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

Percentage Accurate: 76.6% → 93.5%

Time: 7.5s

Alternatives: 10

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (* y (- (+ (/ t (- a t)) 1.0) (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * (((t / (a - t)) + 1.0) - (z / (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 * (((t / (a - t)) + 1.0d0) - (z / (a - t))))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (y * (((t / (a - t)) + 1.0) - (z / (a - t))));
}

Python

def code(x, y, z, t, a):
	return x + (y * (((t / (a - t)) + 1.0) - (z / (a - t))))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(Float64(Float64(t / Float64(a - t)) + 1.0) - Float64(z / Float64(a - t)))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y * (((t / (a - t)) + 1.0) - (z / (a - t))));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.9%

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

   1. associate-*l/ 83.2%

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

3. Simplified 83.2%

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

5. Taylor expanded in y around 0 96.8%

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

6. Final simplification 96.8%

   \[\leadsto x + y \cdot \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \]
7. Add Preprocessing

Alternative 2: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+138}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+75}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{t - z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+138)
   (+ x (/ z (/ t y)))
   (if (<= t 5.5e+75)
     (+ (+ x y) (* y (/ (- t z) (- a t))))
     (+ x (/ y (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+138) {
		tmp = x + (z / (t / y));
	} else if (t <= 5.5e+75) {
		tmp = (x + y) + (y * ((t - z) / (a - t)));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.8d+138)) then
        tmp = x + (z / (t / y))
    else if (t <= 5.5d+75) then
        tmp = (x + y) + (y * ((t - z) / (a - t)))
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+138) {
		tmp = x + (z / (t / y));
	} else if (t <= 5.5e+75) {
		tmp = (x + y) + (y * ((t - z) / (a - t)));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+138:
		tmp = x + (z / (t / y))
	elif t <= 5.5e+75:
		tmp = (x + y) + (y * ((t - z) / (a - t)))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+138)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	elseif (t <= 5.5e+75)
		tmp = Float64(Float64(x + y) + Float64(y * Float64(Float64(t - z) / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+138)
		tmp = x + (z / (t / y));
	elseif (t <= 5.5e+75)
		tmp = (x + y) + (y * ((t - z) / (a - t)));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+138], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+75], N[(N[(x + y), $MachinePrecision] + N[(y * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8000000000000001e138

   1. Initial program 52.7%

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

      1. associate-*l/ 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in y around 0 95.7%

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

   6. Taylor expanded in a around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. associate-/l* 91.8%

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

   8. Simplified 91.8%

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

      1. associate-/r/ 91.7%

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

   10. Applied egg-rr 91.7%

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

       1. *-commutative 91.7%

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

       2. clear-num 91.7%

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

       3. un-div-inv 91.8%

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

   12. Applied egg-rr 91.8%

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

   if -2.8000000000000001e138 < t < 5.5000000000000001e75

   1. Initial program 90.1%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   if 5.5000000000000001e75 < t

   1. Initial program 58.9%

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

      1. associate-*l/ 66.1%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in y around 0 97.7%

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

   6. Taylor expanded in a around 0 85.9%

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

      1. +-commutative 85.9%

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

      2. associate-/l* 95.3%

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

   8. Simplified 95.3%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+138}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+75}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{t - z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+138}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+55}:\\ \;\;\;\;\left(x + y\right) + \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.9e+138)
   (+ x (/ z (/ t y)))
   (if (<= t 9.2e+55)
     (+ (+ x y) (/ (- t z) (/ (- a t) y)))
     (+ x (/ y (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e+138) {
		tmp = x + (z / (t / y));
	} else if (t <= 9.2e+55) {
		tmp = (x + y) + ((t - z) / ((a - t) / y));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.9d+138)) then
        tmp = x + (z / (t / y))
    else if (t <= 9.2d+55) then
        tmp = (x + y) + ((t - z) / ((a - t) / y))
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e+138) {
		tmp = x + (z / (t / y));
	} else if (t <= 9.2e+55) {
		tmp = (x + y) + ((t - z) / ((a - t) / y));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.9e+138:
		tmp = x + (z / (t / y))
	elif t <= 9.2e+55:
		tmp = (x + y) + ((t - z) / ((a - t) / y))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.9e+138)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	elseif (t <= 9.2e+55)
		tmp = Float64(Float64(x + y) + Float64(Float64(t - z) / Float64(Float64(a - t) / y)));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.9e+138)
		tmp = x + (z / (t / y));
	elseif (t <= 9.2e+55)
		tmp = (x + y) + ((t - z) / ((a - t) / y));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.9e+138], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e+55], N[(N[(x + y), $MachinePrecision] + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.90000000000000006e138

   1. Initial program 52.7%

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

      1. associate-*l/ 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in y around 0 95.7%

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

   6. Taylor expanded in a around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. associate-/l* 91.8%

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

   8. Simplified 91.8%

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

      1. associate-/r/ 91.7%

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

   10. Applied egg-rr 91.7%

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

       1. *-commutative 91.7%

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

       2. clear-num 91.7%

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

       3. un-div-inv 91.8%

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

   12. Applied egg-rr 91.8%

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

   if -1.90000000000000006e138 < t < 9.1999999999999995e55

   1. Initial program 90.0%

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

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

      1. associate-/r/ 94.0%

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

   6. Applied egg-rr 94.0%

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

   if 9.1999999999999995e55 < t

   1. Initial program 60.8%

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

      1. associate-*l/ 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in y around 0 97.8%

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

   6. Taylor expanded in a around 0 86.6%

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

      1. +-commutative 86.6%

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

      2. associate-/l* 95.5%

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

   8. Simplified 95.5%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+138}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+55}:\\ \;\;\;\;\left(x + y\right) + \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+122}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+56}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1e+122)
   (+ x (/ z (/ t y)))
   (if (<= t 1.15e+56) (- (+ x y) (/ y (/ (- a t) z))) (+ x (/ y (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1e+122) {
		tmp = x + (z / (t / y));
	} else if (t <= 1.15e+56) {
		tmp = (x + y) - (y / ((a - t) / z));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1d+122)) then
        tmp = x + (z / (t / y))
    else if (t <= 1.15d+56) then
        tmp = (x + y) - (y / ((a - t) / z))
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1e+122) {
		tmp = x + (z / (t / y));
	} else if (t <= 1.15e+56) {
		tmp = (x + y) - (y / ((a - t) / z));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1e+122:
		tmp = x + (z / (t / y))
	elif t <= 1.15e+56:
		tmp = (x + y) - (y / ((a - t) / z))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1e+122)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	elseif (t <= 1.15e+56)
		tmp = Float64(Float64(x + y) - Float64(y / Float64(Float64(a - t) / z)));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1e+122)
		tmp = x + (z / (t / y));
	elseif (t <= 1.15e+56)
		tmp = (x + y) - (y / ((a - t) / z));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1e+122], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+56], N[(N[(x + y), $MachinePrecision] - N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.00000000000000001e122

   1. Initial program 55.4%

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

      1. associate-*l/ 66.0%

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

   3. Simplified 66.0%

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

   5. Taylor expanded in y around 0 96.1%

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

   6. Taylor expanded in a around 0 76.7%

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

      1. +-commutative 76.7%

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

      2. associate-/l* 90.7%

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

   8. Simplified 90.7%

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

      1. associate-/r/ 90.7%

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

   10. Applied egg-rr 90.7%

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

       1. *-commutative 90.7%

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

       2. clear-num 90.6%

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

       3. un-div-inv 90.7%

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

   12. Applied egg-rr 90.7%

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

   if -1.00000000000000001e122 < t < 1.15000000000000007e56

   1. Initial program 90.3%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around inf 90.3%

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

      1. associate-/l* 92.6%

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

   7. Simplified 92.6%

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

   if 1.15000000000000007e56 < t

   1. Initial program 60.8%

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

      1. associate-*l/ 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in y around 0 97.8%

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

   6. Taylor expanded in a around 0 86.6%

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

      1. +-commutative 86.6%

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

      2. associate-/l* 95.5%

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

   8. Simplified 95.5%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+122}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+56}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+31} \lor \neg \left(a \leq 1.05 \cdot 10^{-50}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.8e+31) (not (<= a 1.05e-50)))
   (- (+ x y) (/ y (/ a z)))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e+31) || !(a <= 1.05e-50)) {
		tmp = (x + y) - (y / (a / z));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.8d+31)) .or. (.not. (a <= 1.05d-50))) then
        tmp = (x + y) - (y / (a / z))
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e+31) || !(a <= 1.05e-50)) {
		tmp = (x + y) - (y / (a / z));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.8e+31) or not (a <= 1.05e-50):
		tmp = (x + y) - (y / (a / z))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.8e+31) || !(a <= 1.05e-50))
		tmp = Float64(Float64(x + y) - Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.8e+31) || ~((a <= 1.05e-50)))
		tmp = (x + y) - (y / (a / z));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.8e+31], N[Not[LessEqual[a, 1.05e-50]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.80000000000000017e31 or 1.05e-50 < a

   1. Initial program 84.0%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in t around 0 82.1%

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

      1. +-commutative 82.1%

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

      2. associate-/l* 87.9%

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

   7. Simplified 87.9%

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

   if -2.80000000000000017e31 < a < 1.05e-50

   1. Initial program 71.5%

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

      1. associate-*l/ 72.3%

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

   3. Simplified 72.3%

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

   5. Taylor expanded in y around 0 95.8%

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

   6. Taylor expanded in a around 0 84.3%

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

      1. +-commutative 84.3%

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

      2. associate-/l* 87.4%

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

   8. Simplified 87.4%

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

      1. associate-/r/ 89.6%

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

   10. Applied egg-rr 89.6%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+31} \lor \neg \left(a \leq 1.05 \cdot 10^{-50}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+20} \lor \neg \left(a \leq 7.9 \cdot 10^{+71}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7e+20) (not (<= a 7.9e+71))) (+ x y) (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7e+20) || !(a <= 7.9e+71)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-7d+20)) .or. (.not. (a <= 7.9d+71))) then
        tmp = x + y
    else
        tmp = x + ((y * z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7e+20) || !(a <= 7.9e+71)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7e+20) or not (a <= 7.9e+71):
		tmp = x + y
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7e+20) || !(a <= 7.9e+71))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7e+20) || ~((a <= 7.9e+71)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7e+20], N[Not[LessEqual[a, 7.9e+71]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7e20 or 7.90000000000000028e71 < a

   1. Initial program 83.0%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in a around inf 85.7%

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

      1. +-commutative 85.7%

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

   7. Simplified 85.7%

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

   if -7e20 < a < 7.90000000000000028e71

   1. Initial program 74.6%

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

      1. associate-*l/ 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in y around 0 95.4%

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

   6. Taylor expanded in a around 0 81.8%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+20} \lor \neg \left(a \leq 7.9 \cdot 10^{+71}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+29} \lor \neg \left(a \leq 4.6 \cdot 10^{+70}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.1e+29) (not (<= a 4.6e+70))) (+ x y) (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.1e+29) || !(a <= 4.6e+70)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.1d+29)) .or. (.not. (a <= 4.6d+70))) then
        tmp = x + y
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.1e+29) || !(a <= 4.6e+70)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.1e+29) or not (a <= 4.6e+70):
		tmp = x + y
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.1e+29) || !(a <= 4.6e+70))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.1e+29) || ~((a <= 4.6e+70)))
		tmp = x + y;
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.1e+29], N[Not[LessEqual[a, 4.6e+70]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.1000000000000002e29 or 4.59999999999999987e70 < a

   1. Initial program 83.7%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in a around inf 86.3%

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

      1. +-commutative 86.3%

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

   7. Simplified 86.3%

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

   if -2.1000000000000002e29 < a < 4.59999999999999987e70

   1. Initial program 74.3%

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

      1. associate-*l/ 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in y around 0 95.4%

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

   6. Taylor expanded in a around 0 81.4%

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

      1. +-commutative 81.4%

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

      2. associate-/l* 84.4%

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

   8. Simplified 84.4%

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

      1. associate-/r/ 85.7%

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

   10. Applied egg-rr 85.7%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+29} \lor \neg \left(a \leq 4.6 \cdot 10^{+70}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+55}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.9e+96) x (if (<= t 8.8e+55) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.9e+96) {
		tmp = x;
	} else if (t <= 8.8e+55) {
		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 <= (-3.9d+96)) then
        tmp = x
    else if (t <= 8.8d+55) 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 <= -3.9e+96) {
		tmp = x;
	} else if (t <= 8.8e+55) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.9e+96:
		tmp = x
	elif t <= 8.8e+55:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.9e+96)
		tmp = x;
	elseif (t <= 8.8e+55)
		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 <= -3.9e+96)
		tmp = x;
	elseif (t <= 8.8e+55)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.9e+96], x, If[LessEqual[t, 8.8e+55], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -3.9e96 or 8.80000000000000042e55 < t

   1. Initial program 58.1%

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

      1. associate-*l/ 66.8%

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

   3. Simplified 66.8%

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

   5. Taylor expanded in x around inf 75.3%

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

   if -3.9e96 < t < 8.80000000000000042e55

   1. Initial program 90.7%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in a around inf 72.6%

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

      1. +-commutative 72.6%

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

   7. Simplified 72.6%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+55}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.8% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{+191}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= y 6.2e+191) x y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 6.2e+191) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 6.2d+191) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 6.2e+191) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 6.2e+191:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 6.2e+191)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 6.2e+191)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 6.2e+191], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 6.19999999999999997e191

   1. Initial program 80.1%

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

      1. associate-*l/ 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in x around inf 62.9%

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

   if 6.19999999999999997e191 < y

   1. Initial program 45.1%

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

      1. associate-*l/ 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in t around 0 45.9%

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

      1. +-commutative 45.9%

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

      2. associate-/l* 51.7%

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

   7. Simplified 51.7%

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

   8. Taylor expanded in x around 0 45.9%

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

   9. Taylor expanded in z around 0 35.3%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{+191}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.3% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.9%

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

   1. associate-*l/ 83.2%

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

3. Simplified 83.2%

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

5. Taylor expanded in x around inf 59.5%

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

6. Final simplification 59.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 87.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (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) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (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 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024010 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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