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

Percentage Accurate: 68.2% → 86.8%

Time: 20.0s

Alternatives: 21

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.2% 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: 86.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.1 \cdot 10^{+142}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 1.1e+142)
   (+ x (/ (- y x) (/ (- a t) (- z t))))
   (+ y (* (- y x) (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.1e+142) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 1.1d+142) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + ((y - x) * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.1e+142) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.1e+142:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + ((y - x) * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.1e+142)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 1.1e+142)
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + ((y - x) * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.1e+142], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.09999999999999993e142

   1. Initial program 80.6%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   if 1.09999999999999993e142 < t

   1. Initial program 21.8%

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

      1. associate-/l* 53.3%

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

   3. Simplified 53.3%

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

      1. associate-/l* 21.8%

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

      2. clear-num 21.5%

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

      3. inv-pow 21.5%

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

   5. Applied egg-rr 21.5%

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

      1. unpow-1 21.5%

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

      2. associate-/r* 48.4%

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

   7. Simplified 48.4%

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

      1. div-inv 48.0%

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

   9. Applied egg-rr 48.0%

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

   10. Taylor expanded in t around -inf 65.1%

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

       1. *-commutative 65.1%

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

       2. mul-1-neg 65.1%

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

       3. distribute-rgt-out-- 65.1%

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

       4. *-commutative 65.1%

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

       5. associate-*r/ 82.2%

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

       6. div-sub 82.2%

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

       7. *-commutative 82.2%

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

       8. div-sub 82.2%

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

       9. associate-/r/ 84.9%

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

       10. unsub-neg 84.9%

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

       11. associate-/r/ 82.2%

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

       12. div-sub 82.2%

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

       13. *-commutative 82.2%

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

       14. div-sub 82.2%

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

   12. Simplified 85.0%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.1 \cdot 10^{+142}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]

Alternative 2: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ t_2 := y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{if}\;t \leq -7.4 \cdot 10^{+152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-173}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a}\right)\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+141}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- x y) (- t z)) (- a t))))
        (t_2 (+ y (* (- y x) (/ (- a z) t)))))
   (if (<= t -7.4e+152)
     t_2
     (if (<= t -3e-278)
       t_1
       (if (<= t 2e-173)
         (+ x (* (- y x) (* (- z t) (/ 1.0 a))))
         (if (<= t 1.42e+63)
           t_1
           (if (<= t 3.2e+141) (+ x (/ (- z t) (/ (- a t) y))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((x - y) * (t - z)) / (a - t));
	double t_2 = y + ((y - x) * ((a - z) / t));
	double tmp;
	if (t <= -7.4e+152) {
		tmp = t_2;
	} else if (t <= -3e-278) {
		tmp = t_1;
	} else if (t <= 2e-173) {
		tmp = x + ((y - x) * ((z - t) * (1.0 / a)));
	} else if (t <= 1.42e+63) {
		tmp = t_1;
	} else if (t <= 3.2e+141) {
		tmp = x + ((z - t) / ((a - t) / y));
	} 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 + (((x - y) * (t - z)) / (a - t))
    t_2 = y + ((y - x) * ((a - z) / t))
    if (t <= (-7.4d+152)) then
        tmp = t_2
    else if (t <= (-3d-278)) then
        tmp = t_1
    else if (t <= 2d-173) then
        tmp = x + ((y - x) * ((z - t) * (1.0d0 / a)))
    else if (t <= 1.42d+63) then
        tmp = t_1
    else if (t <= 3.2d+141) then
        tmp = x + ((z - t) / ((a - t) / y))
    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 + (((x - y) * (t - z)) / (a - t));
	double t_2 = y + ((y - x) * ((a - z) / t));
	double tmp;
	if (t <= -7.4e+152) {
		tmp = t_2;
	} else if (t <= -3e-278) {
		tmp = t_1;
	} else if (t <= 2e-173) {
		tmp = x + ((y - x) * ((z - t) * (1.0 / a)));
	} else if (t <= 1.42e+63) {
		tmp = t_1;
	} else if (t <= 3.2e+141) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((x - y) * (t - z)) / (a - t))
	t_2 = y + ((y - x) * ((a - z) / t))
	tmp = 0
	if t <= -7.4e+152:
		tmp = t_2
	elif t <= -3e-278:
		tmp = t_1
	elif t <= 2e-173:
		tmp = x + ((y - x) * ((z - t) * (1.0 / a)))
	elif t <= 1.42e+63:
		tmp = t_1
	elif t <= 3.2e+141:
		tmp = x + ((z - t) / ((a - t) / y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(x - y) * Float64(t - z)) / Float64(a - t)))
	t_2 = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (t <= -7.4e+152)
		tmp = t_2;
	elseif (t <= -3e-278)
		tmp = t_1;
	elseif (t <= 2e-173)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) * Float64(1.0 / a))));
	elseif (t <= 1.42e+63)
		tmp = t_1;
	elseif (t <= 3.2e+141)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((x - y) * (t - z)) / (a - t));
	t_2 = y + ((y - x) * ((a - z) / t));
	tmp = 0.0;
	if (t <= -7.4e+152)
		tmp = t_2;
	elseif (t <= -3e-278)
		tmp = t_1;
	elseif (t <= 2e-173)
		tmp = x + ((y - x) * ((z - t) * (1.0 / a)));
	elseif (t <= 1.42e+63)
		tmp = t_1;
	elseif (t <= 3.2e+141)
		tmp = x + ((z - t) / ((a - t) / y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(x - y), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.4e+152], t$95$2, If[LessEqual[t, -3e-278], t$95$1, If[LessEqual[t, 2e-173], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.42e+63], t$95$1, If[LessEqual[t, 3.2e+141], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.39999999999999992e152 or 3.20000000000000019e141 < t

   1. Initial program 29.7%

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

      1. associate-/l* 63.7%

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

   3. Simplified 63.7%

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

      1. associate-/l* 29.7%

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

      2. clear-num 29.5%

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

      3. inv-pow 29.5%

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

   5. Applied egg-rr 29.5%

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

      1. unpow-1 29.5%

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

      2. associate-/r* 57.2%

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

   7. Simplified 57.2%

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

      1. div-inv 56.9%

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

   9. Applied egg-rr 56.9%

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

   10. Taylor expanded in t around -inf 61.6%

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

       1. *-commutative 61.6%

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

       2. mul-1-neg 61.6%

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

       3. distribute-rgt-out-- 63.3%

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

       4. *-commutative 63.3%

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

       5. associate-*r/ 79.8%

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

       6. div-sub 79.7%

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

       7. *-commutative 79.7%

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

       8. div-sub 79.8%

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

       9. associate-/r/ 82.9%

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

       10. unsub-neg 82.9%

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

       11. associate-/r/ 79.8%

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

       12. div-sub 79.7%

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

       13. *-commutative 79.7%

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

       14. div-sub 79.8%

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

   12. Simplified 82.9%

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

   if -7.39999999999999992e152 < t < -3e-278 or 2.0000000000000001e-173 < t < 1.4200000000000001e63

   1. Initial program 90.0%

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

   if -3e-278 < t < 2.0000000000000001e-173

   1. Initial program 81.7%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

      1. associate-/r/ 97.7%

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

      2. div-inv 97.6%

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

      3. associate-*l* 97.6%

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

   5. Applied egg-rr 97.6%

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

   6. Taylor expanded in a around inf 93.4%

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

   if 1.4200000000000001e63 < t < 3.20000000000000019e141

   1. Initial program 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in y around inf 86.1%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+152}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-278}:\\ \;\;\;\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-173}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a}\right)\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+141}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]

Alternative 3: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a}\right)\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{y - x}{\frac{t - a}{t}}\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+60}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (* (- z t) (/ 1.0 a))))))
   (if (<= a -2.8e+36)
     t_1
     (if (<= a -6.5e-10)
       (+ x (/ (- y x) (/ (- t a) t)))
       (if (<= a -6.6e-54)
         (* y (/ (- z t) (- a t)))
         (if (<= a 1.6e+60) (+ y (* (- y x) (/ (- a z) t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * ((z - t) * (1.0 / a)));
	double tmp;
	if (a <= -2.8e+36) {
		tmp = t_1;
	} else if (a <= -6.5e-10) {
		tmp = x + ((y - x) / ((t - a) / t));
	} else if (a <= -6.6e-54) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 1.6e+60) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) * ((z - t) * (1.0d0 / a)))
    if (a <= (-2.8d+36)) then
        tmp = t_1
    else if (a <= (-6.5d-10)) then
        tmp = x + ((y - x) / ((t - a) / t))
    else if (a <= (-6.6d-54)) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 1.6d+60) then
        tmp = y + ((y - x) * ((a - z) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * ((z - t) * (1.0 / a)));
	double tmp;
	if (a <= -2.8e+36) {
		tmp = t_1;
	} else if (a <= -6.5e-10) {
		tmp = x + ((y - x) / ((t - a) / t));
	} else if (a <= -6.6e-54) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 1.6e+60) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) * ((z - t) * (1.0 / a)))
	tmp = 0
	if a <= -2.8e+36:
		tmp = t_1
	elif a <= -6.5e-10:
		tmp = x + ((y - x) / ((t - a) / t))
	elif a <= -6.6e-54:
		tmp = y * ((z - t) / (a - t))
	elif a <= 1.6e+60:
		tmp = y + ((y - x) * ((a - z) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) * Float64(1.0 / a))))
	tmp = 0.0
	if (a <= -2.8e+36)
		tmp = t_1;
	elseif (a <= -6.5e-10)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(t - a) / t)));
	elseif (a <= -6.6e-54)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 1.6e+60)
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) * ((z - t) * (1.0 / a)));
	tmp = 0.0;
	if (a <= -2.8e+36)
		tmp = t_1;
	elseif (a <= -6.5e-10)
		tmp = x + ((y - x) / ((t - a) / t));
	elseif (a <= -6.6e-54)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 1.6e+60)
		tmp = y + ((y - x) * ((a - z) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e+36], t$95$1, If[LessEqual[a, -6.5e-10], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(t - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.6e-54], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+60], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.8000000000000001e36 or 1.59999999999999995e60 < a

   1. Initial program 70.8%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

      1. associate-/r/ 91.6%

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

      2. div-inv 91.5%

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

      3. associate-*l* 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in a around inf 85.7%

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

   if -2.8000000000000001e36 < a < -6.5000000000000003e-10

   1. Initial program 75.8%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 87.8%

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

      1. associate-*r/ 87.8%

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

      2. neg-mul-1 87.8%

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

   6. Simplified 87.8%

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

   if -6.5000000000000003e-10 < a < -6.59999999999999986e-54

   1. Initial program 93.3%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in x around 0 80.1%

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

      1. associate-*r/ 80.1%

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

   6. Simplified 80.1%

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

   if -6.59999999999999986e-54 < a < 1.59999999999999995e60

   1. Initial program 72.6%

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

      1. associate-/l* 79.6%

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

   3. Simplified 79.6%

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

      1. associate-/l* 72.6%

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

      2. clear-num 72.5%

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

      3. inv-pow 72.5%

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

   5. Applied egg-rr 72.5%

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

      1. unpow-1 72.5%

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

      2. associate-/r* 79.2%

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

   7. Simplified 79.2%

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

      1. div-inv 79.2%

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

   9. Applied egg-rr 79.2%

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

   10. Taylor expanded in t around -inf 73.1%

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

       1. *-commutative 73.1%

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

       2. mul-1-neg 73.1%

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

       3. distribute-rgt-out-- 73.1%

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

       4. *-commutative 73.1%

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

       5. associate-*r/ 79.5%

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

       6. div-sub 75.8%

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

       7. *-commutative 75.8%

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

       8. div-sub 79.5%

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

       9. associate-/r/ 79.4%

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

       10. unsub-neg 79.4%

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

       11. associate-/r/ 79.5%

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

       12. div-sub 75.8%

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

       13. *-commutative 75.8%

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

       14. div-sub 79.5%

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

   12. Simplified 79.4%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+36}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a}\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{y - x}{\frac{t - a}{t}}\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+60}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a}\right)\\ \end{array} \]

Alternative 4: 69.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2900:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-100}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+54} \lor \neg \left(t \leq 1.95 \cdot 10^{+112}\right):\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2900.0)
   (+ y (/ (- x y) (/ t z)))
   (if (<= t -2.9e-100)
     (* x (+ (/ (- t z) (- a t)) 1.0))
     (if (<= t 3.4e+29)
       (+ x (/ (- y x) (/ a z)))
       (if (or (<= t 8e+54) (not (<= t 1.95e+112)))
         (+ y (/ (- z a) (/ t x)))
         (+ x (/ (- z t) (/ a y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2900.0) {
		tmp = y + ((x - y) / (t / z));
	} else if (t <= -2.9e-100) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else if (t <= 3.4e+29) {
		tmp = x + ((y - x) / (a / z));
	} else if ((t <= 8e+54) || !(t <= 1.95e+112)) {
		tmp = y + ((z - a) / (t / x));
	} else {
		tmp = x + ((z - t) / (a / 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 <= (-2900.0d0)) then
        tmp = y + ((x - y) / (t / z))
    else if (t <= (-2.9d-100)) then
        tmp = x * (((t - z) / (a - t)) + 1.0d0)
    else if (t <= 3.4d+29) then
        tmp = x + ((y - x) / (a / z))
    else if ((t <= 8d+54) .or. (.not. (t <= 1.95d+112))) then
        tmp = y + ((z - a) / (t / x))
    else
        tmp = x + ((z - t) / (a / 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 <= -2900.0) {
		tmp = y + ((x - y) / (t / z));
	} else if (t <= -2.9e-100) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else if (t <= 3.4e+29) {
		tmp = x + ((y - x) / (a / z));
	} else if ((t <= 8e+54) || !(t <= 1.95e+112)) {
		tmp = y + ((z - a) / (t / x));
	} else {
		tmp = x + ((z - t) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2900.0:
		tmp = y + ((x - y) / (t / z))
	elif t <= -2.9e-100:
		tmp = x * (((t - z) / (a - t)) + 1.0)
	elif t <= 3.4e+29:
		tmp = x + ((y - x) / (a / z))
	elif (t <= 8e+54) or not (t <= 1.95e+112):
		tmp = y + ((z - a) / (t / x))
	else:
		tmp = x + ((z - t) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2900.0)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	elseif (t <= -2.9e-100)
		tmp = Float64(x * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0));
	elseif (t <= 3.4e+29)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif ((t <= 8e+54) || !(t <= 1.95e+112))
		tmp = Float64(y + Float64(Float64(z - a) / Float64(t / x)));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2900.0)
		tmp = y + ((x - y) / (t / z));
	elseif (t <= -2.9e-100)
		tmp = x * (((t - z) / (a - t)) + 1.0);
	elseif (t <= 3.4e+29)
		tmp = x + ((y - x) / (a / z));
	elseif ((t <= 8e+54) || ~((t <= 1.95e+112)))
		tmp = y + ((z - a) / (t / x));
	else
		tmp = x + ((z - t) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2900.0], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.9e-100], N[(x * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+29], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 8e+54], N[Not[LessEqual[t, 1.95e+112]], $MachinePrecision]], N[(y + N[(N[(z - a), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2900

   1. Initial program 59.0%

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

      1. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in t around -inf 57.4%

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

      1. mul-1-neg 57.4%

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

      2. unsub-neg 57.4%

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

      3. div-sub 57.4%

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

      4. *-commutative 57.4%

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

      5. div-sub 57.4%

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

      6. distribute-rgt-out-- 59.4%

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

   6. Simplified 59.4%

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

   7. Taylor expanded in z around inf 58.4%

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

      1. *-commutative 58.4%

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

      2. associate-/l* 66.0%

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

   9. Simplified 66.0%

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

   if -2900 < t < -2.89999999999999975e-100

   1. Initial program 91.0%

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

      1. associate-/l* 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in x around inf 81.5%

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

      1. mul-1-neg 81.5%

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

      2. unsub-neg 81.5%

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

   6. Simplified 81.5%

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

   if -2.89999999999999975e-100 < t < 3.39999999999999981e29

   1. Initial program 91.2%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in t around 0 87.5%

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

   if 3.39999999999999981e29 < t < 8.0000000000000006e54 or 1.94999999999999984e112 < t

   1. Initial program 33.1%

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

      1. associate-/l* 60.9%

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

   3. Simplified 60.9%

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

   4. Taylor expanded in t around -inf 67.3%

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

      1. mul-1-neg 67.3%

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

      2. unsub-neg 67.3%

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

      3. div-sub 67.3%

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

      4. *-commutative 67.3%

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

      5. div-sub 67.3%

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

      6. distribute-rgt-out-- 67.3%

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

   6. Simplified 67.3%

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

   7. Taylor expanded in y around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. associate-/l* 76.3%

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

      3. distribute-neg-frac 76.3%

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

   9. Simplified 76.3%

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

   if 8.0000000000000006e54 < t < 1.94999999999999984e112

   1. Initial program 68.3%

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

      1. *-commutative 68.3%

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

      2. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around inf 82.6%

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

   5. Taylor expanded in a around inf 75.9%

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

      1. *-commutative 75.9%

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

      2. associate-/l* 82.1%

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

   7. Simplified 82.1%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2900:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-100}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+54} \lor \neg \left(t \leq 1.95 \cdot 10^{+112}\right):\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 69.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -35:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+52} \lor \neg \left(t \leq 1.75 \cdot 10^{+112}\right):\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -35.0)
   (+ y (/ (- x y) (/ t z)))
   (if (<= t 3.2e+30)
     (+ x (/ (- y x) (/ a z)))
     (if (or (<= t 1.08e+52) (not (<= t 1.75e+112)))
       (+ y (/ (- z a) (/ t x)))
       (+ x (/ (- z t) (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -35.0) {
		tmp = y + ((x - y) / (t / z));
	} else if (t <= 3.2e+30) {
		tmp = x + ((y - x) / (a / z));
	} else if ((t <= 1.08e+52) || !(t <= 1.75e+112)) {
		tmp = y + ((z - a) / (t / x));
	} else {
		tmp = x + ((z - t) / (a / 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 <= (-35.0d0)) then
        tmp = y + ((x - y) / (t / z))
    else if (t <= 3.2d+30) then
        tmp = x + ((y - x) / (a / z))
    else if ((t <= 1.08d+52) .or. (.not. (t <= 1.75d+112))) then
        tmp = y + ((z - a) / (t / x))
    else
        tmp = x + ((z - t) / (a / 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 <= -35.0) {
		tmp = y + ((x - y) / (t / z));
	} else if (t <= 3.2e+30) {
		tmp = x + ((y - x) / (a / z));
	} else if ((t <= 1.08e+52) || !(t <= 1.75e+112)) {
		tmp = y + ((z - a) / (t / x));
	} else {
		tmp = x + ((z - t) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -35.0:
		tmp = y + ((x - y) / (t / z))
	elif t <= 3.2e+30:
		tmp = x + ((y - x) / (a / z))
	elif (t <= 1.08e+52) or not (t <= 1.75e+112):
		tmp = y + ((z - a) / (t / x))
	else:
		tmp = x + ((z - t) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -35.0)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	elseif (t <= 3.2e+30)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif ((t <= 1.08e+52) || !(t <= 1.75e+112))
		tmp = Float64(y + Float64(Float64(z - a) / Float64(t / x)));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -35.0)
		tmp = y + ((x - y) / (t / z));
	elseif (t <= 3.2e+30)
		tmp = x + ((y - x) / (a / z));
	elseif ((t <= 1.08e+52) || ~((t <= 1.75e+112)))
		tmp = y + ((z - a) / (t / x));
	else
		tmp = x + ((z - t) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -35.0], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+30], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.08e+52], N[Not[LessEqual[t, 1.75e+112]], $MachinePrecision]], N[(y + N[(N[(z - a), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -35

   1. Initial program 59.8%

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

      1. associate-/l* 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in t around -inf 58.3%

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

      1. mul-1-neg 58.3%

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

      2. unsub-neg 58.3%

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

      3. div-sub 58.3%

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

      4. *-commutative 58.3%

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

      5. div-sub 58.3%

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

      6. distribute-rgt-out-- 60.3%

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

   6. Simplified 60.3%

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

   7. Taylor expanded in z around inf 59.2%

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

      1. *-commutative 59.2%

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

      2. associate-/l* 66.6%

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

   9. Simplified 66.6%

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

   if -35 < t < 3.19999999999999973e30

   1. Initial program 91.1%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in t around 0 82.4%

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

   if 3.19999999999999973e30 < t < 1.07999999999999997e52 or 1.74999999999999998e112 < t

   1. Initial program 33.1%

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

      1. associate-/l* 60.9%

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

   3. Simplified 60.9%

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

   4. Taylor expanded in t around -inf 67.3%

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

      1. mul-1-neg 67.3%

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

      2. unsub-neg 67.3%

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

      3. div-sub 67.3%

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

      4. *-commutative 67.3%

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

      5. div-sub 67.3%

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

      6. distribute-rgt-out-- 67.3%

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

   6. Simplified 67.3%

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

   7. Taylor expanded in y around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. associate-/l* 76.3%

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

      3. distribute-neg-frac 76.3%

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

   9. Simplified 76.3%

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

   if 1.07999999999999997e52 < t < 1.74999999999999998e112

   1. Initial program 68.3%

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

      1. *-commutative 68.3%

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

      2. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around inf 82.6%

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

   5. Taylor expanded in a around inf 75.9%

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

      1. *-commutative 75.9%

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

      2. associate-/l* 82.1%

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

   7. Simplified 82.1%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -35:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+52} \lor \neg \left(t \leq 1.75 \cdot 10^{+112}\right):\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 6: 56.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -115000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-148}:\\ \;\;\;\;\frac{z}{\frac{-t}{y - x}}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -115000.0)
     t_2
     (if (<= t -3.6e-25)
       t_1
       (if (<= t -1.3e-148)
         (/ z (/ (- t) (- y x)))
         (if (<= t 2.9e+85) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -115000.0) {
		tmp = t_2;
	} else if (t <= -3.6e-25) {
		tmp = t_1;
	} else if (t <= -1.3e-148) {
		tmp = z / (-t / (y - x));
	} else if (t <= 2.9e+85) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-115000.0d0)) then
        tmp = t_2
    else if (t <= (-3.6d-25)) then
        tmp = t_1
    else if (t <= (-1.3d-148)) then
        tmp = z / (-t / (y - x))
    else if (t <= 2.9d+85) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -115000.0) {
		tmp = t_2;
	} else if (t <= -3.6e-25) {
		tmp = t_1;
	} else if (t <= -1.3e-148) {
		tmp = z / (-t / (y - x));
	} else if (t <= 2.9e+85) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -115000.0:
		tmp = t_2
	elif t <= -3.6e-25:
		tmp = t_1
	elif t <= -1.3e-148:
		tmp = z / (-t / (y - x))
	elif t <= 2.9e+85:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -115000.0)
		tmp = t_2;
	elseif (t <= -3.6e-25)
		tmp = t_1;
	elseif (t <= -1.3e-148)
		tmp = Float64(z / Float64(Float64(-t) / Float64(y - x)));
	elseif (t <= 2.9e+85)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -115000.0)
		tmp = t_2;
	elseif (t <= -3.6e-25)
		tmp = t_1;
	elseif (t <= -1.3e-148)
		tmp = z / (-t / (y - x));
	elseif (t <= 2.9e+85)
		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[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -115000.0], t$95$2, If[LessEqual[t, -3.6e-25], t$95$1, If[LessEqual[t, -1.3e-148], N[(z / N[((-t) / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+85], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -115000 or 2.89999999999999997e85 < t

   1. Initial program 48.6%

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

      1. associate-/l* 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in x around 0 44.5%

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

      1. associate-*r/ 65.2%

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

   6. Simplified 65.2%

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

   if -115000 < t < -3.5999999999999999e-25 or -1.30000000000000004e-148 < t < 2.89999999999999997e85

   1. Initial program 85.7%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in t around 0 83.0%

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

   5. Taylor expanded in y around inf 64.6%

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

      1. associate-/l* 69.3%

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

      2. associate-/r/ 68.2%

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

   7. Simplified 68.2%

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

   if -3.5999999999999999e-25 < t < -1.30000000000000004e-148

   1. Initial program 95.6%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

      1. associate-/r/ 99.9%

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

      2. div-inv 99.7%

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

      3. associate-*l* 95.2%

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

   5. Applied egg-rr 95.2%

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

   6. Taylor expanded in z around -inf 75.8%

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

      1. associate-/l* 80.1%

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

   8. Simplified 80.1%

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

   9. Taylor expanded in a around 0 61.0%

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

       1. neg-mul-1 61.0%

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

       2. distribute-neg-frac 61.0%

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

   11. Simplified 61.0%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -115000:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-25}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-148}:\\ \;\;\;\;\frac{z}{\frac{-t}{y - x}}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+85}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 7: 52.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ t_2 := \frac{-y}{\frac{a - t}{t}}\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))) (t_2 (/ (- y) (/ (- a t) t))))
   (if (<= t -3.1e+57)
     t_2
     (if (<= t -2.7e-25)
       t_1
       (if (<= t -1.9e-132)
         (* x (/ (- z) (- a t)))
         (if (<= t 1.6e+112) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = -y / ((a - t) / t);
	double tmp;
	if (t <= -3.1e+57) {
		tmp = t_2;
	} else if (t <= -2.7e-25) {
		tmp = t_1;
	} else if (t <= -1.9e-132) {
		tmp = x * (-z / (a - t));
	} else if (t <= 1.6e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    t_2 = -y / ((a - t) / t)
    if (t <= (-3.1d+57)) then
        tmp = t_2
    else if (t <= (-2.7d-25)) then
        tmp = t_1
    else if (t <= (-1.9d-132)) then
        tmp = x * (-z / (a - t))
    else if (t <= 1.6d+112) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = -y / ((a - t) / t);
	double tmp;
	if (t <= -3.1e+57) {
		tmp = t_2;
	} else if (t <= -2.7e-25) {
		tmp = t_1;
	} else if (t <= -1.9e-132) {
		tmp = x * (-z / (a - t));
	} else if (t <= 1.6e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	t_2 = -y / ((a - t) / t)
	tmp = 0
	if t <= -3.1e+57:
		tmp = t_2
	elif t <= -2.7e-25:
		tmp = t_1
	elif t <= -1.9e-132:
		tmp = x * (-z / (a - t))
	elif t <= 1.6e+112:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	t_2 = Float64(Float64(-y) / Float64(Float64(a - t) / t))
	tmp = 0.0
	if (t <= -3.1e+57)
		tmp = t_2;
	elseif (t <= -2.7e-25)
		tmp = t_1;
	elseif (t <= -1.9e-132)
		tmp = Float64(x * Float64(Float64(-z) / Float64(a - t)));
	elseif (t <= 1.6e+112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	t_2 = -y / ((a - t) / t);
	tmp = 0.0;
	if (t <= -3.1e+57)
		tmp = t_2;
	elseif (t <= -2.7e-25)
		tmp = t_1;
	elseif (t <= -1.9e-132)
		tmp = x * (-z / (a - t));
	elseif (t <= 1.6e+112)
		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[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-y) / N[(N[(a - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e+57], t$95$2, If[LessEqual[t, -2.7e-25], t$95$1, If[LessEqual[t, -1.9e-132], N[(x * N[((-z) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+112], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.10000000000000013e57 or 1.59999999999999993e112 < t

   1. Initial program 43.7%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in x around 0 45.0%

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

      1. associate-*r/ 67.7%

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

   6. Simplified 67.7%

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

   7. Taylor expanded in z around 0 41.8%

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

      1. mul-1-neg 41.8%

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

      2. associate-/l* 61.2%

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

      3. distribute-neg-frac 61.2%

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

   9. Simplified 61.2%

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

   if -3.10000000000000013e57 < t < -2.70000000000000016e-25 or -1.8999999999999998e-132 < t < 1.59999999999999993e112

   1. Initial program 85.7%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in t around 0 78.9%

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

   5. Taylor expanded in y around inf 62.3%

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

      1. associate-/l* 66.6%

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

      2. associate-/r/ 65.6%

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

   7. Simplified 65.6%

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

   if -2.70000000000000016e-25 < t < -1.8999999999999998e-132

   1. Initial program 94.5%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

      1. associate-/r/ 99.9%

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

      2. div-inv 99.6%

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

      3. associate-*l* 94.1%

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

   5. Applied egg-rr 94.1%

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

   6. Taylor expanded in z around -inf 75.5%

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

      1. associate-/l* 80.9%

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

   8. Simplified 80.9%

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

   9. Taylor expanded in y around 0 58.6%

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

       1. mul-1-neg 58.6%

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

       2. distribute-neg-frac 58.6%

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

       3. *-commutative 58.6%

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

       4. distribute-lft-neg-out 58.6%

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

       5. associate-*r/ 63.8%

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

       6. distribute-lft-neg-out 63.8%

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

       7. distribute-rgt-neg-in 63.8%

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

   11. Simplified 63.8%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+57}:\\ \;\;\;\;\frac{-y}{\frac{a - t}{t}}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-25}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+112}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{a - t}{t}}\\ \end{array} \]

Alternative 8: 47.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+95}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{-189}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -1.05e+95)
     y
     (if (<= t 6.5e-296)
       t_1
       (if (<= t 1.62e-189) (/ y (/ a z)) (if (<= t 1.18e+114) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.05e+95) {
		tmp = y;
	} else if (t <= 6.5e-296) {
		tmp = t_1;
	} else if (t <= 1.62e-189) {
		tmp = y / (a / z);
	} else if (t <= 1.18e+114) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-1.05d+95)) then
        tmp = y
    else if (t <= 6.5d-296) then
        tmp = t_1
    else if (t <= 1.62d-189) then
        tmp = y / (a / z)
    else if (t <= 1.18d+114) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.05e+95) {
		tmp = y;
	} else if (t <= 6.5e-296) {
		tmp = t_1;
	} else if (t <= 1.62e-189) {
		tmp = y / (a / z);
	} else if (t <= 1.18e+114) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -1.05e+95:
		tmp = y
	elif t <= 6.5e-296:
		tmp = t_1
	elif t <= 1.62e-189:
		tmp = y / (a / z)
	elif t <= 1.18e+114:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -1.05e+95)
		tmp = y;
	elseif (t <= 6.5e-296)
		tmp = t_1;
	elseif (t <= 1.62e-189)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 1.18e+114)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -1.05e+95)
		tmp = y;
	elseif (t <= 6.5e-296)
		tmp = t_1;
	elseif (t <= 1.62e-189)
		tmp = y / (a / z);
	elseif (t <= 1.18e+114)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+95], y, If[LessEqual[t, 6.5e-296], t$95$1, If[LessEqual[t, 1.62e-189], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.18e+114], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05e95 or 1.18000000000000005e114 < t

   1. Initial program 41.5%

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

      1. associate-/l* 71.1%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in t around inf 47.6%

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

   if -1.05e95 < t < 6.49999999999999963e-296 or 1.62e-189 < t < 1.18000000000000005e114

   1. Initial program 84.9%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in t around 0 72.8%

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

   5. Taylor expanded in x around inf 54.9%

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

      1. *-commutative 54.9%

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

      2. mul-1-neg 54.9%

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

      3. unsub-neg 54.9%

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

   7. Simplified 54.9%

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

   if 6.49999999999999963e-296 < t < 1.62e-189

   1. Initial program 90.6%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in x around 0 62.7%

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

      1. associate-*r/ 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in t around 0 57.0%

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

      1. associate-/l* 66.2%

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

   9. Simplified 66.2%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+95}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{-189}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9: 48.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -1.22 \cdot 10^{+92}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-190}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -1.22e+92)
     y
     (if (<= t 9e-296)
       t_1
       (if (<= t 2.5e-190) (* y (/ z (- a t))) (if (<= t 3.9e+112) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.22e+92) {
		tmp = y;
	} else if (t <= 9e-296) {
		tmp = t_1;
	} else if (t <= 2.5e-190) {
		tmp = y * (z / (a - t));
	} else if (t <= 3.9e+112) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-1.22d+92)) then
        tmp = y
    else if (t <= 9d-296) then
        tmp = t_1
    else if (t <= 2.5d-190) then
        tmp = y * (z / (a - t))
    else if (t <= 3.9d+112) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.22e+92) {
		tmp = y;
	} else if (t <= 9e-296) {
		tmp = t_1;
	} else if (t <= 2.5e-190) {
		tmp = y * (z / (a - t));
	} else if (t <= 3.9e+112) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -1.22e+92:
		tmp = y
	elif t <= 9e-296:
		tmp = t_1
	elif t <= 2.5e-190:
		tmp = y * (z / (a - t))
	elif t <= 3.9e+112:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -1.22e+92)
		tmp = y;
	elseif (t <= 9e-296)
		tmp = t_1;
	elseif (t <= 2.5e-190)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 3.9e+112)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -1.22e+92)
		tmp = y;
	elseif (t <= 9e-296)
		tmp = t_1;
	elseif (t <= 2.5e-190)
		tmp = y * (z / (a - t));
	elseif (t <= 3.9e+112)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.22e+92], y, If[LessEqual[t, 9e-296], t$95$1, If[LessEqual[t, 2.5e-190], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e+112], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.22e92 or 3.89999999999999968e112 < t

   1. Initial program 41.5%

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

      1. associate-/l* 71.1%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in t around inf 47.6%

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

   if -1.22e92 < t < 9.0000000000000003e-296 or 2.50000000000000017e-190 < t < 3.89999999999999968e112

   1. Initial program 84.9%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in t around 0 72.8%

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

   5. Taylor expanded in x around inf 54.9%

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

      1. *-commutative 54.9%

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

      2. mul-1-neg 54.9%

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

      3. unsub-neg 54.9%

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

   7. Simplified 54.9%

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

   if 9.0000000000000003e-296 < t < 2.50000000000000017e-190

   1. Initial program 90.6%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in x around 0 62.7%

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

      1. associate-*r/ 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in z around inf 61.3%

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

      1. associate-*r/ 70.5%

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

   9. Simplified 70.5%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+92}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-190}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 10: 58.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-157}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+85}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -3.4e+70)
     t_1
     (if (<= t -9.2e-157)
       (* z (/ (- y x) (- a t)))
       (if (<= t 2.9e+85) (+ x (* z (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -3.4e+70) {
		tmp = t_1;
	} else if (t <= -9.2e-157) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 2.9e+85) {
		tmp = x + (z * (y / 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 = y * ((z - t) / (a - t))
    if (t <= (-3.4d+70)) then
        tmp = t_1
    else if (t <= (-9.2d-157)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 2.9d+85) then
        tmp = x + (z * (y / 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 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -3.4e+70) {
		tmp = t_1;
	} else if (t <= -9.2e-157) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 2.9e+85) {
		tmp = x + (z * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -3.4e+70:
		tmp = t_1
	elif t <= -9.2e-157:
		tmp = z * ((y - x) / (a - t))
	elif t <= 2.9e+85:
		tmp = x + (z * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -3.4e+70)
		tmp = t_1;
	elseif (t <= -9.2e-157)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 2.9e+85)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -3.4e+70)
		tmp = t_1;
	elseif (t <= -9.2e-157)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 2.9e+85)
		tmp = x + (z * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+70], t$95$1, If[LessEqual[t, -9.2e-157], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+85], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4000000000000001e70 or 2.89999999999999997e85 < t

   1. Initial program 44.2%

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

      1. associate-/l* 73.6%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in x around 0 44.8%

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

      1. associate-*r/ 68.8%

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

   6. Simplified 68.8%

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

   if -3.4000000000000001e70 < t < -9.19999999999999954e-157

   1. Initial program 84.2%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in z around inf 64.4%

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

      1. div-sub 64.5%

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

   6. Simplified 64.5%

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

   if -9.19999999999999954e-157 < t < 2.89999999999999997e85

   1. Initial program 86.8%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around 0 83.9%

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

   5. Taylor expanded in y around inf 64.6%

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

      1. associate-/l* 69.0%

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

      2. associate-/r/ 67.8%

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

   7. Simplified 67.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-157}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+85}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 11: 64.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-149}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+85}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -3.9e+70)
     t_1
     (if (<= t -1.2e-149)
       (* z (/ (- y x) (- a t)))
       (if (<= t 4e+85) (+ x (/ z (/ a (- y x)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -3.9e+70) {
		tmp = t_1;
	} else if (t <= -1.2e-149) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 4e+85) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-3.9d+70)) then
        tmp = t_1
    else if (t <= (-1.2d-149)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 4d+85) then
        tmp = x + (z / (a / (y - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -3.9e+70) {
		tmp = t_1;
	} else if (t <= -1.2e-149) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 4e+85) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -3.9e+70:
		tmp = t_1
	elif t <= -1.2e-149:
		tmp = z * ((y - x) / (a - t))
	elif t <= 4e+85:
		tmp = x + (z / (a / (y - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -3.9e+70)
		tmp = t_1;
	elseif (t <= -1.2e-149)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 4e+85)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -3.9e+70)
		tmp = t_1;
	elseif (t <= -1.2e-149)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 4e+85)
		tmp = x + (z / (a / (y - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+70], t$95$1, If[LessEqual[t, -1.2e-149], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+85], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.89999999999999975e70 or 4.0000000000000001e85 < t

   1. Initial program 44.2%

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

      1. associate-/l* 73.6%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in x around 0 44.8%

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

      1. associate-*r/ 68.8%

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

   6. Simplified 68.8%

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

   if -3.89999999999999975e70 < t < -1.2000000000000001e-149

   1. Initial program 84.2%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in z around inf 64.4%

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

      1. div-sub 64.5%

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

   6. Simplified 64.5%

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

   if -1.2000000000000001e-149 < t < 4.0000000000000001e85

   1. Initial program 86.8%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around 0 75.9%

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

      1. +-commutative 75.9%

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

      2. *-commutative 75.9%

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

      3. associate-/l* 82.2%

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

   6. Simplified 82.2%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-149}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+85}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 12: 64.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-149}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+85}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -4.8e+70)
     t_1
     (if (<= t -9.5e-149)
       (* z (/ (- y x) (- a t)))
       (if (<= t 4.2e+85) (+ x (/ (- y x) (/ a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -4.8e+70) {
		tmp = t_1;
	} else if (t <= -9.5e-149) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 4.2e+85) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-4.8d+70)) then
        tmp = t_1
    else if (t <= (-9.5d-149)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 4.2d+85) then
        tmp = x + ((y - x) / (a / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -4.8e+70) {
		tmp = t_1;
	} else if (t <= -9.5e-149) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 4.2e+85) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -4.8e+70:
		tmp = t_1
	elif t <= -9.5e-149:
		tmp = z * ((y - x) / (a - t))
	elif t <= 4.2e+85:
		tmp = x + ((y - x) / (a / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -4.8e+70)
		tmp = t_1;
	elseif (t <= -9.5e-149)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 4.2e+85)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -4.8e+70)
		tmp = t_1;
	elseif (t <= -9.5e-149)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 4.2e+85)
		tmp = x + ((y - x) / (a / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+70], t$95$1, If[LessEqual[t, -9.5e-149], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+85], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.79999999999999974e70 or 4.2000000000000002e85 < t

   1. Initial program 44.2%

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

      1. associate-/l* 73.6%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in x around 0 44.8%

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

      1. associate-*r/ 68.8%

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

   6. Simplified 68.8%

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

   if -4.79999999999999974e70 < t < -9.50000000000000034e-149

   1. Initial program 84.2%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in z around inf 64.4%

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

      1. div-sub 64.5%

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

   6. Simplified 64.5%

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

   if -9.50000000000000034e-149 < t < 4.2000000000000002e85

   1. Initial program 86.8%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around 0 83.9%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-149}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+85}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 13: 74.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-145} \lor \neg \left(a \leq 2.7 \cdot 10^{-15}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.5e-145) (not (<= a 2.7e-15)))
   (+ x (/ (- z t) (/ (- a t) y)))
   (+ y (/ (- x y) (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e-145) || !(a <= 2.7e-15)) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-8.5d-145)) .or. (.not. (a <= 2.7d-15))) then
        tmp = x + ((z - t) / ((a - t) / y))
    else
        tmp = y + ((x - y) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e-145) || !(a <= 2.7e-15)) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.5e-145) or not (a <= 2.7e-15):
		tmp = x + ((z - t) / ((a - t) / y))
	else:
		tmp = y + ((x - y) / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.5e-145) || !(a <= 2.7e-15))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / y)));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8.5e-145) || ~((a <= 2.7e-15)))
		tmp = x + ((z - t) / ((a - t) / y));
	else
		tmp = y + ((x - y) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.5e-145], N[Not[LessEqual[a, 2.7e-15]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.50000000000000043e-145 or 2.70000000000000009e-15 < a

   1. Initial program 71.3%

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

      1. *-commutative 71.3%

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

      2. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in y around inf 75.3%

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

   if -8.50000000000000043e-145 < a < 2.70000000000000009e-15

   1. Initial program 76.5%

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

      1. associate-/l* 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in t around -inf 80.2%

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

      1. mul-1-neg 80.2%

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

      2. unsub-neg 80.2%

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

      3. div-sub 77.8%

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

      4. *-commutative 77.8%

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

      5. div-sub 80.2%

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

      6. distribute-rgt-out-- 80.2%

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

   6. Simplified 80.2%

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

   7. Taylor expanded in z around inf 79.2%

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

      1. *-commutative 79.2%

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

      2. associate-/l* 84.0%

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

   9. Simplified 84.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-145} \lor \neg \left(a \leq 2.7 \cdot 10^{-15}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \]

Alternative 14: 76.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-54} \lor \neg \left(a \leq 1.36 \cdot 10^{+42}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.8e-54) (not (<= a 1.36e+42)))
   (+ x (/ (- z t) (/ (- a t) y)))
   (+ y (* (- y x) (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e-54) || !(a <= 1.36e+42)) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.8d-54)) .or. (.not. (a <= 1.36d+42))) then
        tmp = x + ((z - t) / ((a - t) / y))
    else
        tmp = y + ((y - x) * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e-54) || !(a <= 1.36e+42)) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.8e-54) or not (a <= 1.36e+42):
		tmp = x + ((z - t) / ((a - t) / y))
	else:
		tmp = y + ((y - x) * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.8e-54) || !(a <= 1.36e+42))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / y)));
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.8e-54) || ~((a <= 1.36e+42)))
		tmp = x + ((z - t) / ((a - t) / y));
	else
		tmp = y + ((y - x) * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.8e-54], N[Not[LessEqual[a, 1.36e+42]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.79999999999999988e-54 or 1.35999999999999999e42 < a

   1. Initial program 72.7%

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

      1. *-commutative 72.7%

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

      2. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in y around inf 78.6%

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

   if -1.79999999999999988e-54 < a < 1.35999999999999999e42

   1. Initial program 73.5%

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

      1. associate-/l* 79.9%

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

   3. Simplified 79.9%

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

      1. associate-/l* 73.5%

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

      2. clear-num 73.5%

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

      3. inv-pow 73.5%

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

   5. Applied egg-rr 73.5%

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

      1. unpow-1 73.5%

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

      2. associate-/r* 79.6%

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

   7. Simplified 79.6%

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

      1. div-inv 79.5%

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

   9. Applied egg-rr 79.5%

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

   10. Taylor expanded in t around -inf 74.1%

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

       1. *-commutative 74.1%

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

       2. mul-1-neg 74.1%

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

       3. distribute-rgt-out-- 74.1%

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

       4. *-commutative 74.1%

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

       5. associate-*r/ 79.8%

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

       6. div-sub 76.0%

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

       7. *-commutative 76.0%

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

       8. div-sub 79.8%

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

       9. associate-/r/ 79.8%

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

       10. unsub-neg 79.8%

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

       11. associate-/r/ 79.8%

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

       12. div-sub 76.0%

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

       13. *-commutative 76.0%

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

       14. div-sub 79.8%

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

   12. Simplified 79.8%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-54} \lor \neg \left(a \leq 1.36 \cdot 10^{+42}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]

Alternative 15: 68.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -480:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+86}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -480.0)
   (+ y (/ (- x y) (/ t z)))
   (if (<= t 2.3e+86) (+ x (/ (- y x) (/ a z))) (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -480.0) {
		tmp = y + ((x - y) / (t / z));
	} else if (t <= 2.3e+86) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-480.0d0)) then
        tmp = y + ((x - y) / (t / z))
    else if (t <= 2.3d+86) then
        tmp = x + ((y - x) / (a / z))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -480.0) {
		tmp = y + ((x - y) / (t / z));
	} else if (t <= 2.3e+86) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -480.0:
		tmp = y + ((x - y) / (t / z))
	elif t <= 2.3e+86:
		tmp = x + ((y - x) / (a / z))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -480.0)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	elseif (t <= 2.3e+86)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -480.0)
		tmp = y + ((x - y) / (t / z));
	elseif (t <= 2.3e+86)
		tmp = x + ((y - x) / (a / z));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -480.0], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+86], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -480

   1. Initial program 59.8%

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

      1. associate-/l* 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in t around -inf 58.3%

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

      1. mul-1-neg 58.3%

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

      2. unsub-neg 58.3%

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

      3. div-sub 58.3%

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

      4. *-commutative 58.3%

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

      5. div-sub 58.3%

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

      6. distribute-rgt-out-- 60.3%

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

   6. Simplified 60.3%

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

   7. Taylor expanded in z around inf 59.2%

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

      1. *-commutative 59.2%

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

      2. associate-/l* 66.6%

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

   9. Simplified 66.6%

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

   if -480 < t < 2.2999999999999999e86

   1. Initial program 87.4%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in t around 0 79.5%

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

   if 2.2999999999999999e86 < t

   1. Initial program 36.3%

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

      1. associate-/l* 65.7%

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

   3. Simplified 65.7%

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

   4. Taylor expanded in x around 0 40.7%

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

      1. associate-*r/ 70.1%

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

   6. Simplified 70.1%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -480:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+86}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 16: 55.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+48} \lor \neg \left(t \leq 1.6 \cdot 10^{+112}\right):\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.2e+48) (not (<= t 1.6e+112)))
   (/ (- y) (/ t (- z t)))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.2e+48) || !(t <= 1.6e+112)) {
		tmp = -y / (t / (z - t));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.2d+48)) .or. (.not. (t <= 1.6d+112))) then
        tmp = -y / (t / (z - t))
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.2e+48) || !(t <= 1.6e+112)) {
		tmp = -y / (t / (z - t));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.2e+48) or not (t <= 1.6e+112):
		tmp = -y / (t / (z - t))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.2e+48) || !(t <= 1.6e+112))
		tmp = Float64(Float64(-y) / Float64(t / Float64(z - t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.2e+48) || ~((t <= 1.6e+112)))
		tmp = -y / (t / (z - t));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.2e+48], N[Not[LessEqual[t, 1.6e+112]], $MachinePrecision]], N[((-y) / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2000000000000001e48 or 1.59999999999999993e112 < t

   1. Initial program 43.7%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in x around 0 45.0%

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

      1. associate-*r/ 67.7%

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

   6. Simplified 67.7%

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

   7. Taylor expanded in a around 0 36.1%

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

      1. mul-1-neg 36.1%

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

      2. associate-/l* 51.9%

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

   9. Simplified 51.9%

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

   if -3.2000000000000001e48 < t < 1.59999999999999993e112

   1. Initial program 86.6%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in t around 0 76.4%

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

   5. Taylor expanded in y around inf 58.8%

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

      1. associate-/l* 62.7%

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

      2. associate-/r/ 61.8%

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

   7. Simplified 61.8%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+48} \lor \neg \left(t \leq 1.6 \cdot 10^{+112}\right):\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 17: 39.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+55}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-191}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.2e+55)
   y
   (if (<= t -5.4e-297)
     x
     (if (<= t 8.8e-191) (* y (/ z a)) (if (<= t 1.85e+112) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+55) {
		tmp = y;
	} else if (t <= -5.4e-297) {
		tmp = x;
	} else if (t <= 8.8e-191) {
		tmp = y * (z / a);
	} else if (t <= 1.85e+112) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7.2d+55)) then
        tmp = y
    else if (t <= (-5.4d-297)) then
        tmp = x
    else if (t <= 8.8d-191) then
        tmp = y * (z / a)
    else if (t <= 1.85d+112) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+55) {
		tmp = y;
	} else if (t <= -5.4e-297) {
		tmp = x;
	} else if (t <= 8.8e-191) {
		tmp = y * (z / a);
	} else if (t <= 1.85e+112) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.2e+55:
		tmp = y
	elif t <= -5.4e-297:
		tmp = x
	elif t <= 8.8e-191:
		tmp = y * (z / a)
	elif t <= 1.85e+112:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.2e+55)
		tmp = y;
	elseif (t <= -5.4e-297)
		tmp = x;
	elseif (t <= 8.8e-191)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 1.85e+112)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.2e+55)
		tmp = y;
	elseif (t <= -5.4e-297)
		tmp = x;
	elseif (t <= 8.8e-191)
		tmp = y * (z / a);
	elseif (t <= 1.85e+112)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.2e+55], y, If[LessEqual[t, -5.4e-297], x, If[LessEqual[t, 8.8e-191], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+112], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.19999999999999975e55 or 1.85000000000000002e112 < t

   1. Initial program 43.7%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in t around inf 45.5%

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

   if -7.19999999999999975e55 < t < -5.4000000000000002e-297 or 8.79999999999999992e-191 < t < 1.85000000000000002e112

   1. Initial program 87.7%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in a around inf 39.9%

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

   if -5.4000000000000002e-297 < t < 8.79999999999999992e-191

   1. Initial program 81.8%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in x around 0 51.4%

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

      1. associate-*r/ 60.4%

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

   6. Simplified 60.4%

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

   7. Taylor expanded in t around 0 56.5%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+55}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-191}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 18: 39.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+56}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-188}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.55e+56)
   y
   (if (<= t -1.05e-296)
     x
     (if (<= t 2.45e-188) (/ y (/ a z)) (if (<= t 3.7e+112) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.55e+56) {
		tmp = y;
	} else if (t <= -1.05e-296) {
		tmp = x;
	} else if (t <= 2.45e-188) {
		tmp = y / (a / z);
	} else if (t <= 3.7e+112) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.55d+56)) then
        tmp = y
    else if (t <= (-1.05d-296)) then
        tmp = x
    else if (t <= 2.45d-188) then
        tmp = y / (a / z)
    else if (t <= 3.7d+112) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.55e+56) {
		tmp = y;
	} else if (t <= -1.05e-296) {
		tmp = x;
	} else if (t <= 2.45e-188) {
		tmp = y / (a / z);
	} else if (t <= 3.7e+112) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.55e+56:
		tmp = y
	elif t <= -1.05e-296:
		tmp = x
	elif t <= 2.45e-188:
		tmp = y / (a / z)
	elif t <= 3.7e+112:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.55e+56)
		tmp = y;
	elseif (t <= -1.05e-296)
		tmp = x;
	elseif (t <= 2.45e-188)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 3.7e+112)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.55e+56)
		tmp = y;
	elseif (t <= -1.05e-296)
		tmp = x;
	elseif (t <= 2.45e-188)
		tmp = y / (a / z);
	elseif (t <= 3.7e+112)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.55e+56], y, If[LessEqual[t, -1.05e-296], x, If[LessEqual[t, 2.45e-188], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e+112], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.55000000000000002e56 or 3.70000000000000004e112 < t

   1. Initial program 43.7%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in t around inf 45.5%

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

   if -1.55000000000000002e56 < t < -1.05e-296 or 2.45000000000000002e-188 < t < 3.70000000000000004e112

   1. Initial program 87.7%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in a around inf 39.9%

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

   if -1.05e-296 < t < 2.45000000000000002e-188

   1. Initial program 81.8%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in x around 0 51.4%

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

      1. associate-*r/ 60.4%

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

   6. Simplified 60.4%

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

   7. Taylor expanded in t around 0 47.6%

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

      1. associate-/l* 56.6%

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

   9. Simplified 56.6%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+56}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-188}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 19: 52.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+112}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.1e+51) y (if (<= t 4.8e+112) (+ x (* z (/ y a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.1e+51) {
		tmp = y;
	} else if (t <= 4.8e+112) {
		tmp = x + (z * (y / 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 <= (-3.1d+51)) then
        tmp = y
    else if (t <= 4.8d+112) then
        tmp = x + (z * (y / 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 <= -3.1e+51) {
		tmp = y;
	} else if (t <= 4.8e+112) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.1e+51:
		tmp = y
	elif t <= 4.8e+112:
		tmp = x + (z * (y / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.1e+51)
		tmp = y;
	elseif (t <= 4.8e+112)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.1e+51)
		tmp = y;
	elseif (t <= 4.8e+112)
		tmp = x + (z * (y / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.1e+51], y, If[LessEqual[t, 4.8e+112], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -3.10000000000000011e51 or 4.8e112 < t

   1. Initial program 43.7%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in t around inf 45.5%

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

   if -3.10000000000000011e51 < t < 4.8e112

   1. Initial program 86.6%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in t around 0 76.4%

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

   5. Taylor expanded in y around inf 58.8%

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

      1. associate-/l* 62.7%

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

      2. associate-/r/ 61.8%

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

   7. Simplified 61.8%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+112}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 20: 39.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+56}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.2e+56) y (if (<= t 6.5e+112) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.2e+56) {
		tmp = y;
	} else if (t <= 6.5e+112) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9.2d+56)) then
        tmp = y
    else if (t <= 6.5d+112) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.2e+56) {
		tmp = y;
	} else if (t <= 6.5e+112) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.2e+56:
		tmp = y
	elif t <= 6.5e+112:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.2e+56)
		tmp = y;
	elseif (t <= 6.5e+112)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.2e+56)
		tmp = y;
	elseif (t <= 6.5e+112)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.2e+56], y, If[LessEqual[t, 6.5e+112], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -9.20000000000000058e56 or 6.4999999999999998e112 < t

   1. Initial program 43.7%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in t around inf 45.5%

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

   if -9.20000000000000058e56 < t < 6.4999999999999998e112

   1. Initial program 86.6%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in a around inf 36.4%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+56}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 21: 25.5% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 73.0%

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

   1. associate-/l* 88.2%

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

3. Simplified 88.2%

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

4. Taylor expanded in a around inf 26.9%

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

5. Final simplification 26.9%

   \[\leadsto x \]

Developer target: 86.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023240 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))