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

Percentage Accurate: 85.7% → 98.3%

Time: 9.8s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.1%

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

   1. associate-/l* 96.2%

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

3. Simplified 96.2%

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

5. Taylor expanded in y around 0 86.2%

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

   1. associate-*r/ 86.2%

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

   2. mul-1-neg 86.2%

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

   3. distribute-rgt-neg-out 86.2%

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

   4. associate-*l/ 90.3%

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

   5. +-commutative 90.3%

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

   6. associate-*l/ 95.4%

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

   7. distribute-lft-out 96.2%

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

   8. sub-neg 96.2%

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

   9. associate-*l/ 87.1%

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

   10. associate-*r/ 98.8%

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

7. Simplified 98.8%

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

   1. clear-num 98.8%

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

   2. un-div-inv 98.9%

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

9. Applied egg-rr 98.9%

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

10. Final simplification 98.9%

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

Alternative 2: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+90}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-67}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+90)
   (+ x t)
   (if (<= z -8e-67)
     (- x (/ t (/ z y)))
     (if (<= z 2.75e+22) (+ x (/ t (/ a y))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+90) {
		tmp = x + t;
	} else if (z <= -8e-67) {
		tmp = x - (t / (z / y));
	} else if (z <= 2.75e+22) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x + 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 <= (-6.5d+90)) then
        tmp = x + t
    else if (z <= (-8d-67)) then
        tmp = x - (t / (z / y))
    else if (z <= 2.75d+22) then
        tmp = x + (t / (a / y))
    else
        tmp = x + 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 <= -6.5e+90) {
		tmp = x + t;
	} else if (z <= -8e-67) {
		tmp = x - (t / (z / y));
	} else if (z <= 2.75e+22) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+90:
		tmp = x + t
	elif z <= -8e-67:
		tmp = x - (t / (z / y))
	elif z <= 2.75e+22:
		tmp = x + (t / (a / y))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+90)
		tmp = Float64(x + t);
	elseif (z <= -8e-67)
		tmp = Float64(x - Float64(t / Float64(z / y)));
	elseif (z <= 2.75e+22)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+90)
		tmp = x + t;
	elseif (z <= -8e-67)
		tmp = x - (t / (z / y));
	elseif (z <= 2.75e+22)
		tmp = x + (t / (a / y));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+90], N[(x + t), $MachinePrecision], If[LessEqual[z, -8e-67], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.75e+22], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5000000000000001e90 or 2.7500000000000001e22 < z

   1. Initial program 73.3%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in z around inf 72.1%

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

   if -6.5000000000000001e90 < z < -7.99999999999999954e-67

   1. Initial program 96.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 96.9%

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

      1. associate-*r/ 96.9%

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

      2. mul-1-neg 96.9%

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

      3. distribute-rgt-neg-out 96.9%

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

      4. associate-*l/ 96.9%

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

      5. +-commutative 96.9%

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

      6. associate-*l/ 99.9%

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

      7. distribute-lft-out 99.8%

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

      8. sub-neg 99.8%

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

      9. associate-*l/ 96.9%

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

      10. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   9. Applied egg-rr 99.8%

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

   10. Taylor expanded in y around inf 88.5%

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

   11. Taylor expanded in a around 0 75.4%

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

       1. neg-mul-1 75.4%

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

       2. distribute-neg-frac2 75.4%

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

   13. Simplified 75.4%

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

   if -7.99999999999999954e-67 < z < 2.7500000000000001e22

   1. Initial program 95.5%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in y around 0 95.5%

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

      1. associate-*r/ 95.5%

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

      2. mul-1-neg 95.5%

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

      3. distribute-rgt-neg-out 95.5%

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

      4. associate-*l/ 92.4%

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

      5. +-commutative 92.4%

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

      6. associate-*l/ 95.7%

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

      7. distribute-lft-out 97.3%

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

      8. sub-neg 97.3%

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

      9. associate-*l/ 95.5%

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

      10. associate-*r/ 97.7%

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

   7. Simplified 97.7%

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

      1. clear-num 97.7%

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

      2. un-div-inv 97.9%

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

   9. Applied egg-rr 97.9%

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

   10. Taylor expanded in z around 0 84.0%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+90}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-67}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+91}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-66}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+91)
   (+ x t)
   (if (<= z -1.7e-66)
     (- x (* t (/ y z)))
     (if (<= z 9.5e+22) (+ x (/ t (/ a y))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+91) {
		tmp = x + t;
	} else if (z <= -1.7e-66) {
		tmp = x - (t * (y / z));
	} else if (z <= 9.5e+22) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x + 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 <= (-1.3d+91)) then
        tmp = x + t
    else if (z <= (-1.7d-66)) then
        tmp = x - (t * (y / z))
    else if (z <= 9.5d+22) then
        tmp = x + (t / (a / y))
    else
        tmp = x + 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 <= -1.3e+91) {
		tmp = x + t;
	} else if (z <= -1.7e-66) {
		tmp = x - (t * (y / z));
	} else if (z <= 9.5e+22) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+91:
		tmp = x + t
	elif z <= -1.7e-66:
		tmp = x - (t * (y / z))
	elif z <= 9.5e+22:
		tmp = x + (t / (a / y))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+91)
		tmp = Float64(x + t);
	elseif (z <= -1.7e-66)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 9.5e+22)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+91)
		tmp = x + t;
	elseif (z <= -1.7e-66)
		tmp = x - (t * (y / z));
	elseif (z <= 9.5e+22)
		tmp = x + (t / (a / y));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+91], N[(x + t), $MachinePrecision], If[LessEqual[z, -1.7e-66], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+22], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e91 or 9.49999999999999937e22 < z

   1. Initial program 73.3%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in z around inf 72.1%

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

   if -1.3e91 < z < -1.69999999999999999e-66

   1. Initial program 96.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 88.5%

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

   6. Taylor expanded in a around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. unsub-neg 72.4%

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

      3. associate-/l* 75.4%

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

   8. Simplified 75.4%

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

   if -1.69999999999999999e-66 < z < 9.49999999999999937e22

   1. Initial program 95.5%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in y around 0 95.5%

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

      1. associate-*r/ 95.5%

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

      2. mul-1-neg 95.5%

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

      3. distribute-rgt-neg-out 95.5%

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

      4. associate-*l/ 92.4%

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

      5. +-commutative 92.4%

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

      6. associate-*l/ 95.7%

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

      7. distribute-lft-out 97.3%

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

      8. sub-neg 97.3%

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

      9. associate-*l/ 95.5%

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

      10. associate-*r/ 97.7%

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

   7. Simplified 97.7%

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

      1. clear-num 97.7%

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

      2. un-div-inv 97.9%

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

   9. Applied egg-rr 97.9%

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

   10. Taylor expanded in z around 0 84.0%

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

Alternative 4: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-39} \lor \neg \left(y \leq 4.2 \cdot 10^{-85}\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.3e-39) (not (<= y 4.2e-85)))
   (+ x (/ t (/ (- a z) y)))
   (+ x (* t (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.3e-39) || !(y <= 4.2e-85)) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x + (t * (z / (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 ((y <= (-3.3d-39)) .or. (.not. (y <= 4.2d-85))) then
        tmp = x + (t / ((a - z) / y))
    else
        tmp = x + (t * (z / (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 ((y <= -3.3e-39) || !(y <= 4.2e-85)) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x + (t * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.3e-39) or not (y <= 4.2e-85):
		tmp = x + (t / ((a - z) / y))
	else:
		tmp = x + (t * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.3e-39) || !(y <= 4.2e-85))
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.3e-39) || ~((y <= 4.2e-85)))
		tmp = x + (t / ((a - z) / y));
	else
		tmp = x + (t * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.3e-39], N[Not[LessEqual[y, 4.2e-85]], $MachinePrecision]], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.29999999999999985e-39 or 4.2e-85 < y

   1. Initial program 87.2%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in y around 0 85.7%

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

      1. associate-*r/ 85.7%

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

      2. mul-1-neg 85.7%

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

      3. distribute-rgt-neg-out 85.7%

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

      4. associate-*l/ 86.8%

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

      5. +-commutative 86.8%

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

      6. associate-*l/ 94.9%

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

      7. distribute-lft-out 96.1%

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

      8. sub-neg 96.1%

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

      9. associate-*l/ 87.2%

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

      10. associate-*r/ 98.8%

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

   7. Simplified 98.8%

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

      1. clear-num 98.7%

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

      2. un-div-inv 98.9%

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

   9. Applied egg-rr 98.9%

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

   10. Taylor expanded in y around inf 87.8%

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

   if -3.29999999999999985e-39 < y < 4.2e-85

   1. Initial program 86.9%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around 0 86.9%

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

      1. associate-*r/ 86.9%

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

      2. mul-1-neg 86.9%

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

      3. distribute-rgt-neg-out 86.9%

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

      4. associate-*l/ 96.3%

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

      5. +-commutative 96.3%

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

      6. associate-*l/ 96.3%

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

      7. distribute-lft-out 96.2%

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

      8. sub-neg 96.2%

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

      9. associate-*l/ 86.9%

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

      10. associate-*r/ 98.9%

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

   7. Simplified 98.9%

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

   8. Taylor expanded in y around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. unsub-neg 82.0%

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

      3. associate-/l* 94.0%

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

   10. Simplified 94.0%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-39} \lor \neg \left(y \leq 4.2 \cdot 10^{-85}\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-40} \lor \neg \left(y \leq 4.8 \cdot 10^{-85}\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.55e-40) (not (<= y 4.8e-85)))
   (+ x (/ t (/ (- a z) y)))
   (- x (* z (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.55e-40) || !(y <= 4.8e-85)) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x - (z * (t / (a - 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 ((y <= (-1.55d-40)) .or. (.not. (y <= 4.8d-85))) then
        tmp = x + (t / ((a - z) / y))
    else
        tmp = x - (z * (t / (a - 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 ((y <= -1.55e-40) || !(y <= 4.8e-85)) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x - (z * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.55e-40) or not (y <= 4.8e-85):
		tmp = x + (t / ((a - z) / y))
	else:
		tmp = x - (z * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.55e-40) || !(y <= 4.8e-85))
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(x - Float64(z * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.55e-40) || ~((y <= 4.8e-85)))
		tmp = x + (t / ((a - z) / y));
	else
		tmp = x - (z * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.55e-40], N[Not[LessEqual[y, 4.8e-85]], $MachinePrecision]], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55000000000000005e-40 or 4.8000000000000001e-85 < y

   1. Initial program 87.2%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in y around 0 85.7%

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

      1. associate-*r/ 85.7%

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

      2. mul-1-neg 85.7%

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

      3. distribute-rgt-neg-out 85.7%

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

      4. associate-*l/ 86.8%

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

      5. +-commutative 86.8%

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

      6. associate-*l/ 94.9%

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

      7. distribute-lft-out 96.1%

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

      8. sub-neg 96.1%

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

      9. associate-*l/ 87.2%

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

      10. associate-*r/ 98.8%

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

   7. Simplified 98.8%

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

      1. clear-num 98.7%

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

      2. un-div-inv 98.9%

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

   9. Applied egg-rr 98.9%

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

   10. Taylor expanded in y around inf 87.8%

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

   if -1.55000000000000005e-40 < y < 4.8000000000000001e-85

   1. Initial program 86.9%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around 0 82.0%

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

      1. associate-*r/ 82.0%

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

      2. mul-1-neg 82.0%

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

      3. distribute-rgt-neg-out 82.0%

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

      4. associate-*l/ 92.4%

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

      5. *-commutative 92.4%

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

      6. distribute-lft-neg-out 92.4%

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

      7. distribute-rgt-neg-in 92.4%

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

      8. distribute-frac-neg2 92.4%

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

      9. neg-sub0 92.4%

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

      10. sub-neg 92.4%

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

      11. +-commutative 92.4%

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

      12. associate--r+ 92.4%

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

      13. neg-sub0 92.4%

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

      14. remove-double-neg 92.4%

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

   7. Simplified 92.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-40} \lor \neg \left(y \leq 4.8 \cdot 10^{-85}\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-40} \lor \neg \left(y \leq 4.7 \cdot 10^{-85}\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.8e-40) (not (<= y 4.7e-85)))
   (- x (* y (/ t (- z a))))
   (- x (* z (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.8e-40) || !(y <= 4.7e-85)) {
		tmp = x - (y * (t / (z - a)));
	} else {
		tmp = x - (z * (t / (a - 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 ((y <= (-1.8d-40)) .or. (.not. (y <= 4.7d-85))) then
        tmp = x - (y * (t / (z - a)))
    else
        tmp = x - (z * (t / (a - 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 ((y <= -1.8e-40) || !(y <= 4.7e-85)) {
		tmp = x - (y * (t / (z - a)));
	} else {
		tmp = x - (z * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.8e-40) or not (y <= 4.7e-85):
		tmp = x - (y * (t / (z - a)))
	else:
		tmp = x - (z * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.8e-40) || !(y <= 4.7e-85))
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	else
		tmp = Float64(x - Float64(z * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.8e-40) || ~((y <= 4.7e-85)))
		tmp = x - (y * (t / (z - a)));
	else
		tmp = x - (z * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.8e-40], N[Not[LessEqual[y, 4.7e-85]], $MachinePrecision]], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e-40 or 4.70000000000000009e-85 < y

   1. Initial program 87.2%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in y around inf 87.0%

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

   if -1.8e-40 < y < 4.70000000000000009e-85

   1. Initial program 86.9%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around 0 82.0%

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

      1. associate-*r/ 82.0%

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

      2. mul-1-neg 82.0%

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

      3. distribute-rgt-neg-out 82.0%

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

      4. associate-*l/ 92.4%

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

      5. *-commutative 92.4%

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

      6. distribute-lft-neg-out 92.4%

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

      7. distribute-rgt-neg-in 92.4%

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

      8. distribute-frac-neg2 92.4%

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

      9. neg-sub0 92.4%

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

      10. sub-neg 92.4%

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

      11. +-commutative 92.4%

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

      12. associate--r+ 92.4%

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

      13. neg-sub0 92.4%

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

      14. remove-double-neg 92.4%

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

   7. Simplified 92.4%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-40} \lor \neg \left(y \leq 4.7 \cdot 10^{-85}\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+116} \lor \neg \left(z \leq 2.9 \cdot 10^{+229}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+116) (not (<= z 2.9e+229)))
   (+ x t)
   (- x (* y (/ t (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+116) || !(z <= 2.9e+229)) {
		tmp = x + t;
	} else {
		tmp = x - (y * (t / (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 ((z <= (-1.35d+116)) .or. (.not. (z <= 2.9d+229))) then
        tmp = x + t
    else
        tmp = x - (y * (t / (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 ((z <= -1.35e+116) || !(z <= 2.9e+229)) {
		tmp = x + t;
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e+116) or not (z <= 2.9e+229):
		tmp = x + t
	else:
		tmp = x - (y * (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e+116) || !(z <= 2.9e+229))
		tmp = Float64(x + t);
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.35e+116) || ~((z <= 2.9e+229)))
		tmp = x + t;
	else
		tmp = x - (y * (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e+116], N[Not[LessEqual[z, 2.9e+229]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e116 or 2.89999999999999981e229 < z

   1. Initial program 58.9%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in z around inf 82.4%

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

   if -1.35e116 < z < 2.89999999999999981e229

   1. Initial program 94.8%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in y around inf 86.7%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+116} \lor \neg \left(z \leq 2.9 \cdot 10^{+229}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+76} \lor \neg \left(z \leq 2.15 \cdot 10^{+22}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.9e+76) (not (<= z 2.15e+22))) (+ x t) (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.9e+76) || !(z <= 2.15e+22)) {
		tmp = x + t;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.9d+76)) .or. (.not. (z <= 2.15d+22))) then
        tmp = x + t
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.9e+76) || !(z <= 2.15e+22)) {
		tmp = x + t;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.9e+76) or not (z <= 2.15e+22):
		tmp = x + t
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.9e+76) || !(z <= 2.15e+22))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.9e+76) || ~((z <= 2.15e+22)))
		tmp = x + t;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.9e+76], N[Not[LessEqual[z, 2.15e+22]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.90000000000000026e76 or 2.1500000000000001e22 < z

   1. Initial program 74.1%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around inf 72.0%

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

   if -4.90000000000000026e76 < z < 2.1500000000000001e22

   1. Initial program 95.7%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in y around 0 95.7%

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

      1. associate-*r/ 95.7%

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

      2. mul-1-neg 95.7%

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

      3. distribute-rgt-neg-out 95.7%

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

      4. associate-*l/ 93.1%

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

      5. +-commutative 93.1%

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

      6. associate-*l/ 96.4%

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

      7. distribute-lft-out 97.7%

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

      8. sub-neg 97.7%

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

      9. associate-*l/ 95.7%

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

      10. associate-*r/ 98.1%

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

   7. Simplified 98.1%

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

      1. clear-num 98.1%

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

      2. un-div-inv 98.2%

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

   9. Applied egg-rr 98.2%

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

   10. Taylor expanded in z around 0 78.4%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+76} \lor \neg \left(z \leq 2.15 \cdot 10^{+22}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+78} \lor \neg \left(z \leq 1.66 \cdot 10^{+22}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.8e+78) (not (<= z 1.66e+22))) (+ x t) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e+78) || !(z <= 1.66e+22)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (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 <= (-2.8d+78)) .or. (.not. (z <= 1.66d+22))) then
        tmp = x + t
    else
        tmp = x + (t * (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 <= -2.8e+78) || !(z <= 1.66e+22)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.8e+78) or not (z <= 1.66e+22):
		tmp = x + t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.8e+78) || !(z <= 1.66e+22))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.8e+78) || ~((z <= 1.66e+22)))
		tmp = x + t;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.8e+78], N[Not[LessEqual[z, 1.66e+22]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8000000000000001e78 or 1.66e22 < z

   1. Initial program 74.1%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around inf 72.0%

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

   if -2.8000000000000001e78 < z < 1.66e22

   1. Initial program 95.7%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around 0 76.0%

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

      1. associate-/l* 78.4%

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

   7. Simplified 78.4%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+78} \lor \neg \left(z \leq 1.66 \cdot 10^{+22}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-101} \lor \neg \left(x \leq -1.08 \cdot 10^{-284}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -5.5e-101) (not (<= x -1.08e-284))) (+ x t) (* t (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -5.5e-101) || !(x <= -1.08e-284)) {
		tmp = x + t;
	} else {
		tmp = t * (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 ((x <= (-5.5d-101)) .or. (.not. (x <= (-1.08d-284)))) then
        tmp = x + t
    else
        tmp = t * (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 ((x <= -5.5e-101) || !(x <= -1.08e-284)) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -5.5e-101) or not (x <= -1.08e-284):
		tmp = x + t
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -5.5e-101) || !(x <= -1.08e-284))
		tmp = Float64(x + t);
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -5.5e-101) || ~((x <= -1.08e-284)))
		tmp = x + t;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -5.5e-101], N[Not[LessEqual[x, -1.08e-284]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.49999999999999973e-101 or -1.0799999999999999e-284 < x

   1. Initial program 87.7%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in z around inf 66.8%

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

   if -5.49999999999999973e-101 < x < -1.0799999999999999e-284

   1. Initial program 83.7%

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

      1. +-commutative 83.7%

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

      2. associate-/l* 90.8%

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

      3. fma-define 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in a around inf 60.1%

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

      1. +-commutative 60.1%

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

   7. Simplified 60.1%

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

   8. Taylor expanded in t around inf 58.3%

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

   9. Taylor expanded in y around inf 53.5%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-101} \lor \neg \left(x \leq -1.08 \cdot 10^{-284}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-216} \lor \neg \left(z \leq 1.55 \cdot 10^{-35}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e-216) (not (<= z 1.55e-35))) (+ x t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e-216) || !(z <= 1.55e-35)) {
		tmp = x + t;
	} 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 ((z <= (-4.5d-216)) .or. (.not. (z <= 1.55d-35))) then
        tmp = x + t
    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 ((z <= -4.5e-216) || !(z <= 1.55e-35)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e-216) or not (z <= 1.55e-35):
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e-216) || !(z <= 1.55e-35))
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.5e-216) || ~((z <= 1.55e-35)))
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e-216], N[Not[LessEqual[z, 1.55e-35]], $MachinePrecision]], N[(x + t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999999e-216 or 1.55000000000000006e-35 < z

   1. Initial program 82.2%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in z around inf 65.2%

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

   if -4.4999999999999999e-216 < z < 1.55000000000000006e-35

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. associate-/l* 96.6%

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

      3. fma-define 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in t around 0 58.7%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-216} \lor \neg \left(z \leq 1.55 \cdot 10^{-35}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.1%

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

   1. associate-/l* 96.2%

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

3. Simplified 96.2%

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

5. Taylor expanded in y around 0 86.2%

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

   1. associate-*r/ 86.2%

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

   2. mul-1-neg 86.2%

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

   3. distribute-rgt-neg-out 86.2%

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

   4. associate-*l/ 90.3%

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

   5. +-commutative 90.3%

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

   6. associate-*l/ 95.4%

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

   7. distribute-lft-out 96.2%

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

   8. sub-neg 96.2%

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

   9. associate-*l/ 87.1%

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

   10. associate-*r/ 98.8%

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

7. Simplified 98.8%

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

Alternative 13: 51.6% 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%

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

   1. +-commutative 87.1%

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

   2. associate-/l* 96.2%

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

   3. fma-define 96.2%

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

3. Simplified 96.2%

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

5. Taylor expanded in t around 0 51.5%

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

Developer Target 1: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024137 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -10682974490174067/10000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 312887599100691/80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t)))))

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