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

Percentage Accurate: 85.4% → 98.0%

Time: 11.4s

Alternatives: 13

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: 85.4% 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: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (((z - t) / (a - t)) * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.1%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

   1. clear-num 97.6%

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

   2. associate-/r/ 97.6%

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

   3. clear-num 98.1%

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

6. Applied egg-rr 98.1%

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

7. Final simplification 98.1%

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

Alternative 2: 76.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+91}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-54}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 22000000:\\ \;\;\;\;\frac{z - t}{a - t} \cdot y\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+35}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.5e+91)
   (+ x y)
   (if (<= t 3.9e-54)
     (+ x (* z (/ y a)))
     (if (<= t 22000000.0)
       (* (/ (- z t) (- a t)) y)
       (if (<= t 4.9e+35) (- x (/ t (/ a y))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.5e+91) {
		tmp = x + y;
	} else if (t <= 3.9e-54) {
		tmp = x + (z * (y / a));
	} else if (t <= 22000000.0) {
		tmp = ((z - t) / (a - t)) * y;
	} else if (t <= 4.9e+35) {
		tmp = x - (t / (a / y));
	} 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 <= (-7.5d+91)) then
        tmp = x + y
    else if (t <= 3.9d-54) then
        tmp = x + (z * (y / a))
    else if (t <= 22000000.0d0) then
        tmp = ((z - t) / (a - t)) * y
    else if (t <= 4.9d+35) then
        tmp = x - (t / (a / y))
    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 <= -7.5e+91) {
		tmp = x + y;
	} else if (t <= 3.9e-54) {
		tmp = x + (z * (y / a));
	} else if (t <= 22000000.0) {
		tmp = ((z - t) / (a - t)) * y;
	} else if (t <= 4.9e+35) {
		tmp = x - (t / (a / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.5e+91:
		tmp = x + y
	elif t <= 3.9e-54:
		tmp = x + (z * (y / a))
	elif t <= 22000000.0:
		tmp = ((z - t) / (a - t)) * y
	elif t <= 4.9e+35:
		tmp = x - (t / (a / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.5e+91)
		tmp = Float64(x + y);
	elseif (t <= 3.9e-54)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (t <= 22000000.0)
		tmp = Float64(Float64(Float64(z - t) / Float64(a - t)) * y);
	elseif (t <= 4.9e+35)
		tmp = Float64(x - Float64(t / Float64(a / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.5e+91)
		tmp = x + y;
	elseif (t <= 3.9e-54)
		tmp = x + (z * (y / a));
	elseif (t <= 22000000.0)
		tmp = ((z - t) / (a - t)) * y;
	elseif (t <= 4.9e+35)
		tmp = x - (t / (a / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.5e+91], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.9e-54], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 22000000.0], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 4.9e+35], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.50000000000000033e91 or 4.90000000000000025e35 < t

   1. Initial program 69.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 85.3%

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

      1. +-commutative 85.3%

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

   7. Simplified 85.3%

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

   if -7.50000000000000033e91 < t < 3.9e-54

   1. Initial program 97.2%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. associate-/l* 77.4%

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

   7. Simplified 77.4%

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

      1. associate-/r/ 80.1%

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

   9. Applied egg-rr 80.1%

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

   if 3.9e-54 < t < 2.2e7

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 83.5%

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

      1. div-sub 83.5%

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

   9. Simplified 83.5%

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

   if 2.2e7 < t < 4.90000000000000025e35

   1. Initial program 87.1%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 76.6%

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

      1. +-commutative 76.6%

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

   7. Simplified 76.6%

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

   8. Taylor expanded in z around 0 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

      3. associate-/l* 85.7%

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

   10. Simplified 85.7%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+91}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-54}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 22000000:\\ \;\;\;\;\frac{z - t}{a - t} \cdot y\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+35}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+118} \lor \neg \left(t \leq 6 \cdot 10^{+18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e+118) (not (<= t 6e+18)))
   (+ x y)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+118) || !(t <= 6e+18)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.05d+118)) .or. (.not. (t <= 6d+18))) then
        tmp = x + y
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+118) || !(t <= 6e+18)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e+118) or not (t <= 6e+18):
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e+118) || !(t <= 6e+18))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.05e+118) || ~((t <= 6e+18)))
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e+118], N[Not[LessEqual[t, 6e+18]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e118 or 6e18 < t

   1. Initial program 68.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   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 -1.05e118 < t < 6e18

   1. Initial program 97.5%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around inf 88.0%

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

      1. associate-*l/ 89.8%

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

      2. *-commutative 89.8%

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

   7. Simplified 89.8%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+118} \lor \neg \left(t \leq 6 \cdot 10^{+18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+118} \lor \neg \left(t \leq 4.25 \cdot 10^{-19}\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.1e+118) (not (<= t 4.25e-19)))
   (- x (/ y (/ t (- z t))))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.1e+118) || !(t <= 4.25e-19)) {
		tmp = x - (y / (t / (z - t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.1d+118)) .or. (.not. (t <= 4.25d-19))) then
        tmp = x - (y / (t / (z - t)))
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.1e+118) || !(t <= 4.25e-19)) {
		tmp = x - (y / (t / (z - t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.1e+118) or not (t <= 4.25e-19):
		tmp = x - (y / (t / (z - t)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.1e+118) || !(t <= 4.25e-19))
		tmp = Float64(x - Float64(y / Float64(t / Float64(z - t))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.1e+118) || ~((t <= 4.25e-19)))
		tmp = x - (y / (t / (z - t)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.1e+118], N[Not[LessEqual[t, 4.25e-19]], $MachinePrecision]], N[(x - N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.09999999999999993e118 or 4.25000000000000002e-19 < t

   1. Initial program 72.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. unsub-neg 63.9%

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

      3. associate-/l* 89.0%

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

   7. Simplified 89.0%

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

   if -1.09999999999999993e118 < t < 4.25000000000000002e-19

   1. Initial program 97.3%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in z around inf 89.6%

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

      1. associate-*l/ 92.2%

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

      2. *-commutative 92.2%

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

   7. Simplified 92.2%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+118} \lor \neg \left(t \leq 4.25 \cdot 10^{-19}\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+118}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+112)
   x
   (if (<= a -1.9e+77) (* y (/ z a)) (if (<= a 1.9e+118) (+ x y) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+112) {
		tmp = x;
	} else if (a <= -1.9e+77) {
		tmp = y * (z / a);
	} else if (a <= 1.9e+118) {
		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 <= (-9.5d+112)) then
        tmp = x
    else if (a <= (-1.9d+77)) then
        tmp = y * (z / a)
    else if (a <= 1.9d+118) 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 <= -9.5e+112) {
		tmp = x;
	} else if (a <= -1.9e+77) {
		tmp = y * (z / a);
	} else if (a <= 1.9e+118) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+112:
		tmp = x
	elif a <= -1.9e+77:
		tmp = y * (z / a)
	elif a <= 1.9e+118:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+112)
		tmp = x;
	elseif (a <= -1.9e+77)
		tmp = Float64(y * Float64(z / a));
	elseif (a <= 1.9e+118)
		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 <= -9.5e+112)
		tmp = x;
	elseif (a <= -1.9e+77)
		tmp = y * (z / a);
	elseif (a <= 1.9e+118)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+112], x, If[LessEqual[a, -1.9e+77], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e+118], N[(x + y), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.5000000000000008e112 or 1.90000000000000008e118 < a

   1. Initial program 84.2%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in x around inf 69.5%

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

   if -9.5000000000000008e112 < a < -1.9000000000000001e77

   1. Initial program 99.3%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.6%

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

      3. clear-num 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 99.8%

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

      1. div-sub 99.8%

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

   9. Simplified 99.8%

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

   10. Taylor expanded in t around 0 85.5%

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

   if -1.9000000000000001e77 < a < 1.90000000000000008e118

   1. Initial program 87.7%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around inf 63.9%

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

      1. +-commutative 63.9%

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

   7. Simplified 63.9%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+118}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+219} \lor \neg \left(z \leq 2.1 \cdot 10^{+83}\right):\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e+219) (not (<= z 2.1e+83))) (* y (/ z (- a t))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+219) || !(z <= 2.1e+83)) {
		tmp = y * (z / (a - t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4d+219)) .or. (.not. (z <= 2.1d+83))) then
        tmp = y * (z / (a - t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+219) || !(z <= 2.1e+83)) {
		tmp = y * (z / (a - t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e+219) or not (z <= 2.1e+83):
		tmp = y * (z / (a - t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e+219) || !(z <= 2.1e+83))
		tmp = Float64(y * Float64(z / Float64(a - t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4e+219) || ~((z <= 2.1e+83)))
		tmp = y * (z / (a - t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e+219], N[Not[LessEqual[z, 2.1e+83]], $MachinePrecision]], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999986e219 or 2.10000000000000002e83 < z

   1. Initial program 91.7%

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

      1. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

      1. clear-num 91.6%

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

      2. associate-/r/ 91.6%

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

      3. clear-num 91.6%

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

   6. Applied egg-rr 91.6%

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

   7. Taylor expanded in y around inf 70.8%

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

      1. div-sub 70.8%

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

   9. Simplified 70.8%

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

   10. Taylor expanded in z around inf 65.9%

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

   if -3.99999999999999986e219 < z < 2.10000000000000002e83

   1. Initial program 85.7%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in t around inf 68.9%

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

      1. +-commutative 68.9%

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

   7. Simplified 68.9%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+219} \lor \neg \left(z \leq 2.1 \cdot 10^{+83}\right):\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+91} \lor \neg \left(t \leq 3.8 \cdot 10^{+18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.5e+91) (not (<= t 3.8e+18))) (+ x y) (+ x (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.5e+91) || !(t <= 3.8e+18)) {
		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 <= (-7.5d+91)) .or. (.not. (t <= 3.8d+18))) 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 <= -7.5e+91) || !(t <= 3.8e+18)) {
		tmp = x + y;
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.5e+91) or not (t <= 3.8e+18):
		tmp = x + y
	else:
		tmp = x + ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.5e+91) || !(t <= 3.8e+18))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.5e+91) || ~((t <= 3.8e+18)))
		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, -7.5e+91], N[Not[LessEqual[t, 3.8e+18]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.50000000000000033e91 or 3.8e18 < t

   1. Initial program 69.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 83.9%

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

      1. +-commutative 83.9%

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

   7. Simplified 83.9%

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

   if -7.50000000000000033e91 < t < 3.8e18

   1. Initial program 97.5%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around 0 76.3%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+91} \lor \neg \left(t \leq 3.8 \cdot 10^{+18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+93} \lor \neg \left(t \leq 3.9 \cdot 10^{+18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.45e+93) (not (<= t 3.9e+18))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.45e+93) || !(t <= 3.9e+18)) {
		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 <= (-1.45d+93)) .or. (.not. (t <= 3.9d+18))) 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 <= -1.45e+93) || !(t <= 3.9e+18)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.45e+93) or not (t <= 3.9e+18):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.45e+93) || !(t <= 3.9e+18))
		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 <= -1.45e+93) || ~((t <= 3.9e+18)))
		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, -1.45e+93], N[Not[LessEqual[t, 3.9e+18]], $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 < -1.4499999999999999e93 or 3.9e18 < t

   1. Initial program 69.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 83.9%

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

      1. +-commutative 83.9%

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

   7. Simplified 83.9%

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

   if -1.4499999999999999e93 < t < 3.9e18

   1. Initial program 97.5%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. associate-/l* 75.9%

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

   7. Simplified 75.9%

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

      1. associate-/r/ 77.8%

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

   9. Applied egg-rr 77.8%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+93} \lor \neg \left(t \leq 3.9 \cdot 10^{+18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+219}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+138}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7e+219)
   (* (/ z t) (- y))
   (if (<= z 2.8e+138) (+ x y) (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+219) {
		tmp = (z / t) * -y;
	} else if (z <= 2.8e+138) {
		tmp = x + y;
	} else {
		tmp = (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 (z <= (-7d+219)) then
        tmp = (z / t) * -y
    else if (z <= 2.8d+138) then
        tmp = x + y
    else
        tmp = (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 (z <= -7e+219) {
		tmp = (z / t) * -y;
	} else if (z <= 2.8e+138) {
		tmp = x + y;
	} else {
		tmp = (z * y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7e+219:
		tmp = (z / t) * -y
	elif z <= 2.8e+138:
		tmp = x + y
	else:
		tmp = (z * y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7e+219)
		tmp = Float64(Float64(z / t) * Float64(-y));
	elseif (z <= 2.8e+138)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(z * y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7e+219)
		tmp = (z / t) * -y;
	elseif (z <= 2.8e+138)
		tmp = x + y;
	else
		tmp = (z * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7e+219], N[(N[(z / t), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[z, 2.8e+138], N[(x + y), $MachinePrecision], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.0000000000000002e219

   1. Initial program 89.5%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

      1. clear-num 89.3%

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

      2. associate-/r/ 89.4%

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

      3. clear-num 89.4%

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

   6. Applied egg-rr 89.4%

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

   7. Taylor expanded in y around inf 72.7%

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

      1. div-sub 72.7%

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

   9. Simplified 72.7%

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

   10. Taylor expanded in a around 0 61.8%

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

       1. associate-*r/ 61.8%

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

       2. neg-mul-1 61.8%

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

   12. Simplified 61.8%

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

   13. Taylor expanded in z around inf 56.6%

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

       1. associate-*r/ 56.6%

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

       2. neg-mul-1 56.6%

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

   15. Simplified 56.6%

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

   if -7.0000000000000002e219 < z < 2.8000000000000001e138

   1. Initial program 86.4%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in t around inf 67.6%

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

      1. +-commutative 67.6%

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

   7. Simplified 67.6%

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

   if 2.8000000000000001e138 < z

   1. Initial program 90.3%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

      1. clear-num 90.1%

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

      2. associate-/r/ 90.1%

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

      3. clear-num 90.1%

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

   6. Applied egg-rr 90.1%

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

   7. Taylor expanded in y around inf 72.9%

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

      1. div-sub 72.9%

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

   9. Simplified 72.9%

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

   10. Taylor expanded in t around 0 45.5%

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

       1. *-commutative 45.5%

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

       2. associate-*l/ 53.9%

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

   12. Applied egg-rr 53.9%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+219}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+138}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 10^{+118}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2e+25) x (if (<= a 1e+118) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e+25) {
		tmp = x;
	} else if (a <= 1e+118) {
		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 <= (-2d+25)) then
        tmp = x
    else if (a <= 1d+118) 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 <= -2e+25) {
		tmp = x;
	} else if (a <= 1e+118) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2e+25:
		tmp = x
	elif a <= 1e+118:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2e+25)
		tmp = x;
	elseif (a <= 1e+118)
		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 <= -2e+25)
		tmp = x;
	elseif (a <= 1e+118)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2e+25], x, If[LessEqual[a, 1e+118], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.00000000000000018e25 or 9.99999999999999967e117 < a

   1. Initial program 86.3%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in x around inf 65.5%

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

   if -2.00000000000000018e25 < a < 9.99999999999999967e117

   1. Initial program 87.5%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in t around inf 63.3%

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

      1. +-commutative 63.3%

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

   7. Simplified 63.3%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 10^{+118}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+100}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 10^{+150}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -9.2e+100) y (if (<= y 1e+150) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9.2e+100) {
		tmp = y;
	} else if (y <= 1e+150) {
		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 <= (-9.2d+100)) then
        tmp = y
    else if (y <= 1d+150) 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 <= -9.2e+100) {
		tmp = y;
	} else if (y <= 1e+150) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -9.2e+100:
		tmp = y
	elif y <= 1e+150:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -9.2e+100)
		tmp = y;
	elseif (y <= 1e+150)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -9.2e+100)
		tmp = y;
	elseif (y <= 1e+150)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -9.2e+100], y, If[LessEqual[y, 1e+150], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -9.1999999999999996e100 or 9.99999999999999981e149 < y

   1. Initial program 67.6%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

      1. clear-num 98.5%

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

      2. associate-/r/ 98.6%

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

      3. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 85.5%

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

      1. div-sub 85.5%

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

   9. Simplified 85.5%

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

   10. Taylor expanded in t around inf 34.9%

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

   if -9.1999999999999996e100 < y < 9.99999999999999981e149

   1. Initial program 95.6%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in x around inf 63.7%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+100}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 10^{+150}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 6.5 \cdot 10^{+138}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 6.5e+138) (+ x y) (/ (* z y) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 6.5e+138) {
		tmp = x + y;
	} else {
		tmp = (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 (z <= 6.5d+138) then
        tmp = x + y
    else
        tmp = (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 (z <= 6.5e+138) {
		tmp = x + y;
	} else {
		tmp = (z * y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 6.5e+138:
		tmp = x + y
	else:
		tmp = (z * y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 6.5e+138)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(z * y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 6.5e+138)
		tmp = x + y;
	else
		tmp = (z * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 6.5e+138], N[(x + y), $MachinePrecision], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6.50000000000000054e138

   1. Initial program 86.6%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in t around inf 64.2%

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

      1. +-commutative 64.2%

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

   7. Simplified 64.2%

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

   if 6.50000000000000054e138 < z

   1. Initial program 90.3%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

      1. clear-num 90.1%

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

      2. associate-/r/ 90.1%

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

      3. clear-num 90.1%

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

   6. Applied egg-rr 90.1%

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

   7. Taylor expanded in y around inf 72.9%

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

      1. div-sub 72.9%

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

   9. Simplified 72.9%

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

   10. Taylor expanded in t around 0 45.5%

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

       1. *-commutative 45.5%

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

       2. associate-*l/ 53.9%

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

   12. Applied egg-rr 53.9%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6.5 \cdot 10^{+138}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.7% 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 87.1%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

5. Taylor expanded in x around inf 48.9%

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

6. Final simplification 48.9%

   \[\leadsto x \]
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 2024019 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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