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

Percentage Accurate: 85.7% → 98.3%

Time: 10.1s

Alternatives: 15

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: 85.7% 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: 98.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+163}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.4e+163)
   (+ x (* (- z t) (/ y (- a t))))
   (+ x (/ y (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e+163) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = x + (y / ((a - t) / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.4d+163)) then
        tmp = x + ((z - t) * (y / (a - t)))
    else
        tmp = x + (y / ((a - t) / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e+163) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = x + (y / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.4e+163:
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = x + (y / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.4e+163)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.4e+163)
		tmp = x + ((z - t) * (y / (a - t)));
	else
		tmp = x + (y / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.4e+163], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.40000000000000007e163

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

      2. associate-/l* 97.2%

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

   4. Applied egg-rr 97.2%

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

   if -1.40000000000000007e163 < z

   1. Initial program 81.1%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

Alternative 2: 76.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-49}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-21}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+118}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6e-49)
   (+ x y)
   (if (<= t 5.9e-21)
     (+ x (* z (/ y a)))
     (if (<= t 2.4e+118) (- x (/ y (/ t z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6e-49) {
		tmp = x + y;
	} else if (t <= 5.9e-21) {
		tmp = x + (z * (y / a));
	} else if (t <= 2.4e+118) {
		tmp = x - (y / (t / z));
	} 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 <= (-6d-49)) then
        tmp = x + y
    else if (t <= 5.9d-21) then
        tmp = x + (z * (y / a))
    else if (t <= 2.4d+118) then
        tmp = x - (y / (t / z))
    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 <= -6e-49) {
		tmp = x + y;
	} else if (t <= 5.9e-21) {
		tmp = x + (z * (y / a));
	} else if (t <= 2.4e+118) {
		tmp = x - (y / (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6e-49:
		tmp = x + y
	elif t <= 5.9e-21:
		tmp = x + (z * (y / a))
	elif t <= 2.4e+118:
		tmp = x - (y / (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6e-49)
		tmp = Float64(x + y);
	elseif (t <= 5.9e-21)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (t <= 2.4e+118)
		tmp = Float64(x - Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6e-49)
		tmp = x + y;
	elseif (t <= 5.9e-21)
		tmp = x + (z * (y / a));
	elseif (t <= 2.4e+118)
		tmp = x - (y / (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6e-49], N[(x + y), $MachinePrecision], If[LessEqual[t, 5.9e-21], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+118], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6e-49 or 2.4e118 < t

   1. Initial program 66.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 t around inf 84.2%

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

   if -6e-49 < t < 5.9000000000000003e-21

   1. Initial program 97.2%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around 0 81.5%

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

      1. *-commutative 81.5%

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

      2. associate-/l* 82.3%

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

   7. Applied egg-rr 82.3%

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

   if 5.9000000000000003e-21 < t < 2.4e118

   1. Initial program 89.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 100.0%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around inf 83.4%

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

   8. Taylor expanded in a around 0 75.2%

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

      1. neg-mul-1 75.2%

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

      2. distribute-neg-frac2 75.2%

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

   10. Simplified 75.2%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-49}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-21}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+118}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-51}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-24}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+118}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.6e-51)
   (+ x y)
   (if (<= t 7.8e-24)
     (+ x (* z (/ y a)))
     (if (<= t 2.9e+118) (- x (* y (/ z t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e-51) {
		tmp = x + y;
	} else if (t <= 7.8e-24) {
		tmp = x + (z * (y / a));
	} else if (t <= 2.9e+118) {
		tmp = x - (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.6d-51)) then
        tmp = x + y
    else if (t <= 7.8d-24) then
        tmp = x + (z * (y / a))
    else if (t <= 2.9d+118) then
        tmp = x - (y * (z / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e-51) {
		tmp = x + y;
	} else if (t <= 7.8e-24) {
		tmp = x + (z * (y / a));
	} else if (t <= 2.9e+118) {
		tmp = x - (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.6e-51:
		tmp = x + y
	elif t <= 7.8e-24:
		tmp = x + (z * (y / a))
	elif t <= 2.9e+118:
		tmp = x - (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.6e-51)
		tmp = Float64(x + y);
	elseif (t <= 7.8e-24)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (t <= 2.9e+118)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.6e-51)
		tmp = x + y;
	elseif (t <= 7.8e-24)
		tmp = x + (z * (y / a));
	elseif (t <= 2.9e+118)
		tmp = x - (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.6e-51], N[(x + y), $MachinePrecision], If[LessEqual[t, 7.8e-24], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+118], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.6e-51 or 2.90000000000000016e118 < t

   1. Initial program 66.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 t around inf 84.2%

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

   if -3.6e-51 < t < 7.8e-24

   1. Initial program 97.2%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around 0 81.5%

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

      1. *-commutative 81.5%

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

      2. associate-/l* 82.3%

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

   7. Applied egg-rr 82.3%

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

   if 7.8e-24 < t < 2.90000000000000016e118

   1. Initial program 89.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 75.4%

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

      1. associate-/l* 83.4%

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

   7. Simplified 83.4%

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

   8. Taylor expanded in a around 0 72.5%

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

      1. metadata-eval 72.5%

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

      2. associate-*r/ 75.2%

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

      3. cancel-sign-sub-inv 75.2%

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

      4. *-commutative 75.2%

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

      5. *-rgt-identity 75.2%

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

   10. Simplified 75.2%

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

Alternative 4: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+39} \lor \neg \left(t \leq 12.5\right):\\ \;\;\;\;x + \left(y - y \cdot \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.2e+39) (not (<= t 12.5)))
   (+ x (- y (* y (/ z t))))
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.2e+39) || !(t <= 12.5)) {
		tmp = x + (y - (y * (z / t)));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8.2d+39)) .or. (.not. (t <= 12.5d0))) then
        tmp = x + (y - (y * (z / t)))
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.2e+39) || !(t <= 12.5)) {
		tmp = x + (y - (y * (z / t)));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.2e+39) or not (t <= 12.5):
		tmp = x + (y - (y * (z / t)))
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.2e+39) || !(t <= 12.5))
		tmp = Float64(x + Float64(y - Float64(y * Float64(z / t))));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.2e+39) || ~((t <= 12.5)))
		tmp = x + (y - (y * (z / t)));
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.2e+39], N[Not[LessEqual[t, 12.5]], $MachinePrecision]], N[(x + N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.20000000000000008e39 or 12.5 < t

   1. Initial program 66.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 a around 0 60.6%

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

      1. mul-1-neg 60.6%

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

      2. associate-/l* 90.5%

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

      3. div-sub 90.5%

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

      4. *-inverses 90.5%

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

      5. sub-neg 90.5%

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

      6. metadata-eval 90.5%

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

      7. distribute-lft-out 90.5%

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

      8. +-commutative 90.5%

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

      9. distribute-neg-in 90.5%

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

      10. distribute-rgt-neg-in 90.5%

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

      11. metadata-eval 90.5%

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

      12. *-rgt-identity 90.5%

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

      13. unsub-neg 90.5%

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

   9. Simplified 90.5%

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

   if -8.20000000000000008e39 < t < 12.5

   1. Initial program 97.1%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in z around inf 88.1%

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

      1. associate-/l* 86.0%

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

   7. Simplified 86.0%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+39} \lor \neg \left(t \leq 12.5\right):\\ \;\;\;\;x + \left(y - y \cdot \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+120} \lor \neg \left(t \leq 1.55 \cdot 10^{+112}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3e+120) (not (<= t 1.55e+112)))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3e+120) || !(t <= 1.55e+112)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3d+120)) .or. (.not. (t <= 1.55d+112))) then
        tmp = x + y
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3e+120) || !(t <= 1.55e+112)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3e+120) or not (t <= 1.55e+112):
		tmp = x + y
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3e+120) || !(t <= 1.55e+112))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3e+120) || ~((t <= 1.55e+112)))
		tmp = x + y;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3e+120], N[Not[LessEqual[t, 1.55e+112]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3e120 or 1.54999999999999991e112 < t

   1. Initial program 56.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 t around inf 88.7%

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

   if -3e120 < t < 1.54999999999999991e112

   1. Initial program 95.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 84.1%

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

      1. associate-/l* 83.5%

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

   7. Simplified 83.5%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+120} \lor \neg \left(t \leq 1.55 \cdot 10^{+112}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-6}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-16}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e-6)
   (+ x (/ (* z y) (- a t)))
   (if (<= z 8e-16) (+ x (* y (/ t (- t a)))) (+ x (/ y (/ (- a t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e-6) {
		tmp = x + ((z * y) / (a - t));
	} else if (z <= 8e-16) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9d-6)) then
        tmp = x + ((z * y) / (a - t))
    else if (z <= 8d-16) then
        tmp = x + (y * (t / (t - a)))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e-6) {
		tmp = x + ((z * y) / (a - t));
	} else if (z <= 8e-16) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9e-6:
		tmp = x + ((z * y) / (a - t))
	elif z <= 8e-16:
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e-6)
		tmp = Float64(x + Float64(Float64(z * y) / Float64(a - t)));
	elseif (z <= 8e-16)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9e-6)
		tmp = x + ((z * y) / (a - t));
	elseif (z <= 8e-16)
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e-6], N[(x + N[(N[(z * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-16], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.00000000000000023e-6

   1. Initial program 90.9%

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

      1. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in z around inf 85.4%

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

   if -9.00000000000000023e-6 < z < 7.9999999999999998e-16

   1. Initial program 79.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 z around 0 76.1%

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

      1. associate-*r/ 76.1%

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

      2. mul-1-neg 76.1%

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

      3. distribute-lft-neg-out 76.1%

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

      4. *-commutative 76.1%

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

      5. associate-/l* 96.4%

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

      6. distribute-neg-frac 96.4%

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

      7. distribute-neg-frac2 96.4%

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

      8. neg-sub0 96.4%

         \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(a - t\right)}} \]

      9. associate--r- 96.4%

         \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - a\right) + t}} \]

      10. neg-sub0 96.4%

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

   7. Simplified 96.4%

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

   if 7.9999999999999998e-16 < z

   1. Initial program 78.9%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

      1. clear-num 98.5%

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

      2. un-div-inv 99.2%

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

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in z around inf 82.2%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-6}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-16}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00195:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.00195)
   (+ x (/ (* z y) (- a t)))
   (if (<= z 8.2e-13) (+ x (/ y (- 1.0 (/ a t)))) (+ x (/ y (/ (- a t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.00195) {
		tmp = x + ((z * y) / (a - t));
	} else if (z <= 8.2e-13) {
		tmp = x + (y / (1.0 - (a / t)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-0.00195d0)) then
        tmp = x + ((z * y) / (a - t))
    else if (z <= 8.2d-13) then
        tmp = x + (y / (1.0d0 - (a / t)))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.00195) {
		tmp = x + ((z * y) / (a - t));
	} else if (z <= 8.2e-13) {
		tmp = x + (y / (1.0 - (a / t)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.00195:
		tmp = x + ((z * y) / (a - t))
	elif z <= 8.2e-13:
		tmp = x + (y / (1.0 - (a / t)))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.00195)
		tmp = Float64(x + Float64(Float64(z * y) / Float64(a - t)));
	elseif (z <= 8.2e-13)
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.00195)
		tmp = x + ((z * y) / (a - t));
	elseif (z <= 8.2e-13)
		tmp = x + (y / (1.0 - (a / t)));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.00195], N[(x + N[(N[(z * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-13], N[(x + N[(y / N[(1.0 - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0019499999999999999

   1. Initial program 90.9%

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

      1. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in z around inf 85.4%

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

   if -0.0019499999999999999 < z < 8.2000000000000004e-13

   1. Initial program 79.7%

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

      1. div-sub 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in z around 0 96.3%

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

       1. mul-1-neg 96.3%

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

       2. unsub-neg 96.3%

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

   11. Simplified 96.3%

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

   if 8.2000000000000004e-13 < z

   1. Initial program 78.9%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

      1. clear-num 98.5%

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

      2. un-div-inv 99.2%

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

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in z around inf 82.2%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00195:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \mathbf{elif}\;t \leq 15:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - y \cdot \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.6e-49)
   (+ x (/ y (- 1.0 (/ a t))))
   (if (<= t 15.0) (+ x (/ y (/ (- a t) z))) (+ x (- y (* y (/ z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e-49) {
		tmp = x + (y / (1.0 - (a / t)));
	} else if (t <= 15.0) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x + (y - (y * (z / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.6d-49)) then
        tmp = x + (y / (1.0d0 - (a / t)))
    else if (t <= 15.0d0) then
        tmp = x + (y / ((a - t) / z))
    else
        tmp = x + (y - (y * (z / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e-49) {
		tmp = x + (y / (1.0 - (a / t)));
	} else if (t <= 15.0) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x + (y - (y * (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.6e-49:
		tmp = x + (y / (1.0 - (a / t)))
	elif t <= 15.0:
		tmp = x + (y / ((a - t) / z))
	else:
		tmp = x + (y - (y * (z / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.6e-49)
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / t))));
	elseif (t <= 15.0)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	else
		tmp = Float64(x + Float64(y - Float64(y * Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.6e-49)
		tmp = x + (y / (1.0 - (a / t)));
	elseif (t <= 15.0)
		tmp = x + (y / ((a - t) / z));
	else
		tmp = x + (y - (y * (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.6e-49], N[(x + N[(y / N[(1.0 - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 15.0], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5999999999999997e-49

   1. Initial program 73.0%

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

      1. div-sub 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in z around 0 90.3%

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

       1. mul-1-neg 90.3%

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

       2. unsub-neg 90.3%

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

   11. Simplified 90.3%

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

   if -3.5999999999999997e-49 < t < 15

   1. Initial program 96.6%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

      1. clear-num 94.1%

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

      2. un-div-inv 94.6%

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

   6. Applied egg-rr 94.6%

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

   7. Taylor expanded in z around inf 86.5%

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

   if 15 < t

   1. Initial program 69.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 100.0%

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

      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 a around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. associate-/l* 90.0%

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

      3. div-sub 90.0%

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

      4. *-inverses 90.0%

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

      5. sub-neg 90.0%

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

      6. metadata-eval 90.0%

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

      7. distribute-lft-out 90.0%

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

      8. +-commutative 90.0%

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

      9. distribute-neg-in 90.0%

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

      10. distribute-rgt-neg-in 90.0%

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

      11. metadata-eval 90.0%

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

      12. *-rgt-identity 90.0%

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

      13. unsub-neg 90.0%

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

   9. Simplified 90.0%

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

Alternative 9: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \mathbf{elif}\;t \leq 9.5:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - y \cdot \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.1e-49)
   (+ x (/ y (- 1.0 (/ a t))))
   (if (<= t 9.5) (+ x (* y (/ z (- a t)))) (+ x (- y (* y (/ z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e-49) {
		tmp = x + (y / (1.0 - (a / t)));
	} else if (t <= 9.5) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (y - (y * (z / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.1d-49)) then
        tmp = x + (y / (1.0d0 - (a / t)))
    else if (t <= 9.5d0) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = x + (y - (y * (z / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e-49) {
		tmp = x + (y / (1.0 - (a / t)));
	} else if (t <= 9.5) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (y - (y * (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.1e-49:
		tmp = x + (y / (1.0 - (a / t)))
	elif t <= 9.5:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + (y - (y * (z / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.1e-49)
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / t))));
	elseif (t <= 9.5)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y - Float64(y * Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.1e-49)
		tmp = x + (y / (1.0 - (a / t)));
	elseif (t <= 9.5)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + (y - (y * (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.1e-49], N[(x + N[(y / N[(1.0 - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0999999999999999e-49

   1. Initial program 73.0%

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

      1. div-sub 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in z around 0 90.3%

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

       1. mul-1-neg 90.3%

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

       2. unsub-neg 90.3%

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

   11. Simplified 90.3%

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

   if -2.0999999999999999e-49 < t < 9.5

   1. Initial program 96.6%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in z around inf 88.4%

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

      1. associate-/l* 86.0%

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

   7. Simplified 86.0%

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

   if 9.5 < t

   1. Initial program 69.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 100.0%

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

      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 a around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. associate-/l* 90.0%

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

      3. div-sub 90.0%

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

      4. *-inverses 90.0%

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

      5. sub-neg 90.0%

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

      6. metadata-eval 90.0%

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

      7. distribute-lft-out 90.0%

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

      8. +-commutative 90.0%

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

      9. distribute-neg-in 90.0%

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

      10. distribute-rgt-neg-in 90.0%

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

      11. metadata-eval 90.0%

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

      12. *-rgt-identity 90.0%

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

      13. unsub-neg 90.0%

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

   9. Simplified 90.0%

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

Alternative 10: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-50} \lor \neg \left(t \leq 50\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.2e-50) (not (<= t 50.0))) (+ 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-50) || !(t <= 50.0)) {
		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-50)) .or. (.not. (t <= 50.0d0))) 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-50) || !(t <= 50.0)) {
		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-50) or not (t <= 50.0):
		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-50) || !(t <= 50.0))
		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-50) || ~((t <= 50.0)))
		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-50], N[Not[LessEqual[t, 50.0]], $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 < -6.2000000000000004e-50 or 50 < t

   1. Initial program 71.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 80.9%

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

   if -6.2000000000000004e-50 < t < 50

   1. Initial program 96.6%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in t around 0 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-/l* 80.0%

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

   7. Applied egg-rr 80.0%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-50} \lor \neg \left(t \leq 50\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-51} \lor \neg \left(t \leq 15.5\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.7e-51) (not (<= t 15.5))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.7e-51) || !(t <= 15.5)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.7d-51)) .or. (.not. (t <= 15.5d0))) then
        tmp = x + y
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.7e-51) || !(t <= 15.5)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.7e-51) or not (t <= 15.5):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.7e-51) || !(t <= 15.5))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.7e-51) || ~((t <= 15.5)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.7e-51], N[Not[LessEqual[t, 15.5]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.6999999999999997e-51 or 15.5 < t

   1. Initial program 71.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 80.9%

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

   if -4.6999999999999997e-51 < t < 15.5

   1. Initial program 96.6%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in t around 0 78.4%

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

      1. associate-/l* 78.3%

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

   7. Simplified 78.3%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-51} \lor \neg \left(t \leq 15.5\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+163}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+163)
   (+ x (* (- z t) (/ y (- a t))))
   (+ x (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+163) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.15d+163)) then
        tmp = x + ((z - t) * (y / (a - t)))
    else
        tmp = x + (y * ((z - t) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+163) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+163:
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = x + (y * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+163)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e+163)
		tmp = x + ((z - t) * (y / (a - t)));
	else
		tmp = x + (y * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+163], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000001e163

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

      2. associate-/l* 97.2%

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

   4. Applied egg-rr 97.2%

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

   if -1.15000000000000001e163 < z

   1. Initial program 81.1%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

Alternative 13: 63.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-154} \lor \neg \left(t \leq 9.5 \cdot 10^{-62}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.35e-154) (not (<= t 9.5e-62))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.35e-154) || !(t <= 9.5e-62)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.35d-154)) .or. (.not. (t <= 9.5d-62))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.35e-154) || !(t <= 9.5e-62)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.35e-154) or not (t <= 9.5e-62):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.35e-154) || !(t <= 9.5e-62))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.35e-154) || ~((t <= 9.5e-62)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.35e-154], N[Not[LessEqual[t, 9.5e-62]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.34999999999999995e-154 or 9.49999999999999951e-62 < t

   1. Initial program 76.3%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in t around inf 70.8%

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

   if -1.34999999999999995e-154 < t < 9.49999999999999951e-62

   1. Initial program 98.6%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in z around inf 93.5%

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

      1. associate-/l* 88.4%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in x around inf 52.2%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-154} \lor \neg \left(t \leq 9.5 \cdot 10^{-62}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.6%

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

   1. associate-/l* 97.3%

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

3. Simplified 97.3%

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

Alternative 15: 51.2% 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 82.6%

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

   1. associate-/l* 97.3%

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

3. Simplified 97.3%

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

5. Taylor expanded in z around inf 72.0%

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

   1. associate-/l* 72.3%

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

7. Simplified 72.3%

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

8. Taylor expanded in x around inf 48.6%

   \[\leadsto \color{blue}{x} \]
9. Add Preprocessing

Developer target: 98.3% 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 2024085 
(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))))