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

Percentage Accurate: 98.0% → 98.1%

Time: 11.9s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

   1. *-commutative N/A

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

   2. associate-*l/ N/A

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

   3. associate-/l* N/A

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

   4. cancel-sign-sub N/A

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

   5. neg-sub0 N/A

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

   6. associate-+l- N/A

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

   7. neg-sub0 N/A

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

   8. +-commutative N/A

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

   9. sub-neg N/A

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

   10. *-commutative N/A

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

   11. --lowering--.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z - a} \cdot \left(t - z\right)\right)}\right) \]

   12. sub-neg N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

   13. +-commutative N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(\left(\mathsf{neg}\left(z\right)\right) + \color{blue}{t}\right)\right)\right) \]

   14. neg-sub0 N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(\left(0 - z\right) + t\right)\right)\right) \]

   15. associate-+l- N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(0 - \color{blue}{\left(z - t\right)}\right)\right)\right) \]

   16. neg-sub0 N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)\right)\right) \]

   17. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\frac{y}{z - a} \cdot \left(z - t\right)\right)\right)\right) \]

   18. distribute-lft-neg-in N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z - a}\right)\right) \cdot \color{blue}{\left(z - t\right)}\right)\right) \]

   19. distribute-frac-neg2 N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot \left(\color{blue}{z} - t\right)\right)\right) \]

   20. associate-*l/ N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(z - t\right)}{\color{blue}{\mathsf{neg}\left(\left(z - a\right)\right)}}\right)\right) \]

   21. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(z - t\right)\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - a\right)\right)\right)}\right)\right) \]

3. Simplified 84.4%

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

   1. associate-/l* N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\frac{z - t}{a - z}}\right)\right) \]

   2. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{a - z}{z - t}}}\right)\right) \]

   3. un-div-inv N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{a - z}{z - t}}}\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a - z}{z - t}\right)}\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\left(a - z\right), \color{blue}{\left(z - t\right)}\right)\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \left(\color{blue}{z} - t\right)\right)\right)\right) \]

   7. --lowering--.f64 98.6%

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

6. Applied egg-rr 98.6%

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

7. Final simplification 98.6%

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

Alternative 2: 81.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-108}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-151}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5e-108)
   (+ x (* y (/ z (- z a))))
   (if (<= z 4.4e-151) (+ x (* y (/ t a))) (- x (/ y (+ (/ a z) -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e-108) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 4.4e-151) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (y / ((a / z) + -1.0));
	}
	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 <= (-5d-108)) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= 4.4d-151) then
        tmp = x + (y * (t / a))
    else
        tmp = x - (y / ((a / z) + (-1.0d0)))
    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 <= -5e-108) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 4.4e-151) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (y / ((a / z) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5e-108:
		tmp = x + (y * (z / (z - a)))
	elif z <= 4.4e-151:
		tmp = x + (y * (t / a))
	else:
		tmp = x - (y / ((a / z) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5e-108)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= 4.4e-151)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(a / z) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5e-108)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= 4.4e-151)
		tmp = x + (y * (t / a));
	else
		tmp = x - (y / ((a / z) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5e-108], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e-151], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5e-108

   1. Initial program 97.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. cancel-sign-sub N/A

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

      5. neg-sub0 N/A

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

      6. associate-+l- N/A

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

      7. neg-sub0 N/A

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

      8. +-commutative N/A

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

      9. sub-neg N/A

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

      10. *-commutative N/A

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

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z - a} \cdot \left(t - z\right)\right)}\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(\left(\mathsf{neg}\left(z\right)\right) + \color{blue}{t}\right)\right)\right) \]

      14. neg-sub0 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(\left(0 - z\right) + t\right)\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(0 - \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      16. neg-sub0 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\frac{y}{z - a} \cdot \left(z - t\right)\right)\right)\right) \]

      18. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z - a}\right)\right) \cdot \color{blue}{\left(z - t\right)}\right)\right) \]

      19. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot \left(\color{blue}{z} - t\right)\right)\right) \]

      20. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(z - t\right)}{\color{blue}{\mathsf{neg}\left(\left(z - a\right)\right)}}\right)\right) \]

      21. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(z - t\right)\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - a\right)\right)\right)}\right)\right) \]

   3. Simplified 82.2%

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

   5. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{a - z}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\frac{z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{a - z}\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      5. --lowering--.f64 87.1%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   7. Simplified 87.1%

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

   if -5e-108 < z < 4.3999999999999999e-151

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 84.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 84.0%

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

   if 4.3999999999999999e-151 < z

   1. Initial program 100.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. cancel-sign-sub N/A

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

      5. neg-sub0 N/A

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

      6. associate-+l- N/A

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

      7. neg-sub0 N/A

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

      8. +-commutative N/A

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

      9. sub-neg N/A

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

      10. *-commutative N/A

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

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z - a} \cdot \left(t - z\right)\right)}\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(\left(\mathsf{neg}\left(z\right)\right) + \color{blue}{t}\right)\right)\right) \]

      14. neg-sub0 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(\left(0 - z\right) + t\right)\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(0 - \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      16. neg-sub0 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\frac{y}{z - a} \cdot \left(z - t\right)\right)\right)\right) \]

      18. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z - a}\right)\right) \cdot \color{blue}{\left(z - t\right)}\right)\right) \]

      19. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot \left(\color{blue}{z} - t\right)\right)\right) \]

      20. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(z - t\right)}{\color{blue}{\mathsf{neg}\left(\left(z - a\right)\right)}}\right)\right) \]

      21. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(z - t\right)\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - a\right)\right)\right)}\right)\right) \]

   3. Simplified 79.0%

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

   5. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{a - z}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\frac{z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{a - z}\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      5. --lowering--.f64 87.7%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   7. Simplified 87.7%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(y \cdot \frac{z}{a - z}\right)}\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{a - z}{z}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{a - z}{z}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a - z}{z}\right)}\right)\right) \]

      5. div-sub N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \left(\frac{a}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \left(\frac{a}{z} + \color{blue}{\left(\mathsf{neg}\left(\frac{z}{z}\right)\right)}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \left(\frac{a}{z} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \left(\frac{a}{z} + -1\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{a}{z}\right), \color{blue}{-1}\right)\right)\right) \]

      10. /-lowering-/.f64 87.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(a, z\right), -1\right)\right)\right) \]

   9. Applied egg-rr 87.7%

      \[\leadsto \color{blue}{x - \frac{y}{\frac{a}{z} + -1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-108}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-151}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-157}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))))
   (if (<= z -2.7e-108) t_1 (if (<= z 1.35e-157) (+ x (* y (/ t a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double tmp;
	if (z <= -2.7e-108) {
		tmp = t_1;
	} else if (z <= 1.35e-157) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / (z - a)))
    if (z <= (-2.7d-108)) then
        tmp = t_1
    else if (z <= 1.35d-157) then
        tmp = x + (y * (t / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double tmp;
	if (z <= -2.7e-108) {
		tmp = t_1;
	} else if (z <= 1.35e-157) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (z - a)))
	tmp = 0
	if z <= -2.7e-108:
		tmp = t_1
	elif z <= 1.35e-157:
		tmp = x + (y * (t / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(z - a))))
	tmp = 0.0
	if (z <= -2.7e-108)
		tmp = t_1;
	elseif (z <= 1.35e-157)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / (z - a)));
	tmp = 0.0;
	if (z <= -2.7e-108)
		tmp = t_1;
	elseif (z <= 1.35e-157)
		tmp = x + (y * (t / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e-108], t$95$1, If[LessEqual[z, 1.35e-157], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.70000000000000005e-108 or 1.35e-157 < z

   1. Initial program 98.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. cancel-sign-sub N/A

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

      5. neg-sub0 N/A

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

      6. associate-+l- N/A

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

      7. neg-sub0 N/A

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

      8. +-commutative N/A

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

      9. sub-neg N/A

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

      10. *-commutative N/A

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

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z - a} \cdot \left(t - z\right)\right)}\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(\left(\mathsf{neg}\left(z\right)\right) + \color{blue}{t}\right)\right)\right) \]

      14. neg-sub0 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(\left(0 - z\right) + t\right)\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(0 - \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      16. neg-sub0 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z - a} \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\mathsf{neg}\left(\frac{y}{z - a} \cdot \left(z - t\right)\right)\right)\right) \]

      18. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z - a}\right)\right) \cdot \color{blue}{\left(z - t\right)}\right)\right) \]

      19. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot \left(\color{blue}{z} - t\right)\right)\right) \]

      20. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(z - t\right)}{\color{blue}{\mathsf{neg}\left(\left(z - a\right)\right)}}\right)\right) \]

      21. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(z - t\right)\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - a\right)\right)\right)}\right)\right) \]

   3. Simplified 80.8%

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

   5. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{a - z}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\frac{z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{a - z}\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      5. --lowering--.f64 87.4%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   7. Simplified 87.4%

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

   if -2.70000000000000005e-108 < z < 1.35e-157

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 84.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 84.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-108}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-157}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-136}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+26)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 1.45e-136) (+ x (* y (/ t a))) (+ x (* y (/ (- z t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+26) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 1.45e-136) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.2d+26)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 1.45d-136) then
        tmp = x + (y * (t / a))
    else
        tmp = x + (y * ((z - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+26) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 1.45e-136) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+26:
		tmp = x + (y / (z / (z - t)))
	elif z <= 1.45e-136:
		tmp = x + (y * (t / a))
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+26)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 1.45e-136)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e+26)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 1.45e-136)
		tmp = x + (y * (t / a));
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+26], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-136], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.20000000000000029e26

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \color{blue}{z}\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 82.0%

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

      1. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{z}{z - t}}}\right)\right) \]

      2. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{z}{z - t}}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{z}{z - t}\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      5. --lowering--.f64 82.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   7. Applied egg-rr 82.1%

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

   if -3.20000000000000029e26 < z < 1.44999999999999997e-136

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 80.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 80.2%

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

   if 1.44999999999999997e-136 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \color{blue}{z}\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 86.0%

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

Alternative 5: 80.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-136}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) z)))))
   (if (<= z -1.35e+28) t_1 (if (<= z 1.45e-136) (+ x (* y (/ t a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -1.35e+28) {
		tmp = t_1;
	} else if (z <= 1.45e-136) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / z))
    if (z <= (-1.35d+28)) then
        tmp = t_1
    else if (z <= 1.45d-136) then
        tmp = x + (y * (t / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -1.35e+28) {
		tmp = t_1;
	} else if (z <= 1.45e-136) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / z))
	tmp = 0
	if z <= -1.35e+28:
		tmp = t_1
	elif z <= 1.45e-136:
		tmp = x + (y * (t / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / z)))
	tmp = 0.0
	if (z <= -1.35e+28)
		tmp = t_1;
	elseif (z <= 1.45e-136)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / z));
	tmp = 0.0;
	if (z <= -1.35e+28)
		tmp = t_1;
	elseif (z <= 1.45e-136)
		tmp = x + (y * (t / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+28], t$95$1, If[LessEqual[z, 1.45e-136], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3500000000000001e28 or 1.44999999999999997e-136 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \color{blue}{z}\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 84.2%

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

   if -1.3500000000000001e28 < z < 1.44999999999999997e-136

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 80.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 80.2%

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

Alternative 6: 75.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -60000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-118}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -60000000000.0)
   (+ x y)
   (if (<= z 1.4e-118) (+ x (* y (/ t a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -60000000000.0) {
		tmp = x + y;
	} else if (z <= 1.4e-118) {
		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 <= (-60000000000.0d0)) then
        tmp = x + y
    else if (z <= 1.4d-118) 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 <= -60000000000.0) {
		tmp = x + y;
	} else if (z <= 1.4e-118) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -60000000000.0:
		tmp = x + y
	elif z <= 1.4e-118:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -60000000000.0)
		tmp = Float64(x + y);
	elseif (z <= 1.4e-118)
		tmp = Float64(x + Float64(y * Float64(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 <= -60000000000.0)
		tmp = x + y;
	elseif (z <= 1.4e-118)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -60000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.4e-118], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6e10 or 1.4e-118 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 78.1%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 78.1%

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

   if -6e10 < z < 1.4e-118

   1. Initial program 95.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 78.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 78.5%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -60000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-118}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+183}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+125}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.6e+183) x (if (<= a 4e+125) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e+183) {
		tmp = x;
	} else if (a <= 4e+125) {
		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 <= (-2.6d+183)) then
        tmp = x
    else if (a <= 4d+125) 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 <= -2.6e+183) {
		tmp = x;
	} else if (a <= 4e+125) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.6e+183:
		tmp = x
	elif a <= 4e+125:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.6e+183)
		tmp = x;
	elseif (a <= 4e+125)
		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 <= -2.6e+183)
		tmp = x;
	elseif (a <= 4e+125)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.6e+183], x, If[LessEqual[a, 4e+125], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.5999999999999999e183 or 3.9999999999999997e125 < a

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 70.5%

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

   if -2.5999999999999999e183 < a < 3.9999999999999997e125

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 71.0%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 71.0%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+183}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+125}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-185}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-119}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.2e-185) x (if (<= x 5.8e-119) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.2e-185) {
		tmp = x;
	} else if (x <= 5.8e-119) {
		tmp = 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 (x <= (-2.2d-185)) then
        tmp = x
    else if (x <= 5.8d-119) then
        tmp = 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 (x <= -2.2e-185) {
		tmp = x;
	} else if (x <= 5.8e-119) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.2e-185:
		tmp = x
	elif x <= 5.8e-119:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.2e-185)
		tmp = x;
	elseif (x <= 5.8e-119)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.2e-185)
		tmp = x;
	elseif (x <= 5.8e-119)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.2e-185], x, If[LessEqual[x, 5.8e-119], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2e-185 or 5.8e-119 < x

   1. Initial program 97.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 67.8%

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

   if -2.2e-185 < x < 5.8e-119

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 44.5%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 44.5%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   7. Step-by-step derivation

   8. Simplified 39.6%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 98.0% accurate, 1.0× speedup

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.3%

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

Alternative 10: 50.0% 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 98.3%

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

3. Taylor expanded in x around inf

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

5. Simplified 51.8%

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

Developer Target 1: 98.1% 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 2024191 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- z a) (- z t)))))

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