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

Percentage Accurate: 85.3% → 98.3%

Time: 11.8s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.3% 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, 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]

Derivation

1. Initial program 85.2%

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

   1. associate-/l* 98.5%

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

3. Simplified 98.5%

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

5. Final simplification 98.5%

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

Alternative 2: 84.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a - t}\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+79}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-215}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y (- a t))))))
   (if (<= t -3.3e+79)
     (+ x y)
     (if (<= t -2.8e-137)
       t_1
       (if (<= t -1.6e-215)
         (+ x (/ y (/ a (- z t))))
         (if (<= t 1.2e+145) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (a - t)));
	double tmp;
	if (t <= -3.3e+79) {
		tmp = x + y;
	} else if (t <= -2.8e-137) {
		tmp = t_1;
	} else if (t <= -1.6e-215) {
		tmp = x + (y / (a / (z - t)));
	} else if (t <= 1.2e+145) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / (a - t)))
    if (t <= (-3.3d+79)) then
        tmp = x + y
    else if (t <= (-2.8d-137)) then
        tmp = t_1
    else if (t <= (-1.6d-215)) then
        tmp = x + (y / (a / (z - t)))
    else if (t <= 1.2d+145) then
        tmp = t_1
    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 t_1 = x + (z * (y / (a - t)));
	double tmp;
	if (t <= -3.3e+79) {
		tmp = x + y;
	} else if (t <= -2.8e-137) {
		tmp = t_1;
	} else if (t <= -1.6e-215) {
		tmp = x + (y / (a / (z - t)));
	} else if (t <= 1.2e+145) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / (a - t)))
	tmp = 0
	if t <= -3.3e+79:
		tmp = x + y
	elif t <= -2.8e-137:
		tmp = t_1
	elif t <= -1.6e-215:
		tmp = x + (y / (a / (z - t)))
	elif t <= 1.2e+145:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / Float64(a - t))))
	tmp = 0.0
	if (t <= -3.3e+79)
		tmp = Float64(x + y);
	elseif (t <= -2.8e-137)
		tmp = t_1;
	elseif (t <= -1.6e-215)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (t <= 1.2e+145)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / (a - t)));
	tmp = 0.0;
	if (t <= -3.3e+79)
		tmp = x + y;
	elseif (t <= -2.8e-137)
		tmp = t_1;
	elseif (t <= -1.6e-215)
		tmp = x + (y / (a / (z - t)));
	elseif (t <= 1.2e+145)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e+79], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.8e-137], t$95$1, If[LessEqual[t, -1.6e-215], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+145], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3000000000000002e79 or 1.19999999999999996e145 < t

   1. Initial program 68.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 83.0%

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

      1. +-commutative 83.0%

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

   7. Simplified 83.0%

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

   if -3.3000000000000002e79 < t < -2.7999999999999999e-137 or -1.6000000000000001e-215 < t < 1.19999999999999996e145

   1. Initial program 91.2%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around inf 81.9%

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

      1. associate-*l/ 87.3%

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

      2. *-commutative 87.3%

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

   7. Simplified 87.3%

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

   if -2.7999999999999999e-137 < t < -1.6000000000000001e-215

   1. Initial program 95.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+79}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-137}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-215}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+145}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+45}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+145}:\\ \;\;\;\;x + \frac{z}{\frac{-t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.5e+45)
   (+ x y)
   (if (<= t 2.2e-81)
     (+ x (/ z (/ a y)))
     (if (<= t 6.5e+145) (+ x (/ z (/ (- t) y))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.5e+45) {
		tmp = x + y;
	} else if (t <= 2.2e-81) {
		tmp = x + (z / (a / y));
	} else if (t <= 6.5e+145) {
		tmp = x + (z / (-t / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.5d+45)) then
        tmp = x + y
    else if (t <= 2.2d-81) then
        tmp = x + (z / (a / y))
    else if (t <= 6.5d+145) then
        tmp = x + (z / (-t / y))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.5e+45) {
		tmp = x + y;
	} else if (t <= 2.2e-81) {
		tmp = x + (z / (a / y));
	} else if (t <= 6.5e+145) {
		tmp = x + (z / (-t / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.5e+45:
		tmp = x + y
	elif t <= 2.2e-81:
		tmp = x + (z / (a / y))
	elif t <= 6.5e+145:
		tmp = x + (z / (-t / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.5e+45)
		tmp = Float64(x + y);
	elseif (t <= 2.2e-81)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif (t <= 6.5e+145)
		tmp = Float64(x + Float64(z / Float64(Float64(-t) / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.5e+45)
		tmp = x + y;
	elseif (t <= 2.2e-81)
		tmp = x + (z / (a / y));
	elseif (t <= 6.5e+145)
		tmp = x + (z / (-t / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.5e+45], N[(x + y), $MachinePrecision], If[LessEqual[t, 2.2e-81], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+145], N[(x + N[(z / N[((-t) / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.50000000000000023e45 or 6.50000000000000034e145 < t

   1. Initial program 68.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 79.5%

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

      1. +-commutative 79.5%

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

   7. Simplified 79.5%

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

   if -3.50000000000000023e45 < t < 2.1999999999999999e-81

   1. Initial program 93.5%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in z around inf 83.2%

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

      1. associate-*l/ 87.1%

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

      2. *-commutative 87.1%

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

   7. Simplified 87.1%

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

      1. associate-*r/ 83.2%

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

      2. frac-2neg 83.2%

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

      3. sub-neg 83.2%

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

      4. distribute-neg-in 83.2%

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

      5. add-sqr-sqrt 51.3%

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

      6. sqrt-unprod 78.6%

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

      7. sqr-neg 78.6%

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

      8. sqrt-unprod 27.3%

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

      9. add-sqr-sqrt 72.8%

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

      10. add-sqr-sqrt 45.4%

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

      11. sqrt-unprod 75.0%

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

      12. sqr-neg 75.0%

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

      13. sqrt-unprod 31.9%

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

      14. add-sqr-sqrt 83.2%

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

   9. Applied egg-rr 83.2%

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

       1. distribute-rgt-neg-in 83.2%

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

       2. associate-/l* 87.4%

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

       3. +-commutative 87.4%

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

       4. unsub-neg 87.4%

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

   11. Simplified 87.4%

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

   12. Taylor expanded in t around 0 78.1%

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

   if 2.1999999999999999e-81 < t < 6.50000000000000034e145

   1. Initial program 90.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 80.6%

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

      1. associate-*l/ 84.7%

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

      2. *-commutative 84.7%

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

   7. Simplified 84.7%

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

      1. associate-*r/ 80.6%

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

      2. frac-2neg 80.6%

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

      3. sub-neg 80.6%

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

      4. distribute-neg-in 80.6%

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

      5. add-sqr-sqrt 0.0%

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

      6. sqrt-unprod 57.1%

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

      7. sqr-neg 57.1%

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

      8. sqrt-unprod 57.1%

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

      9. add-sqr-sqrt 57.1%

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

      10. add-sqr-sqrt 0.0%

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

      11. sqrt-unprod 80.6%

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

      12. sqr-neg 80.6%

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

      13. sqrt-unprod 80.5%

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

      14. add-sqr-sqrt 80.6%

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

   9. Applied egg-rr 80.6%

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

       1. distribute-rgt-neg-in 80.6%

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

       2. associate-/l* 84.7%

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

       3. +-commutative 84.7%

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

       4. unsub-neg 84.7%

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

   11. Simplified 84.7%

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

   12. Taylor expanded in t around inf 76.6%

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

       1. associate-*r/ 76.6%

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

       2. neg-mul-1 76.6%

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

   14. Simplified 76.6%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+45}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+145}:\\ \;\;\;\;x + \frac{z}{\frac{-t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+46}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+145}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.85e+46)
   (+ x y)
   (if (<= t 4.8e-84)
     (+ x (/ z (/ a y)))
     (if (<= t 1.35e+145) (- x (* z (/ y t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.85e+46) {
		tmp = x + y;
	} else if (t <= 4.8e-84) {
		tmp = x + (z / (a / y));
	} else if (t <= 1.35e+145) {
		tmp = x - (z * (y / 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 <= (-1.85d+46)) then
        tmp = x + y
    else if (t <= 4.8d-84) then
        tmp = x + (z / (a / y))
    else if (t <= 1.35d+145) then
        tmp = x - (z * (y / 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 <= -1.85e+46) {
		tmp = x + y;
	} else if (t <= 4.8e-84) {
		tmp = x + (z / (a / y));
	} else if (t <= 1.35e+145) {
		tmp = x - (z * (y / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.85e+46:
		tmp = x + y
	elif t <= 4.8e-84:
		tmp = x + (z / (a / y))
	elif t <= 1.35e+145:
		tmp = x - (z * (y / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.85e+46)
		tmp = Float64(x + y);
	elseif (t <= 4.8e-84)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif (t <= 1.35e+145)
		tmp = Float64(x - Float64(z * Float64(y / 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 <= -1.85e+46)
		tmp = x + y;
	elseif (t <= 4.8e-84)
		tmp = x + (z / (a / y));
	elseif (t <= 1.35e+145)
		tmp = x - (z * (y / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.85e+46], N[(x + y), $MachinePrecision], If[LessEqual[t, 4.8e-84], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+145], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.84999999999999995e46 or 1.35000000000000011e145 < t

   1. Initial program 68.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 79.5%

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

      1. +-commutative 79.5%

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

   7. Simplified 79.5%

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

   if -1.84999999999999995e46 < t < 4.80000000000000035e-84

   1. Initial program 93.5%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in z around inf 83.2%

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

      1. associate-*l/ 87.1%

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

      2. *-commutative 87.1%

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

   7. Simplified 87.1%

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

      1. associate-*r/ 83.2%

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

      2. frac-2neg 83.2%

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

      3. sub-neg 83.2%

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

      4. distribute-neg-in 83.2%

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

      5. add-sqr-sqrt 51.3%

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

      6. sqrt-unprod 78.6%

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

      7. sqr-neg 78.6%

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

      8. sqrt-unprod 27.3%

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

      9. add-sqr-sqrt 72.8%

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

      10. add-sqr-sqrt 45.4%

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

      11. sqrt-unprod 75.0%

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

      12. sqr-neg 75.0%

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

      13. sqrt-unprod 31.9%

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

      14. add-sqr-sqrt 83.2%

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

   9. Applied egg-rr 83.2%

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

       1. distribute-rgt-neg-in 83.2%

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

       2. associate-/l* 87.4%

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

       3. +-commutative 87.4%

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

       4. unsub-neg 87.4%

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

   11. Simplified 87.4%

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

   12. Taylor expanded in t around 0 78.1%

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

   if 4.80000000000000035e-84 < t < 1.35000000000000011e145

   1. Initial program 90.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 80.6%

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

      1. associate-*l/ 84.7%

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

      2. *-commutative 84.7%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in a around 0 72.0%

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

      1. mul-1-neg 72.0%

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

      2. unsub-neg 72.0%

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

      3. associate-/l* 76.0%

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

   10. Simplified 76.0%

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

       1. associate-/r/ 76.6%

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

   12. Applied egg-rr 76.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+46}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+145}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+79} \lor \neg \left(t \leq 1.6 \cdot 10^{+145}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.8e+79) (not (<= t 1.6e+145)))
   (+ x y)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e+79) || !(t <= 1.6e+145)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.8d+79)) .or. (.not. (t <= 1.6d+145))) then
        tmp = x + y
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e+79) || !(t <= 1.6e+145)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.8e+79) or not (t <= 1.6e+145):
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.8e+79) || !(t <= 1.6e+145))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.8e+79) || ~((t <= 1.6e+145)))
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.8e+79], N[Not[LessEqual[t, 1.6e+145]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.79999999999999971e79 or 1.60000000000000004e145 < t

   1. Initial program 68.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 83.0%

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

      1. +-commutative 83.0%

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

   7. Simplified 83.0%

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

   if -4.79999999999999971e79 < t < 1.60000000000000004e145

   1. Initial program 91.8%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around inf 82.2%

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

      1. associate-*l/ 86.5%

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

      2. *-commutative 86.5%

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

   7. Simplified 86.5%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+79} \lor \neg \left(t \leq 1.6 \cdot 10^{+145}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-78} \lor \neg \left(z \leq 6 \cdot 10^{-44}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1e-78) (not (<= z 6e-44)))
   (+ x (* z (/ y (- a t))))
   (+ x (/ (* y t) (- t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1e-78) || !(z <= 6e-44)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + ((y * t) / (t - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1d-78)) .or. (.not. (z <= 6d-44))) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + ((y * t) / (t - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1e-78) || !(z <= 6e-44)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + ((y * t) / (t - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1e-78) or not (z <= 6e-44):
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + ((y * t) / (t - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1e-78) || !(z <= 6e-44))
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(Float64(y * t) / Float64(t - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1e-78) || ~((z <= 6e-44)))
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + ((y * t) / (t - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1e-78], N[Not[LessEqual[z, 6e-44]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.99999999999999999e-79 or 6.0000000000000005e-44 < z

   1. Initial program 82.4%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in z around inf 79.4%

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

      1. associate-*l/ 86.5%

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

      2. *-commutative 86.5%

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

   7. Simplified 86.5%

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

   if -9.99999999999999999e-79 < z < 6.0000000000000005e-44

   1. Initial program 89.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. mul-1-neg 83.4%

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

      3. *-commutative 83.4%

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

      4. associate-*l/ 89.2%

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

      5. distribute-rgt-neg-out 89.2%

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

   7. Simplified 89.2%

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

      1. associate-*l/ 83.4%

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

      2. frac-2neg 83.4%

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

      3. add-sqr-sqrt 44.6%

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

      4. sqrt-unprod 57.6%

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

      5. sqr-neg 57.6%

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

      6. sqrt-unprod 26.7%

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

      7. add-sqr-sqrt 58.1%

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

      8. distribute-rgt-neg-out 58.1%

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

      9. add-sqr-sqrt 31.4%

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

      10. sqrt-unprod 57.8%

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

      11. sqr-neg 57.8%

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

      12. sqrt-unprod 38.7%

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

      13. add-sqr-sqrt 83.4%

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

      14. sub-neg 83.4%

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

      15. distribute-neg-in 83.4%

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

      16. add-sqr-sqrt 44.6%

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

      17. sqrt-unprod 71.4%

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

      18. sqr-neg 71.4%

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

      19. sqrt-unprod 30.6%

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

      20. add-sqr-sqrt 68.5%

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

      21. add-sqr-sqrt 37.9%

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

      22. sqrt-unprod 74.1%

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

      23. sqr-neg 74.1%

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

   9. Applied egg-rr 83.4%

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

       1. *-commutative 83.4%

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

       2. +-commutative 83.4%

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

       3. unsub-neg 83.4%

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

   11. Simplified 83.4%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-78} \lor \neg \left(z \leq 6 \cdot 10^{-44}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-78} \lor \neg \left(z \leq 8.8 \cdot 10^{+112}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.5e-78) (not (<= z 8.8e+112)))
   (+ x (* z (/ y (- a t))))
   (- x (/ t (/ (- a t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e-78) || !(z <= 8.8e+112)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (t / ((a - t) / 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 <= (-6.5d-78)) .or. (.not. (z <= 8.8d+112))) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x - (t / ((a - t) / 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 <= -6.5e-78) || !(z <= 8.8e+112)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (t / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.5e-78) or not (z <= 8.8e+112):
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x - (t / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.5e-78) || !(z <= 8.8e+112))
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x - Float64(t / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.5e-78) || ~((z <= 8.8e+112)))
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x - (t / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.5e-78], N[Not[LessEqual[z, 8.8e+112]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5000000000000003e-78 or 8.7999999999999997e112 < z

   1. Initial program 82.6%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in z around inf 80.6%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

   7. Simplified 90.0%

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

   if -6.5000000000000003e-78 < z < 8.7999999999999997e112

   1. Initial program 87.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

      3. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 79.6%

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

      1. mul-1-neg 79.6%

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

      2. unsub-neg 79.6%

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

      3. associate-/l* 88.0%

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

   9. Simplified 88.0%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-78} \lor \neg \left(z \leq 8.8 \cdot 10^{+112}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a - t}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{-78} \lor \neg \left(z \leq 1.85 \cdot 10^{+114}\right):\\ \;\;\;\;x + z \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- a t))))
   (if (or (<= z -7.2e-78) (not (<= z 1.85e+114)))
     (+ x (* z t_1))
     (- x (* t t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a - t);
	double tmp;
	if ((z <= -7.2e-78) || !(z <= 1.85e+114)) {
		tmp = x + (z * t_1);
	} else {
		tmp = x - (t * t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (a - t)
    if ((z <= (-7.2d-78)) .or. (.not. (z <= 1.85d+114))) then
        tmp = x + (z * t_1)
    else
        tmp = x - (t * t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a - t);
	double tmp;
	if ((z <= -7.2e-78) || !(z <= 1.85e+114)) {
		tmp = x + (z * t_1);
	} else {
		tmp = x - (t * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a - t)
	tmp = 0
	if (z <= -7.2e-78) or not (z <= 1.85e+114):
		tmp = x + (z * t_1)
	else:
		tmp = x - (t * t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a - t))
	tmp = 0.0
	if ((z <= -7.2e-78) || !(z <= 1.85e+114))
		tmp = Float64(x + Float64(z * t_1));
	else
		tmp = Float64(x - Float64(t * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a - t);
	tmp = 0.0;
	if ((z <= -7.2e-78) || ~((z <= 1.85e+114)))
		tmp = x + (z * t_1);
	else
		tmp = x - (t * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -7.2e-78], N[Not[LessEqual[z, 1.85e+114]], $MachinePrecision]], N[(x + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2000000000000005e-78 or 1.85e114 < z

   1. Initial program 82.6%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in z around inf 80.6%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

   7. Simplified 90.0%

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

   if -7.2000000000000005e-78 < z < 1.85e114

   1. Initial program 87.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 79.6%

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

      1. +-commutative 79.6%

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

      2. mul-1-neg 79.6%

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

      3. *-commutative 79.6%

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

      4. associate-*l/ 88.2%

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

      5. distribute-rgt-neg-out 88.2%

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

   7. Simplified 88.2%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-78} \lor \neg \left(z \leq 1.85 \cdot 10^{+114}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+46} \lor \neg \left(t \leq 1.9 \cdot 10^{+37}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.5e+46) (not (<= t 1.9e+37))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.5e+46) || !(t <= 1.9e+37)) {
		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 <= (-3.5d+46)) .or. (.not. (t <= 1.9d+37))) 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 <= -3.5e+46) || !(t <= 1.9e+37)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.5e+46) or not (t <= 1.9e+37):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.5e+46) || !(t <= 1.9e+37))
		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 <= -3.5e+46) || ~((t <= 1.9e+37)))
		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, -3.5e+46], N[Not[LessEqual[t, 1.9e+37]], $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 < -3.49999999999999985e46 or 1.89999999999999995e37 < t

   1. Initial program 70.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 74.9%

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

      1. +-commutative 74.9%

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

   7. Simplified 74.9%

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

   if -3.49999999999999985e46 < t < 1.89999999999999995e37

   1. Initial program 94.5%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

      1. clear-num 97.5%

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

      2. associate-/r/ 97.3%

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

      3. clear-num 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in t around 0 74.6%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+46} \lor \neg \left(t \leq 1.9 \cdot 10^{+37}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+43} \lor \neg \left(t \leq 1.16 \cdot 10^{+33}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.8e+43) (not (<= t 1.16e+33))) (+ x y) (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.8e+43) || !(t <= 1.16e+33)) {
		tmp = x + y;
	} else {
		tmp = x + (z / (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 ((t <= (-5.8d+43)) .or. (.not. (t <= 1.16d+33))) then
        tmp = x + y
    else
        tmp = x + (z / (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 ((t <= -5.8e+43) || !(t <= 1.16e+33)) {
		tmp = x + y;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.8e+43) or not (t <= 1.16e+33):
		tmp = x + y
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.8e+43) || !(t <= 1.16e+33))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.8e+43) || ~((t <= 1.16e+33)))
		tmp = x + y;
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.8e+43], N[Not[LessEqual[t, 1.16e+33]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.8000000000000004e43 or 1.16000000000000001e33 < t

   1. Initial program 70.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 74.9%

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

      1. +-commutative 74.9%

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

   7. Simplified 74.9%

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

   if -5.8000000000000004e43 < t < 1.16000000000000001e33

   1. Initial program 94.5%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in z around inf 84.0%

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

      1. associate-*l/ 87.3%

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

      2. *-commutative 87.3%

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

   7. Simplified 87.3%

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

      1. associate-*r/ 84.0%

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

      2. frac-2neg 84.0%

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

      3. sub-neg 84.0%

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

      4. distribute-neg-in 84.0%

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

      5. add-sqr-sqrt 43.0%

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

      6. sqrt-unprod 75.0%

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

      7. sqr-neg 75.0%

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

      8. sqrt-unprod 32.0%

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

      9. add-sqr-sqrt 70.1%

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

      10. add-sqr-sqrt 38.1%

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

      11. sqrt-unprod 77.2%

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

      12. sqr-neg 77.2%

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

      13. sqrt-unprod 40.9%

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

      14. add-sqr-sqrt 84.0%

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

   9. Applied egg-rr 84.0%

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

       1. distribute-rgt-neg-in 84.0%

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

       2. associate-/l* 87.6%

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

       3. +-commutative 87.6%

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

       4. unsub-neg 87.6%

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

   11. Simplified 87.6%

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

   12. Taylor expanded in t around 0 75.3%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+43} \lor \neg \left(t \leq 1.16 \cdot 10^{+33}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+130}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.7e+131) x (if (<= a 4e+130) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.7e+131) {
		tmp = x;
	} else if (a <= 4e+130) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.7d+131)) then
        tmp = x
    else if (a <= 4d+130) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.7e+131) {
		tmp = x;
	} else if (a <= 4e+130) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.7e+131:
		tmp = x
	elif a <= 4e+130:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.7e+131)
		tmp = x;
	elseif (a <= 4e+130)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.7e+131)
		tmp = x;
	elseif (a <= 4e+130)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.7e+131], x, If[LessEqual[a, 4e+130], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.7e131 or 4.0000000000000002e130 < a

   1. Initial program 80.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 66.9%

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

   if -5.7e131 < a < 4.0000000000000002e130

   1. Initial program 87.2%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around inf 60.1%

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

      1. +-commutative 60.1%

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

   7. Simplified 60.1%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+130}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.2% 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 85.2%

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

   1. associate-/l* 98.5%

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

3. Simplified 98.5%

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

   1. clear-num 98.4%

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

   2. associate-/r/ 98.3%

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

   3. clear-num 98.4%

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

6. Applied egg-rr 98.4%

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

7. Final simplification 98.4%

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

Alternative 13: 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 85.2%

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

   1. associate-/l* 98.5%

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

3. Simplified 98.5%

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

5. Taylor expanded in x around inf 51.1%

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

6. Final simplification 51.1%

   \[\leadsto x \]
7. 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 2024036 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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