Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B

Percentage Accurate: 85.3% → 98.5%

Time: 12.2s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{a - t}{z - t}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (y / ((a - t) / (z - 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 / ((a - t) / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

   1. associate-/l* 98.8%

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

3. Simplified 98.8%

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

   1. clear-num 98.7%

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

   2. un-div-inv 98.8%

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

6. Applied egg-rr 98.8%

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

7. Final simplification 98.8%

   \[\leadsto x + \frac{y}{\frac{a - t}{z - t}} \]
8. Add Preprocessing

Alternative 2: 59.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;a \leq -9.6 \cdot 10^{-195}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-253}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-276}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+126}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))))
   (if (<= a -9.6e-195)
     (+ x y)
     (if (<= a -1.55e-221)
       t_1
       (if (<= a -7e-253)
         (+ x y)
         (if (<= a 4.8e-276) t_1 (if (<= a 1.25e+126) (+ x y) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (a <= -9.6e-195) {
		tmp = x + y;
	} else if (a <= -1.55e-221) {
		tmp = t_1;
	} else if (a <= -7e-253) {
		tmp = x + y;
	} else if (a <= 4.8e-276) {
		tmp = t_1;
	} else if (a <= 1.25e+126) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / (a - t))
    if (a <= (-9.6d-195)) then
        tmp = x + y
    else if (a <= (-1.55d-221)) then
        tmp = t_1
    else if (a <= (-7d-253)) then
        tmp = x + y
    else if (a <= 4.8d-276) then
        tmp = t_1
    else if (a <= 1.25d+126) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (a <= -9.6e-195) {
		tmp = x + y;
	} else if (a <= -1.55e-221) {
		tmp = t_1;
	} else if (a <= -7e-253) {
		tmp = x + y;
	} else if (a <= 4.8e-276) {
		tmp = t_1;
	} else if (a <= 1.25e+126) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	tmp = 0
	if a <= -9.6e-195:
		tmp = x + y
	elif a <= -1.55e-221:
		tmp = t_1
	elif a <= -7e-253:
		tmp = x + y
	elif a <= 4.8e-276:
		tmp = t_1
	elif a <= 1.25e+126:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (a <= -9.6e-195)
		tmp = Float64(x + y);
	elseif (a <= -1.55e-221)
		tmp = t_1;
	elseif (a <= -7e-253)
		tmp = Float64(x + y);
	elseif (a <= 4.8e-276)
		tmp = t_1;
	elseif (a <= 1.25e+126)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	tmp = 0.0;
	if (a <= -9.6e-195)
		tmp = x + y;
	elseif (a <= -1.55e-221)
		tmp = t_1;
	elseif (a <= -7e-253)
		tmp = x + y;
	elseif (a <= 4.8e-276)
		tmp = t_1;
	elseif (a <= 1.25e+126)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.6e-195], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.55e-221], t$95$1, If[LessEqual[a, -7e-253], N[(x + y), $MachinePrecision], If[LessEqual[a, 4.8e-276], t$95$1, If[LessEqual[a, 1.25e+126], N[(x + y), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.6e-195 or -1.55e-221 < a < -7.00000000000000045e-253 or 4.79999999999999965e-276 < a < 1.24999999999999994e126

   1. Initial program 85.8%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in t around inf 65.1%

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

      1. +-commutative 65.1%

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

   7. Simplified 65.1%

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

   if -9.6e-195 < a < -1.55e-221 or -7.00000000000000045e-253 < a < 4.79999999999999965e-276

   1. Initial program 87.7%

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

      1. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in y around inf 92.0%

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

      1. associate--l+ 92.0%

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

      2. div-sub 92.0%

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

   7. Simplified 92.0%

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

   8. Taylor expanded in z around inf 73.6%

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

   if 1.24999999999999994e126 < a

   1. Initial program 86.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 83.4%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{-195}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-221}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-253}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-276}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+126}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-35}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-119} \lor \neg \left(t \leq 3.5 \cdot 10^{+93}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.4e+46)
   (+ x y)
   (if (<= t -2.9e-35)
     (- x (* t (/ y a)))
     (if (or (<= t -1.2e-119) (not (<= t 3.5e+93)))
       (+ x y)
       (+ x (* y (/ z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e+46) {
		tmp = x + y;
	} else if (t <= -2.9e-35) {
		tmp = x - (t * (y / a));
	} else if ((t <= -1.2e-119) || !(t <= 3.5e+93)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / 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 <= (-2.4d+46)) then
        tmp = x + y
    else if (t <= (-2.9d-35)) then
        tmp = x - (t * (y / a))
    else if ((t <= (-1.2d-119)) .or. (.not. (t <= 3.5d+93))) then
        tmp = x + y
    else
        tmp = x + (y * (z / 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 <= -2.4e+46) {
		tmp = x + y;
	} else if (t <= -2.9e-35) {
		tmp = x - (t * (y / a));
	} else if ((t <= -1.2e-119) || !(t <= 3.5e+93)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.4e+46:
		tmp = x + y
	elif t <= -2.9e-35:
		tmp = x - (t * (y / a))
	elif (t <= -1.2e-119) or not (t <= 3.5e+93):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.4e+46)
		tmp = Float64(x + y);
	elseif (t <= -2.9e-35)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	elseif ((t <= -1.2e-119) || !(t <= 3.5e+93))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.4e+46)
		tmp = x + y;
	elseif (t <= -2.9e-35)
		tmp = x - (t * (y / a));
	elseif ((t <= -1.2e-119) || ~((t <= 3.5e+93)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.4e+46], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.9e-35], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.2e-119], N[Not[LessEqual[t, 3.5e+93]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.40000000000000008e46 or -2.9000000000000002e-35 < t < -1.20000000000000004e-119 or 3.49999999999999998e93 < t

   1. Initial program 76.0%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around inf 72.3%

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

      1. +-commutative 72.3%

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

   7. Simplified 72.3%

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

   if -2.40000000000000008e46 < t < -2.9000000000000002e-35

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around 0 92.7%

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

      1. mul-1-neg 92.7%

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

      2. unsub-neg 92.7%

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

      3. associate-/l* 92.5%

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

   9. Simplified 92.5%

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

   10. Taylor expanded in t around 0 85.5%

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

       1. associate-/l* 85.4%

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

   12. Simplified 85.4%

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

   if -1.20000000000000004e-119 < t < 3.49999999999999998e93

   1. Initial program 92.8%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around 0 72.0%

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

      1. +-commutative 72.0%

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

      2. associate-/l* 76.9%

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

   7. Simplified 76.9%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-35}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-119} \lor \neg \left(t \leq 3.5 \cdot 10^{+93}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+104}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ z t)))))
   (if (<= t -1.7e+104)
     (+ x y)
     (if (<= t -3.5e-137)
       t_1
       (if (<= t 2.1e-48)
         (+ x (* y (/ z a)))
         (if (<= t 8.2e+128) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (z / t));
	double tmp;
	if (t <= -1.7e+104) {
		tmp = x + y;
	} else if (t <= -3.5e-137) {
		tmp = t_1;
	} else if (t <= 2.1e-48) {
		tmp = x + (y * (z / a));
	} else if (t <= 8.2e+128) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * (z / t))
    if (t <= (-1.7d+104)) then
        tmp = x + y
    else if (t <= (-3.5d-137)) then
        tmp = t_1
    else if (t <= 2.1d-48) then
        tmp = x + (y * (z / a))
    else if (t <= 8.2d+128) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (z / t));
	double tmp;
	if (t <= -1.7e+104) {
		tmp = x + y;
	} else if (t <= -3.5e-137) {
		tmp = t_1;
	} else if (t <= 2.1e-48) {
		tmp = x + (y * (z / a));
	} else if (t <= 8.2e+128) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (z / t))
	tmp = 0
	if t <= -1.7e+104:
		tmp = x + y
	elif t <= -3.5e-137:
		tmp = t_1
	elif t <= 2.1e-48:
		tmp = x + (y * (z / a))
	elif t <= 8.2e+128:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -1.7e+104)
		tmp = Float64(x + y);
	elseif (t <= -3.5e-137)
		tmp = t_1;
	elseif (t <= 2.1e-48)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 8.2e+128)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (z / t));
	tmp = 0.0;
	if (t <= -1.7e+104)
		tmp = x + y;
	elseif (t <= -3.5e-137)
		tmp = t_1;
	elseif (t <= 2.1e-48)
		tmp = x + (y * (z / a));
	elseif (t <= 8.2e+128)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+104], N[(x + y), $MachinePrecision], If[LessEqual[t, -3.5e-137], t$95$1, If[LessEqual[t, 2.1e-48], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e+128], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6999999999999998e104 or 8.20000000000000023e128 < t

   1. Initial program 68.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 81.0%

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

      1. +-commutative 81.0%

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

   7. Simplified 81.0%

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

   if -1.6999999999999998e104 < t < -3.5000000000000001e-137 or 2.09999999999999989e-48 < t < 8.20000000000000023e128

   1. Initial program 92.7%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in z around inf 81.7%

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

   6. Taylor expanded in a around 0 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

      3. associate-/l* 73.2%

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

   8. Simplified 73.2%

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

   if -3.5000000000000001e-137 < t < 2.09999999999999989e-48

   1. Initial program 92.8%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in t around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. associate-/l* 83.5%

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

   7. Simplified 83.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+104}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-137}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+128}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+102}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-145}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-46}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+129}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.25e+102)
   (+ x y)
   (if (<= t -1.35e-145)
     (- x (* z (/ y t)))
     (if (<= t 1.9e-46)
       (+ x (* y (/ z a)))
       (if (<= t 1.35e+129) (- x (* y (/ z t))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e+102) {
		tmp = x + y;
	} else if (t <= -1.35e-145) {
		tmp = x - (z * (y / t));
	} else if (t <= 1.9e-46) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.35e+129) {
		tmp = x - (y * (z / t));
	} else {
		tmp = x + 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 <= (-1.25d+102)) then
        tmp = x + y
    else if (t <= (-1.35d-145)) then
        tmp = x - (z * (y / t))
    else if (t <= 1.9d-46) then
        tmp = x + (y * (z / a))
    else if (t <= 1.35d+129) then
        tmp = x - (y * (z / t))
    else
        tmp = x + 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 <= -1.25e+102) {
		tmp = x + y;
	} else if (t <= -1.35e-145) {
		tmp = x - (z * (y / t));
	} else if (t <= 1.9e-46) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.35e+129) {
		tmp = x - (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.25e+102:
		tmp = x + y
	elif t <= -1.35e-145:
		tmp = x - (z * (y / t))
	elif t <= 1.9e-46:
		tmp = x + (y * (z / a))
	elif t <= 1.35e+129:
		tmp = x - (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.25e+102)
		tmp = Float64(x + y);
	elseif (t <= -1.35e-145)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	elseif (t <= 1.9e-46)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 1.35e+129)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.25e+102)
		tmp = x + y;
	elseif (t <= -1.35e-145)
		tmp = x - (z * (y / t));
	elseif (t <= 1.9e-46)
		tmp = x + (y * (z / a));
	elseif (t <= 1.35e+129)
		tmp = x - (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.25e+102], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.35e-145], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-46], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+129], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.25e102 or 1.35e129 < t

   1. Initial program 68.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 81.0%

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

      1. +-commutative 81.0%

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

   7. Simplified 81.0%

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

   if -1.25e102 < t < -1.35e-145

   1. Initial program 95.7%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in z around inf 80.2%

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

   6. Taylor expanded in a around 0 71.4%

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

      1. mul-1-neg 71.4%

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

      2. unsub-neg 71.4%

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

      3. associate-/l* 69.3%

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

   8. Simplified 69.3%

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

   9. Taylor expanded in y around 0 71.4%

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

       1. *-rgt-identity 71.4%

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

       2. times-frac 71.7%

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

       3. /-rgt-identity 71.7%

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

       4. associate-/r/ 69.8%

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

   11. Simplified 69.8%

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

       1. associate-/r/ 71.7%

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

   13. Applied egg-rr 71.7%

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

   if -1.35e-145 < t < 1.8999999999999998e-46

   1. Initial program 92.8%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in t around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. associate-/l* 83.5%

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

   7. Simplified 83.5%

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

   if 1.8999999999999998e-46 < t < 1.35e129

   1. Initial program 89.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 83.1%

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

   6. Taylor expanded in a around 0 72.9%

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

      1. mul-1-neg 72.9%

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

      2. unsub-neg 72.9%

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

      3. associate-/l* 76.9%

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

   8. Simplified 76.9%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+102}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-145}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-46}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+129}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-60} \lor \neg \left(x \leq 3 \cdot 10^{-182}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.1e-60) (not (<= x 3e-182)))
   (+ x (* z (/ y (- a t))))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.1e-60) || !(x <= 3e-182)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-2.1d-60)) .or. (.not. (x <= 3d-182))) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.1e-60) || !(x <= 3e-182)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.1e-60) or not (x <= 3e-182):
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.1e-60) || !(x <= 3e-182))
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.1e-60) || ~((x <= 3e-182)))
		tmp = x + (z * (y / (a - t)));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.1e-60], N[Not[LessEqual[x, 3e-182]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.09999999999999991e-60 or 3.0000000000000001e-182 < x

   1. Initial program 88.0%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in z around inf 83.7%

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

      1. div-inv 83.7%

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

      2. *-commutative 83.7%

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

      3. associate-*l* 89.1%

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

      4. div-inv 89.2%

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

   7. Applied egg-rr 89.2%

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

   if -2.09999999999999991e-60 < x < 3.0000000000000001e-182

   1. Initial program 81.9%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around inf 98.6%

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

      1. associate--l+ 98.6%

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

      2. div-sub 98.6%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in x around 0 80.4%

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

      1. div-sub 80.4%

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

   10. Simplified 80.4%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-60} \lor \neg \left(x \leq 3 \cdot 10^{-182}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+101} \lor \neg \left(t \leq 8.2 \cdot 10^{+122}\right):\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.7e+101) (not (<= t 8.2e+122)))
   (- x (* y (+ (/ z t) -1.0)))
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.7e+101) || !(t <= 8.2e+122)) {
		tmp = x - (y * ((z / t) + -1.0));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.7d+101)) .or. (.not. (t <= 8.2d+122))) then
        tmp = x - (y * ((z / t) + (-1.0d0)))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.7e+101) || !(t <= 8.2e+122)) {
		tmp = x - (y * ((z / t) + -1.0));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.7e+101) or not (t <= 8.2e+122):
		tmp = x - (y * ((z / t) + -1.0))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.7e+101) || !(t <= 8.2e+122))
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.7e+101) || ~((t <= 8.2e+122)))
		tmp = x - (y * ((z / t) + -1.0));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.7e+101], N[Not[LessEqual[t, 8.2e+122]], $MachinePrecision]], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.6999999999999997e101 or 8.2000000000000004e122 < t

   1. Initial program 69.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. unsub-neg 65.4%

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

      3. associate-/l* 93.1%

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

      4. div-sub 93.0%

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

      5. sub-neg 93.0%

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

      6. *-inverses 93.0%

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

      7. metadata-eval 93.0%

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

   7. Simplified 93.0%

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

   if -3.6999999999999997e101 < t < 8.2000000000000004e122

   1. Initial program 92.7%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

      1. clear-num 98.3%

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

      2. un-div-inv 98.4%

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

   6. Applied egg-rr 98.4%

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

   7. Taylor expanded in z around inf 87.8%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+101} \lor \neg \left(t \leq 8.2 \cdot 10^{+122}\right):\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-60}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.3e-60)
   (+ x (* y (/ z a)))
   (if (<= x 2.25e-7) (* y (/ (- z t) (- a t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.3e-60) {
		tmp = x + (y * (z / a));
	} else if (x <= 2.25e-7) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + 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 (x <= (-2.3d-60)) then
        tmp = x + (y * (z / a))
    else if (x <= 2.25d-7) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + 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 (x <= -2.3e-60) {
		tmp = x + (y * (z / a));
	} else if (x <= 2.25e-7) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.3e-60:
		tmp = x + (y * (z / a))
	elif x <= 2.25e-7:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.3e-60)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (x <= 2.25e-7)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.3e-60)
		tmp = x + (y * (z / a));
	elseif (x <= 2.25e-7)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.3e-60], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.25e-7], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.3000000000000001e-60

   1. Initial program 87.1%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in t around 0 70.0%

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

      1. +-commutative 70.0%

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

      2. associate-/l* 76.2%

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

   7. Simplified 76.2%

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

   if -2.3000000000000001e-60 < x < 2.2499999999999999e-7

   1. Initial program 83.0%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in y around inf 98.9%

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

      1. associate--l+ 98.9%

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

      2. div-sub 98.9%

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

   7. Simplified 98.9%

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

   8. Taylor expanded in x around 0 77.5%

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

      1. div-sub 77.5%

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

   10. Simplified 77.5%

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

   if 2.2499999999999999e-7 < x

   1. Initial program 89.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 76.5%

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

      1. +-commutative 76.5%

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

   7. Simplified 76.5%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-60}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-60}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-182}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.8e-60)
   (+ x (* z (/ y (- a t))))
   (if (<= x 3.5e-182) (* y (/ (- z t) (- a t))) (+ x (/ y (/ (- a t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.8e-60) {
		tmp = x + (z * (y / (a - t)));
	} else if (x <= 3.5e-182) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.8d-60)) then
        tmp = x + (z * (y / (a - t)))
    else if (x <= 3.5d-182) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.8e-60) {
		tmp = x + (z * (y / (a - t)));
	} else if (x <= 3.5e-182) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.8e-60:
		tmp = x + (z * (y / (a - t)))
	elif x <= 3.5e-182:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.8e-60)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	elseif (x <= 3.5e-182)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.8e-60)
		tmp = x + (z * (y / (a - t)));
	elseif (x <= 3.5e-182)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.8e-60], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e-182], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8e-60

   1. Initial program 87.1%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in z around inf 83.1%

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

      1. div-inv 83.1%

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

      2. *-commutative 83.1%

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

      3. associate-*l* 93.3%

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

      4. div-inv 93.3%

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

   7. Applied egg-rr 93.3%

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

   if -1.8e-60 < x < 3.49999999999999983e-182

   1. Initial program 81.9%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around inf 98.6%

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

      1. associate--l+ 98.6%

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

      2. div-sub 98.6%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in x around 0 80.4%

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

      1. div-sub 80.4%

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

   10. Simplified 80.4%

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

   if 3.49999999999999983e-182 < x

   1. Initial program 88.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around inf 88.0%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-60}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-182}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-127}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-180}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5.7e-127)
   (+ x (/ z (/ (- a t) y)))
   (if (<= x 2.2e-180) (* y (/ (- z t) (- a t))) (+ x (/ y (/ (- a t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.7e-127) {
		tmp = x + (z / ((a - t) / y));
	} else if (x <= 2.2e-180) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-5.7d-127)) then
        tmp = x + (z / ((a - t) / y))
    else if (x <= 2.2d-180) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.7e-127) {
		tmp = x + (z / ((a - t) / y));
	} else if (x <= 2.2e-180) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -5.7e-127:
		tmp = x + (z / ((a - t) / y))
	elif x <= 2.2e-180:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5.7e-127)
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	elseif (x <= 2.2e-180)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5.7e-127)
		tmp = x + (z / ((a - t) / y));
	elseif (x <= 2.2e-180)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5.7e-127], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e-180], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.69999999999999963e-127

   1. Initial program 85.4%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in z around inf 80.1%

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

      1. div-inv 80.0%

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

      2. *-commutative 80.0%

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

      3. associate-*l* 88.9%

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

      4. div-inv 88.9%

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

   7. Applied egg-rr 88.9%

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

      1. clear-num 88.9%

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

      2. un-div-inv 89.8%

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

   9. Applied egg-rr 89.8%

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

   if -5.69999999999999963e-127 < x < 2.20000000000000013e-180

   1. Initial program 82.9%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in y around inf 98.4%

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

      1. associate--l+ 98.4%

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

      2. div-sub 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in x around 0 82.6%

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

      1. div-sub 82.6%

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

   10. Simplified 82.6%

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

   if 2.20000000000000013e-180 < x

   1. Initial program 88.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around inf 88.0%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-127}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-180}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-44}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-107}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.3e-44)
   (+ x (* z (/ y (- a t))))
   (if (<= z 4.7e-107) (+ x (* t (/ y (- t a)))) (+ x (/ y (/ (- a t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e-44) {
		tmp = x + (z * (y / (a - t)));
	} else if (z <= 4.7e-107) {
		tmp = x + (t * (y / (t - a)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.3d-44)) then
        tmp = x + (z * (y / (a - t)))
    else if (z <= 4.7d-107) then
        tmp = x + (t * (y / (t - a)))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e-44) {
		tmp = x + (z * (y / (a - t)));
	} else if (z <= 4.7e-107) {
		tmp = x + (t * (y / (t - a)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.3e-44:
		tmp = x + (z * (y / (a - t)))
	elif z <= 4.7e-107:
		tmp = x + (t * (y / (t - a)))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.3e-44)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	elseif (z <= 4.7e-107)
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.3e-44)
		tmp = x + (z * (y / (a - t)));
	elseif (z <= 4.7e-107)
		tmp = x + (t * (y / (t - a)));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.3e-44], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e-107], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.30000000000000013e-44

   1. Initial program 82.4%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in z around inf 77.4%

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

      1. div-inv 77.3%

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

      2. *-commutative 77.3%

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

      3. associate-*l* 89.0%

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

      4. div-inv 89.0%

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

   7. Applied egg-rr 89.0%

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

   if -4.30000000000000013e-44 < z < 4.69999999999999998e-107

   1. Initial program 91.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 85.1%

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

      1. mul-1-neg 85.1%

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

      2. unsub-neg 85.1%

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

      3. associate-/l* 91.3%

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

   9. Simplified 91.3%

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

   if 4.69999999999999998e-107 < z

   1. Initial program 83.0%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

      1. clear-num 98.6%

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

      2. un-div-inv 98.5%

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

   6. Applied egg-rr 98.5%

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

   7. Taylor expanded in z around inf 84.9%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-44}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-107}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-44}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-107}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.3e-44)
   (+ x (* z (/ y (- a t))))
   (if (<= z 5e-107) (+ x (* y (/ t (- t a)))) (+ x (/ y (/ (- a t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e-44) {
		tmp = x + (z * (y / (a - t)));
	} else if (z <= 5e-107) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.3d-44)) then
        tmp = x + (z * (y / (a - t)))
    else if (z <= 5d-107) then
        tmp = x + (y * (t / (t - a)))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e-44) {
		tmp = x + (z * (y / (a - t)));
	} else if (z <= 5e-107) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.3e-44:
		tmp = x + (z * (y / (a - t)))
	elif z <= 5e-107:
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.3e-44)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	elseif (z <= 5e-107)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.3e-44)
		tmp = x + (z * (y / (a - t)));
	elseif (z <= 5e-107)
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.3e-44], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-107], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.30000000000000013e-44

   1. Initial program 82.4%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in z around inf 77.4%

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

      1. div-inv 77.3%

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

      2. *-commutative 77.3%

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

      3. associate-*l* 89.0%

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

      4. div-inv 89.0%

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

   7. Applied egg-rr 89.0%

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

   if -4.30000000000000013e-44 < z < 4.99999999999999971e-107

   1. Initial program 91.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 85.1%

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

      1. mul-1-neg 85.1%

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

      2. unsub-neg 85.1%

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

      3. *-commutative 85.1%

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

      4. associate-/l* 94.1%

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

   7. Simplified 94.1%

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

   if 4.99999999999999971e-107 < z

   1. Initial program 83.0%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

      1. clear-num 98.6%

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

      2. un-div-inv 98.5%

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

   6. Applied egg-rr 98.5%

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

   7. Taylor expanded in z around inf 84.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-44}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-107}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-119} \lor \neg \left(t \leq 1.8 \cdot 10^{+93}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.2e-119) (not (<= t 1.8e+93))) (+ x y) (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e-119) || !(t <= 1.8e+93)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / 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 <= (-1.2d-119)) .or. (.not. (t <= 1.8d+93))) then
        tmp = x + y
    else
        tmp = x + ((y * z) / 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 <= -1.2e-119) || !(t <= 1.8e+93)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.2e-119) or not (t <= 1.8e+93):
		tmp = x + y
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.2e-119) || !(t <= 1.8e+93))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.2e-119) || ~((t <= 1.8e+93)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.2e-119], N[Not[LessEqual[t, 1.8e+93]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.20000000000000004e-119 or 1.8e93 < t

   1. Initial program 78.6%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around inf 69.8%

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

      1. +-commutative 69.8%

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

   7. Simplified 69.8%

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

   if -1.20000000000000004e-119 < t < 1.8e93

   1. Initial program 92.8%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around 0 72.0%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-119} \lor \neg \left(t \leq 1.8 \cdot 10^{+93}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-119} \lor \neg \left(t \leq 1.8 \cdot 10^{+93}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.2e-119) (not (<= t 1.8e+93))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e-119) || !(t <= 1.8e+93)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / 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 <= (-1.2d-119)) .or. (.not. (t <= 1.8d+93))) then
        tmp = x + y
    else
        tmp = x + (y * (z / 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 <= -1.2e-119) || !(t <= 1.8e+93)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.2e-119) or not (t <= 1.8e+93):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.2e-119) || !(t <= 1.8e+93))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.2e-119) || ~((t <= 1.8e+93)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.2e-119], N[Not[LessEqual[t, 1.8e+93]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.20000000000000004e-119 or 1.8e93 < t

   1. Initial program 78.6%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around inf 69.8%

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

      1. +-commutative 69.8%

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

   7. Simplified 69.8%

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

   if -1.20000000000000004e-119 < t < 1.8e93

   1. Initial program 92.8%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around 0 72.0%

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

      1. +-commutative 72.0%

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

      2. associate-/l* 76.9%

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

   7. Simplified 76.9%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-119} \lor \neg \left(t \leq 1.8 \cdot 10^{+93}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

   1. associate-/l* 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

   \[\leadsto x + y \cdot \frac{z - t}{a - t} \]
6. Add Preprocessing

Alternative 16: 61.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 8 \cdot 10^{+124}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 8e+124) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 8e+124) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= 8d+124) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 8e+124) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 8e+124:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 8e+124)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 8e+124)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 8e+124], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 7.99999999999999959e124

   1. Initial program 86.0%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in t around inf 60.2%

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

      1. +-commutative 60.2%

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

   7. Simplified 60.2%

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

   if 7.99999999999999959e124 < a

   1. Initial program 86.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 83.4%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 8 \cdot 10^{+124}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.9% accurate, 11.0× 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 86.0%

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

   1. associate-/l* 98.8%

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

3. Simplified 98.8%

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

5. Taylor expanded in x around inf 50.3%

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

6. Final simplification 50.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{a - t}{z - t}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (y / ((a - t) / (z - 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 / ((a - t) / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024066 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (+ x (/ y (/ (- a t) (- z t))))

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