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

Percentage Accurate: 98.3% → 98.4%

Time: 8.9s

Alternatives: 15

Speedup: 1.0×

Specification

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]

Initial Program: 98.3% 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]

Alternative 1: 98.4% 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 98.0%

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

   1. clear-num 98.0%

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

   2. un-div-inv 98.1%

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

4. Applied egg-rr 98.1%

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

5. Final simplification 98.1%

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

Alternative 2: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))))
   (if (<= t -7.2e+76)
     (+ x y)
     (if (<= t 2.65e-45)
       t_1
       (if (<= t 5.8e+53)
         (* y (- 1.0 (/ z t)))
         (if (<= t 3.6e+84) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (t <= -7.2e+76) {
		tmp = x + y;
	} else if (t <= 2.65e-45) {
		tmp = t_1;
	} else if (t <= 5.8e+53) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= 3.6e+84) {
		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 / (a / z))
    if (t <= (-7.2d+76)) then
        tmp = x + y
    else if (t <= 2.65d-45) then
        tmp = t_1
    else if (t <= 5.8d+53) then
        tmp = y * (1.0d0 - (z / t))
    else if (t <= 3.6d+84) 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 / (a / z));
	double tmp;
	if (t <= -7.2e+76) {
		tmp = x + y;
	} else if (t <= 2.65e-45) {
		tmp = t_1;
	} else if (t <= 5.8e+53) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= 3.6e+84) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	tmp = 0
	if t <= -7.2e+76:
		tmp = x + y
	elif t <= 2.65e-45:
		tmp = t_1
	elif t <= 5.8e+53:
		tmp = y * (1.0 - (z / t))
	elif t <= 3.6e+84:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (t <= -7.2e+76)
		tmp = Float64(x + y);
	elseif (t <= 2.65e-45)
		tmp = t_1;
	elseif (t <= 5.8e+53)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (t <= 3.6e+84)
		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 / (a / z));
	tmp = 0.0;
	if (t <= -7.2e+76)
		tmp = x + y;
	elseif (t <= 2.65e-45)
		tmp = t_1;
	elseif (t <= 5.8e+53)
		tmp = y * (1.0 - (z / t));
	elseif (t <= 3.6e+84)
		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[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+76], N[(x + y), $MachinePrecision], If[LessEqual[t, 2.65e-45], t$95$1, If[LessEqual[t, 5.8e+53], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+84], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.2000000000000006e76 or 3.5999999999999999e84 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 88.3%

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

      1. +-commutative 88.3%

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

   5. Simplified 88.3%

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

   if -7.2000000000000006e76 < t < 2.6499999999999999e-45 or 5.8000000000000004e53 < t < 3.5999999999999999e84

   1. Initial program 96.4%

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

      1. clear-num 96.4%

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

      2. un-div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in t around 0 79.3%

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

   if 2.6499999999999999e-45 < t < 5.8000000000000004e53

   1. Initial program 99.7%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around 0 85.6%

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

      1. mul-1-neg 85.6%

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

      2. unsub-neg 85.6%

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

      3. associate-/l* 85.3%

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

      4. div-sub 85.3%

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

      5. *-inverses 85.3%

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

   7. Simplified 85.3%

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

   8. Taylor expanded in x around 0 58.8%

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

      1. mul-1-neg 58.8%

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

      2. sub-neg 58.8%

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

      3. metadata-eval 58.8%

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

      4. distribute-rgt-neg-in 58.8%

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

      5. +-commutative 58.8%

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

      6. distribute-neg-in 58.8%

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

      7. metadata-eval 58.8%

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

      8. sub-neg 58.8%

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

   10. Simplified 58.8%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+84}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+220}:\\ \;\;\;\;\frac{z}{\frac{t}{-y}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+185} \lor \neg \left(z \leq 9 \cdot 10^{+228}\right) \land z \leq 7 \cdot 10^{+251}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+220)
   (/ z (/ t (- y)))
   (if (or (<= z 1.6e+185) (and (not (<= z 9e+228)) (<= z 7e+251)))
     (+ x y)
     (* (/ z t) (- y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+220) {
		tmp = z / (t / -y);
	} else if ((z <= 1.6e+185) || (!(z <= 9e+228) && (z <= 7e+251))) {
		tmp = x + y;
	} else {
		tmp = (z / t) * -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 (z <= (-8d+220)) then
        tmp = z / (t / -y)
    else if ((z <= 1.6d+185) .or. (.not. (z <= 9d+228)) .and. (z <= 7d+251)) then
        tmp = x + y
    else
        tmp = (z / t) * -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 (z <= -8e+220) {
		tmp = z / (t / -y);
	} else if ((z <= 1.6e+185) || (!(z <= 9e+228) && (z <= 7e+251))) {
		tmp = x + y;
	} else {
		tmp = (z / t) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+220:
		tmp = z / (t / -y)
	elif (z <= 1.6e+185) or (not (z <= 9e+228) and (z <= 7e+251)):
		tmp = x + y
	else:
		tmp = (z / t) * -y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+220)
		tmp = Float64(z / Float64(t / Float64(-y)));
	elseif ((z <= 1.6e+185) || (!(z <= 9e+228) && (z <= 7e+251)))
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(z / t) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e+220)
		tmp = z / (t / -y);
	elseif ((z <= 1.6e+185) || (~((z <= 9e+228)) && (z <= 7e+251)))
		tmp = x + y;
	else
		tmp = (z / t) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+220], N[(z / N[(t / (-y)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.6e+185], And[N[Not[LessEqual[z, 9e+228]], $MachinePrecision], LessEqual[z, 7e+251]]], N[(x + y), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8e220

   1. Initial program 90.1%

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

      1. clear-num 90.1%

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

      2. un-div-inv 90.2%

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

   4. Applied egg-rr 90.2%

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

   5. Taylor expanded in a around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

      3. associate-/l* 69.7%

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

      4. div-sub 69.7%

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

      5. *-inverses 69.7%

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

   7. Simplified 69.7%

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

   8. Taylor expanded in z around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. associate-*r/ 54.5%

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

      3. distribute-lft-neg-in 54.5%

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

      4. *-commutative 54.5%

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

   10. Simplified 54.5%

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

       1. frac-2neg 54.5%

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

       2. associate-*l/ 64.3%

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

       3. associate-*r/ 64.2%

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

       4. frac-2neg 64.2%

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

       5. clear-num 64.2%

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

       6. un-div-inv 64.1%

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

   12. Applied egg-rr 64.1%

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

   if -8e220 < z < 1.60000000000000003e185 or 8.99999999999999966e228 < z < 7.00000000000000008e251

   1. Initial program 99.0%

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

   3. Taylor expanded in t around inf 68.2%

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

      1. +-commutative 68.2%

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

   5. Simplified 68.2%

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

   if 1.60000000000000003e185 < z < 8.99999999999999966e228 or 7.00000000000000008e251 < z

   1. Initial program 96.3%

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

      1. clear-num 96.4%

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

      2. un-div-inv 96.4%

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in a around 0 51.5%

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

      1. mul-1-neg 51.5%

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

      2. unsub-neg 51.5%

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

      3. associate-/l* 58.3%

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

      4. div-sub 58.3%

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

      5. *-inverses 58.3%

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

   7. Simplified 58.3%

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

   8. Taylor expanded in z around inf 47.8%

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

      1. mul-1-neg 47.8%

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

      2. associate-*r/ 50.9%

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

      3. distribute-lft-neg-in 50.9%

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

      4. *-commutative 50.9%

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

   10. Simplified 50.9%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+220}:\\ \;\;\;\;\frac{z}{\frac{t}{-y}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+185} \lor \neg \left(z \leq 9 \cdot 10^{+228}\right) \land z \leq 7 \cdot 10^{+251}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+220}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+185} \lor \neg \left(z \leq 2.2 \cdot 10^{+229}\right) \land z \leq 4.4 \cdot 10^{+253}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e+220)
   (/ (* y z) (- t))
   (if (or (<= z 1.65e+185) (and (not (<= z 2.2e+229)) (<= z 4.4e+253)))
     (+ x y)
     (* (/ z t) (- y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e+220) {
		tmp = (y * z) / -t;
	} else if ((z <= 1.65e+185) || (!(z <= 2.2e+229) && (z <= 4.4e+253))) {
		tmp = x + y;
	} else {
		tmp = (z / t) * -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 (z <= (-4.4d+220)) then
        tmp = (y * z) / -t
    else if ((z <= 1.65d+185) .or. (.not. (z <= 2.2d+229)) .and. (z <= 4.4d+253)) then
        tmp = x + y
    else
        tmp = (z / t) * -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 (z <= -4.4e+220) {
		tmp = (y * z) / -t;
	} else if ((z <= 1.65e+185) || (!(z <= 2.2e+229) && (z <= 4.4e+253))) {
		tmp = x + y;
	} else {
		tmp = (z / t) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.4e+220:
		tmp = (y * z) / -t
	elif (z <= 1.65e+185) or (not (z <= 2.2e+229) and (z <= 4.4e+253)):
		tmp = x + y
	else:
		tmp = (z / t) * -y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e+220)
		tmp = Float64(Float64(y * z) / Float64(-t));
	elseif ((z <= 1.65e+185) || (!(z <= 2.2e+229) && (z <= 4.4e+253)))
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(z / t) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.4e+220)
		tmp = (y * z) / -t;
	elseif ((z <= 1.65e+185) || (~((z <= 2.2e+229)) && (z <= 4.4e+253)))
		tmp = x + y;
	else
		tmp = (z / t) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e+220], N[(N[(y * z), $MachinePrecision] / (-t)), $MachinePrecision], If[Or[LessEqual[z, 1.65e+185], And[N[Not[LessEqual[z, 2.2e+229]], $MachinePrecision], LessEqual[z, 4.4e+253]]], N[(x + y), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.39999999999999978e220

   1. Initial program 90.1%

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

      1. clear-num 90.1%

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

      2. un-div-inv 90.2%

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

   4. Applied egg-rr 90.2%

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

   5. Taylor expanded in a around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

      3. associate-/l* 69.7%

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

      4. div-sub 69.7%

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

      5. *-inverses 69.7%

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

   7. Simplified 69.7%

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

   8. Taylor expanded in z around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. associate-*r/ 54.5%

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

      3. distribute-lft-neg-in 54.5%

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

      4. *-commutative 54.5%

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

   10. Simplified 54.5%

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

       1. frac-2neg 54.5%

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

       2. associate-*l/ 64.3%

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

       3. associate-*r/ 64.2%

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

       4. frac-2neg 64.2%

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

       5. associate-*r/ 64.3%

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

   12. Applied egg-rr 64.3%

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

   if -4.39999999999999978e220 < z < 1.65000000000000006e185 or 2.20000000000000004e229 < z < 4.40000000000000011e253

   1. Initial program 99.0%

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

   3. Taylor expanded in t around inf 68.2%

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

      1. +-commutative 68.2%

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

   5. Simplified 68.2%

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

   if 1.65000000000000006e185 < z < 2.20000000000000004e229 or 4.40000000000000011e253 < z

   1. Initial program 96.3%

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

      1. clear-num 96.4%

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

      2. un-div-inv 96.4%

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in a around 0 51.5%

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

      1. mul-1-neg 51.5%

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

      2. unsub-neg 51.5%

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

      3. associate-/l* 58.3%

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

      4. div-sub 58.3%

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

      5. *-inverses 58.3%

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

   7. Simplified 58.3%

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

   8. Taylor expanded in z around inf 47.8%

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

      1. mul-1-neg 47.8%

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

      2. associate-*r/ 50.9%

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

      3. distribute-lft-neg-in 50.9%

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

      4. *-commutative 50.9%

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

   10. Simplified 50.9%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+220}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+185} \lor \neg \left(z \leq 2.2 \cdot 10^{+229}\right) \land z \leq 4.4 \cdot 10^{+253}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+88}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.2e+76)
   (+ x y)
   (if (<= t 1.45e-90)
     (+ x (/ y (/ a z)))
     (if (<= t 1.75e+88) (- x (* y (/ z t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.2e+76) {
		tmp = x + y;
	} else if (t <= 1.45e-90) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.75e+88) {
		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 <= (-9.2d+76)) then
        tmp = x + y
    else if (t <= 1.45d-90) then
        tmp = x + (y / (a / z))
    else if (t <= 1.75d+88) 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 <= -9.2e+76) {
		tmp = x + y;
	} else if (t <= 1.45e-90) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.75e+88) {
		tmp = x - (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.2e+76:
		tmp = x + y
	elif t <= 1.45e-90:
		tmp = x + (y / (a / z))
	elif t <= 1.75e+88:
		tmp = x - (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.2e+76)
		tmp = Float64(x + y);
	elseif (t <= 1.45e-90)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.75e+88)
		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 <= -9.2e+76)
		tmp = x + y;
	elseif (t <= 1.45e-90)
		tmp = x + (y / (a / z));
	elseif (t <= 1.75e+88)
		tmp = x - (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.2e+76], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.45e-90], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e+88], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.20000000000000005e76 or 1.7499999999999999e88 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 88.3%

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

      1. +-commutative 88.3%

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

   5. Simplified 88.3%

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

   if -9.20000000000000005e76 < t < 1.44999999999999992e-90

   1. Initial program 95.9%

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

      1. clear-num 95.9%

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

      2. un-div-inv 96.0%

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in t around 0 80.4%

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

   if 1.44999999999999992e-90 < t < 1.7499999999999999e88

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 86.8%

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

      1. associate-/l* 86.6%

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

   5. Simplified 86.6%

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

   6. Taylor expanded in a around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. unsub-neg 79.3%

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

      3. associate-/l* 79.1%

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

   8. Simplified 79.1%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+88}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+87}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1e+77)
   (+ x y)
   (if (<= t 1.22e-89)
     (+ x (/ y (/ a z)))
     (if (<= t 4e+87) (- x (* z (/ y t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1e+77) {
		tmp = x + y;
	} else if (t <= 1.22e-89) {
		tmp = x + (y / (a / z));
	} else if (t <= 4e+87) {
		tmp = x - (z * (y / 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 <= (-1d+77)) then
        tmp = x + y
    else if (t <= 1.22d-89) then
        tmp = x + (y / (a / z))
    else if (t <= 4d+87) then
        tmp = x - (z * (y / 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 <= -1e+77) {
		tmp = x + y;
	} else if (t <= 1.22e-89) {
		tmp = x + (y / (a / z));
	} else if (t <= 4e+87) {
		tmp = x - (z * (y / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1e+77:
		tmp = x + y
	elif t <= 1.22e-89:
		tmp = x + (y / (a / z))
	elif t <= 4e+87:
		tmp = x - (z * (y / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1e+77)
		tmp = Float64(x + y);
	elseif (t <= 1.22e-89)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 4e+87)
		tmp = Float64(x - Float64(z * Float64(y / 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 <= -1e+77)
		tmp = x + y;
	elseif (t <= 1.22e-89)
		tmp = x + (y / (a / z));
	elseif (t <= 4e+87)
		tmp = x - (z * (y / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1e+77], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.22e-89], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+87], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.99999999999999983e76 or 3.9999999999999998e87 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 88.3%

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

      1. +-commutative 88.3%

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

   5. Simplified 88.3%

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

   if -9.99999999999999983e76 < t < 1.22e-89

   1. Initial program 95.9%

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

      1. clear-num 95.9%

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

      2. un-div-inv 96.0%

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in t around 0 80.4%

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

   if 1.22e-89 < t < 3.9999999999999998e87

   1. Initial program 99.8%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing
   3. 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 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in a around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. unsub-neg 82.3%

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

      3. associate-/l* 82.1%

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

      4. div-sub 82.1%

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

      5. *-inverses 82.1%

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

   7. Simplified 82.1%

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

   8. Taylor expanded in z around inf 79.3%

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

      1. *-commutative 79.3%

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

      2. associate-*r/ 79.2%

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

   10. Simplified 79.2%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+87}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.55e+77)
   (+ x y)
   (if (<= t 1.25e-89)
     (+ x (/ y (/ a z)))
     (if (<= t 3.2e+87) (- x (/ (* y z) t)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.55e+77) {
		tmp = x + y;
	} else if (t <= 1.25e-89) {
		tmp = x + (y / (a / z));
	} else if (t <= 3.2e+87) {
		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 <= (-1.55d+77)) then
        tmp = x + y
    else if (t <= 1.25d-89) then
        tmp = x + (y / (a / z))
    else if (t <= 3.2d+87) 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 <= -1.55e+77) {
		tmp = x + y;
	} else if (t <= 1.25e-89) {
		tmp = x + (y / (a / z));
	} else if (t <= 3.2e+87) {
		tmp = x - ((y * z) / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.55e+77:
		tmp = x + y
	elif t <= 1.25e-89:
		tmp = x + (y / (a / z))
	elif t <= 3.2e+87:
		tmp = x - ((y * z) / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.55e+77)
		tmp = Float64(x + y);
	elseif (t <= 1.25e-89)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 3.2e+87)
		tmp = Float64(x - Float64(Float64(y * 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 <= -1.55e+77)
		tmp = x + y;
	elseif (t <= 1.25e-89)
		tmp = x + (y / (a / z));
	elseif (t <= 3.2e+87)
		tmp = x - ((y * z) / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.55e+77], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.25e-89], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+87], N[(x - N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.54999999999999999e77 or 3.2e87 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 88.3%

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

      1. +-commutative 88.3%

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

   5. Simplified 88.3%

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

   if -1.54999999999999999e77 < t < 1.24999999999999992e-89

   1. Initial program 95.9%

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

      1. clear-num 95.9%

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

      2. un-div-inv 96.0%

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in t around 0 80.4%

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

   if 1.24999999999999992e-89 < t < 3.2e87

   1. Initial program 99.8%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing
   3. 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 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in a around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. unsub-neg 82.3%

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

      3. associate-/l* 82.1%

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

      4. div-sub 82.1%

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

      5. *-inverses 82.1%

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

   7. Simplified 82.1%

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

   8. Taylor expanded in z around inf 79.3%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+180} \lor \neg \left(t \leq 3.3 \cdot 10^{+89}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8e+180) (not (<= t 3.3e+89)))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e+180) || !(t <= 3.3e+89)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8d+180)) .or. (.not. (t <= 3.3d+89))) then
        tmp = x + y
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e+180) || !(t <= 3.3e+89)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8e+180) or not (t <= 3.3e+89):
		tmp = x + y
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8e+180) || !(t <= 3.3e+89))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8e+180) || ~((t <= 3.3e+89)))
		tmp = x + y;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8e+180], N[Not[LessEqual[t, 3.3e+89]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.0000000000000001e180 or 3.29999999999999974e89 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 90.9%

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

      1. +-commutative 90.9%

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

   5. Simplified 90.9%

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

   if -8.0000000000000001e180 < t < 3.29999999999999974e89

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 85.6%

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

      1. associate-/l* 86.7%

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

   5. Simplified 86.7%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+180} \lor \neg \left(t \leq 3.3 \cdot 10^{+89}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+88}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.8e+63)
   (+ x (/ y (- 1.0 (/ a t))))
   (if (<= t 1.65e+88) (+ x (* y (/ z (- a t)))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+63) {
		tmp = x + (y / (1.0 - (a / t)));
	} else if (t <= 1.65e+88) {
		tmp = x + (y * (z / (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 (t <= (-3.8d+63)) then
        tmp = x + (y / (1.0d0 - (a / t)))
    else if (t <= 1.65d+88) then
        tmp = x + (y * (z / (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 (t <= -3.8e+63) {
		tmp = x + (y / (1.0 - (a / t)));
	} else if (t <= 1.65e+88) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.8e+63:
		tmp = x + (y / (1.0 - (a / t)))
	elif t <= 1.65e+88:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.8e+63)
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / t))));
	elseif (t <= 1.65e+88)
		tmp = Float64(x + Float64(y * Float64(z / 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 (t <= -3.8e+63)
		tmp = x + (y / (1.0 - (a / t)));
	elseif (t <= 1.65e+88)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.8e+63], N[(x + N[(y / N[(1.0 - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e+88], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8000000000000001e63

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing
   3. 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 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 88.4%

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

      1. associate-*r/ 88.4%

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

      2. neg-mul-1 88.4%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in a around 0 88.4%

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

      1. mul-1-neg 88.4%

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

      2. unsub-neg 88.4%

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

   10. Simplified 88.4%

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

   if -3.8000000000000001e63 < t < 1.6500000000000002e88

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 88.9%

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

      1. associate-/l* 88.9%

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

   5. Simplified 88.9%

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

   if 1.6500000000000002e88 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 92.8%

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

      1. +-commutative 92.8%

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

   5. Simplified 92.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+88}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \mathbf{elif}\;t \leq 1.04 \cdot 10^{+86}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.35e+63)
   (+ x (/ y (- 1.0 (/ a t))))
   (if (<= t 1.04e+86) (+ x (/ (* y z) (- a t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.35e+63) {
		tmp = x + (y / (1.0 - (a / t)));
	} else if (t <= 1.04e+86) {
		tmp = x + ((y * z) / (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 (t <= (-1.35d+63)) then
        tmp = x + (y / (1.0d0 - (a / t)))
    else if (t <= 1.04d+86) then
        tmp = x + ((y * z) / (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 (t <= -1.35e+63) {
		tmp = x + (y / (1.0 - (a / t)));
	} else if (t <= 1.04e+86) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.35e+63:
		tmp = x + (y / (1.0 - (a / t)))
	elif t <= 1.04e+86:
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.35e+63)
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / t))));
	elseif (t <= 1.04e+86)
		tmp = Float64(x + Float64(Float64(y * z) / 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 (t <= -1.35e+63)
		tmp = x + (y / (1.0 - (a / t)));
	elseif (t <= 1.04e+86)
		tmp = x + ((y * z) / (a - t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.35e+63], N[(x + N[(y / N[(1.0 - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.04e+86], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35000000000000009e63

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing
   3. 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 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 88.4%

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

      1. associate-*r/ 88.4%

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

      2. neg-mul-1 88.4%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in a around 0 88.4%

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

      1. mul-1-neg 88.4%

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

      2. unsub-neg 88.4%

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

   10. Simplified 88.4%

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

   if -1.35000000000000009e63 < t < 1.04000000000000004e86

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 88.9%

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

   if 1.04000000000000004e86 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 92.8%

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

      1. +-commutative 92.8%

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

   5. Simplified 92.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \mathbf{elif}\;t \leq 1.04 \cdot 10^{+86}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+87}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.5e+61)
   (+ x (/ y (- 1.0 (/ a t))))
   (if (<= t 1.15e+87)
     (+ x (/ (* y z) (- a t)))
     (- x (* y (+ (/ z t) -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.5e+61) {
		tmp = x + (y / (1.0 - (a / t)));
	} else if (t <= 1.15e+87) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x - (y * ((z / t) + -1.0));
	}
	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 <= (-8.5d+61)) then
        tmp = x + (y / (1.0d0 - (a / t)))
    else if (t <= 1.15d+87) then
        tmp = x + ((y * z) / (a - t))
    else
        tmp = x - (y * ((z / t) + (-1.0d0)))
    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 <= -8.5e+61) {
		tmp = x + (y / (1.0 - (a / t)));
	} else if (t <= 1.15e+87) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x - (y * ((z / t) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.5e+61:
		tmp = x + (y / (1.0 - (a / t)))
	elif t <= 1.15e+87:
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = x - (y * ((z / t) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.5e+61)
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / t))));
	elseif (t <= 1.15e+87)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8.5e+61)
		tmp = x + (y / (1.0 - (a / t)));
	elseif (t <= 1.15e+87)
		tmp = x + ((y * z) / (a - t));
	else
		tmp = x - (y * ((z / t) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.5e+61], N[(x + N[(y / N[(1.0 - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+87], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.50000000000000035e61

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing
   3. 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 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 88.4%

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

      1. associate-*r/ 88.4%

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

      2. neg-mul-1 88.4%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in a around 0 88.4%

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

      1. mul-1-neg 88.4%

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

      2. unsub-neg 88.4%

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

   10. Simplified 88.4%

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

   if -8.50000000000000035e61 < t < 1.1500000000000001e87

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 88.9%

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

   if 1.1500000000000001e87 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. unsub-neg 74.3%

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

      3. associate-/l* 100.0%

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

      4. div-sub 100.0%

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

      5. sub-neg 100.0%

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

      6. *-inverses 100.0%

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

      7. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+87}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+83} \lor \neg \left(y \leq 9 \cdot 10^{+169}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -8.5e+83) (not (<= y 9e+169))) (* y (- 1.0 (/ z t))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8.5e+83) || !(y <= 9e+169)) {
		tmp = y * (1.0 - (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 ((y <= (-8.5d+83)) .or. (.not. (y <= 9d+169))) then
        tmp = y * (1.0d0 - (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 ((y <= -8.5e+83) || !(y <= 9e+169)) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -8.5e+83) or not (y <= 9e+169):
		tmp = y * (1.0 - (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -8.5e+83) || !(y <= 9e+169))
		tmp = Float64(y * Float64(1.0 - 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 ((y <= -8.5e+83) || ~((y <= 9e+169)))
		tmp = y * (1.0 - (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -8.5e+83], N[Not[LessEqual[y, 9e+169]], $MachinePrecision]], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4999999999999995e83 or 8.9999999999999999e169 < y

   1. Initial program 98.6%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing
   3. 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 98.7%

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

   4. Applied egg-rr 98.7%

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

   5. Taylor expanded in a around 0 39.4%

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

      1. mul-1-neg 39.4%

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

      2. unsub-neg 39.4%

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

      3. associate-/l* 65.8%

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

      4. div-sub 65.8%

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

      5. *-inverses 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in x around 0 60.1%

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

      1. mul-1-neg 60.1%

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

      2. sub-neg 60.1%

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

      3. metadata-eval 60.1%

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

      4. distribute-rgt-neg-in 60.1%

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

      5. +-commutative 60.1%

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

      6. distribute-neg-in 60.1%

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

      7. metadata-eval 60.1%

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

      8. sub-neg 60.1%

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

   10. Simplified 60.1%

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

   if -8.4999999999999995e83 < y < 8.9999999999999999e169

   1. Initial program 97.8%

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

   3. Taylor expanded in t around inf 67.0%

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

      1. +-commutative 67.0%

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

   5. Simplified 67.0%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+83} \lor \neg \left(y \leq 9 \cdot 10^{+169}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-114} \lor \neg \left(t \leq 4.7 \cdot 10^{-160}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.75e-114) (not (<= t 4.7e-160))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.75e-114) || !(t <= 4.7e-160)) {
		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 ((t <= (-2.75d-114)) .or. (.not. (t <= 4.7d-160))) 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 ((t <= -2.75e-114) || !(t <= 4.7e-160)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.75e-114) or not (t <= 4.7e-160):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.75e-114) || !(t <= 4.7e-160))
		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 ((t <= -2.75e-114) || ~((t <= 4.7e-160)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.75e-114], N[Not[LessEqual[t, 4.7e-160]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -2.75000000000000005e-114 or 4.6999999999999998e-160 < t

   1. Initial program 98.9%

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

   3. Taylor expanded in t around inf 68.8%

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

      1. +-commutative 68.8%

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

   5. Simplified 68.8%

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

   if -2.75000000000000005e-114 < t < 4.6999999999999998e-160

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf 46.3%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-114} \lor \neg \left(t \leq 4.7 \cdot 10^{-160}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 98.3% 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 98.0%

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

3. Final simplification 98.0%

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

Alternative 15: 49.9% 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 98.0%

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

3. Taylor expanded in x around inf 48.0%

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

4. Final simplification 48.0%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024095 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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