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

Percentage Accurate: 85.1% → 96.6%

Time: 10.5s

Alternatives: 11

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-265}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{z - a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.4e-265)
   (fma y (/ (- z t) (- z a)) x)
   (fma (- z t) (/ y (- z a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.4e-265) {
		tmp = fma(y, ((z - t) / (z - a)), x);
	} else {
		tmp = fma((z - t), (y / (z - a)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.4e-265)
		tmp = fma(y, Float64(Float64(z - t) / Float64(z - a)), x);
	else
		tmp = fma(Float64(z - t), Float64(y / Float64(z - a)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.4e-265], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.3999999999999999e-265

   1. Initial program 90.2%

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

      1. +-commutative 90.2%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   if -6.3999999999999999e-265 < x

   1. Initial program 85.6%

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

      1. +-commutative 85.6%

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

      2. *-commutative 85.6%

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

      3. associate-/l* 99.1%

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

      4. fma-define 99.0%

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

   3. Simplified 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y}{z - a}, x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-265}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{z - a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

   1. +-commutative 87.9%

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

   2. associate-/l* 97.7%

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

   3. fma-define 97.7%

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

3. Simplified 97.7%

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

5. Final simplification 97.7%

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

Alternative 3: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+133}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{-106}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 10000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.6e+133)
   (+ x y)
   (if (<= z -1.56e-106)
     (- x (* t (/ y z)))
     (if (<= z 10000.0) (+ x (/ (* y t) a)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+133) {
		tmp = x + y;
	} else if (z <= -1.56e-106) {
		tmp = x - (t * (y / z));
	} else if (z <= 10000.0) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.6d+133)) then
        tmp = x + y
    else if (z <= (-1.56d-106)) then
        tmp = x - (t * (y / z))
    else if (z <= 10000.0d0) then
        tmp = x + ((y * t) / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+133) {
		tmp = x + y;
	} else if (z <= -1.56e-106) {
		tmp = x - (t * (y / z));
	} else if (z <= 10000.0) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.6e+133:
		tmp = x + y
	elif z <= -1.56e-106:
		tmp = x - (t * (y / z))
	elif z <= 10000.0:
		tmp = x + ((y * t) / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.6e+133)
		tmp = Float64(x + y);
	elseif (z <= -1.56e-106)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 10000.0)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.6e+133)
		tmp = x + y;
	elseif (z <= -1.56e-106)
		tmp = x - (t * (y / z));
	elseif (z <= 10000.0)
		tmp = x + ((y * t) / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.6e+133], N[(x + y), $MachinePrecision], If[LessEqual[z, -1.56e-106], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 10000.0], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.6e133 or 1e4 < z

   1. Initial program 70.4%

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

   3. Taylor expanded in z around inf 79.0%

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

      1. +-commutative 79.0%

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

   5. Simplified 79.0%

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

   if -6.6e133 < z < -1.56e-106

   1. Initial program 94.9%

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

      1. clear-num 94.7%

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

      2. associate-/r/ 94.8%

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

   4. Applied egg-rr 94.8%

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

   5. Taylor expanded in t around inf 76.9%

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

      1. associate-/l* 80.1%

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

      2. associate-*r* 80.1%

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

      3. neg-mul-1 80.1%

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

      4. *-commutative 80.1%

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

   7. Simplified 80.1%

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

      1. distribute-rgt-neg-out 80.1%

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

      2. distribute-lft-neg-in 80.1%

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

      3. add-sqr-sqrt 46.6%

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

      4. sqrt-unprod 55.1%

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

      5. sqr-neg 55.1%

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

      6. sqrt-unprod 19.2%

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

      7. add-sqr-sqrt 52.9%

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

      8. cancel-sign-sub-inv 52.9%

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

      9. associate-*l/ 52.8%

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

      10. associate-/l* 52.9%

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

      11. add-sqr-sqrt 19.2%

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

      12. sqrt-unprod 55.2%

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

      13. sqr-neg 55.2%

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

      14. sqrt-unprod 48.4%

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

      15. add-sqr-sqrt 80.2%

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

   9. Applied egg-rr 80.2%

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

   10. Taylor expanded in z around inf 69.6%

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

       1. associate-*r/ 72.8%

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

   12. Simplified 72.8%

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

   if -1.56e-106 < z < 1e4

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 84.0%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+133}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{-106}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 10000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+122}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+117}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4e+122)
   (- x (* y (/ (- t z) z)))
   (if (<= z 4e+117)
     (+ x (/ (* y (- z t)) (- z a)))
     (+ x (* y (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e+122) {
		tmp = x - (y * ((t - z) / z));
	} else if (z <= 4e+117) {
		tmp = x + ((y * (z - t)) / (z - a));
	} else {
		tmp = x + (y * (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 (z <= (-4d+122)) then
        tmp = x - (y * ((t - z) / z))
    else if (z <= 4d+117) then
        tmp = x + ((y * (z - t)) / (z - a))
    else
        tmp = x + (y * (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 (z <= -4e+122) {
		tmp = x - (y * ((t - z) / z));
	} else if (z <= 4e+117) {
		tmp = x + ((y * (z - t)) / (z - a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4e+122:
		tmp = x - (y * ((t - z) / z))
	elif z <= 4e+117:
		tmp = x + ((y * (z - t)) / (z - a))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4e+122)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	elseif (z <= 4e+117)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(z - a)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4e+122)
		tmp = x - (y * ((t - z) / z));
	elseif (z <= 4e+117)
		tmp = x + ((y * (z - t)) / (z - a));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4e+122], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+117], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.00000000000000006e122

   1. Initial program 67.3%

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

   3. Taylor expanded in a around 0 64.0%

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

      1. +-commutative 64.0%

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

      2. associate-/l* 88.5%

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

   5. Simplified 88.5%

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

   if -4.00000000000000006e122 < z < 4.0000000000000002e117

   1. Initial program 97.8%

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

   if 4.0000000000000002e117 < z

   1. Initial program 61.8%

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

   3. Taylor expanded in t around 0 61.8%

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

      1. +-commutative 61.8%

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

      2. associate-/l* 95.4%

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

   5. Simplified 95.4%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+122}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+117}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-177} \lor \neg \left(z \leq 1.12 \cdot 10^{-54}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e-177) (not (<= z 1.12e-54)))
   (+ x (* y (/ z (- z a))))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e-177) || !(z <= 1.12e-54)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.35d-177)) .or. (.not. (z <= 1.12d-54))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e-177) || !(z <= 1.12e-54)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e-177) or not (z <= 1.12e-54):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e-177) || !(z <= 1.12e-54))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.35e-177) || ~((z <= 1.12e-54)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e-177], N[Not[LessEqual[z, 1.12e-54]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3500000000000001e-177 or 1.11999999999999994e-54 < z

   1. Initial program 83.3%

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

   3. Taylor expanded in t around 0 70.3%

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

      1. +-commutative 70.3%

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

      2. associate-/l* 81.8%

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

   5. Simplified 81.8%

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

   if -1.3500000000000001e-177 < z < 1.11999999999999994e-54

   1. Initial program 98.6%

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

   3. Taylor expanded in z around 0 88.4%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-177} \lor \neg \left(z \leq 1.12 \cdot 10^{-54}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-121} \lor \neg \left(z \leq 1.15 \cdot 10^{-32}\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3e-121) (not (<= z 1.15e-32)))
   (- x (* y (/ (- t z) z)))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e-121) || !(z <= 1.15e-32)) {
		tmp = x - (y * ((t - z) / z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3d-121)) .or. (.not. (z <= 1.15d-32))) then
        tmp = x - (y * ((t - z) / z))
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e-121) || !(z <= 1.15e-32)) {
		tmp = x - (y * ((t - z) / z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3e-121) or not (z <= 1.15e-32):
		tmp = x - (y * ((t - z) / z))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3e-121) || !(z <= 1.15e-32))
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3e-121) || ~((z <= 1.15e-32)))
		tmp = x - (y * ((t - z) / z));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3e-121], N[Not[LessEqual[z, 1.15e-32]], $MachinePrecision]], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9999999999999999e-121 or 1.15e-32 < z

   1. Initial program 81.0%

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

   3. Taylor expanded in a around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. associate-/l* 85.2%

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

   5. Simplified 85.2%

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

   if -2.9999999999999999e-121 < z < 1.15e-32

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 87.0%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-121} \lor \neg \left(z \leq 1.15 \cdot 10^{-32}\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+60} \lor \neg \left(t \leq 2.2 \cdot 10^{+32}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3e+60) (not (<= t 2.2e+32)))
   (+ x (* y (/ t (- a z))))
   (+ x (* y (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3e+60) || !(t <= 2.2e+32)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (y * (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 ((t <= (-3d+60)) .or. (.not. (t <= 2.2d+32))) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + (y * (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 ((t <= -3e+60) || !(t <= 2.2e+32)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3e+60) or not (t <= 2.2e+32):
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3e+60) || !(t <= 2.2e+32))
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3e+60) || ~((t <= 2.2e+32)))
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3e+60], N[Not[LessEqual[t, 2.2e+32]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9999999999999998e60 or 2.20000000000000001e32 < t

   1. Initial program 80.8%

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

      1. clear-num 80.7%

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

      2. associate-/r/ 80.6%

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

   4. Applied egg-rr 80.6%

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

   5. Taylor expanded in t around inf 77.7%

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

      1. associate-/l* 85.8%

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

      2. associate-*r* 85.8%

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

      3. neg-mul-1 85.8%

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

      4. *-commutative 85.8%

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

   7. Simplified 85.8%

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

      1. distribute-rgt-neg-out 85.8%

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

      2. distribute-lft-neg-in 85.8%

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

      3. add-sqr-sqrt 46.6%

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

      4. sqrt-unprod 29.8%

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

      5. sqr-neg 29.8%

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

      6. sqrt-unprod 12.6%

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

      7. add-sqr-sqrt 34.3%

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

      8. cancel-sign-sub-inv 34.3%

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

      9. associate-*l/ 33.2%

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

      10. associate-/l* 34.3%

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

      11. add-sqr-sqrt 12.6%

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

      12. sqrt-unprod 30.2%

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

      13. sqr-neg 30.2%

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

      14. sqrt-unprod 47.9%

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

      15. add-sqr-sqrt 83.2%

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

   9. Applied egg-rr 83.2%

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

   if -2.9999999999999998e60 < t < 2.20000000000000001e32

   1. Initial program 92.2%

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

   3. Taylor expanded in t around 0 84.3%

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

      1. +-commutative 84.3%

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

      2. associate-/l* 92.0%

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

   5. Simplified 92.0%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+60} \lor \neg \left(t \leq 2.2 \cdot 10^{+32}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+53}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.8e+53)
   (+ x (* t (/ y (- a z))))
   (if (<= t 5.2e+31) (+ x (* y (/ z (- z a)))) (+ x (* y (/ t (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+53) {
		tmp = x + (t * (y / (a - z)));
	} else if (t <= 5.2e+31) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y * (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 (t <= (-3.8d+53)) then
        tmp = x + (t * (y / (a - z)))
    else if (t <= 5.2d+31) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + (y * (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 (t <= -3.8e+53) {
		tmp = x + (t * (y / (a - z)));
	} else if (t <= 5.2e+31) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.8e+53:
		tmp = x + (t * (y / (a - z)))
	elif t <= 5.2e+31:
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.8e+53)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	elseif (t <= 5.2e+31)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.8e+53)
		tmp = x + (t * (y / (a - z)));
	elseif (t <= 5.2e+31)
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.8e+53], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+31], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.79999999999999997e53

   1. Initial program 73.5%

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

   3. Taylor expanded in t around inf 69.0%

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

      1. mul-1-neg 69.0%

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

      2. associate-/l* 83.1%

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

      3. distribute-rgt-neg-in 83.1%

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

      4. distribute-frac-neg2 83.1%

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

      5. sub-neg 83.1%

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

      6. mul-1-neg 83.1%

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

      7. distribute-neg-in 83.1%

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

      8. mul-1-neg 83.1%

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

      9. remove-double-neg 83.1%

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

   5. Simplified 83.1%

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

   if -3.79999999999999997e53 < t < 5.2e31

   1. Initial program 92.2%

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

   3. Taylor expanded in t around 0 84.3%

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

      1. +-commutative 84.3%

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

      2. associate-/l* 92.0%

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

   5. Simplified 92.0%

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

   if 5.2e31 < t

   1. Initial program 87.3%

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

      1. clear-num 87.2%

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

      2. associate-/r/ 87.2%

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

   4. Applied egg-rr 87.2%

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

   5. Taylor expanded in t around inf 85.3%

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

      1. associate-/l* 88.2%

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

      2. associate-*r* 88.2%

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

      3. neg-mul-1 88.2%

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

      4. *-commutative 88.2%

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

   7. Simplified 88.2%

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

      1. distribute-rgt-neg-out 88.2%

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

      2. distribute-lft-neg-in 88.2%

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

      3. add-sqr-sqrt 87.9%

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

      4. sqrt-unprod 47.6%

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

      5. sqr-neg 47.6%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 40.9%

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

      8. cancel-sign-sub-inv 40.9%

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

      9. associate-*l/ 40.7%

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

      10. associate-/l* 40.8%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 48.1%

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

      13. sqr-neg 48.1%

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

      14. sqrt-unprod 90.2%

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

      15. add-sqr-sqrt 90.5%

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

   9. Applied egg-rr 90.5%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+53}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-30} \lor \neg \left(z \leq 5500\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e-30) (not (<= z 5500.0))) (+ x y) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-30) || !(z <= 5500.0)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.7d-30)) .or. (.not. (z <= 5500.0d0))) then
        tmp = x + y
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-30) || !(z <= 5500.0)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e-30) or not (z <= 5500.0):
		tmp = x + y
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e-30) || !(z <= 5500.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.7e-30) || ~((z <= 5500.0)))
		tmp = x + y;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e-30], N[Not[LessEqual[z, 5500.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.69999999999999987e-30 or 5500 < z

   1. Initial program 76.4%

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

   3. Taylor expanded in z around inf 74.9%

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

      1. +-commutative 74.9%

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

   5. Simplified 74.9%

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

   if -2.69999999999999987e-30 < z < 5500

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 80.9%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-30} \lor \neg \left(z \leq 5500\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-121} \lor \neg \left(z \leq 5.5 \cdot 10^{-13}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.75e-121) (not (<= z 5.5e-13))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.75e-121) || !(z <= 5.5e-13)) {
		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 ((z <= (-1.75d-121)) .or. (.not. (z <= 5.5d-13))) 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 ((z <= -1.75e-121) || !(z <= 5.5e-13)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.75e-121) or not (z <= 5.5e-13):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.75e-121) || !(z <= 5.5e-13))
		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 ((z <= -1.75e-121) || ~((z <= 5.5e-13)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.75e-121], N[Not[LessEqual[z, 5.5e-13]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.74999999999999996e-121 or 5.49999999999999979e-13 < z

   1. Initial program 80.3%

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

   3. Taylor expanded in z around inf 71.8%

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

      1. +-commutative 71.8%

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

   5. Simplified 71.8%

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

   if -1.74999999999999996e-121 < z < 5.49999999999999979e-13

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 61.5%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-121} \lor \neg \left(z \leq 5.5 \cdot 10^{-13}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.8% 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 87.9%

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

3. Taylor expanded in x around inf 53.7%

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

4. Final simplification 53.7%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024053 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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