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

Percentage Accurate: 68.6% → 88.6%

Time: 16.5s

Alternatives: 25

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{+127} \lor \neg \left(t \leq 2 \cdot 10^{+105}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.15e+127) (not (<= t 2e+105)))
   (+ y (* (- z a) (/ (- x y) t)))
   (fma (- y x) (/ (- z t) (- a t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.15e+127) || !(t <= 2e+105)) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.15e+127) || !(t <= 2e+105))
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	else
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.15e+127], N[Not[LessEqual[t, 2e+105]], $MachinePrecision]], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.15000000000000024e127 or 1.9999999999999999e105 < 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 68.2%

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

      1. associate--l+ 68.2%

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

      2. distribute-lft-out-- 68.2%

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

      3. div-sub 68.2%

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

      4. mul-1-neg 68.2%

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

      5. unsub-neg 68.2%

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

      6. div-sub 68.2%

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

      7. associate-/l* 74.9%

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

      8. associate-/l* 88.6%

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

      9. distribute-rgt-out-- 88.6%

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

   5. Simplified 88.6%

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

   if -3.15000000000000024e127 < t < 1.9999999999999999e105

   1. Initial program 84.3%

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

      1. +-commutative 84.3%

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

      2. associate-/l* 93.6%

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

      3. fma-define 93.6%

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

   3. Simplified 93.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{+127} \lor \neg \left(t \leq 2 \cdot 10^{+105}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 49.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{z}{a}\\ t_2 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t \leq -5.1 \cdot 10^{+230}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{+115}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.1:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.04 \cdot 10^{-147}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+61}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ z a)))) (t_2 (* y (/ z (- a t)))))
   (if (<= t -5.1e+230)
     y
     (if (<= t -4.9e+115)
       (* (- z a) (/ x t))
       (if (<= t -3.9e+87)
         t_1
         (if (<= t -2.6e+80)
           t_2
           (if (<= t -1.1)
             y
             (if (<= t -3.9e-98)
               t_1
               (if (<= t -1.04e-147)
                 t_2
                 (if (<= t 3.2e+61) (+ x (* y (/ z a))) y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (z / a));
	double t_2 = y * (z / (a - t));
	double tmp;
	if (t <= -5.1e+230) {
		tmp = y;
	} else if (t <= -4.9e+115) {
		tmp = (z - a) * (x / t);
	} else if (t <= -3.9e+87) {
		tmp = t_1;
	} else if (t <= -2.6e+80) {
		tmp = t_2;
	} else if (t <= -1.1) {
		tmp = y;
	} else if (t <= -3.9e-98) {
		tmp = t_1;
	} else if (t <= -1.04e-147) {
		tmp = t_2;
	} else if (t <= 3.2e+61) {
		tmp = x + (y * (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (x * (z / a))
    t_2 = y * (z / (a - t))
    if (t <= (-5.1d+230)) then
        tmp = y
    else if (t <= (-4.9d+115)) then
        tmp = (z - a) * (x / t)
    else if (t <= (-3.9d+87)) then
        tmp = t_1
    else if (t <= (-2.6d+80)) then
        tmp = t_2
    else if (t <= (-1.1d0)) then
        tmp = y
    else if (t <= (-3.9d-98)) then
        tmp = t_1
    else if (t <= (-1.04d-147)) then
        tmp = t_2
    else if (t <= 3.2d+61) then
        tmp = x + (y * (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 t_1 = x - (x * (z / a));
	double t_2 = y * (z / (a - t));
	double tmp;
	if (t <= -5.1e+230) {
		tmp = y;
	} else if (t <= -4.9e+115) {
		tmp = (z - a) * (x / t);
	} else if (t <= -3.9e+87) {
		tmp = t_1;
	} else if (t <= -2.6e+80) {
		tmp = t_2;
	} else if (t <= -1.1) {
		tmp = y;
	} else if (t <= -3.9e-98) {
		tmp = t_1;
	} else if (t <= -1.04e-147) {
		tmp = t_2;
	} else if (t <= 3.2e+61) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (z / a))
	t_2 = y * (z / (a - t))
	tmp = 0
	if t <= -5.1e+230:
		tmp = y
	elif t <= -4.9e+115:
		tmp = (z - a) * (x / t)
	elif t <= -3.9e+87:
		tmp = t_1
	elif t <= -2.6e+80:
		tmp = t_2
	elif t <= -1.1:
		tmp = y
	elif t <= -3.9e-98:
		tmp = t_1
	elif t <= -1.04e-147:
		tmp = t_2
	elif t <= 3.2e+61:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(z / a)))
	t_2 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (t <= -5.1e+230)
		tmp = y;
	elseif (t <= -4.9e+115)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif (t <= -3.9e+87)
		tmp = t_1;
	elseif (t <= -2.6e+80)
		tmp = t_2;
	elseif (t <= -1.1)
		tmp = y;
	elseif (t <= -3.9e-98)
		tmp = t_1;
	elseif (t <= -1.04e-147)
		tmp = t_2;
	elseif (t <= 3.2e+61)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (z / a));
	t_2 = y * (z / (a - t));
	tmp = 0.0;
	if (t <= -5.1e+230)
		tmp = y;
	elseif (t <= -4.9e+115)
		tmp = (z - a) * (x / t);
	elseif (t <= -3.9e+87)
		tmp = t_1;
	elseif (t <= -2.6e+80)
		tmp = t_2;
	elseif (t <= -1.1)
		tmp = y;
	elseif (t <= -3.9e-98)
		tmp = t_1;
	elseif (t <= -1.04e-147)
		tmp = t_2;
	elseif (t <= 3.2e+61)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.1e+230], y, If[LessEqual[t, -4.9e+115], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.9e+87], t$95$1, If[LessEqual[t, -2.6e+80], t$95$2, If[LessEqual[t, -1.1], y, If[LessEqual[t, -3.9e-98], t$95$1, If[LessEqual[t, -1.04e-147], t$95$2, If[LessEqual[t, 3.2e+61], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.1e230 or -2.59999999999999982e80 < t < -1.1000000000000001 or 3.1999999999999998e61 < t

   1. Initial program 38.3%

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

   3. Taylor expanded in t around inf 50.9%

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

   if -5.1e230 < t < -4.89999999999999964e115

   1. Initial program 37.8%

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

   3. Taylor expanded in t around inf 42.7%

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

      1. associate--l+ 42.7%

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

      2. distribute-lft-out-- 42.7%

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

      3. div-sub 42.7%

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

      4. mul-1-neg 42.7%

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

      5. unsub-neg 42.7%

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

      6. div-sub 42.7%

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

      7. associate-/l* 57.0%

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

      8. associate-/l* 76.5%

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

      9. distribute-rgt-out-- 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in y around 0 29.1%

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

      1. *-commutative 29.1%

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

      2. associate-/l* 45.0%

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

   8. Simplified 45.0%

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

   if -4.89999999999999964e115 < t < -3.9000000000000002e87 or -1.1000000000000001 < t < -3.89999999999999971e-98

   1. Initial program 64.3%

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

   3. Taylor expanded in t around 0 42.1%

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

   4. Taylor expanded in y around 0 41.9%

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

      1. mul-1-neg 41.9%

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

      2. unsub-neg 41.9%

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

      3. associate-/l* 64.0%

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

   6. Simplified 64.0%

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

   if -3.9000000000000002e87 < t < -2.59999999999999982e80 or -3.89999999999999971e-98 < t < -1.04000000000000003e-147

   1. Initial program 86.1%

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

      1. +-commutative 86.1%

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

      2. associate-/l* 90.8%

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

      3. fma-define 90.8%

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

   3. Simplified 90.8%

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

      1. clear-num 90.7%

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

      2. associate-/r/ 90.6%

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

   6. Applied egg-rr 90.6%

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

   7. Taylor expanded in y around inf 72.2%

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

      1. div-sub 72.2%

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

      2. associate-*r/ 67.5%

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

      3. *-commutative 67.5%

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

      4. associate-*r/ 67.6%

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

   9. Simplified 67.6%

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

   10. Taylor expanded in z around inf 58.2%

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

       1. associate-/l* 62.9%

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

   12. Simplified 62.9%

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

   if -1.04000000000000003e-147 < t < 3.1999999999999998e61

   1. Initial program 92.3%

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

   3. Taylor expanded in t around 0 71.9%

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

   4. Taylor expanded in y around inf 64.6%

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

      1. associate-/l* 36.9%

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

   6. Simplified 69.4%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+230}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{+115}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{+87}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -1.1:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-98}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.04 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+61}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 29.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - a}{t}\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.82 \cdot 10^{+149}:\\ \;\;\;\;z \cdot \frac{x}{-a}\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4200000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-190}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-107}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-67}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 10^{+102}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- z a) t))))
   (if (<= x -1.4e+222)
     t_1
     (if (<= x -1.82e+149)
       (* z (/ x (- a)))
       (if (<= x -1.2e+68)
         t_1
         (if (<= x -4200000000000.0)
           x
           (if (<= x 9.5e-190)
             y
             (if (<= x 1.85e-107)
               (* y (/ z a))
               (if (<= x 3.8e-67) y (if (<= x 1e+102) (/ (* x z) t) x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (x <= -1.4e+222) {
		tmp = t_1;
	} else if (x <= -1.82e+149) {
		tmp = z * (x / -a);
	} else if (x <= -1.2e+68) {
		tmp = t_1;
	} else if (x <= -4200000000000.0) {
		tmp = x;
	} else if (x <= 9.5e-190) {
		tmp = y;
	} else if (x <= 1.85e-107) {
		tmp = y * (z / a);
	} else if (x <= 3.8e-67) {
		tmp = y;
	} else if (x <= 1e+102) {
		tmp = (x * z) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((z - a) / t)
    if (x <= (-1.4d+222)) then
        tmp = t_1
    else if (x <= (-1.82d+149)) then
        tmp = z * (x / -a)
    else if (x <= (-1.2d+68)) then
        tmp = t_1
    else if (x <= (-4200000000000.0d0)) then
        tmp = x
    else if (x <= 9.5d-190) then
        tmp = y
    else if (x <= 1.85d-107) then
        tmp = y * (z / a)
    else if (x <= 3.8d-67) then
        tmp = y
    else if (x <= 1d+102) then
        tmp = (x * z) / t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (x <= -1.4e+222) {
		tmp = t_1;
	} else if (x <= -1.82e+149) {
		tmp = z * (x / -a);
	} else if (x <= -1.2e+68) {
		tmp = t_1;
	} else if (x <= -4200000000000.0) {
		tmp = x;
	} else if (x <= 9.5e-190) {
		tmp = y;
	} else if (x <= 1.85e-107) {
		tmp = y * (z / a);
	} else if (x <= 3.8e-67) {
		tmp = y;
	} else if (x <= 1e+102) {
		tmp = (x * z) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((z - a) / t)
	tmp = 0
	if x <= -1.4e+222:
		tmp = t_1
	elif x <= -1.82e+149:
		tmp = z * (x / -a)
	elif x <= -1.2e+68:
		tmp = t_1
	elif x <= -4200000000000.0:
		tmp = x
	elif x <= 9.5e-190:
		tmp = y
	elif x <= 1.85e-107:
		tmp = y * (z / a)
	elif x <= 3.8e-67:
		tmp = y
	elif x <= 1e+102:
		tmp = (x * z) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(z - a) / t))
	tmp = 0.0
	if (x <= -1.4e+222)
		tmp = t_1;
	elseif (x <= -1.82e+149)
		tmp = Float64(z * Float64(x / Float64(-a)));
	elseif (x <= -1.2e+68)
		tmp = t_1;
	elseif (x <= -4200000000000.0)
		tmp = x;
	elseif (x <= 9.5e-190)
		tmp = y;
	elseif (x <= 1.85e-107)
		tmp = Float64(y * Float64(z / a));
	elseif (x <= 3.8e-67)
		tmp = y;
	elseif (x <= 1e+102)
		tmp = Float64(Float64(x * z) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((z - a) / t);
	tmp = 0.0;
	if (x <= -1.4e+222)
		tmp = t_1;
	elseif (x <= -1.82e+149)
		tmp = z * (x / -a);
	elseif (x <= -1.2e+68)
		tmp = t_1;
	elseif (x <= -4200000000000.0)
		tmp = x;
	elseif (x <= 9.5e-190)
		tmp = y;
	elseif (x <= 1.85e-107)
		tmp = y * (z / a);
	elseif (x <= 3.8e-67)
		tmp = y;
	elseif (x <= 1e+102)
		tmp = (x * z) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e+222], t$95$1, If[LessEqual[x, -1.82e+149], N[(z * N[(x / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.2e+68], t$95$1, If[LessEqual[x, -4200000000000.0], x, If[LessEqual[x, 9.5e-190], y, If[LessEqual[x, 1.85e-107], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e-67], y, If[LessEqual[x, 1e+102], N[(N[(x * z), $MachinePrecision] / t), $MachinePrecision], x]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.4000000000000001e222 or -1.8199999999999999e149 < x < -1.20000000000000004e68

   1. Initial program 51.7%

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

   3. Taylor expanded in x around -inf 59.8%

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

      1. associate-*r* 59.8%

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

      2. neg-mul-1 59.8%

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

      3. +-commutative 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in t around -inf 42.0%

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

      1. associate-/l* 50.7%

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

   8. Simplified 50.7%

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

   if -1.4000000000000001e222 < x < -1.8199999999999999e149

   1. Initial program 76.8%

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

   3. Taylor expanded in t around 0 76.1%

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

   4. Taylor expanded in z around inf 67.0%

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

      1. div-sub 67.0%

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

   6. Simplified 67.0%

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

   7. Taylor expanded in y around 0 67.0%

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

      1. neg-mul-1 67.0%

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

      2. distribute-neg-frac2 67.0%

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

   9. Simplified 67.0%

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

   if -1.20000000000000004e68 < x < -4.2e12 or 9.99999999999999977e101 < x

   1. Initial program 62.8%

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

   3. Taylor expanded in a around inf 47.1%

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

   if -4.2e12 < x < 9.50000000000000055e-190 or 1.8500000000000001e-107 < x < 3.79999999999999988e-67

   1. Initial program 74.1%

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

   3. Taylor expanded in t around inf 44.5%

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

   if 9.50000000000000055e-190 < x < 1.8500000000000001e-107

   1. Initial program 79.6%

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

   3. Taylor expanded in t around 0 58.5%

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

   4. Taylor expanded in z around -inf 58.4%

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

   5. Taylor expanded in y around inf 45.1%

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

      1. associate-/l* 58.8%

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

   7. Simplified 58.8%

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

   if 3.79999999999999988e-67 < x < 9.99999999999999977e101

   1. Initial program 73.2%

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

   3. Taylor expanded in x around -inf 53.2%

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

      1. associate-*r* 53.2%

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

      2. neg-mul-1 53.2%

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

      3. +-commutative 53.2%

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

   5. Simplified 53.2%

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

   6. Taylor expanded in a around 0 42.0%

      \[\leadsto \color{blue}{\frac{x \cdot z}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;x \leq -1.82 \cdot 10^{+149}:\\ \;\;\;\;z \cdot \frac{x}{-a}\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;x \leq -4200000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-190}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-107}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-67}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 10^{+102}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a - t}\\ t_2 := x + z \cdot \frac{y - x}{a}\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-98}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-231}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ y (- a t)))) (t_2 (+ x (* z (/ (- y x) a)))))
   (if (<= a -1.55e-12)
     t_2
     (if (<= a -2e-82)
       t_1
       (if (<= a -1.42e-98)
         (- x (* x (/ z a)))
         (if (<= a -6.2e-196)
           t_1
           (if (<= a -1e-211)
             (* x (/ (- z a) t))
             (if (<= a 5.5e-231)
               (* z (/ (- y x) (- a t)))
               (if (<= a 1.35e+50) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (a - t));
	double t_2 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -1.55e-12) {
		tmp = t_2;
	} else if (a <= -2e-82) {
		tmp = t_1;
	} else if (a <= -1.42e-98) {
		tmp = x - (x * (z / a));
	} else if (a <= -6.2e-196) {
		tmp = t_1;
	} else if (a <= -1e-211) {
		tmp = x * ((z - a) / t);
	} else if (a <= 5.5e-231) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 1.35e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z - t) * (y / (a - t))
    t_2 = x + (z * ((y - x) / a))
    if (a <= (-1.55d-12)) then
        tmp = t_2
    else if (a <= (-2d-82)) then
        tmp = t_1
    else if (a <= (-1.42d-98)) then
        tmp = x - (x * (z / a))
    else if (a <= (-6.2d-196)) then
        tmp = t_1
    else if (a <= (-1d-211)) then
        tmp = x * ((z - a) / t)
    else if (a <= 5.5d-231) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 1.35d+50) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (a - t));
	double t_2 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -1.55e-12) {
		tmp = t_2;
	} else if (a <= -2e-82) {
		tmp = t_1;
	} else if (a <= -1.42e-98) {
		tmp = x - (x * (z / a));
	} else if (a <= -6.2e-196) {
		tmp = t_1;
	} else if (a <= -1e-211) {
		tmp = x * ((z - a) / t);
	} else if (a <= 5.5e-231) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 1.35e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * (y / (a - t))
	t_2 = x + (z * ((y - x) / a))
	tmp = 0
	if a <= -1.55e-12:
		tmp = t_2
	elif a <= -2e-82:
		tmp = t_1
	elif a <= -1.42e-98:
		tmp = x - (x * (z / a))
	elif a <= -6.2e-196:
		tmp = t_1
	elif a <= -1e-211:
		tmp = x * ((z - a) / t)
	elif a <= 5.5e-231:
		tmp = z * ((y - x) / (a - t))
	elif a <= 1.35e+50:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * Float64(y / Float64(a - t)))
	t_2 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (a <= -1.55e-12)
		tmp = t_2;
	elseif (a <= -2e-82)
		tmp = t_1;
	elseif (a <= -1.42e-98)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (a <= -6.2e-196)
		tmp = t_1;
	elseif (a <= -1e-211)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (a <= 5.5e-231)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 1.35e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * (y / (a - t));
	t_2 = x + (z * ((y - x) / a));
	tmp = 0.0;
	if (a <= -1.55e-12)
		tmp = t_2;
	elseif (a <= -2e-82)
		tmp = t_1;
	elseif (a <= -1.42e-98)
		tmp = x - (x * (z / a));
	elseif (a <= -6.2e-196)
		tmp = t_1;
	elseif (a <= -1e-211)
		tmp = x * ((z - a) / t);
	elseif (a <= 5.5e-231)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 1.35e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e-12], t$95$2, If[LessEqual[a, -2e-82], t$95$1, If[LessEqual[a, -1.42e-98], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.2e-196], t$95$1, If[LessEqual[a, -1e-211], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-231], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+50], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.5500000000000001e-12 or 1.35e50 < a

   1. Initial program 66.5%

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

   3. Taylor expanded in t around 0 59.7%

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

      1. associate-/l* 70.8%

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

   5. Simplified 70.8%

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

   if -1.5500000000000001e-12 < a < -2e-82 or -1.41999999999999999e-98 < a < -6.19999999999999986e-196 or 5.49999999999999951e-231 < a < 1.35e50

   1. Initial program 68.4%

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

      1. +-commutative 68.4%

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

      2. associate-/l* 80.8%

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

      3. fma-define 80.8%

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

   3. Simplified 80.8%

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

      1. clear-num 80.7%

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

      2. associate-/r/ 80.5%

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

   6. Applied egg-rr 80.5%

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

   7. Taylor expanded in y around inf 73.5%

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

      1. div-sub 73.5%

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

      2. associate-*r/ 59.1%

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

      3. *-commutative 59.1%

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

      4. associate-*r/ 62.7%

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

   9. Simplified 62.7%

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

   if -2e-82 < a < -1.41999999999999999e-98

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 99.7%

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

   4. Taylor expanded in y around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

      3. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   if -6.19999999999999986e-196 < a < -1.00000000000000009e-211

   1. Initial program 72.5%

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

   3. Taylor expanded in x around -inf 99.8%

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

      1. associate-*r* 99.8%

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

      2. neg-mul-1 99.8%

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

      3. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around -inf 59.1%

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

      1. associate-/l* 86.4%

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

   8. Simplified 86.4%

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

   if -1.00000000000000009e-211 < a < 5.49999999999999951e-231

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-/l* 75.5%

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

      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. associate-/r/ 75.2%

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

   6. Applied egg-rr 75.2%

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

   7. Taylor expanded in z around inf 67.0%

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

      1. div-sub 71.9%

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

   9. Simplified 71.9%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-12}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-82}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-98}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-196}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-231}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+50}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a - t}\\ t_2 := x + z \cdot \frac{y - x}{a}\\ \mathbf{if}\;a \leq -9 \cdot 10^{-14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-218}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ y (- a t)))) (t_2 (+ x (* z (/ (- y x) a)))))
   (if (<= a -9e-14)
     t_2
     (if (<= a -1.8e-69)
       t_1
       (if (<= a -1.4e-98)
         (+ x (/ (* (- y x) z) a))
         (if (<= a -7.2e-196)
           t_1
           (if (<= a -1e-211)
             (* x (/ (- z a) t))
             (if (<= a 1.2e-218)
               (* z (/ (- y x) (- a t)))
               (if (<= a 4.8e+50) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (a - t));
	double t_2 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -9e-14) {
		tmp = t_2;
	} else if (a <= -1.8e-69) {
		tmp = t_1;
	} else if (a <= -1.4e-98) {
		tmp = x + (((y - x) * z) / a);
	} else if (a <= -7.2e-196) {
		tmp = t_1;
	} else if (a <= -1e-211) {
		tmp = x * ((z - a) / t);
	} else if (a <= 1.2e-218) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 4.8e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z - t) * (y / (a - t))
    t_2 = x + (z * ((y - x) / a))
    if (a <= (-9d-14)) then
        tmp = t_2
    else if (a <= (-1.8d-69)) then
        tmp = t_1
    else if (a <= (-1.4d-98)) then
        tmp = x + (((y - x) * z) / a)
    else if (a <= (-7.2d-196)) then
        tmp = t_1
    else if (a <= (-1d-211)) then
        tmp = x * ((z - a) / t)
    else if (a <= 1.2d-218) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 4.8d+50) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (a - t));
	double t_2 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -9e-14) {
		tmp = t_2;
	} else if (a <= -1.8e-69) {
		tmp = t_1;
	} else if (a <= -1.4e-98) {
		tmp = x + (((y - x) * z) / a);
	} else if (a <= -7.2e-196) {
		tmp = t_1;
	} else if (a <= -1e-211) {
		tmp = x * ((z - a) / t);
	} else if (a <= 1.2e-218) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 4.8e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * (y / (a - t))
	t_2 = x + (z * ((y - x) / a))
	tmp = 0
	if a <= -9e-14:
		tmp = t_2
	elif a <= -1.8e-69:
		tmp = t_1
	elif a <= -1.4e-98:
		tmp = x + (((y - x) * z) / a)
	elif a <= -7.2e-196:
		tmp = t_1
	elif a <= -1e-211:
		tmp = x * ((z - a) / t)
	elif a <= 1.2e-218:
		tmp = z * ((y - x) / (a - t))
	elif a <= 4.8e+50:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * Float64(y / Float64(a - t)))
	t_2 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (a <= -9e-14)
		tmp = t_2;
	elseif (a <= -1.8e-69)
		tmp = t_1;
	elseif (a <= -1.4e-98)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / a));
	elseif (a <= -7.2e-196)
		tmp = t_1;
	elseif (a <= -1e-211)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (a <= 1.2e-218)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 4.8e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * (y / (a - t));
	t_2 = x + (z * ((y - x) / a));
	tmp = 0.0;
	if (a <= -9e-14)
		tmp = t_2;
	elseif (a <= -1.8e-69)
		tmp = t_1;
	elseif (a <= -1.4e-98)
		tmp = x + (((y - x) * z) / a);
	elseif (a <= -7.2e-196)
		tmp = t_1;
	elseif (a <= -1e-211)
		tmp = x * ((z - a) / t);
	elseif (a <= 1.2e-218)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 4.8e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e-14], t$95$2, If[LessEqual[a, -1.8e-69], t$95$1, If[LessEqual[a, -1.4e-98], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.2e-196], t$95$1, If[LessEqual[a, -1e-211], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-218], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e+50], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -8.9999999999999995e-14 or 4.8000000000000004e50 < a

   1. Initial program 66.5%

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

   3. Taylor expanded in t around 0 59.7%

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

      1. associate-/l* 70.8%

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

   5. Simplified 70.8%

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

   if -8.9999999999999995e-14 < a < -1.80000000000000009e-69 or -1.3999999999999999e-98 < a < -7.2000000000000001e-196 or 1.2e-218 < a < 4.8000000000000004e50

   1. Initial program 68.0%

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

      1. +-commutative 68.0%

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

      2. associate-/l* 80.5%

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

      3. fma-define 80.5%

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

   3. Simplified 80.5%

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

      1. clear-num 80.4%

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

      2. associate-/r/ 80.2%

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

   6. Applied egg-rr 80.2%

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

   7. Taylor expanded in y around inf 73.2%

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

      1. div-sub 73.2%

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

      2. associate-*r/ 58.6%

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

      3. *-commutative 58.6%

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

      4. associate-*r/ 62.2%

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

   9. Simplified 62.2%

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

   if -1.80000000000000009e-69 < a < -1.3999999999999999e-98

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 99.8%

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

   if -7.2000000000000001e-196 < a < -1.00000000000000009e-211

   1. Initial program 72.5%

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

   3. Taylor expanded in x around -inf 99.8%

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

      1. associate-*r* 99.8%

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

      2. neg-mul-1 99.8%

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

      3. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around -inf 59.1%

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

      1. associate-/l* 86.4%

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

   8. Simplified 86.4%

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

   if -1.00000000000000009e-211 < a < 1.2e-218

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-/l* 75.5%

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

      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. associate-/r/ 75.2%

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

   6. Applied egg-rr 75.2%

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

   7. Taylor expanded in z around inf 67.0%

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

      1. div-sub 71.9%

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

   9. Simplified 71.9%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-14}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-69}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-196}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-218}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+50}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a - t}\\ t_2 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-156}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 9.9 \cdot 10^{-141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ y (- a t)))) (t_2 (* z (/ (- y x) (- a t)))))
   (if (<= z -5.8e+64)
     t_2
     (if (<= z -1.16e-145)
       t_1
       (if (<= z 1.02e-156)
         (- x (* y (/ t a)))
         (if (<= z 9.9e-141)
           t_1
           (if (<= z 7.5e+17) (+ x (* y (/ z a))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -5.8e+64) {
		tmp = t_2;
	} else if (z <= -1.16e-145) {
		tmp = t_1;
	} else if (z <= 1.02e-156) {
		tmp = x - (y * (t / a));
	} else if (z <= 9.9e-141) {
		tmp = t_1;
	} else if (z <= 7.5e+17) {
		tmp = x + (y * (z / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z - t) * (y / (a - t))
    t_2 = z * ((y - x) / (a - t))
    if (z <= (-5.8d+64)) then
        tmp = t_2
    else if (z <= (-1.16d-145)) then
        tmp = t_1
    else if (z <= 1.02d-156) then
        tmp = x - (y * (t / a))
    else if (z <= 9.9d-141) then
        tmp = t_1
    else if (z <= 7.5d+17) then
        tmp = x + (y * (z / a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -5.8e+64) {
		tmp = t_2;
	} else if (z <= -1.16e-145) {
		tmp = t_1;
	} else if (z <= 1.02e-156) {
		tmp = x - (y * (t / a));
	} else if (z <= 9.9e-141) {
		tmp = t_1;
	} else if (z <= 7.5e+17) {
		tmp = x + (y * (z / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * (y / (a - t))
	t_2 = z * ((y - x) / (a - t))
	tmp = 0
	if z <= -5.8e+64:
		tmp = t_2
	elif z <= -1.16e-145:
		tmp = t_1
	elif z <= 1.02e-156:
		tmp = x - (y * (t / a))
	elif z <= 9.9e-141:
		tmp = t_1
	elif z <= 7.5e+17:
		tmp = x + (y * (z / a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * Float64(y / Float64(a - t)))
	t_2 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (z <= -5.8e+64)
		tmp = t_2;
	elseif (z <= -1.16e-145)
		tmp = t_1;
	elseif (z <= 1.02e-156)
		tmp = Float64(x - Float64(y * Float64(t / a)));
	elseif (z <= 9.9e-141)
		tmp = t_1;
	elseif (z <= 7.5e+17)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * (y / (a - t));
	t_2 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (z <= -5.8e+64)
		tmp = t_2;
	elseif (z <= -1.16e-145)
		tmp = t_1;
	elseif (z <= 1.02e-156)
		tmp = x - (y * (t / a));
	elseif (z <= 9.9e-141)
		tmp = t_1;
	elseif (z <= 7.5e+17)
		tmp = x + (y * (z / a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+64], t$95$2, If[LessEqual[z, -1.16e-145], t$95$1, If[LessEqual[z, 1.02e-156], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.9e-141], t$95$1, If[LessEqual[z, 7.5e+17], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.79999999999999986e64 or 7.5e17 < z

   1. Initial program 71.2%

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

      1. +-commutative 71.2%

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

      2. associate-/l* 93.3%

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

      3. fma-define 93.2%

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

   3. Simplified 93.2%

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

      1. clear-num 93.1%

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

      2. associate-/r/ 93.1%

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

   6. Applied egg-rr 93.1%

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

   7. Taylor expanded in z around inf 77.9%

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

      1. div-sub 79.7%

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

   9. Simplified 79.7%

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

   if -5.79999999999999986e64 < z < -1.16000000000000004e-145 or 1.02e-156 < z < 9.9000000000000006e-141

   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* 79.7%

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

      3. fma-define 79.7%

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

   3. Simplified 79.7%

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

      1. clear-num 79.6%

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

      2. associate-/r/ 79.6%

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

   6. Applied egg-rr 79.6%

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

   7. Taylor expanded in y around inf 64.4%

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

      1. div-sub 64.4%

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

      2. associate-*r/ 53.4%

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

      3. *-commutative 53.4%

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

      4. associate-*r/ 59.9%

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

   9. Simplified 59.9%

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

   if -1.16000000000000004e-145 < z < 1.02e-156

   1. Initial program 65.3%

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

   3. Taylor expanded in z around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. unsub-neg 63.9%

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

      3. associate-/l* 60.9%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in t around 0 50.9%

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

   7. Taylor expanded in y around inf 52.0%

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

      1. *-commutative 52.0%

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

      2. associate-*r/ 56.3%

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

   9. Simplified 56.3%

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

   if 9.9000000000000006e-141 < z < 7.5e17

   1. Initial program 70.8%

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

   3. Taylor expanded in t around 0 44.8%

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

   4. Taylor expanded in y around inf 45.5%

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

      1. associate-/l* 12.0%

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

   6. Simplified 45.5%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-145}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-156}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 9.9 \cdot 10^{-141}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.62 \cdot 10^{-69}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-161}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+88}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) a)))))
   (if (<= a -6.2e-12)
     t_1
     (if (<= a -1.62e-69)
       (* (- z t) (/ y (- a t)))
       (if (<= a -1.42e-98)
         (+ x (/ (* (- y x) z) a))
         (if (<= a 1.25e-161)
           (+ y (/ (* z (- x y)) t))
           (if (<= a 2.7e+88) (+ y (* x (/ (- z a) t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -6.2e-12) {
		tmp = t_1;
	} else if (a <= -1.62e-69) {
		tmp = (z - t) * (y / (a - t));
	} else if (a <= -1.42e-98) {
		tmp = x + (((y - x) * z) / a);
	} else if (a <= 1.25e-161) {
		tmp = y + ((z * (x - y)) / t);
	} else if (a <= 2.7e+88) {
		tmp = y + (x * ((z - a) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * ((y - x) / a))
    if (a <= (-6.2d-12)) then
        tmp = t_1
    else if (a <= (-1.62d-69)) then
        tmp = (z - t) * (y / (a - t))
    else if (a <= (-1.42d-98)) then
        tmp = x + (((y - x) * z) / a)
    else if (a <= 1.25d-161) then
        tmp = y + ((z * (x - y)) / t)
    else if (a <= 2.7d+88) then
        tmp = y + (x * ((z - a) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -6.2e-12) {
		tmp = t_1;
	} else if (a <= -1.62e-69) {
		tmp = (z - t) * (y / (a - t));
	} else if (a <= -1.42e-98) {
		tmp = x + (((y - x) * z) / a);
	} else if (a <= 1.25e-161) {
		tmp = y + ((z * (x - y)) / t);
	} else if (a <= 2.7e+88) {
		tmp = y + (x * ((z - a) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / a))
	tmp = 0
	if a <= -6.2e-12:
		tmp = t_1
	elif a <= -1.62e-69:
		tmp = (z - t) * (y / (a - t))
	elif a <= -1.42e-98:
		tmp = x + (((y - x) * z) / a)
	elif a <= 1.25e-161:
		tmp = y + ((z * (x - y)) / t)
	elif a <= 2.7e+88:
		tmp = y + (x * ((z - a) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (a <= -6.2e-12)
		tmp = t_1;
	elseif (a <= -1.62e-69)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (a <= -1.42e-98)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / a));
	elseif (a <= 1.25e-161)
		tmp = Float64(y + Float64(Float64(z * Float64(x - y)) / t));
	elseif (a <= 2.7e+88)
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / a));
	tmp = 0.0;
	if (a <= -6.2e-12)
		tmp = t_1;
	elseif (a <= -1.62e-69)
		tmp = (z - t) * (y / (a - t));
	elseif (a <= -1.42e-98)
		tmp = x + (((y - x) * z) / a);
	elseif (a <= 1.25e-161)
		tmp = y + ((z * (x - y)) / t);
	elseif (a <= 2.7e+88)
		tmp = y + (x * ((z - a) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e-12], t$95$1, If[LessEqual[a, -1.62e-69], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.42e-98], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e-161], N[(y + N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+88], N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.2000000000000002e-12 or 2.70000000000000016e88 < 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 t around 0 61.8%

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

      1. associate-/l* 73.0%

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

   5. Simplified 73.0%

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

   if -6.2000000000000002e-12 < a < -1.62e-69

   1. Initial program 82.5%

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

      1. +-commutative 82.5%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 91.0%

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

      1. div-sub 91.0%

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

      2. associate-*r/ 73.4%

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

      3. *-commutative 73.4%

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

      4. associate-*r/ 91.0%

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

   9. Simplified 91.0%

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

   if -1.62e-69 < a < -1.41999999999999999e-98

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 99.8%

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

   if -1.41999999999999999e-98 < a < 1.25e-161

   1. Initial program 68.2%

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

   3. Taylor expanded in t around inf 85.3%

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

      1. associate--l+ 85.3%

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

      2. distribute-lft-out-- 85.3%

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

      3. div-sub 85.3%

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

      4. mul-1-neg 85.3%

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

      5. unsub-neg 85.3%

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

      6. div-sub 85.3%

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

      7. associate-/l* 87.5%

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

      8. associate-/l* 78.8%

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

      9. distribute-rgt-out-- 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in z around inf 82.6%

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

   if 1.25e-161 < a < 2.70000000000000016e88

   1. Initial program 61.0%

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

   3. Taylor expanded in t around inf 56.5%

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

      1. associate--l+ 56.5%

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

      2. distribute-lft-out-- 56.5%

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

      3. div-sub 56.7%

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

      4. mul-1-neg 56.7%

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

      5. unsub-neg 56.7%

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

      6. div-sub 56.5%

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

      7. associate-/l* 58.5%

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

      8. associate-/l* 63.9%

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

      9. distribute-rgt-out-- 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in y around 0 57.4%

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

      1. mul-1-neg 57.4%

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

      2. associate-/l* 63.0%

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

      3. distribute-rgt-neg-in 63.0%

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

      4. distribute-frac-neg2 63.0%

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

   8. Simplified 63.0%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-12}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -1.62 \cdot 10^{-69}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-161}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+88}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a}\\ \mathbf{if}\;a \leq -6 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-69}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-147}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+88}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) a)))))
   (if (<= a -6e-13)
     t_1
     (if (<= a -1.7e-69)
       (* (- z t) (/ y (- a t)))
       (if (<= a -1.42e-98)
         (+ x (/ (* (- y x) z) a))
         (if (<= a 1.18e-147)
           (+ y (/ (* z (- x y)) t))
           (if (<= a 5e+88) (+ y (* (- z a) (/ x t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -6e-13) {
		tmp = t_1;
	} else if (a <= -1.7e-69) {
		tmp = (z - t) * (y / (a - t));
	} else if (a <= -1.42e-98) {
		tmp = x + (((y - x) * z) / a);
	} else if (a <= 1.18e-147) {
		tmp = y + ((z * (x - y)) / t);
	} else if (a <= 5e+88) {
		tmp = y + ((z - a) * (x / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * ((y - x) / a))
    if (a <= (-6d-13)) then
        tmp = t_1
    else if (a <= (-1.7d-69)) then
        tmp = (z - t) * (y / (a - t))
    else if (a <= (-1.42d-98)) then
        tmp = x + (((y - x) * z) / a)
    else if (a <= 1.18d-147) then
        tmp = y + ((z * (x - y)) / t)
    else if (a <= 5d+88) then
        tmp = y + ((z - a) * (x / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -6e-13) {
		tmp = t_1;
	} else if (a <= -1.7e-69) {
		tmp = (z - t) * (y / (a - t));
	} else if (a <= -1.42e-98) {
		tmp = x + (((y - x) * z) / a);
	} else if (a <= 1.18e-147) {
		tmp = y + ((z * (x - y)) / t);
	} else if (a <= 5e+88) {
		tmp = y + ((z - a) * (x / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / a))
	tmp = 0
	if a <= -6e-13:
		tmp = t_1
	elif a <= -1.7e-69:
		tmp = (z - t) * (y / (a - t))
	elif a <= -1.42e-98:
		tmp = x + (((y - x) * z) / a)
	elif a <= 1.18e-147:
		tmp = y + ((z * (x - y)) / t)
	elif a <= 5e+88:
		tmp = y + ((z - a) * (x / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (a <= -6e-13)
		tmp = t_1;
	elseif (a <= -1.7e-69)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (a <= -1.42e-98)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / a));
	elseif (a <= 1.18e-147)
		tmp = Float64(y + Float64(Float64(z * Float64(x - y)) / t));
	elseif (a <= 5e+88)
		tmp = Float64(y + Float64(Float64(z - a) * Float64(x / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / a));
	tmp = 0.0;
	if (a <= -6e-13)
		tmp = t_1;
	elseif (a <= -1.7e-69)
		tmp = (z - t) * (y / (a - t));
	elseif (a <= -1.42e-98)
		tmp = x + (((y - x) * z) / a);
	elseif (a <= 1.18e-147)
		tmp = y + ((z * (x - y)) / t);
	elseif (a <= 5e+88)
		tmp = y + ((z - a) * (x / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e-13], t$95$1, If[LessEqual[a, -1.7e-69], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.42e-98], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.18e-147], N[(y + N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+88], N[(y + N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.99999999999999968e-13 or 4.99999999999999997e88 < 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 t around 0 61.8%

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

      1. associate-/l* 73.0%

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

   5. Simplified 73.0%

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

   if -5.99999999999999968e-13 < a < -1.70000000000000004e-69

   1. Initial program 82.5%

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

      1. +-commutative 82.5%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 91.0%

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

      1. div-sub 91.0%

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

      2. associate-*r/ 73.4%

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

      3. *-commutative 73.4%

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

      4. associate-*r/ 91.0%

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

   9. Simplified 91.0%

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

   if -1.70000000000000004e-69 < a < -1.41999999999999999e-98

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 99.8%

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

   if -1.41999999999999999e-98 < a < 1.18000000000000003e-147

   1. Initial program 69.0%

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

   3. Taylor expanded in t around inf 85.7%

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

      1. associate--l+ 85.7%

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

      2. distribute-lft-out-- 85.7%

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

      3. div-sub 85.7%

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

      4. mul-1-neg 85.7%

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

      5. unsub-neg 85.7%

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

      6. div-sub 85.7%

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

      7. associate-/l* 86.7%

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

      8. associate-/l* 78.1%

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

      9. distribute-rgt-out-- 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in z around inf 83.1%

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

   if 1.18000000000000003e-147 < a < 4.99999999999999997e88

   1. Initial program 59.3%

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

   3. Taylor expanded in t around inf 54.7%

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

      1. associate--l+ 54.7%

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

      2. distribute-lft-out-- 54.7%

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

      3. div-sub 54.9%

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

      4. mul-1-neg 54.9%

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

      5. unsub-neg 54.9%

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

      6. div-sub 54.7%

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

      7. associate-/l* 58.6%

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

      8. associate-/l* 64.5%

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

      9. distribute-rgt-out-- 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in y around 0 63.4%

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

      1. neg-mul-1 63.4%

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

      2. distribute-neg-frac2 63.4%

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

   8. Simplified 63.4%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-13}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-69}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-147}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+88}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a}\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-82}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-148}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+88}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) a)))))
   (if (<= a -1.3e-12)
     t_1
     (if (<= a -3.7e-82)
       (* (- z t) (/ y (- a t)))
       (if (<= a -5.1e-99)
         (* x (+ (/ (- z t) (- t a)) 1.0))
         (if (<= a 9.5e-148)
           (+ y (/ (* z (- x y)) t))
           (if (<= a 4.8e+88) (+ y (* (- z a) (/ x t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -1.3e-12) {
		tmp = t_1;
	} else if (a <= -3.7e-82) {
		tmp = (z - t) * (y / (a - t));
	} else if (a <= -5.1e-99) {
		tmp = x * (((z - t) / (t - a)) + 1.0);
	} else if (a <= 9.5e-148) {
		tmp = y + ((z * (x - y)) / t);
	} else if (a <= 4.8e+88) {
		tmp = y + ((z - a) * (x / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * ((y - x) / a))
    if (a <= (-1.3d-12)) then
        tmp = t_1
    else if (a <= (-3.7d-82)) then
        tmp = (z - t) * (y / (a - t))
    else if (a <= (-5.1d-99)) then
        tmp = x * (((z - t) / (t - a)) + 1.0d0)
    else if (a <= 9.5d-148) then
        tmp = y + ((z * (x - y)) / t)
    else if (a <= 4.8d+88) then
        tmp = y + ((z - a) * (x / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -1.3e-12) {
		tmp = t_1;
	} else if (a <= -3.7e-82) {
		tmp = (z - t) * (y / (a - t));
	} else if (a <= -5.1e-99) {
		tmp = x * (((z - t) / (t - a)) + 1.0);
	} else if (a <= 9.5e-148) {
		tmp = y + ((z * (x - y)) / t);
	} else if (a <= 4.8e+88) {
		tmp = y + ((z - a) * (x / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / a))
	tmp = 0
	if a <= -1.3e-12:
		tmp = t_1
	elif a <= -3.7e-82:
		tmp = (z - t) * (y / (a - t))
	elif a <= -5.1e-99:
		tmp = x * (((z - t) / (t - a)) + 1.0)
	elif a <= 9.5e-148:
		tmp = y + ((z * (x - y)) / t)
	elif a <= 4.8e+88:
		tmp = y + ((z - a) * (x / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (a <= -1.3e-12)
		tmp = t_1;
	elseif (a <= -3.7e-82)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (a <= -5.1e-99)
		tmp = Float64(x * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0));
	elseif (a <= 9.5e-148)
		tmp = Float64(y + Float64(Float64(z * Float64(x - y)) / t));
	elseif (a <= 4.8e+88)
		tmp = Float64(y + Float64(Float64(z - a) * Float64(x / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / a));
	tmp = 0.0;
	if (a <= -1.3e-12)
		tmp = t_1;
	elseif (a <= -3.7e-82)
		tmp = (z - t) * (y / (a - t));
	elseif (a <= -5.1e-99)
		tmp = x * (((z - t) / (t - a)) + 1.0);
	elseif (a <= 9.5e-148)
		tmp = y + ((z * (x - y)) / t);
	elseif (a <= 4.8e+88)
		tmp = y + ((z - a) * (x / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.3e-12], t$95$1, If[LessEqual[a, -3.7e-82], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.1e-99], N[(x * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-148], N[(y + N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e+88], N[(y + N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.29999999999999991e-12 or 4.7999999999999998e88 < 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 t around 0 61.8%

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

      1. associate-/l* 73.0%

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

   5. Simplified 73.0%

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

   if -1.29999999999999991e-12 < a < -3.7000000000000001e-82

   1. Initial program 83.9%

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

      1. +-commutative 83.9%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 91.7%

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

      1. div-sub 91.7%

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

      2. associate-*r/ 75.6%

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

      3. *-commutative 75.6%

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

      4. associate-*r/ 91.7%

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

   9. Simplified 91.7%

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

   if -3.7000000000000001e-82 < a < -5.0999999999999999e-99

   1. Initial program 86.3%

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

   3. Taylor expanded in x around inf 86.9%

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

      1. mul-1-neg 86.9%

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

      2. unsub-neg 86.9%

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

   5. Simplified 86.9%

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

   if -5.0999999999999999e-99 < a < 9.50000000000000069e-148

   1. Initial program 69.8%

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

   3. Taylor expanded in t around inf 86.7%

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

      1. associate--l+ 86.7%

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

      2. distribute-lft-out-- 86.7%

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

      3. div-sub 86.7%

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

      4. mul-1-neg 86.7%

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

      5. unsub-neg 86.7%

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

      6. div-sub 86.7%

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

      7. associate-/l* 86.6%

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

      8. associate-/l* 77.8%

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

      9. distribute-rgt-out-- 86.6%

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

   5. Simplified 86.6%

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

   6. Taylor expanded in z around inf 84.0%

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

   if 9.50000000000000069e-148 < a < 4.7999999999999998e88

   1. Initial program 59.3%

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

   3. Taylor expanded in t around inf 54.7%

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

      1. associate--l+ 54.7%

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

      2. distribute-lft-out-- 54.7%

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

      3. div-sub 54.9%

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

      4. mul-1-neg 54.9%

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

      5. unsub-neg 54.9%

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

      6. div-sub 54.7%

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

      7. associate-/l* 58.6%

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

      8. associate-/l* 64.5%

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

      9. distribute-rgt-out-- 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in y around 0 63.4%

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

      1. neg-mul-1 63.4%

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

      2. distribute-neg-frac2 63.4%

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

   8. Simplified 63.4%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-12}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-82}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-148}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+88}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{t}\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{-194}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-242}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-269}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+52}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ z t))))
   (if (<= a -3.7e+27)
     x
     (if (<= a -1.26e-194)
       y
       (if (<= a -2.9e-242)
         t_1
         (if (<= a -2.85e-269)
           y
           (if (<= a 2.55e-248) t_1 (if (<= a 6e+52) y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (a <= -3.7e+27) {
		tmp = x;
	} else if (a <= -1.26e-194) {
		tmp = y;
	} else if (a <= -2.9e-242) {
		tmp = t_1;
	} else if (a <= -2.85e-269) {
		tmp = y;
	} else if (a <= 2.55e-248) {
		tmp = t_1;
	} else if (a <= 6e+52) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / t)
    if (a <= (-3.7d+27)) then
        tmp = x
    else if (a <= (-1.26d-194)) then
        tmp = y
    else if (a <= (-2.9d-242)) then
        tmp = t_1
    else if (a <= (-2.85d-269)) then
        tmp = y
    else if (a <= 2.55d-248) then
        tmp = t_1
    else if (a <= 6d+52) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (a <= -3.7e+27) {
		tmp = x;
	} else if (a <= -1.26e-194) {
		tmp = y;
	} else if (a <= -2.9e-242) {
		tmp = t_1;
	} else if (a <= -2.85e-269) {
		tmp = y;
	} else if (a <= 2.55e-248) {
		tmp = t_1;
	} else if (a <= 6e+52) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (z / t)
	tmp = 0
	if a <= -3.7e+27:
		tmp = x
	elif a <= -1.26e-194:
		tmp = y
	elif a <= -2.9e-242:
		tmp = t_1
	elif a <= -2.85e-269:
		tmp = y
	elif a <= 2.55e-248:
		tmp = t_1
	elif a <= 6e+52:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(z / t))
	tmp = 0.0
	if (a <= -3.7e+27)
		tmp = x;
	elseif (a <= -1.26e-194)
		tmp = y;
	elseif (a <= -2.9e-242)
		tmp = t_1;
	elseif (a <= -2.85e-269)
		tmp = y;
	elseif (a <= 2.55e-248)
		tmp = t_1;
	elseif (a <= 6e+52)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (z / t);
	tmp = 0.0;
	if (a <= -3.7e+27)
		tmp = x;
	elseif (a <= -1.26e-194)
		tmp = y;
	elseif (a <= -2.9e-242)
		tmp = t_1;
	elseif (a <= -2.85e-269)
		tmp = y;
	elseif (a <= 2.55e-248)
		tmp = t_1;
	elseif (a <= 6e+52)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.7e+27], x, If[LessEqual[a, -1.26e-194], y, If[LessEqual[a, -2.9e-242], t$95$1, If[LessEqual[a, -2.85e-269], y, If[LessEqual[a, 2.55e-248], t$95$1, If[LessEqual[a, 6e+52], y, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.70000000000000002e27 or 6e52 < a

   1. Initial program 65.3%

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

   3. Taylor expanded in a around inf 43.7%

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

   if -3.70000000000000002e27 < a < -1.26e-194 or -2.9000000000000001e-242 < a < -2.84999999999999985e-269 or 2.54999999999999986e-248 < a < 6e52

   1. Initial program 71.2%

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

   3. Taylor expanded in t around inf 40.3%

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

   if -1.26e-194 < a < -2.9000000000000001e-242 or -2.84999999999999985e-269 < a < 2.54999999999999986e-248

   1. Initial program 71.9%

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

   3. Taylor expanded in x around -inf 72.7%

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

      1. associate-*r* 72.7%

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

      2. neg-mul-1 72.7%

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

      3. +-commutative 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in a around 0 51.1%

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

      1. associate-/l* 61.6%

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

   8. Simplified 61.6%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{-194}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-269}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+52}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-142}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+53}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+110)
   x
   (if (<= a -4.7e+51)
     (* y (/ z a))
     (if (<= a -4.2e+27)
       x
       (if (<= a -2.8e-142)
         y
         (if (<= a 9e-248) (* x (/ z t)) (if (<= a 1.65e+53) y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e+110) {
		tmp = x;
	} else if (a <= -4.7e+51) {
		tmp = y * (z / a);
	} else if (a <= -4.2e+27) {
		tmp = x;
	} else if (a <= -2.8e-142) {
		tmp = y;
	} else if (a <= 9e-248) {
		tmp = x * (z / t);
	} else if (a <= 1.65e+53) {
		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 <= (-3.4d+110)) then
        tmp = x
    else if (a <= (-4.7d+51)) then
        tmp = y * (z / a)
    else if (a <= (-4.2d+27)) then
        tmp = x
    else if (a <= (-2.8d-142)) then
        tmp = y
    else if (a <= 9d-248) then
        tmp = x * (z / t)
    else if (a <= 1.65d+53) 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 <= -3.4e+110) {
		tmp = x;
	} else if (a <= -4.7e+51) {
		tmp = y * (z / a);
	} else if (a <= -4.2e+27) {
		tmp = x;
	} else if (a <= -2.8e-142) {
		tmp = y;
	} else if (a <= 9e-248) {
		tmp = x * (z / t);
	} else if (a <= 1.65e+53) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.4e+110:
		tmp = x
	elif a <= -4.7e+51:
		tmp = y * (z / a)
	elif a <= -4.2e+27:
		tmp = x
	elif a <= -2.8e-142:
		tmp = y
	elif a <= 9e-248:
		tmp = x * (z / t)
	elif a <= 1.65e+53:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.4e+110)
		tmp = x;
	elseif (a <= -4.7e+51)
		tmp = Float64(y * Float64(z / a));
	elseif (a <= -4.2e+27)
		tmp = x;
	elseif (a <= -2.8e-142)
		tmp = y;
	elseif (a <= 9e-248)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 1.65e+53)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.4e+110)
		tmp = x;
	elseif (a <= -4.7e+51)
		tmp = y * (z / a);
	elseif (a <= -4.2e+27)
		tmp = x;
	elseif (a <= -2.8e-142)
		tmp = y;
	elseif (a <= 9e-248)
		tmp = x * (z / t);
	elseif (a <= 1.65e+53)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.4e+110], x, If[LessEqual[a, -4.7e+51], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.2e+27], x, If[LessEqual[a, -2.8e-142], y, If[LessEqual[a, 9e-248], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e+53], y, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.4000000000000001e110 or -4.7000000000000002e51 < a < -4.19999999999999989e27 or 1.6500000000000001e53 < a

   1. Initial program 65.9%

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

   3. Taylor expanded in a around inf 50.2%

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

   if -3.4000000000000001e110 < a < -4.7000000000000002e51

   1. Initial program 61.7%

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

   3. Taylor expanded in t around 0 47.9%

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

   4. Taylor expanded in z around -inf 47.4%

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

   5. Taylor expanded in y around inf 48.2%

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

      1. associate-/l* 48.4%

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

   7. Simplified 48.4%

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

   if -4.19999999999999989e27 < a < -2.80000000000000004e-142 or 8.9999999999999992e-248 < a < 1.6500000000000001e53

   1. Initial program 70.0%

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

   3. Taylor expanded in t around inf 38.0%

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

   if -2.80000000000000004e-142 < a < 8.9999999999999992e-248

   1. Initial program 73.8%

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

   3. Taylor expanded in x around -inf 55.9%

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

      1. associate-*r* 55.9%

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

      2. neg-mul-1 55.9%

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

      3. +-commutative 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in a around 0 41.4%

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

      1. associate-/l* 48.4%

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

   8. Simplified 48.4%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-142}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+53}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-142}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-248}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+55}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e+111)
   x
   (if (<= a -1.65e+52)
     (* y (/ z a))
     (if (<= a -9e+27)
       x
       (if (<= a -1.4e-142)
         y
         (if (<= a 1.75e-248) (/ x (/ t z)) (if (<= a 5.2e+55) y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+111) {
		tmp = x;
	} else if (a <= -1.65e+52) {
		tmp = y * (z / a);
	} else if (a <= -9e+27) {
		tmp = x;
	} else if (a <= -1.4e-142) {
		tmp = y;
	} else if (a <= 1.75e-248) {
		tmp = x / (t / z);
	} else if (a <= 5.2e+55) {
		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+111)) then
        tmp = x
    else if (a <= (-1.65d+52)) then
        tmp = y * (z / a)
    else if (a <= (-9d+27)) then
        tmp = x
    else if (a <= (-1.4d-142)) then
        tmp = y
    else if (a <= 1.75d-248) then
        tmp = x / (t / z)
    else if (a <= 5.2d+55) 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+111) {
		tmp = x;
	} else if (a <= -1.65e+52) {
		tmp = y * (z / a);
	} else if (a <= -9e+27) {
		tmp = x;
	} else if (a <= -1.4e-142) {
		tmp = y;
	} else if (a <= 1.75e-248) {
		tmp = x / (t / z);
	} else if (a <= 5.2e+55) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e+111:
		tmp = x
	elif a <= -1.65e+52:
		tmp = y * (z / a)
	elif a <= -9e+27:
		tmp = x
	elif a <= -1.4e-142:
		tmp = y
	elif a <= 1.75e-248:
		tmp = x / (t / z)
	elif a <= 5.2e+55:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e+111)
		tmp = x;
	elseif (a <= -1.65e+52)
		tmp = Float64(y * Float64(z / a));
	elseif (a <= -9e+27)
		tmp = x;
	elseif (a <= -1.4e-142)
		tmp = y;
	elseif (a <= 1.75e-248)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 5.2e+55)
		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+111)
		tmp = x;
	elseif (a <= -1.65e+52)
		tmp = y * (z / a);
	elseif (a <= -9e+27)
		tmp = x;
	elseif (a <= -1.4e-142)
		tmp = y;
	elseif (a <= 1.75e-248)
		tmp = x / (t / z);
	elseif (a <= 5.2e+55)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e+111], x, If[LessEqual[a, -1.65e+52], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9e+27], x, If[LessEqual[a, -1.4e-142], y, If[LessEqual[a, 1.75e-248], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e+55], y, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.20000000000000003e111 or -1.65e52 < a < -8.9999999999999998e27 or 5.2e55 < a

   1. Initial program 65.9%

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

   3. Taylor expanded in a around inf 50.2%

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

   if -1.20000000000000003e111 < a < -1.65e52

   1. Initial program 61.7%

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

   3. Taylor expanded in t around 0 47.9%

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

   4. Taylor expanded in z around -inf 47.4%

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

   5. Taylor expanded in y around inf 48.2%

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

      1. associate-/l* 48.4%

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

   7. Simplified 48.4%

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

   if -8.9999999999999998e27 < a < -1.40000000000000002e-142 or 1.74999999999999991e-248 < a < 5.2e55

   1. Initial program 70.0%

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

   3. Taylor expanded in t around inf 38.0%

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

   if -1.40000000000000002e-142 < a < 1.74999999999999991e-248

   1. Initial program 73.8%

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

   3. Taylor expanded in x around -inf 55.9%

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

      1. associate-*r* 55.9%

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

      2. neg-mul-1 55.9%

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

      3. +-commutative 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in a around 0 41.4%

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

      1. associate-/l* 48.4%

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

   8. Simplified 48.4%

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

      1. clear-num 48.5%

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

      2. un-div-inv 48.6%

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

   10. Applied egg-rr 48.6%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-142}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-248}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+55}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z - t}{t - a}\\ \mathbf{if}\;t \leq -7 \cdot 10^{+118}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-252}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- z t) (- t a))))))
   (if (<= t -7e+118)
     (+ y (* x (/ (- z a) t)))
     (if (<= t -1.25e-194)
       t_1
       (if (<= t 1.16e-252)
         (+ x (/ (* (- y x) z) a))
         (if (<= t 5.6e+98) t_1 (+ y (* (- z a) (/ x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((z - t) / (t - a)));
	double tmp;
	if (t <= -7e+118) {
		tmp = y + (x * ((z - a) / t));
	} else if (t <= -1.25e-194) {
		tmp = t_1;
	} else if (t <= 1.16e-252) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= 5.6e+98) {
		tmp = t_1;
	} else {
		tmp = y + ((z - a) * (x / 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 * ((z - t) / (t - a)))
    if (t <= (-7d+118)) then
        tmp = y + (x * ((z - a) / t))
    else if (t <= (-1.25d-194)) then
        tmp = t_1
    else if (t <= 1.16d-252) then
        tmp = x + (((y - x) * z) / a)
    else if (t <= 5.6d+98) then
        tmp = t_1
    else
        tmp = y + ((z - a) * (x / 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 * ((z - t) / (t - a)));
	double tmp;
	if (t <= -7e+118) {
		tmp = y + (x * ((z - a) / t));
	} else if (t <= -1.25e-194) {
		tmp = t_1;
	} else if (t <= 1.16e-252) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= 5.6e+98) {
		tmp = t_1;
	} else {
		tmp = y + ((z - a) * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((z - t) / (t - a)))
	tmp = 0
	if t <= -7e+118:
		tmp = y + (x * ((z - a) / t))
	elif t <= -1.25e-194:
		tmp = t_1
	elif t <= 1.16e-252:
		tmp = x + (((y - x) * z) / a)
	elif t <= 5.6e+98:
		tmp = t_1
	else:
		tmp = y + ((z - a) * (x / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(z - t) / Float64(t - a))))
	tmp = 0.0
	if (t <= -7e+118)
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	elseif (t <= -1.25e-194)
		tmp = t_1;
	elseif (t <= 1.16e-252)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / a));
	elseif (t <= 5.6e+98)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(z - a) * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((z - t) / (t - a)));
	tmp = 0.0;
	if (t <= -7e+118)
		tmp = y + (x * ((z - a) / t));
	elseif (t <= -1.25e-194)
		tmp = t_1;
	elseif (t <= 1.16e-252)
		tmp = x + (((y - x) * z) / a);
	elseif (t <= 5.6e+98)
		tmp = t_1;
	else
		tmp = y + ((z - a) * (x / t));
	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]}, If[LessEqual[t, -7e+118], N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.25e-194], t$95$1, If[LessEqual[t, 1.16e-252], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+98], t$95$1, N[(y + N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.00000000000000033e118

   1. Initial program 28.4%

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

   3. Taylor expanded in t around inf 54.1%

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

      1. associate--l+ 54.1%

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

      2. distribute-lft-out-- 54.1%

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

      3. div-sub 54.1%

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

      4. mul-1-neg 54.1%

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

      5. unsub-neg 54.1%

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

      6. div-sub 54.1%

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

      7. associate-/l* 63.2%

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

      8. associate-/l* 84.9%

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

      9. distribute-rgt-out-- 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in y around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. associate-/l* 82.7%

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

      3. distribute-rgt-neg-in 82.7%

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

      4. distribute-frac-neg2 82.7%

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

   8. Simplified 82.7%

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

   if -7.00000000000000033e118 < t < -1.2500000000000001e-194 or 1.1599999999999999e-252 < t < 5.6000000000000001e98

   1. Initial program 82.6%

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

   3. Taylor expanded in y around inf 72.0%

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

      1. associate-/l* 79.9%

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

   5. Simplified 79.9%

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

   if -1.2500000000000001e-194 < t < 1.1599999999999999e-252

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 96.0%

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

   if 5.6000000000000001e98 < t

   1. Initial program 32.4%

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

   3. Taylor expanded in t around inf 82.9%

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

      1. associate--l+ 82.9%

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

      2. distribute-lft-out-- 82.9%

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

      3. div-sub 82.9%

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

      4. mul-1-neg 82.9%

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

      5. unsub-neg 82.9%

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

      6. div-sub 82.9%

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

      7. associate-/l* 85.8%

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

      8. associate-/l* 91.3%

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

      9. distribute-rgt-out-- 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in y around 0 91.3%

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

      1. neg-mul-1 91.3%

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

      2. distribute-neg-frac2 91.3%

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

   8. Simplified 91.3%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+118}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-194}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-252}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+98}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 77.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z - t}{t - a}\\ \mathbf{if}\;t \leq -8 \cdot 10^{+116}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-116}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- z t) (- t a))))))
   (if (<= t -8e+116)
     (+ y (* x (/ (- z a) t)))
     (if (<= t -9.5e-140)
       t_1
       (if (<= t 8.5e-116)
         (+ x (/ (* (- y x) z) (- a t)))
         (if (<= t 5.8e+102) t_1 (+ y (* (- z a) (/ x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((z - t) / (t - a)));
	double tmp;
	if (t <= -8e+116) {
		tmp = y + (x * ((z - a) / t));
	} else if (t <= -9.5e-140) {
		tmp = t_1;
	} else if (t <= 8.5e-116) {
		tmp = x + (((y - x) * z) / (a - t));
	} else if (t <= 5.8e+102) {
		tmp = t_1;
	} else {
		tmp = y + ((z - a) * (x / 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 * ((z - t) / (t - a)))
    if (t <= (-8d+116)) then
        tmp = y + (x * ((z - a) / t))
    else if (t <= (-9.5d-140)) then
        tmp = t_1
    else if (t <= 8.5d-116) then
        tmp = x + (((y - x) * z) / (a - t))
    else if (t <= 5.8d+102) then
        tmp = t_1
    else
        tmp = y + ((z - a) * (x / 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 * ((z - t) / (t - a)));
	double tmp;
	if (t <= -8e+116) {
		tmp = y + (x * ((z - a) / t));
	} else if (t <= -9.5e-140) {
		tmp = t_1;
	} else if (t <= 8.5e-116) {
		tmp = x + (((y - x) * z) / (a - t));
	} else if (t <= 5.8e+102) {
		tmp = t_1;
	} else {
		tmp = y + ((z - a) * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((z - t) / (t - a)))
	tmp = 0
	if t <= -8e+116:
		tmp = y + (x * ((z - a) / t))
	elif t <= -9.5e-140:
		tmp = t_1
	elif t <= 8.5e-116:
		tmp = x + (((y - x) * z) / (a - t))
	elif t <= 5.8e+102:
		tmp = t_1
	else:
		tmp = y + ((z - a) * (x / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(z - t) / Float64(t - a))))
	tmp = 0.0
	if (t <= -8e+116)
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	elseif (t <= -9.5e-140)
		tmp = t_1;
	elseif (t <= 8.5e-116)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / Float64(a - t)));
	elseif (t <= 5.8e+102)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(z - a) * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((z - t) / (t - a)));
	tmp = 0.0;
	if (t <= -8e+116)
		tmp = y + (x * ((z - a) / t));
	elseif (t <= -9.5e-140)
		tmp = t_1;
	elseif (t <= 8.5e-116)
		tmp = x + (((y - x) * z) / (a - t));
	elseif (t <= 5.8e+102)
		tmp = t_1;
	else
		tmp = y + ((z - a) * (x / t));
	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]}, If[LessEqual[t, -8e+116], N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.5e-140], t$95$1, If[LessEqual[t, 8.5e-116], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+102], t$95$1, N[(y + N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.00000000000000012e116

   1. Initial program 28.4%

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

   3. Taylor expanded in t around inf 54.1%

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

      1. associate--l+ 54.1%

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

      2. distribute-lft-out-- 54.1%

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

      3. div-sub 54.1%

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

      4. mul-1-neg 54.1%

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

      5. unsub-neg 54.1%

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

      6. div-sub 54.1%

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

      7. associate-/l* 63.2%

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

      8. associate-/l* 84.9%

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

      9. distribute-rgt-out-- 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in y around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. associate-/l* 82.7%

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

      3. distribute-rgt-neg-in 82.7%

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

      4. distribute-frac-neg2 82.7%

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

   8. Simplified 82.7%

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

   if -8.00000000000000012e116 < t < -9.50000000000000019e-140 or 8.4999999999999995e-116 < t < 5.8000000000000005e102

   1. Initial program 78.8%

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

   3. Taylor expanded in y around inf 70.9%

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

      1. associate-/l* 78.8%

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

   5. Simplified 78.8%

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

   if -9.50000000000000019e-140 < t < 8.4999999999999995e-116

   1. Initial program 94.5%

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

   3. Taylor expanded in z around inf 92.4%

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

   if 5.8000000000000005e102 < t

   1. Initial program 32.4%

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

   3. Taylor expanded in t around inf 82.9%

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

      1. associate--l+ 82.9%

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

      2. distribute-lft-out-- 82.9%

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

      3. div-sub 82.9%

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

      4. mul-1-neg 82.9%

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

      5. unsub-neg 82.9%

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

      6. div-sub 82.9%

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

      7. associate-/l* 85.8%

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

      8. associate-/l* 91.3%

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

      9. distribute-rgt-out-- 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in y around 0 91.3%

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

      1. neg-mul-1 91.3%

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

      2. distribute-neg-frac2 91.3%

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

   8. Simplified 91.3%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+116}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-140}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-116}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+102}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 78.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z - t}{t - a}\\ t_2 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+117}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-115}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -1.7e+117)
     t_2
     (if (<= t -3.3e-139)
       t_1
       (if (<= t 1.35e-115)
         (+ x (/ (* (- y x) z) (- a t)))
         (if (<= t 3.2e+97) 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 <= -1.7e+117) {
		tmp = t_2;
	} else if (t <= -3.3e-139) {
		tmp = t_1;
	} else if (t <= 1.35e-115) {
		tmp = x + (((y - x) * z) / (a - t));
	} else if (t <= 3.2e+97) {
		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 <= (-1.7d+117)) then
        tmp = t_2
    else if (t <= (-3.3d-139)) then
        tmp = t_1
    else if (t <= 1.35d-115) then
        tmp = x + (((y - x) * z) / (a - t))
    else if (t <= 3.2d+97) 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 <= -1.7e+117) {
		tmp = t_2;
	} else if (t <= -3.3e-139) {
		tmp = t_1;
	} else if (t <= 1.35e-115) {
		tmp = x + (((y - x) * z) / (a - t));
	} else if (t <= 3.2e+97) {
		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 <= -1.7e+117:
		tmp = t_2
	elif t <= -3.3e-139:
		tmp = t_1
	elif t <= 1.35e-115:
		tmp = x + (((y - x) * z) / (a - t))
	elif t <= 3.2e+97:
		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 <= -1.7e+117)
		tmp = t_2;
	elseif (t <= -3.3e-139)
		tmp = t_1;
	elseif (t <= 1.35e-115)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / Float64(a - t)));
	elseif (t <= 3.2e+97)
		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 <= -1.7e+117)
		tmp = t_2;
	elseif (t <= -3.3e-139)
		tmp = t_1;
	elseif (t <= 1.35e-115)
		tmp = x + (((y - x) * z) / (a - t));
	elseif (t <= 3.2e+97)
		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, -1.7e+117], t$95$2, If[LessEqual[t, -3.3e-139], t$95$1, If[LessEqual[t, 1.35e-115], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+97], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7e117 or 3.20000000000000016e97 < t

   1. Initial program 30.2%

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

   3. Taylor expanded in t around inf 67.0%

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

      1. associate--l+ 67.0%

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

      2. distribute-lft-out-- 67.0%

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

      3. div-sub 67.0%

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

      4. mul-1-neg 67.0%

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

      5. unsub-neg 67.0%

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

      6. div-sub 67.0%

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

      7. associate-/l* 73.3%

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

      8. associate-/l* 87.7%

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

      9. distribute-rgt-out-- 87.7%

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

   5. Simplified 87.7%

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

   if -1.7e117 < t < -3.3e-139 or 1.35e-115 < t < 3.20000000000000016e97

   1. Initial program 78.8%

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

   3. Taylor expanded in y around inf 70.9%

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

      1. associate-/l* 78.8%

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

   5. Simplified 78.8%

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

   if -3.3e-139 < t < 1.35e-115

   1. Initial program 94.5%

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

   3. Taylor expanded in z around inf 92.4%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+117}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-139}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-115}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+97}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 68.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a}\\ \mathbf{if}\;a \leq -8 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-69}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-21}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) a)))))
   (if (<= a -8e-14)
     t_1
     (if (<= a -2e-69)
       (* (- z t) (/ y (- a t)))
       (if (<= a -8.5e-99)
         (+ x (/ (* (- y x) z) a))
         (if (<= a 2.55e-21) (+ y (/ (* z (- x y)) t)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -8e-14) {
		tmp = t_1;
	} else if (a <= -2e-69) {
		tmp = (z - t) * (y / (a - t));
	} else if (a <= -8.5e-99) {
		tmp = x + (((y - x) * z) / a);
	} else if (a <= 2.55e-21) {
		tmp = y + ((z * (x - y)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * ((y - x) / a))
    if (a <= (-8d-14)) then
        tmp = t_1
    else if (a <= (-2d-69)) then
        tmp = (z - t) * (y / (a - t))
    else if (a <= (-8.5d-99)) then
        tmp = x + (((y - x) * z) / a)
    else if (a <= 2.55d-21) then
        tmp = y + ((z * (x - y)) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -8e-14) {
		tmp = t_1;
	} else if (a <= -2e-69) {
		tmp = (z - t) * (y / (a - t));
	} else if (a <= -8.5e-99) {
		tmp = x + (((y - x) * z) / a);
	} else if (a <= 2.55e-21) {
		tmp = y + ((z * (x - y)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / a))
	tmp = 0
	if a <= -8e-14:
		tmp = t_1
	elif a <= -2e-69:
		tmp = (z - t) * (y / (a - t))
	elif a <= -8.5e-99:
		tmp = x + (((y - x) * z) / a)
	elif a <= 2.55e-21:
		tmp = y + ((z * (x - y)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (a <= -8e-14)
		tmp = t_1;
	elseif (a <= -2e-69)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (a <= -8.5e-99)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / a));
	elseif (a <= 2.55e-21)
		tmp = Float64(y + Float64(Float64(z * Float64(x - y)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / a));
	tmp = 0.0;
	if (a <= -8e-14)
		tmp = t_1;
	elseif (a <= -2e-69)
		tmp = (z - t) * (y / (a - t));
	elseif (a <= -8.5e-99)
		tmp = x + (((y - x) * z) / a);
	elseif (a <= 2.55e-21)
		tmp = y + ((z * (x - y)) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e-14], t$95$1, If[LessEqual[a, -2e-69], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.5e-99], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.55e-21], N[(y + N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.99999999999999999e-14 or 2.55000000000000002e-21 < a

   1. Initial program 66.5%

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

   3. Taylor expanded in t around 0 57.5%

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

      1. associate-/l* 67.5%

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

   5. Simplified 67.5%

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

   if -7.99999999999999999e-14 < a < -1.9999999999999999e-69

   1. Initial program 82.5%

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

      1. +-commutative 82.5%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 91.0%

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

      1. div-sub 91.0%

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

      2. associate-*r/ 73.4%

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

      3. *-commutative 73.4%

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

      4. associate-*r/ 91.0%

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

   9. Simplified 91.0%

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

   if -1.9999999999999999e-69 < a < -8.5000000000000004e-99

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 99.8%

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

   if -8.5000000000000004e-99 < a < 2.55000000000000002e-21

   1. Initial program 68.1%

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

   3. Taylor expanded in t around inf 81.7%

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

      1. associate--l+ 81.7%

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

      2. distribute-lft-out-- 81.7%

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

      3. div-sub 81.8%

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

      4. mul-1-neg 81.8%

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

      5. unsub-neg 81.8%

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

      6. div-sub 81.7%

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

      7. associate-/l* 83.4%

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

      8. associate-/l* 76.7%

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

      9. distribute-rgt-out-- 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in z around inf 75.9%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-14}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-69}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-21}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 34.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-125} \lor \neg \left(z \leq 1.5 \cdot 10^{+21}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))))
   (if (<= z -6.8e+149)
     t_1
     (if (<= z -2.35e+115)
       (* x (/ z t))
       (if (or (<= z -1.75e-125) (not (<= z 1.5e+21))) t_1 x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (z <= -6.8e+149) {
		tmp = t_1;
	} else if (z <= -2.35e+115) {
		tmp = x * (z / t);
	} else if ((z <= -1.75e-125) || !(z <= 1.5e+21)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / (a - t))
    if (z <= (-6.8d+149)) then
        tmp = t_1
    else if (z <= (-2.35d+115)) then
        tmp = x * (z / t)
    else if ((z <= (-1.75d-125)) .or. (.not. (z <= 1.5d+21))) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (z <= -6.8e+149) {
		tmp = t_1;
	} else if (z <= -2.35e+115) {
		tmp = x * (z / t);
	} else if ((z <= -1.75e-125) || !(z <= 1.5e+21)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	tmp = 0
	if z <= -6.8e+149:
		tmp = t_1
	elif z <= -2.35e+115:
		tmp = x * (z / t)
	elif (z <= -1.75e-125) or not (z <= 1.5e+21):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (z <= -6.8e+149)
		tmp = t_1;
	elseif (z <= -2.35e+115)
		tmp = Float64(x * Float64(z / t));
	elseif ((z <= -1.75e-125) || !(z <= 1.5e+21))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	tmp = 0.0;
	if (z <= -6.8e+149)
		tmp = t_1;
	elseif (z <= -2.35e+115)
		tmp = x * (z / t);
	elseif ((z <= -1.75e-125) || ~((z <= 1.5e+21)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+149], t$95$1, If[LessEqual[z, -2.35e+115], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.75e-125], N[Not[LessEqual[z, 1.5e+21]], $MachinePrecision]], t$95$1, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.7999999999999997e149 or -2.3499999999999998e115 < z < -1.74999999999999999e-125 or 1.5e21 < z

   1. Initial program 71.6%

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

      1. +-commutative 71.6%

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

      2. associate-/l* 91.5%

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

      3. fma-define 91.4%

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

   3. Simplified 91.4%

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

      1. clear-num 91.4%

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

      2. associate-/r/ 91.3%

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

   6. Applied egg-rr 91.3%

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

   7. Taylor expanded in y around inf 63.4%

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

      1. div-sub 63.4%

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

      2. associate-*r/ 47.1%

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

      3. *-commutative 47.1%

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

      4. associate-*r/ 58.2%

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

   9. Simplified 58.2%

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

   10. Taylor expanded in z around inf 38.7%

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

       1. associate-/l* 46.4%

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

   12. Simplified 46.4%

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

   if -6.7999999999999997e149 < z < -2.3499999999999998e115

   1. Initial program 52.2%

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

   3. Taylor expanded in x around -inf 75.4%

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

      1. associate-*r* 75.4%

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

      2. neg-mul-1 75.4%

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

      3. +-commutative 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in a around 0 52.7%

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

      1. associate-/l* 60.1%

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

   8. Simplified 60.1%

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

   if -1.74999999999999999e-125 < z < 1.5e21

   1. Initial program 67.2%

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

   3. Taylor expanded in a around inf 41.7%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+149}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-125} \lor \neg \left(z \leq 1.5 \cdot 10^{+21}\right):\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{if}\;a \leq -1.42 \cdot 10^{-98}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y t) (- t z))))
   (if (<= a -1.42e-98)
     (+ x (* y (/ z a)))
     (if (<= a -6.2e-196)
       t_1
       (if (<= a -9.2e-233)
         (* x (/ (- z a) t))
         (if (<= a 9e-83) t_1 (+ x (/ y (/ a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / t) * (t - z);
	double tmp;
	if (a <= -1.42e-98) {
		tmp = x + (y * (z / a));
	} else if (a <= -6.2e-196) {
		tmp = t_1;
	} else if (a <= -9.2e-233) {
		tmp = x * ((z - a) / t);
	} else if (a <= 9e-83) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (y / t) * (t - z)
    if (a <= (-1.42d-98)) then
        tmp = x + (y * (z / a))
    else if (a <= (-6.2d-196)) then
        tmp = t_1
    else if (a <= (-9.2d-233)) then
        tmp = x * ((z - a) / t)
    else if (a <= 9d-83) then
        tmp = t_1
    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 t_1 = (y / t) * (t - z);
	double tmp;
	if (a <= -1.42e-98) {
		tmp = x + (y * (z / a));
	} else if (a <= -6.2e-196) {
		tmp = t_1;
	} else if (a <= -9.2e-233) {
		tmp = x * ((z - a) / t);
	} else if (a <= 9e-83) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / t) * (t - z)
	tmp = 0
	if a <= -1.42e-98:
		tmp = x + (y * (z / a))
	elif a <= -6.2e-196:
		tmp = t_1
	elif a <= -9.2e-233:
		tmp = x * ((z - a) / t)
	elif a <= 9e-83:
		tmp = t_1
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / t) * Float64(t - z))
	tmp = 0.0
	if (a <= -1.42e-98)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (a <= -6.2e-196)
		tmp = t_1;
	elseif (a <= -9.2e-233)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (a <= 9e-83)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / t) * (t - z);
	tmp = 0.0;
	if (a <= -1.42e-98)
		tmp = x + (y * (z / a));
	elseif (a <= -6.2e-196)
		tmp = t_1;
	elseif (a <= -9.2e-233)
		tmp = x * ((z - a) / t);
	elseif (a <= 9e-83)
		tmp = t_1;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.42e-98], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.2e-196], t$95$1, If[LessEqual[a, -9.2e-233], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-83], t$95$1, N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.41999999999999999e-98

   1. Initial program 74.3%

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

   3. Taylor expanded in t around 0 61.7%

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

   4. Taylor expanded in y around inf 58.0%

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

      1. associate-/l* 31.7%

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

   6. Simplified 65.6%

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

   if -1.41999999999999999e-98 < a < -6.19999999999999986e-196 or -9.2000000000000007e-233 < a < 8.99999999999999995e-83

   1. Initial program 66.6%

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

      1. +-commutative 66.6%

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

      2. associate-/l* 75.1%

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

      3. fma-define 75.1%

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

   3. Simplified 75.1%

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

      1. clear-num 75.0%

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

      2. associate-/r/ 74.8%

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

   6. Applied egg-rr 74.8%

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

   7. Taylor expanded in y around inf 67.8%

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

      1. div-sub 67.8%

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

      2. associate-*r/ 59.5%

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

      3. *-commutative 59.5%

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

      4. associate-*r/ 56.3%

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

   9. Simplified 56.3%

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

   10. Taylor expanded in a around 0 55.9%

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

       1. associate-*r/ 55.9%

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

       2. neg-mul-1 55.9%

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

   12. Simplified 55.9%

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

   if -6.19999999999999986e-196 < a < -9.2000000000000007e-233

   1. Initial program 77.7%

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

   3. Taylor expanded in x around -inf 99.8%

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

      1. associate-*r* 99.8%

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

      2. neg-mul-1 99.8%

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

      3. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around -inf 55.4%

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

      1. associate-/l* 77.2%

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

   8. Simplified 77.2%

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

   if 8.99999999999999995e-83 < a

   1. Initial program 63.4%

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

   3. Taylor expanded in t around 0 53.6%

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

   4. Taylor expanded in y around inf 47.4%

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

      1. associate-/l* 24.1%

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

   6. Simplified 53.4%

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

      1. clear-num 53.4%

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

      2. un-div-inv 53.5%

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

   8. Applied egg-rr 53.5%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{-98}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-196}:\\ \;\;\;\;\frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-83}:\\ \;\;\;\;\frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 64.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-126}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+19}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) (- a t)))))
   (if (<= z -5.8e+65)
     t_1
     (if (<= z -5.5e-126)
       (* (- z t) (/ y (- a t)))
       (if (<= z 2.8e+19) (+ x (* t (/ y (- t a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -5.8e+65) {
		tmp = t_1;
	} else if (z <= -5.5e-126) {
		tmp = (z - t) * (y / (a - t));
	} else if (z <= 2.8e+19) {
		tmp = x + (t * (y / (t - a)));
	} 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 = z * ((y - x) / (a - t))
    if (z <= (-5.8d+65)) then
        tmp = t_1
    else if (z <= (-5.5d-126)) then
        tmp = (z - t) * (y / (a - t))
    else if (z <= 2.8d+19) then
        tmp = x + (t * (y / (t - a)))
    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 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -5.8e+65) {
		tmp = t_1;
	} else if (z <= -5.5e-126) {
		tmp = (z - t) * (y / (a - t));
	} else if (z <= 2.8e+19) {
		tmp = x + (t * (y / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / (a - t))
	tmp = 0
	if z <= -5.8e+65:
		tmp = t_1
	elif z <= -5.5e-126:
		tmp = (z - t) * (y / (a - t))
	elif z <= 2.8e+19:
		tmp = x + (t * (y / (t - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (z <= -5.8e+65)
		tmp = t_1;
	elseif (z <= -5.5e-126)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (z <= 2.8e+19)
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (z <= -5.8e+65)
		tmp = t_1;
	elseif (z <= -5.5e-126)
		tmp = (z - t) * (y / (a - t));
	elseif (z <= 2.8e+19)
		tmp = x + (t * (y / (t - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+65], t$95$1, If[LessEqual[z, -5.5e-126], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+19], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8000000000000001e65 or 2.8e19 < z

   1. Initial program 71.2%

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

      1. +-commutative 71.2%

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

      2. associate-/l* 93.3%

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

      3. fma-define 93.2%

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

   3. Simplified 93.2%

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

      1. clear-num 93.1%

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

      2. associate-/r/ 93.1%

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

   6. Applied egg-rr 93.1%

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

   7. Taylor expanded in z around inf 77.9%

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

      1. div-sub 79.7%

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

   9. Simplified 79.7%

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

   if -5.8000000000000001e65 < z < -5.49999999999999987e-126

   1. Initial program 66.9%

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

      1. +-commutative 66.9%

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

      2. associate-/l* 80.5%

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

      3. fma-define 80.5%

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

   3. Simplified 80.5%

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

      1. clear-num 80.5%

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

      2. associate-/r/ 80.4%

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

   6. Applied egg-rr 80.4%

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

   7. Taylor expanded in y around inf 61.8%

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

      1. div-sub 61.8%

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

      2. associate-*r/ 51.0%

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

      3. *-commutative 51.0%

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

      4. associate-*r/ 56.2%

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

   9. Simplified 56.2%

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

   if -5.49999999999999987e-126 < z < 2.8e19

   1. Initial program 66.9%

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

   3. Taylor expanded in y around inf 64.7%

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

      1. *-commutative 64.7%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in z around 0 59.3%

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

      1. mul-1-neg 59.3%

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

      2. unsub-neg 59.3%

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

      3. associate-/l* 62.0%

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

   8. Simplified 62.0%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+65}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-126}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+19}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+115} \lor \neg \left(t \leq 2.05 \cdot 10^{+61}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.2e+115) (not (<= t 2.05e+61)))
   (+ y (* (- z a) (/ (- x y) t)))
   (+ x (/ (* (- y x) (- z t)) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.2e+115) || !(t <= 2.05e+61)) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-6.2d+115)) .or. (.not. (t <= 2.05d+61))) then
        tmp = y + ((z - a) * ((x - y) / t))
    else
        tmp = x + (((y - x) * (z - t)) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.2e+115) || !(t <= 2.05e+61)) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.2e+115) or not (t <= 2.05e+61):
		tmp = y + ((z - a) * ((x - y) / t))
	else:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.2e+115) || !(t <= 2.05e+61))
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.2e+115) || ~((t <= 2.05e+61)))
		tmp = y + ((z - a) * ((x - y) / t));
	else
		tmp = x + (((y - x) * (z - t)) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.2e+115], N[Not[LessEqual[t, 2.05e+61]], $MachinePrecision]], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.2000000000000001e115 or 2.04999999999999986e61 < t

   1. Initial program 33.7%

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

   3. Taylor expanded in t around inf 66.7%

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

      1. associate--l+ 66.7%

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

      2. distribute-lft-out-- 66.7%

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

      3. div-sub 66.7%

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

      4. mul-1-neg 66.7%

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

      5. unsub-neg 66.7%

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

      6. div-sub 66.7%

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

      7. associate-/l* 73.4%

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

      8. associate-/l* 85.9%

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

      9. distribute-rgt-out-- 85.9%

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

   5. Simplified 85.9%

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

   if -6.2000000000000001e115 < t < 2.04999999999999986e61

   1. Initial program 86.9%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+115} \lor \neg \left(t \leq 2.05 \cdot 10^{+61}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 37.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-145}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.6e+19)
   (* z (/ (- y x) a))
   (if (<= z -4.8e-145) y (if (<= z 1.4e+22) x (* y (/ z (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e+19) {
		tmp = z * ((y - x) / a);
	} else if (z <= -4.8e-145) {
		tmp = y;
	} else if (z <= 1.4e+22) {
		tmp = x;
	} else {
		tmp = y * (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) :: tmp
    if (z <= (-3.6d+19)) then
        tmp = z * ((y - x) / a)
    else if (z <= (-4.8d-145)) then
        tmp = y
    else if (z <= 1.4d+22) then
        tmp = x
    else
        tmp = y * (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 tmp;
	if (z <= -3.6e+19) {
		tmp = z * ((y - x) / a);
	} else if (z <= -4.8e-145) {
		tmp = y;
	} else if (z <= 1.4e+22) {
		tmp = x;
	} else {
		tmp = y * (z / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.6e+19:
		tmp = z * ((y - x) / a)
	elif z <= -4.8e-145:
		tmp = y
	elif z <= 1.4e+22:
		tmp = x
	else:
		tmp = y * (z / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.6e+19)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (z <= -4.8e-145)
		tmp = y;
	elseif (z <= 1.4e+22)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.6e+19)
		tmp = z * ((y - x) / a);
	elseif (z <= -4.8e-145)
		tmp = y;
	elseif (z <= 1.4e+22)
		tmp = x;
	else
		tmp = y * (z / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.6e+19], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e-145], y, If[LessEqual[z, 1.4e+22], x, N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6e19

   1. Initial program 69.8%

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

   3. Taylor expanded in t around 0 50.7%

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

   4. Taylor expanded in z around inf 53.3%

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

      1. div-sub 53.3%

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

   6. Simplified 53.3%

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

   if -3.6e19 < z < -4.8000000000000003e-145

   1. Initial program 72.7%

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

   3. Taylor expanded in t around inf 36.9%

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

   if -4.8000000000000003e-145 < z < 1.4e22

   1. Initial program 67.2%

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

   3. Taylor expanded in a around inf 41.9%

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

   if 1.4e22 < z

   1. Initial program 68.5%

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

      1. +-commutative 68.5%

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

      2. associate-/l* 93.5%

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

      3. fma-define 93.4%

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

   3. Simplified 93.4%

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

      1. clear-num 93.2%

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

      2. associate-/r/ 93.2%

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

   6. Applied egg-rr 93.2%

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

   7. Taylor expanded in y around inf 61.7%

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

      1. div-sub 61.7%

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

      2. associate-*r/ 38.7%

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

      3. *-commutative 38.7%

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

      4. associate-*r/ 54.4%

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

   9. Simplified 54.4%

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

   10. Taylor expanded in z around inf 36.3%

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

       1. associate-/l* 48.6%

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

   12. Simplified 48.6%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-145}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+230}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -6 \cdot 10^{+115}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+60}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.6e+230)
   y
   (if (<= t -6e+115)
     (* (- z a) (/ x t))
     (if (<= t 4.8e+60) (+ x (* y (/ z a))) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.6e+230) {
		tmp = y;
	} else if (t <= -6e+115) {
		tmp = (z - a) * (x / t);
	} else if (t <= 4.8e+60) {
		tmp = x + (y * (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 <= (-4.6d+230)) then
        tmp = y
    else if (t <= (-6d+115)) then
        tmp = (z - a) * (x / t)
    else if (t <= 4.8d+60) then
        tmp = x + (y * (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 <= -4.6e+230) {
		tmp = y;
	} else if (t <= -6e+115) {
		tmp = (z - a) * (x / t);
	} else if (t <= 4.8e+60) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.6e+230:
		tmp = y
	elif t <= -6e+115:
		tmp = (z - a) * (x / t)
	elif t <= 4.8e+60:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.6e+230)
		tmp = y;
	elseif (t <= -6e+115)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif (t <= 4.8e+60)
		tmp = Float64(x + Float64(y * 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 <= -4.6e+230)
		tmp = y;
	elseif (t <= -6e+115)
		tmp = (z - a) * (x / t);
	elseif (t <= 4.8e+60)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.6e+230], y, If[LessEqual[t, -6e+115], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+60], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.5999999999999996e230 or 4.8e60 < t

   1. Initial program 31.8%

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

   3. Taylor expanded in t around inf 52.0%

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

   if -4.5999999999999996e230 < t < -6.0000000000000001e115

   1. Initial program 37.8%

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

   3. Taylor expanded in t around inf 42.7%

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

      1. associate--l+ 42.7%

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

      2. distribute-lft-out-- 42.7%

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

      3. div-sub 42.7%

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

      4. mul-1-neg 42.7%

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

      5. unsub-neg 42.7%

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

      6. div-sub 42.7%

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

      7. associate-/l* 57.0%

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

      8. associate-/l* 76.5%

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

      9. distribute-rgt-out-- 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in y around 0 29.1%

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

      1. *-commutative 29.1%

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

      2. associate-/l* 45.0%

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

   8. Simplified 45.0%

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

   if -6.0000000000000001e115 < t < 4.8e60

   1. Initial program 86.9%

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

   3. Taylor expanded in t around 0 61.3%

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

   4. Taylor expanded in y around inf 54.4%

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

      1. associate-/l* 32.0%

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

   6. Simplified 60.5%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+230}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -6 \cdot 10^{+115}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+60}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 55.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+23}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-218}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-81}:\\ \;\;\;\;\frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.8e+23)
   (+ x (* y (/ z a)))
   (if (<= a 1.2e-218)
     (* z (/ (- y x) (- a t)))
     (if (<= a 2.2e-81) (* (/ y t) (- t z)) (+ x (/ y (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.8e+23) {
		tmp = x + (y * (z / a));
	} else if (a <= 1.2e-218) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 2.2e-81) {
		tmp = (y / t) * (t - z);
	} 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 (a <= (-7.8d+23)) then
        tmp = x + (y * (z / a))
    else if (a <= 1.2d-218) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 2.2d-81) then
        tmp = (y / t) * (t - z)
    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 (a <= -7.8e+23) {
		tmp = x + (y * (z / a));
	} else if (a <= 1.2e-218) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 2.2e-81) {
		tmp = (y / t) * (t - z);
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.8e+23:
		tmp = x + (y * (z / a))
	elif a <= 1.2e-218:
		tmp = z * ((y - x) / (a - t))
	elif a <= 2.2e-81:
		tmp = (y / t) * (t - z)
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.8e+23)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (a <= 1.2e-218)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 2.2e-81)
		tmp = Float64(Float64(y / t) * Float64(t - z));
	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 (a <= -7.8e+23)
		tmp = x + (y * (z / a));
	elseif (a <= 1.2e-218)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 2.2e-81)
		tmp = (y / t) * (t - z);
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.8e+23], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-218], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-81], N[(N[(y / t), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.8000000000000001e23

   1. Initial program 68.0%

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

   3. Taylor expanded in t around 0 60.0%

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

   4. Taylor expanded in y around inf 61.6%

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

      1. associate-/l* 27.5%

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

   6. Simplified 69.1%

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

   if -7.8000000000000001e23 < a < 1.2e-218

   1. Initial program 74.5%

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

      1. +-commutative 74.5%

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

      2. associate-/l* 82.8%

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

      3. fma-define 82.8%

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

   3. Simplified 82.8%

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

      1. clear-num 82.7%

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

      2. associate-/r/ 82.6%

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

   6. Applied egg-rr 82.6%

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

   7. Taylor expanded in z around inf 62.0%

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

      1. div-sub 65.3%

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

   9. Simplified 65.3%

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

   if 1.2e-218 < a < 2.1999999999999999e-81

   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* 74.7%

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

      3. fma-define 74.7%

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

   3. Simplified 74.7%

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

      1. clear-num 74.6%

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

      2. associate-/r/ 74.4%

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

   6. Applied egg-rr 74.4%

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

   7. Taylor expanded in y around inf 66.8%

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

      1. div-sub 66.8%

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

      2. associate-*r/ 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-*r/ 58.5%

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

   9. Simplified 58.5%

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

   10. Taylor expanded in a around 0 57.3%

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

       1. associate-*r/ 57.3%

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

       2. neg-mul-1 57.3%

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

   12. Simplified 57.3%

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

   if 2.1999999999999999e-81 < a

   1. Initial program 63.4%

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

   3. Taylor expanded in t around 0 53.6%

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

   4. Taylor expanded in y around inf 47.4%

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

      1. associate-/l* 24.1%

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

   6. Simplified 53.4%

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

      1. clear-num 53.4%

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

      2. un-div-inv 53.5%

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

   8. Applied egg-rr 53.5%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+23}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-218}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-81}:\\ \;\;\;\;\frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 39.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.86 \cdot 10^{+56}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e+27) x (if (<= a 1.86e+56) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e+27) {
		tmp = x;
	} else if (a <= 1.86e+56) {
		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 <= (-3.2d+27)) then
        tmp = x
    else if (a <= 1.86d+56) 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 <= -3.2e+27) {
		tmp = x;
	} else if (a <= 1.86e+56) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e+27:
		tmp = x
	elif a <= 1.86e+56:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e+27)
		tmp = x;
	elseif (a <= 1.86e+56)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e+27)
		tmp = x;
	elseif (a <= 1.86e+56)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e+27], x, If[LessEqual[a, 1.86e+56], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.20000000000000015e27 or 1.86000000000000007e56 < a

   1. Initial program 65.3%

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

   3. Taylor expanded in a around inf 43.7%

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

   if -3.20000000000000015e27 < a < 1.86000000000000007e56

   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 t around inf 33.9%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.86 \cdot 10^{+56}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 26.0% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 68.8%

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

3. Taylor expanded in a around inf 24.4%

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

4. Final simplification 24.4%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 87.4% 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 2024115 
(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))))