif t <= -4.5e-180:
		tmp = z * ((x - y) / t)
	elif t <= 1.7e+63:
		tmp = x + (y / (a / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(x * Float64(z / t)))
	tmp = 0.0
	if (t <= -2.25e+111)
		tmp = t_1;
	elseif (t <= -1.12e-107)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= -4.5e-180)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (t <= 1.7e+63)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (x * (z / t));
	tmp = 0.0;
	if (t <= -2.25e+111)
		tmp = t_1;
	elseif (t <= -1.12e-107)
		tmp = x + (y * (z / a));
	elseif (t <= -4.5e-180)
		tmp = z * ((x - y) / t);
	elseif (t <= 1.7e+63)
		tmp = x + (y / (a / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.25e+111], t$95$1, If[LessEqual[t, -1.12e-107], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.5e-180], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+63], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.25e111 or 1.6999999999999999e63 < t

   1. Initial program 29.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 29.8%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 66.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 66.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 66.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

      2. inv-pow 66.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 66.7%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 66.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   8. Simplified 66.7%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   9. Taylor expanded in t around inf 65.5%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   10. Step-by-step derivation

       1. associate--l+ 65.5%

          \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

       2. associate-*r/ 65.5%

          \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

       3. associate-*r/ 65.5%

          \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

       4. mul-1-neg 65.5%

          \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \frac{\color{blue}{-a \cdot \left(y - x\right)}}{t}\right) \]

       5. div-sub 65.5%

          \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - \left(-a \cdot \left(y - x\right)\right)}{t}} \]

       6. mul-1-neg 65.5%

          \[\leadsto y + \frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

       7. distribute-lft-out-- 65.5%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

       8. associate-*r/ 65.5%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       9. mul-1-neg 65.5%

          \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

       10. unsub-neg 65.5%

           \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       11. distribute-rgt-out-- 65.6%

           \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   11. Simplified 65.6%

       \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   12. Taylor expanded in y around 0 68.1%

       \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   13. Step-by-step derivation

       1. mul-1-neg 68.1%

          \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

       2. associate-/l* 81.7%

          \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

       3. distribute-rgt-neg-in 81.7%

          \[\leadsto y - \color{blue}{x \cdot \left(-\frac{z - a}{t}\right)} \]

       4. distribute-neg-frac2 81.7%

          \[\leadsto y - x \cdot \color{blue}{\frac{z - a}{-t}} \]

   14. Simplified 81.7%

       \[\leadsto y - \color{blue}{x \cdot \frac{z - a}{-t}} \]

   15. Taylor expanded in z around inf 62.4%

       \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
   16. Step-by-step derivation

       1. mul-1-neg 62.4%

          \[\leadsto y - \color{blue}{\left(-\frac{x \cdot z}{t}\right)} \]

       2. associate-/l* 74.0%

          \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z}{t}}\right) \]

       3. distribute-rgt-neg-in 74.0%

          \[\leadsto y - \color{blue}{x \cdot \left(-\frac{z}{t}\right)} \]

       4. mul-1-neg 74.0%

          \[\leadsto y - x \cdot \color{blue}{\left(-1 \cdot \frac{z}{t}\right)} \]

       5. associate-*r/ 74.0%

          \[\leadsto y - x \cdot \color{blue}{\frac{-1 \cdot z}{t}} \]

       6. neg-mul-1 74.0%

          \[\leadsto y - x \cdot \frac{\color{blue}{-z}}{t} \]

   17. Simplified 74.0%

       \[\leadsto y - \color{blue}{x \cdot \frac{-z}{t}} \]

   if -2.25e111 < t < -1.12e-107

   1. Initial program 79.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 50.9%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in y around inf 46.3%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 48.5%

         \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]

   6. Simplified 48.5%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]

   if -1.12e-107 < t < -4.50000000000000009e-180

   1. Initial program 99.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 99.3%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 83.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 83.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 83.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 83.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

      2. inv-pow 83.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 83.9%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 83.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   8. Simplified 83.9%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   9. Taylor expanded in z around -inf 83.3%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   10. Taylor expanded in a around 0 65.1%

       \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right)}{t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 65.1%

          \[\leadsto \color{blue}{-\frac{z \cdot \left(y - x\right)}{t}} \]

       2. associate-/l* 65.1%

          \[\leadsto -\color{blue}{z \cdot \frac{y - x}{t}} \]

       3. distribute-rgt-neg-in 65.1%

          \[\leadsto \color{blue}{z \cdot \left(-\frac{y - x}{t}\right)} \]

       4. distribute-neg-frac2 65.1%

          \[\leadsto z \cdot \color{blue}{\frac{y - x}{-t}} \]

   12. Simplified 65.1%

       \[\leadsto \color{blue}{z \cdot \frac{y - x}{-t}} \]

   if -4.50000000000000009e-180 < t < 1.6999999999999999e63

   1. Initial program 89.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 74.6%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in y around inf 61.7%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 64.6%

         \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]

   6. Simplified 64.6%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]
   7. Step-by-step derivation

      1. clear-num 64.5%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a}{z}}} \]

      2. un-div-inv 64.6%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   8. Applied egg-rr 64.6%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+111}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-107}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-180}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 61.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{t - z}{a}\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-172}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- t z) a)))))
   (if (<= a -1.1e-66)
     t_1
     (if (<= a 1.9e-172)
       (+ y (* x (/ z t)))
       (if (<= a 2.4e+71) (* z (/ (- y x) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((t - z) / a));
	double tmp;
	if (a <= -1.1e-66) {
		tmp = t_1;
	} else if (a <= 1.9e-172) {
		tmp = y + (x * (z / t));
	} else if (a <= 2.4e+71) {
		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 - (y * ((t - z) / a))
    if (a <= (-1.1d-66)) then
        tmp = t_1
    else if (a <= 1.9d-172) then
        tmp = y + (x * (z / t))
    else if (a <= 2.4d+71) 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 - (y * ((t - z) / a));
	double tmp;
	if (a <= -1.1e-66) {
		tmp = t_1;
	} else if (a <= 1.9e-172) {
		tmp = y + (x * (z / t));
	} else if (a <= 2.4e+71) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((t - z) / a))
	tmp = 0
	if a <= -1.1e-66:
		tmp = t_1
	elif a <= 1.9e-172:
		tmp = y + (x * (z / t))
	elif a <= 2.4e+71:
		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(y * Float64(Float64(t - z) / a)))
	tmp = 0.0
	if (a <= -1.1e-66)
		tmp = t_1;
	elseif (a <= 1.9e-172)
		tmp = Float64(y + Float64(x * Float64(z / t)));
	elseif (a <= 2.4e+71)
		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 - (y * ((t - z) / a));
	tmp = 0.0;
	if (a <= -1.1e-66)
		tmp = t_1;
	elseif (a <= 1.9e-172)
		tmp = y + (x * (z / t));
	elseif (a <= 2.4e+71)
		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[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.1e-66], t$95$1, If[LessEqual[a, 1.9e-172], N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e+71], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.1000000000000001e-66 or 2.39999999999999981e71 < a

   1. Initial program 69.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 66.2%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. *-commutative 66.2%

         \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot y}}{a - t} \]

   5. Simplified 66.2%

      \[\leadsto x + \color{blue}{\frac{\left(z - t\right) \cdot y}{a - t}} \]

   6. Taylor expanded in a around inf 62.0%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 68.8%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a}} \]

   8. Simplified 68.8%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a}} \]

   if -1.1000000000000001e-66 < a < 1.89999999999999993e-172

   1. Initial program 58.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 58.1%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 77.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 78.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 78.0%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

      2. inv-pow 78.0%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 78.0%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 78.0%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   8. Simplified 78.0%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   9. Taylor expanded in t around inf 80.3%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   10. Step-by-step derivation

       1. associate--l+ 80.3%

          \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

       2. associate-*r/ 80.3%

          \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

       3. associate-*r/ 80.3%

          \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

       4. mul-1-neg 80.3%

          \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \frac{\color{blue}{-a \cdot \left(y - x\right)}}{t}\right) \]

       5. div-sub 80.3%

          \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - \left(-a \cdot \left(y - x\right)\right)}{t}} \]

       6. mul-1-neg 80.3%

          \[\leadsto y + \frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

       7. distribute-lft-out-- 80.3%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

       8. associate-*r/ 80.3%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       9. mul-1-neg 80.3%

          \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

       10. unsub-neg 80.3%

           \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       11. distribute-rgt-out-- 80.3%

           \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   11. Simplified 80.3%

       \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   12. Taylor expanded in y around 0 67.8%

       \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   13. Step-by-step derivation

       1. mul-1-neg 67.8%

          \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

       2. associate-/l* 74.7%

          \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

       3. distribute-rgt-neg-in 74.7%

          \[\leadsto y - \color{blue}{x \cdot \left(-\frac{z - a}{t}\right)} \]

       4. distribute-neg-frac2 74.7%

          \[\leadsto y - x \cdot \color{blue}{\frac{z - a}{-t}} \]

   14. Simplified 74.7%

       \[\leadsto y - \color{blue}{x \cdot \frac{z - a}{-t}} \]

   15. Taylor expanded in z around inf 64.8%

       \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
   16. Step-by-step derivation

       1. mul-1-neg 64.8%

          \[\leadsto y - \color{blue}{\left(-\frac{x \cdot z}{t}\right)} \]

       2. associate-/l* 72.9%

          \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z}{t}}\right) \]

       3. distribute-rgt-neg-in 72.9%

          \[\leadsto y - \color{blue}{x \cdot \left(-\frac{z}{t}\right)} \]

       4. mul-1-neg 72.9%

          \[\leadsto y - x \cdot \color{blue}{\left(-1 \cdot \frac{z}{t}\right)} \]

       5. associate-*r/ 72.9%

          \[\leadsto y - x \cdot \color{blue}{\frac{-1 \cdot z}{t}} \]

       6. neg-mul-1 72.9%

          \[\leadsto y - x \cdot \frac{\color{blue}{-z}}{t} \]

   17. Simplified 72.9%

       \[\leadsto y - \color{blue}{x \cdot \frac{-z}{t}} \]

   if 1.89999999999999993e-172 < a < 2.39999999999999981e71

   1. Initial program 65.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 65.2%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 75.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 75.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 75.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 75.4%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

      2. inv-pow 75.4%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 75.4%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 75.4%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   8. Simplified 75.4%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   9. Taylor expanded in z around inf 59.7%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   10. Step-by-step derivation

       1. div-sub 61.5%

          \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   11. Simplified 61.5%

       \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-66}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-172}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+111}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8e+111)
   y
   (if (<= t 2.5e+59)
     (+ x (/ y (/ a z)))
     (if (<= t 2.5e+116) (* x (/ (- z a) t)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8e+111) {
		tmp = y;
	} else if (t <= 2.5e+59) {
		tmp = x + (y / (a / z));
	} else if (t <= 2.5e+116) {
		tmp = x * ((z - a) / 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 <= (-8d+111)) then
        tmp = y
    else if (t <= 2.5d+59) then
        tmp = x + (y / (a / z))
    else if (t <= 2.5d+116) then
        tmp = x * ((z - a) / 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 <= -8e+111) {
		tmp = y;
	} else if (t <= 2.5e+59) {
		tmp = x + (y / (a / z));
	} else if (t <= 2.5e+116) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8e+111:
		tmp = y
	elif t <= 2.5e+59:
		tmp = x + (y / (a / z))
	elif t <= 2.5e+116:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8e+111)
		tmp = y;
	elseif (t <= 2.5e+59)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 2.5e+116)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8e+111)
		tmp = y;
	elseif (t <= 2.5e+59)
		tmp = x + (y / (a / z));
	elseif (t <= 2.5e+116)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8e+111], y, If[LessEqual[t, 2.5e+59], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+116], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.99999999999999965e111 or 2.50000000000000013e116 < t

   1. Initial program 29.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 65.0%

      \[\leadsto \color{blue}{y} \]

   if -7.99999999999999965e111 < t < 2.4999999999999999e59

   1. Initial program 87.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 65.8%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in y around inf 53.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 56.3%

         \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]

   6. Simplified 56.3%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]
   7. Step-by-step derivation

      1. clear-num 56.3%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a}{z}}} \]

      2. un-div-inv 56.4%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   8. Applied egg-rr 56.4%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   if 2.4999999999999999e59 < t < 2.50000000000000013e116

   1. Initial program 30.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 30.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 61.1%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 61.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 61.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 61.2%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

      2. inv-pow 61.2%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 61.2%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 61.2%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   8. Simplified 61.2%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   9. Taylor expanded in t around inf 56.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   10. Step-by-step derivation

       1. associate--l+ 56.8%

          \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

       2. associate-*r/ 56.8%

          \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

       3. associate-*r/ 56.8%

          \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

       4. mul-1-neg 56.8%

          \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \frac{\color{blue}{-a \cdot \left(y - x\right)}}{t}\right) \]

       5. div-sub 56.8%

          \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - \left(-a \cdot \left(y - x\right)\right)}{t}} \]

       6. mul-1-neg 56.8%

          \[\leadsto y + \frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

       7. distribute-lft-out-- 56.8%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

       8. associate-*r/ 56.8%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       9. mul-1-neg 56.8%

          \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

       10. unsub-neg 56.8%

           \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       11. distribute-rgt-out-- 56.8%

           \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   11. Simplified 56.8%

       \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   12. Taylor expanded in y around 0 28.7%

       \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   13. Step-by-step derivation

       1. associate-/l* 58.8%

          \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   14. Simplified 58.8%

       \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 52.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+111}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+66}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.2e+111)
   y
   (if (<= t 7.2e+66)
     (+ x (* y (/ z a)))
     (if (<= t 1.12e+116) (* x (/ (- z a) t)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.2e+111) {
		tmp = y;
	} else if (t <= 7.2e+66) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.12e+116) {
		tmp = x * ((z - a) / 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 <= (-9.2d+111)) then
        tmp = y
    else if (t <= 7.2d+66) then
        tmp = x + (y * (z / a))
    else if (t <= 1.12d+116) then
        tmp = x * ((z - a) / 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 <= -9.2e+111) {
		tmp = y;
	} else if (t <= 7.2e+66) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.12e+116) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.2e+111:
		tmp = y
	elif t <= 7.2e+66:
		tmp = x + (y * (z / a))
	elif t <= 1.12e+116:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.2e+111)
		tmp = y;
	elseif (t <= 7.2e+66)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 1.12e+116)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.2e+111)
		tmp = y;
	elseif (t <= 7.2e+66)
		tmp = x + (y * (z / a));
	elseif (t <= 1.12e+116)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.2e+111], y, If[LessEqual[t, 7.2e+66], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e+116], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.20000000000000008e111 or 1.12e116 < t

   1. Initial program 29.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 65.0%

      \[\leadsto \color{blue}{y} \]

   if -9.20000000000000008e111 < t < 7.2e66

   1. Initial program 87.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 65.8%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in y around inf 53.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 56.3%

         \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]

   6. Simplified 56.3%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]

   if 7.2e66 < t < 1.12e116

   1. Initial program 30.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 30.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 61.1%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 61.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 61.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 61.2%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

      2. inv-pow 61.2%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 61.2%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 61.2%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   8. Simplified 61.2%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   9. Taylor expanded in t around inf 56.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   10. Step-by-step derivation

       1. associate--l+ 56.8%

          \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

       2. associate-*r/ 56.8%

          \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

       3. associate-*r/ 56.8%

          \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

       4. mul-1-neg 56.8%

          \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \frac{\color{blue}{-a \cdot \left(y - x\right)}}{t}\right) \]

       5. div-sub 56.8%

          \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - \left(-a \cdot \left(y - x\right)\right)}{t}} \]

       6. mul-1-neg 56.8%

          \[\leadsto y + \frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

       7. distribute-lft-out-- 56.8%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

       8. associate-*r/ 56.8%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       9. mul-1-neg 56.8%

          \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

       10. unsub-neg 56.8%

           \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       11. distribute-rgt-out-- 56.8%

           \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   11. Simplified 56.8%

       \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   12. Taylor expanded in y around 0 28.7%

       \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   13. Step-by-step derivation

       1. associate-/l* 58.8%

          \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   14. Simplified 58.8%

       \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 47.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+111}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.8e+111)
   y
   (if (<= t 1.6e+58)
     (* x (- 1.0 (/ z a)))
     (if (<= t 1.2e+115) (* x (/ (- z a) t)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+111) {
		tmp = y;
	} else if (t <= 1.6e+58) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.2e+115) {
		tmp = x * ((z - a) / 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 <= (-3.8d+111)) then
        tmp = y
    else if (t <= 1.6d+58) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 1.2d+115) then
        tmp = x * ((z - a) / 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 <= -3.8e+111) {
		tmp = y;
	} else if (t <= 1.6e+58) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.2e+115) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.8e+111:
		tmp = y
	elif t <= 1.6e+58:
		tmp = x * (1.0 - (z / a))
	elif t <= 1.2e+115:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.8e+111)
		tmp = y;
	elseif (t <= 1.6e+58)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 1.2e+115)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.8e+111)
		tmp = y;
	elseif (t <= 1.6e+58)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 1.2e+115)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.8e+111], y, If[LessEqual[t, 1.6e+58], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+115], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.79999999999999976e111 or 1.2e115 < t

   1. Initial program 29.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 65.0%

      \[\leadsto \color{blue}{y} \]

   if -3.79999999999999976e111 < t < 1.60000000000000008e58

   1. Initial program 87.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 65.8%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in x around inf 50.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 50.3%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   6. Simplified 50.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]

   if 1.60000000000000008e58 < t < 1.2e115

   1. Initial program 30.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 30.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 61.1%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 61.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 61.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 61.2%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

      2. inv-pow 61.2%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 61.2%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 61.2%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   8. Simplified 61.2%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   9. Taylor expanded in t around inf 56.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   10. Step-by-step derivation

       1. associate--l+ 56.8%

          \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

       2. associate-*r/ 56.8%

          \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

       3. associate-*r/ 56.8%

          \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

       4. mul-1-neg 56.8%

          \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \frac{\color{blue}{-a \cdot \left(y - x\right)}}{t}\right) \]

       5. div-sub 56.8%

          \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - \left(-a \cdot \left(y - x\right)\right)}{t}} \]

       6. mul-1-neg 56.8%

          \[\leadsto y + \frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

       7. distribute-lft-out-- 56.8%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

       8. associate-*r/ 56.8%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       9. mul-1-neg 56.8%

          \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

       10. unsub-neg 56.8%

           \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       11. distribute-rgt-out-- 56.8%

           \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   11. Simplified 56.8%

       \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   12. Taylor expanded in y around 0 28.7%

       \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   13. Step-by-step derivation

       1. associate-/l* 58.8%

          \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   14. Simplified 58.8%

       \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 35.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+111}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.2e+111)
   y
   (if (<= t -4e-6)
     x
     (if (<= t -5.1e-250) (* x (/ z (- a))) (if (<= t 1.7e+64) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+111) {
		tmp = y;
	} else if (t <= -4e-6) {
		tmp = x;
	} else if (t <= -5.1e-250) {
		tmp = x * (z / -a);
	} else if (t <= 1.7e+64) {
		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 <= (-4.2d+111)) then
        tmp = y
    else if (t <= (-4d-6)) then
        tmp = x
    else if (t <= (-5.1d-250)) then
        tmp = x * (z / -a)
    else if (t <= 1.7d+64) 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 <= -4.2e+111) {
		tmp = y;
	} else if (t <= -4e-6) {
		tmp = x;
	} else if (t <= -5.1e-250) {
		tmp = x * (z / -a);
	} else if (t <= 1.7e+64) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.2e+111:
		tmp = y
	elif t <= -4e-6:
		tmp = x
	elif t <= -5.1e-250:
		tmp = x * (z / -a)
	elif t <= 1.7e+64:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.2e+111)
		tmp = y;
	elseif (t <= -4e-6)
		tmp = x;
	elseif (t <= -5.1e-250)
		tmp = Float64(x * Float64(z / Float64(-a)));
	elseif (t <= 1.7e+64)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.2e+111)
		tmp = y;
	elseif (t <= -4e-6)
		tmp = x;
	elseif (t <= -5.1e-250)
		tmp = x * (z / -a);
	elseif (t <= 1.7e+64)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.2e+111], y, If[LessEqual[t, -4e-6], x, If[LessEqual[t, -5.1e-250], N[(x * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+64], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.1999999999999999e111 or 1.7000000000000001e64 < t

   1. Initial program 29.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 57.6%

      \[\leadsto \color{blue}{y} \]

   if -4.1999999999999999e111 < t < -3.99999999999999982e-6 or -5.1000000000000002e-250 < t < 1.7000000000000001e64

   1. Initial program 85.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 38.0%

      \[\leadsto \color{blue}{x} \]

   if -3.99999999999999982e-6 < t < -5.1000000000000002e-250

   1. Initial program 90.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 66.8%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in y around 0 47.3%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot z}{a}} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.3%

         \[\leadsto x + \color{blue}{\left(-\frac{x \cdot z}{a}\right)} \]

      2. unsub-neg 47.3%

         \[\leadsto \color{blue}{x - \frac{x \cdot z}{a}} \]

      3. associate-/l* 52.8%

         \[\leadsto x - \color{blue}{x \cdot \frac{z}{a}} \]

   6. Simplified 52.8%

      \[\leadsto \color{blue}{x - x \cdot \frac{z}{a}} \]

   7. Taylor expanded in z around inf 30.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{a}} \]
   8. Step-by-step derivation

      1. mul-1-neg 30.0%

         \[\leadsto \color{blue}{-\frac{x \cdot z}{a}} \]

      2. associate-*r/ 33.5%

         \[\leadsto -\color{blue}{x \cdot \frac{z}{a}} \]

      3. distribute-rgt-neg-in 33.5%

         \[\leadsto \color{blue}{x \cdot \left(-\frac{z}{a}\right)} \]

      4. distribute-neg-frac2 33.5%

         \[\leadsto x \cdot \color{blue}{\frac{z}{-a}} \]

   9. Simplified 33.5%

      \[\leadsto \color{blue}{x \cdot \frac{z}{-a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 22: 37.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-198}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -7.7 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+80}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1e+75)
   x
   (if (<= a -2.05e-198)
     y
     (if (<= a -7.7e-261) (* x (/ z t)) (if (<= a 4.5e+80) y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+75) {
		tmp = x;
	} else if (a <= -2.05e-198) {
		tmp = y;
	} else if (a <= -7.7e-261) {
		tmp = x * (z / t);
	} else if (a <= 4.5e+80) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1d+75)) then
        tmp = x
    else if (a <= (-2.05d-198)) then
        tmp = y
    else if (a <= (-7.7d-261)) then
        tmp = x * (z / t)
    else if (a <= 4.5d+80) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+75) {
		tmp = x;
	} else if (a <= -2.05e-198) {
		tmp = y;
	} else if (a <= -7.7e-261) {
		tmp = x * (z / t);
	} else if (a <= 4.5e+80) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1e+75:
		tmp = x
	elif a <= -2.05e-198:
		tmp = y
	elif a <= -7.7e-261:
		tmp = x * (z / t)
	elif a <= 4.5e+80:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1e+75)
		tmp = x;
	elseif (a <= -2.05e-198)
		tmp = y;
	elseif (a <= -7.7e-261)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 4.5e+80)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1e+75)
		tmp = x;
	elseif (a <= -2.05e-198)
		tmp = y;
	elseif (a <= -7.7e-261)
		tmp = x * (z / t);
	elseif (a <= 4.5e+80)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1e+75], x, If[LessEqual[a, -2.05e-198], y, If[LessEqual[a, -7.7e-261], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+80], y, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.99999999999999927e74 or 4.50000000000000007e80 < a

   1. Initial program 71.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 53.1%

      \[\leadsto \color{blue}{x} \]

   if -9.99999999999999927e74 < a < -2.05000000000000006e-198 or -7.6999999999999997e-261 < a < 4.50000000000000007e80

   1. Initial program 60.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 37.7%

      \[\leadsto \color{blue}{y} \]

   if -2.05000000000000006e-198 < a < -7.6999999999999997e-261

   1. Initial program 66.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 66.2%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 79.1%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 79.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 79.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 79.1%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

      2. inv-pow 79.1%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 79.1%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 79.1%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   8. Simplified 79.1%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   9. Taylor expanded in t around inf 80.4%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   10. Step-by-step derivation

       1. associate--l+ 80.4%

          \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

       2. associate-*r/ 80.4%

          \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

       3. associate-*r/ 80.4%

          \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

       4. mul-1-neg 80.4%

          \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \frac{\color{blue}{-a \cdot \left(y - x\right)}}{t}\right) \]

       5. div-sub 80.4%

          \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - \left(-a \cdot \left(y - x\right)\right)}{t}} \]

       6. mul-1-neg 80.4%

          \[\leadsto y + \frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

       7. distribute-lft-out-- 80.4%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

       8. associate-*r/ 80.4%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       9. mul-1-neg 80.4%

          \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

       10. unsub-neg 80.4%

           \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       11. distribute-rgt-out-- 80.4%

           \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   11. Simplified 80.4%

       \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   12. Taylor expanded in y around 0 53.0%

       \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   13. Step-by-step derivation

       1. mul-1-neg 53.0%

          \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

       2. associate-/l* 72.6%

          \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

       3. distribute-rgt-neg-in 72.6%

          \[\leadsto y - \color{blue}{x \cdot \left(-\frac{z - a}{t}\right)} \]

       4. distribute-neg-frac2 72.6%

          \[\leadsto y - x \cdot \color{blue}{\frac{z - a}{-t}} \]

   14. Simplified 72.6%

       \[\leadsto y - \color{blue}{x \cdot \frac{z - a}{-t}} \]

   15. Taylor expanded in z around inf 36.5%

       \[\leadsto \color{blue}{\frac{x \cdot z}{t}} \]
   16. Step-by-step derivation

       1. associate-/l* 56.0%

          \[\leadsto \color{blue}{x \cdot \frac{z}{t}} \]

   17. Simplified 56.0%

       \[\leadsto \color{blue}{x \cdot \frac{z}{t}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 23: 67.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-47} \lor \neg \left(a \leq 1.25 \cdot 10^{+81}\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.3e-47) (not (<= a 1.25e+81)))
   (- x (* y (/ (- t z) a)))
   (+ y (* z (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.3e-47) || !(a <= 1.25e+81)) {
		tmp = x - (y * ((t - z) / a));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.3d-47)) .or. (.not. (a <= 1.25d+81))) then
        tmp = x - (y * ((t - z) / a))
    else
        tmp = y + (z * ((x - y) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.3e-47) || !(a <= 1.25e+81)) {
		tmp = x - (y * ((t - z) / a));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.3e-47) or not (a <= 1.25e+81):
		tmp = x - (y * ((t - z) / a))
	else:
		tmp = y + (z * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.3e-47) || !(a <= 1.25e+81))
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.3e-47) || ~((a <= 1.25e+81)))
		tmp = x - (y * ((t - z) / a));
	else
		tmp = y + (z * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.3e-47], N[Not[LessEqual[a, 1.25e+81]], $MachinePrecision]], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.29999999999999982e-47 or 1.25e81 < a

   1. Initial program 69.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 66.6%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. *-commutative 66.6%

         \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot y}}{a - t} \]

   5. Simplified 66.6%

      \[\leadsto x + \color{blue}{\frac{\left(z - t\right) \cdot y}{a - t}} \]

   6. Taylor expanded in a around inf 63.1%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 70.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a}} \]

   8. Simplified 70.2%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a}} \]

   if -2.29999999999999982e-47 < a < 1.25e81

   1. Initial program 60.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 60.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 77.3%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 77.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 77.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 77.4%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

      2. inv-pow 77.4%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 77.4%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 77.4%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   8. Simplified 77.4%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   9. Taylor expanded in t around inf 69.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   10. Step-by-step derivation

       1. associate--l+ 69.7%

          \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

       2. associate-*r/ 69.7%

          \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

       3. associate-*r/ 69.7%

          \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

       4. mul-1-neg 69.7%

          \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \frac{\color{blue}{-a \cdot \left(y - x\right)}}{t}\right) \]

       5. div-sub 69.7%

          \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - \left(-a \cdot \left(y - x\right)\right)}{t}} \]

       6. mul-1-neg 69.7%

          \[\leadsto y + \frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

       7. distribute-lft-out-- 69.7%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

       8. associate-*r/ 69.7%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       9. mul-1-neg 69.7%

          \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

       10. unsub-neg 69.7%

           \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       11. distribute-rgt-out-- 69.8%

           \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   11. Simplified 69.8%

       \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   12. Taylor expanded in z around inf 66.2%

       \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   13. Step-by-step derivation

       1. associate-/l* 74.5%

          \[\leadsto y - \color{blue}{z \cdot \frac{y - x}{t}} \]

   14. Simplified 74.5%

       \[\leadsto y - \color{blue}{z \cdot \frac{y - x}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-47} \lor \neg \left(a \leq 1.25 \cdot 10^{+81}\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 56.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+111} \lor \neg \left(t \leq 7.5 \cdot 10^{+60}\right):\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.6e+111) (not (<= t 7.5e+60)))
   (- y (* x (/ a t)))
   (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.6e+111) || !(t <= 7.5e+60)) {
		tmp = y - (x * (a / t));
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.6d+111)) .or. (.not. (t <= 7.5d+60))) then
        tmp = y - (x * (a / t))
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.6e+111) || !(t <= 7.5e+60)) {
		tmp = y - (x * (a / t));
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.6e+111) or not (t <= 7.5e+60):
		tmp = y - (x * (a / t))
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.6e+111) || !(t <= 7.5e+60))
		tmp = Float64(y - Float64(x * Float64(a / t)));
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.6e+111) || ~((t <= 7.5e+60)))
		tmp = y - (x * (a / t));
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.6e+111], N[Not[LessEqual[t, 7.5e+60]], $MachinePrecision]], N[(y - N[(x * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.60000000000000004e111 or 7.5e60 < t

   1. Initial program 29.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 29.8%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 66.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 66.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 66.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

      2. inv-pow 66.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 66.7%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 66.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   8. Simplified 66.7%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

   9. Taylor expanded in t around inf 65.5%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   10. Step-by-step derivation

       1. associate--l+ 65.5%

          \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

       2. associate-*r/ 65.5%

          \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

       3. associate-*r/ 65.5%

          \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

       4. mul-1-neg 65.5%

          \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \frac{\color{blue}{-a \cdot \left(y - x\right)}}{t}\right) \]

       5. div-sub 65.5%

          \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - \left(-a \cdot \left(y - x\right)\right)}{t}} \]

       6. mul-1-neg 65.5%

          \[\leadsto y + \frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

       7. distribute-lft-out-- 65.5%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

       8. associate-*r/ 65.5%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       9. mul-1-neg 65.5%

          \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

       10. unsub-neg 65.5%

           \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

       11. distribute-rgt-out-- 65.6%

           \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   11. Simplified 65.6%

       \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   12. Taylor expanded in y around 0 68.1%

       \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   13. Step-by-step derivation

       1. mul-1-neg 68.1%

          \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

       2. associate-/l* 81.7%

          \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

       3. distribute-rgt-neg-in 81.7%

          \[\leadsto y - \color{blue}{x \cdot \left(-\frac{z - a}{t}\right)} \]

       4. distribute-neg-frac2 81.7%

          \[\leadsto y - x \cdot \color{blue}{\frac{z - a}{-t}} \]

   14. Simplified 81.7%

       \[\leadsto y - \color{blue}{x \cdot \frac{z - a}{-t}} \]

   15. Taylor expanded in z around 0 65.4%

       \[\leadsto y - x \cdot \color{blue}{\frac{a}{t}} \]

   if -4.60000000000000004e111 < t < 7.5e60

   1. Initial program 87.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 65.8%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in y around inf 53.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 56.3%

         \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]

   6. Simplified 56.3%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]
   7. Step-by-step derivation

      1. clear-num 56.3%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a}{z}}} \]

      2. un-div-inv 56.4%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   8. Applied egg-rr 56.4%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+111} \lor \neg \left(t \leq 7.5 \cdot 10^{+60}\right):\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 48.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+111}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.25e+111) y (if (<= t 1.85e+59) (* x (- 1.0 (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.25e+111) {
		tmp = y;
	} else if (t <= 1.85e+59) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.25d+111)) then
        tmp = y
    else if (t <= 1.85d+59) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.25e+111) {
		tmp = y;
	} else if (t <= 1.85e+59) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.25e+111:
		tmp = y
	elif t <= 1.85e+59:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.25e+111)
		tmp = y;
	elseif (t <= 1.85e+59)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.25e+111)
		tmp = y;
	elseif (t <= 1.85e+59)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.25e+111], y, If[LessEqual[t, 1.85e+59], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -2.25e111 or 1.84999999999999999e59 < t

   1. Initial program 29.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 57.6%

      \[\leadsto \color{blue}{y} \]

   if -2.25e111 < t < 1.84999999999999999e59

   1. Initial program 87.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 65.8%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in x around inf 50.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 50.3%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   6. Simplified 50.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 26: 38.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+83}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e+79) x (if (<= a 7e+83) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+79) {
		tmp = x;
	} else if (a <= 7e+83) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.2d+79)) then
        tmp = x
    else if (a <= 7d+83) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+79) {
		tmp = x;
	} else if (a <= 7e+83) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e+79:
		tmp = x
	elif a <= 7e+83:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e+79)
		tmp = x;
	elseif (a <= 7e+83)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.2e+79)
		tmp = x;
	elseif (a <= 7e+83)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e+79], x, If[LessEqual[a, 7e+83], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.19999999999999993e79 or 6.99999999999999954e83 < a

   1. Initial program 71.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 53.1%

      \[\leadsto \color{blue}{x} \]

   if -1.19999999999999993e79 < a < 6.99999999999999954e83

   1. Initial program 61.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 35.9%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 27: 24.5% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x;
}

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 64.9%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Add Preprocessing

3. Taylor expanded in a around inf 23.0%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 85.9% accurate, 0.5× 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 2024085 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (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))))