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

Percentage Accurate: 85.1% → 98.2%

Time: 8.9s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.4%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

   1. clear-num 97.6%

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

   2. un-div-inv 98.0%

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

6. Applied egg-rr 98.0%

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

7. Final simplification 98.0%

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

Alternative 2: 83.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+201}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+119}:\\ \;\;\;\;x - \frac{y}{\frac{t - a}{z}}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+86}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+43}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+134}:\\ \;\;\;\;x - z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.1e+201)
   (+ x y)
   (if (<= t -4.2e+119)
     (- x (/ y (/ (- t a) z)))
     (if (<= t -5.5e+86)
       (+ x y)
       (if (<= t -1.25e+43)
         (- x (* y (/ (- t z) a)))
         (if (<= t 5.3e+134) (- x (* z (/ y (- t a)))) (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.1e+201) {
		tmp = x + y;
	} else if (t <= -4.2e+119) {
		tmp = x - (y / ((t - a) / z));
	} else if (t <= -5.5e+86) {
		tmp = x + y;
	} else if (t <= -1.25e+43) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= 5.3e+134) {
		tmp = x - (z * (y / (t - a)));
	} 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 <= (-1.1d+201)) then
        tmp = x + y
    else if (t <= (-4.2d+119)) then
        tmp = x - (y / ((t - a) / z))
    else if (t <= (-5.5d+86)) then
        tmp = x + y
    else if (t <= (-1.25d+43)) then
        tmp = x - (y * ((t - z) / a))
    else if (t <= 5.3d+134) then
        tmp = x - (z * (y / (t - a)))
    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 <= -1.1e+201) {
		tmp = x + y;
	} else if (t <= -4.2e+119) {
		tmp = x - (y / ((t - a) / z));
	} else if (t <= -5.5e+86) {
		tmp = x + y;
	} else if (t <= -1.25e+43) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= 5.3e+134) {
		tmp = x - (z * (y / (t - a)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.1e+201:
		tmp = x + y
	elif t <= -4.2e+119:
		tmp = x - (y / ((t - a) / z))
	elif t <= -5.5e+86:
		tmp = x + y
	elif t <= -1.25e+43:
		tmp = x - (y * ((t - z) / a))
	elif t <= 5.3e+134:
		tmp = x - (z * (y / (t - a)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.1e+201)
		tmp = Float64(x + y);
	elseif (t <= -4.2e+119)
		tmp = Float64(x - Float64(y / Float64(Float64(t - a) / z)));
	elseif (t <= -5.5e+86)
		tmp = Float64(x + y);
	elseif (t <= -1.25e+43)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / a)));
	elseif (t <= 5.3e+134)
		tmp = Float64(x - Float64(z * Float64(y / Float64(t - a))));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.1e+201)
		tmp = x + y;
	elseif (t <= -4.2e+119)
		tmp = x - (y / ((t - a) / z));
	elseif (t <= -5.5e+86)
		tmp = x + y;
	elseif (t <= -1.25e+43)
		tmp = x - (y * ((t - z) / a));
	elseif (t <= 5.3e+134)
		tmp = x - (z * (y / (t - a)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.1e+201], N[(x + y), $MachinePrecision], If[LessEqual[t, -4.2e+119], N[(x - N[(y / N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.5e+86], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.25e+43], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.3e+134], N[(x - N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.1e201 or -4.19999999999999966e119 < t < -5.5000000000000002e86 or 5.3000000000000002e134 < t

   1. Initial program 67.2%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 86.6%

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

      1. +-commutative 86.6%

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

   7. Simplified 86.6%

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

   if -1.1e201 < t < -4.19999999999999966e119

   1. Initial program 72.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around inf 73.8%

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

   if -5.5000000000000002e86 < t < -1.2500000000000001e43

   1. Initial program 91.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around inf 67.7%

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

      1. +-commutative 67.7%

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

      2. associate-/l* 75.7%

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

   7. Simplified 75.7%

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

   if -1.2500000000000001e43 < t < 5.3000000000000002e134

   1. Initial program 93.6%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in z around inf 86.0%

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

      1. *-commutative 86.0%

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

      2. associate-/l* 90.3%

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

   7. Applied egg-rr 90.3%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+201}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+119}:\\ \;\;\;\;x - \frac{y}{\frac{t - a}{z}}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+86}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+43}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+134}:\\ \;\;\;\;x - z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+179}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{+120}:\\ \;\;\;\;x - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+86} \lor \neg \left(t \leq 6.2 \cdot 10^{-127}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.8e+179)
   (+ x y)
   (if (<= t -1.22e+120)
     (- x (/ z (/ t y)))
     (if (or (<= t -8e+86) (not (<= t 6.2e-127)))
       (+ x y)
       (+ x (* z (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.8e+179) {
		tmp = x + y;
	} else if (t <= -1.22e+120) {
		tmp = x - (z / (t / y));
	} else if ((t <= -8e+86) || !(t <= 6.2e-127)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7.8d+179)) then
        tmp = x + y
    else if (t <= (-1.22d+120)) then
        tmp = x - (z / (t / y))
    else if ((t <= (-8d+86)) .or. (.not. (t <= 6.2d-127))) then
        tmp = x + y
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.8e+179) {
		tmp = x + y;
	} else if (t <= -1.22e+120) {
		tmp = x - (z / (t / y));
	} else if ((t <= -8e+86) || !(t <= 6.2e-127)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.8e+179:
		tmp = x + y
	elif t <= -1.22e+120:
		tmp = x - (z / (t / y))
	elif (t <= -8e+86) or not (t <= 6.2e-127):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.8e+179)
		tmp = Float64(x + y);
	elseif (t <= -1.22e+120)
		tmp = Float64(x - Float64(z / Float64(t / y)));
	elseif ((t <= -8e+86) || !(t <= 6.2e-127))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.8e+179)
		tmp = x + y;
	elseif (t <= -1.22e+120)
		tmp = x - (z / (t / y));
	elseif ((t <= -8e+86) || ~((t <= 6.2e-127)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.8e+179], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.22e+120], N[(x - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -8e+86], N[Not[LessEqual[t, 6.2e-127]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.79999999999999947e179 or -1.22e120 < t < -8.0000000000000001e86 or 6.2e-127 < t

   1. Initial program 74.5%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around inf 76.1%

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

      1. +-commutative 76.1%

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

   7. Simplified 76.1%

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

   if -7.79999999999999947e179 < t < -1.22e120

   1. Initial program 70.9%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 71.1%

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

      1. *-commutative 71.1%

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

      2. associate-/l* 79.6%

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

   7. Applied egg-rr 79.6%

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

   8. Taylor expanded in a around 0 79.6%

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

      1. associate-*r/ 79.6%

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

      2. neg-mul-1 79.6%

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

   10. Simplified 79.6%

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

       1. distribute-frac-neg 79.6%

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

       2. distribute-rgt-neg-out 79.6%

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

       3. div-inv 79.6%

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

       4. add-sqr-sqrt 48.6%

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

       5. sqrt-unprod 63.4%

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

       6. sqr-neg 63.4%

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

       7. sqrt-unprod 23.5%

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

       8. add-sqr-sqrt 55.1%

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

       9. div-inv 55.1%

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

       10. clear-num 55.1%

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

       11. un-div-inv 55.1%

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

       12. add-sqr-sqrt 23.5%

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

       13. sqrt-unprod 63.4%

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

       14. sqr-neg 63.4%

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

       15. sqrt-unprod 48.6%

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

       16. add-sqr-sqrt 79.6%

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

   12. Applied egg-rr 79.6%

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

   if -8.0000000000000001e86 < t < 6.2e-127

   1. Initial program 95.9%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t around 0 77.4%

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

      1. *-commutative 77.4%

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

      2. associate-/l* 79.7%

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

   7. Applied egg-rr 79.7%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+179}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{+120}:\\ \;\;\;\;x - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+86} \lor \neg \left(t \leq 6.2 \cdot 10^{-127}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+179}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+119}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{+86} \lor \neg \left(t \leq 6.2 \cdot 10^{-127}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7e+179)
   (+ x y)
   (if (<= t -7.2e+119)
     (- x (* y (/ z t)))
     (if (or (<= t -6.6e+86) (not (<= t 6.2e-127)))
       (+ x y)
       (+ x (* z (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+179) {
		tmp = x + y;
	} else if (t <= -7.2e+119) {
		tmp = x - (y * (z / t));
	} else if ((t <= -6.6e+86) || !(t <= 6.2e-127)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7d+179)) then
        tmp = x + y
    else if (t <= (-7.2d+119)) then
        tmp = x - (y * (z / t))
    else if ((t <= (-6.6d+86)) .or. (.not. (t <= 6.2d-127))) then
        tmp = x + y
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+179) {
		tmp = x + y;
	} else if (t <= -7.2e+119) {
		tmp = x - (y * (z / t));
	} else if ((t <= -6.6e+86) || !(t <= 6.2e-127)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7e+179:
		tmp = x + y
	elif t <= -7.2e+119:
		tmp = x - (y * (z / t))
	elif (t <= -6.6e+86) or not (t <= 6.2e-127):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7e+179)
		tmp = Float64(x + y);
	elseif (t <= -7.2e+119)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif ((t <= -6.6e+86) || !(t <= 6.2e-127))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7e+179)
		tmp = x + y;
	elseif (t <= -7.2e+119)
		tmp = x - (y * (z / t));
	elseif ((t <= -6.6e+86) || ~((t <= 6.2e-127)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7e+179], N[(x + y), $MachinePrecision], If[LessEqual[t, -7.2e+119], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -6.6e+86], N[Not[LessEqual[t, 6.2e-127]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.0000000000000003e179 or -7.20000000000000003e119 < t < -6.5999999999999998e86 or 6.2e-127 < t

   1. Initial program 74.5%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around inf 76.1%

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

      1. +-commutative 76.1%

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

   7. Simplified 76.1%

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

   if -7.0000000000000003e179 < t < -7.20000000000000003e119

   1. Initial program 70.9%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 71.1%

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

   6. Taylor expanded in a around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. associate-/l* 79.6%

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

      3. distribute-rgt-neg-in 79.6%

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

      4. distribute-neg-frac2 79.6%

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

   8. Simplified 79.6%

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

   if -6.5999999999999998e86 < t < 6.2e-127

   1. Initial program 95.9%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t around 0 77.4%

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

      1. *-commutative 77.4%

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

      2. associate-/l* 79.7%

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

   7. Applied egg-rr 79.7%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+179}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+119}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{+86} \lor \neg \left(t \leq 6.2 \cdot 10^{-127}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t - a}\\ t_2 := x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+146}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+55}:\\ \;\;\;\;x + t \cdot t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+135}:\\ \;\;\;\;x - z \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- t a))) (t_2 (- x (* y (+ (/ z t) -1.0)))))
   (if (<= t -7.5e+146)
     t_2
     (if (<= t -2.35e+55)
       (+ x (* t t_1))
       (if (<= t 4.2e+135) (- x (* z t_1)) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (t - a);
	double t_2 = x - (y * ((z / t) + -1.0));
	double tmp;
	if (t <= -7.5e+146) {
		tmp = t_2;
	} else if (t <= -2.35e+55) {
		tmp = x + (t * t_1);
	} else if (t <= 4.2e+135) {
		tmp = x - (z * t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y / (t - a)
    t_2 = x - (y * ((z / t) + (-1.0d0)))
    if (t <= (-7.5d+146)) then
        tmp = t_2
    else if (t <= (-2.35d+55)) then
        tmp = x + (t * t_1)
    else if (t <= 4.2d+135) then
        tmp = x - (z * t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (t - a);
	double t_2 = x - (y * ((z / t) + -1.0));
	double tmp;
	if (t <= -7.5e+146) {
		tmp = t_2;
	} else if (t <= -2.35e+55) {
		tmp = x + (t * t_1);
	} else if (t <= 4.2e+135) {
		tmp = x - (z * t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (t - a)
	t_2 = x - (y * ((z / t) + -1.0))
	tmp = 0
	if t <= -7.5e+146:
		tmp = t_2
	elif t <= -2.35e+55:
		tmp = x + (t * t_1)
	elif t <= 4.2e+135:
		tmp = x - (z * t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(t - a))
	t_2 = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)))
	tmp = 0.0
	if (t <= -7.5e+146)
		tmp = t_2;
	elseif (t <= -2.35e+55)
		tmp = Float64(x + Float64(t * t_1));
	elseif (t <= 4.2e+135)
		tmp = Float64(x - Float64(z * t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (t - a);
	t_2 = x - (y * ((z / t) + -1.0));
	tmp = 0.0;
	if (t <= -7.5e+146)
		tmp = t_2;
	elseif (t <= -2.35e+55)
		tmp = x + (t * t_1);
	elseif (t <= 4.2e+135)
		tmp = x - (z * t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+146], t$95$2, If[LessEqual[t, -2.35e+55], N[(x + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+135], N[(x - N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.49999999999999983e146 or 4.20000000000000019e135 < t

   1. Initial program 64.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 63.5%

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

      1. mul-1-neg 63.5%

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

      2. unsub-neg 63.5%

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

      3. associate-/l* 93.9%

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

      4. div-sub 93.9%

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

      5. sub-neg 93.9%

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

      6. *-inverses 93.9%

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

      7. metadata-eval 93.9%

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

   7. Simplified 93.9%

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

   if -7.49999999999999983e146 < t < -2.35e55

   1. Initial program 90.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 86.2%

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

      1. mul-1-neg 86.2%

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

      2. unsub-neg 86.2%

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

      3. associate-/l* 95.4%

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

   7. Simplified 95.4%

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

   if -2.35e55 < t < 4.20000000000000019e135

   1. Initial program 93.3%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around inf 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-/l* 89.4%

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

   7. Applied egg-rr 89.4%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+146}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+55}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+135}:\\ \;\;\;\;x - z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+201} \lor \neg \left(t \leq 3.8 \cdot 10^{+133}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.35e+201) (not (<= t 3.8e+133)))
   (+ x y)
   (- x (* z (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.35e+201) || !(t <= 3.8e+133)) {
		tmp = x + y;
	} else {
		tmp = x - (z * (y / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.35d+201)) .or. (.not. (t <= 3.8d+133))) then
        tmp = x + y
    else
        tmp = x - (z * (y / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.35e+201) || !(t <= 3.8e+133)) {
		tmp = x + y;
	} else {
		tmp = x - (z * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.35e+201) or not (t <= 3.8e+133):
		tmp = x + y
	else:
		tmp = x - (z * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.35e+201) || !(t <= 3.8e+133))
		tmp = Float64(x + y);
	else
		tmp = Float64(x - Float64(z * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.35e+201) || ~((t <= 3.8e+133)))
		tmp = x + y;
	else
		tmp = x - (z * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.35e+201], N[Not[LessEqual[t, 3.8e+133]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x - N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35e201 or 3.8000000000000002e133 < t

   1. Initial program 63.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 87.6%

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

      1. +-commutative 87.6%

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

   7. Simplified 87.6%

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

   if -1.35e201 < t < 3.8000000000000002e133

   1. Initial program 91.1%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around inf 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-/l* 84.6%

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

   7. Applied egg-rr 84.6%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+201} \lor \neg \left(t \leq 3.8 \cdot 10^{+133}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t - a}\\ \mathbf{if}\;t \leq -2.06 \cdot 10^{+55} \lor \neg \left(t \leq 5.1 \cdot 10^{+119}\right):\\ \;\;\;\;x + t \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- t a))))
   (if (or (<= t -2.06e+55) (not (<= t 5.1e+119)))
     (+ x (* t t_1))
     (- x (* z t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (t - a);
	double tmp;
	if ((t <= -2.06e+55) || !(t <= 5.1e+119)) {
		tmp = x + (t * t_1);
	} else {
		tmp = x - (z * t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (t - a)
    if ((t <= (-2.06d+55)) .or. (.not. (t <= 5.1d+119))) then
        tmp = x + (t * t_1)
    else
        tmp = x - (z * 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 / (t - a);
	double tmp;
	if ((t <= -2.06e+55) || !(t <= 5.1e+119)) {
		tmp = x + (t * t_1);
	} else {
		tmp = x - (z * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (t - a)
	tmp = 0
	if (t <= -2.06e+55) or not (t <= 5.1e+119):
		tmp = x + (t * t_1)
	else:
		tmp = x - (z * t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(t - a))
	tmp = 0.0
	if ((t <= -2.06e+55) || !(t <= 5.1e+119))
		tmp = Float64(x + Float64(t * t_1));
	else
		tmp = Float64(x - Float64(z * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (t - a);
	tmp = 0.0;
	if ((t <= -2.06e+55) || ~((t <= 5.1e+119)))
		tmp = x + (t * t_1);
	else
		tmp = x - (z * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -2.06e+55], N[Not[LessEqual[t, 5.1e+119]], $MachinePrecision]], N[(x + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.06e55 or 5.09999999999999984e119 < t

   1. Initial program 71.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 66.3%

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

      1. mul-1-neg 66.3%

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

      2. unsub-neg 66.3%

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

      3. associate-/l* 85.3%

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

   7. Simplified 85.3%

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

   if -2.06e55 < t < 5.09999999999999984e119

   1. Initial program 93.1%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in z around inf 85.6%

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

      1. *-commutative 85.6%

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

      2. associate-/l* 89.8%

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

   7. Applied egg-rr 89.8%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.06 \cdot 10^{+55} \lor \neg \left(t \leq 5.1 \cdot 10^{+119}\right):\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+86} \lor \neg \left(t \leq 6.2 \cdot 10^{-127}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.2e+86) (not (<= t 6.2e-127))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.2e+86) || !(t <= 6.2e-127)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-6.2d+86)) .or. (.not. (t <= 6.2d-127))) then
        tmp = x + y
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.2e+86) || !(t <= 6.2e-127)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.2e+86) or not (t <= 6.2e-127):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.2e+86) || !(t <= 6.2e-127))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.2e+86) || ~((t <= 6.2e-127)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.2e+86], N[Not[LessEqual[t, 6.2e-127]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.2000000000000004e86 or 6.2e-127 < t

   1. Initial program 74.1%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around inf 72.9%

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

      1. +-commutative 72.9%

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

   7. Simplified 72.9%

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

   if -6.2000000000000004e86 < t < 6.2e-127

   1. Initial program 95.9%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t around 0 77.4%

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

      1. *-commutative 77.4%

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

      2. associate-/l* 79.7%

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

   7. Applied egg-rr 79.7%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+86} \lor \neg \left(t \leq 6.2 \cdot 10^{-127}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+183}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+134}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.1e+183) x (if (<= a 1.35e+134) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.1e+183) {
		tmp = x;
	} else if (a <= 1.35e+134) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.1d+183)) then
        tmp = x
    else if (a <= 1.35d+134) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.1e+183) {
		tmp = x;
	} else if (a <= 1.35e+134) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.1e+183:
		tmp = x
	elif a <= 1.35e+134:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.1e+183)
		tmp = x;
	elseif (a <= 1.35e+134)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.1e+183)
		tmp = x;
	elseif (a <= 1.35e+134)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.1e+183], x, If[LessEqual[a, 1.35e+134], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.10000000000000015e183 or 1.35e134 < a

   1. Initial program 82.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 70.1%

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

   if -4.10000000000000015e183 < a < 1.35e134

   1. Initial program 85.4%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in t around inf 63.4%

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

      1. +-commutative 63.4%

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

   7. Simplified 63.4%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+183}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+134}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.4%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

5. Final simplification 97.7%

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

Alternative 11: 50.9% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.4%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

5. Taylor expanded in x around inf 49.4%

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

6. Final simplification 49.4%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024079 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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