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

Percentage Accurate: 77.2% → 85.9%

Time: 12.7s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 85.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -4 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-78}:\\ \;\;\;\;x - \frac{y \cdot a - y \cdot z}{t}\\ \mathbf{elif}\;a \leq 50000000000000:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* y (/ z a)))))
   (if (<= a -4e+56)
     t_1
     (if (<= a -3.8e+35)
       (+ x (/ y (/ t (- z a))))
       (if (<= a -1.8e-33)
         t_1
         (if (<= a -2.05e-78)
           (- x (/ (- (* y a) (* y z)) t))
           (if (<= a 50000000000000.0) (- x (/ (* y z) (- a t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (y * (z / a));
	double tmp;
	if (a <= -4e+56) {
		tmp = t_1;
	} else if (a <= -3.8e+35) {
		tmp = x + (y / (t / (z - a)));
	} else if (a <= -1.8e-33) {
		tmp = t_1;
	} else if (a <= -2.05e-78) {
		tmp = x - (((y * a) - (y * z)) / t);
	} else if (a <= 50000000000000.0) {
		tmp = x - ((y * z) / (a - t));
	} 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 = (y + x) - (y * (z / a))
    if (a <= (-4d+56)) then
        tmp = t_1
    else if (a <= (-3.8d+35)) then
        tmp = x + (y / (t / (z - a)))
    else if (a <= (-1.8d-33)) then
        tmp = t_1
    else if (a <= (-2.05d-78)) then
        tmp = x - (((y * a) - (y * z)) / t)
    else if (a <= 50000000000000.0d0) then
        tmp = x - ((y * z) / (a - t))
    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 = (y + x) - (y * (z / a));
	double tmp;
	if (a <= -4e+56) {
		tmp = t_1;
	} else if (a <= -3.8e+35) {
		tmp = x + (y / (t / (z - a)));
	} else if (a <= -1.8e-33) {
		tmp = t_1;
	} else if (a <= -2.05e-78) {
		tmp = x - (((y * a) - (y * z)) / t);
	} else if (a <= 50000000000000.0) {
		tmp = x - ((y * z) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (y * (z / a))
	tmp = 0
	if a <= -4e+56:
		tmp = t_1
	elif a <= -3.8e+35:
		tmp = x + (y / (t / (z - a)))
	elif a <= -1.8e-33:
		tmp = t_1
	elif a <= -2.05e-78:
		tmp = x - (((y * a) - (y * z)) / t)
	elif a <= 50000000000000.0:
		tmp = x - ((y * z) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -4e+56)
		tmp = t_1;
	elseif (a <= -3.8e+35)
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	elseif (a <= -1.8e-33)
		tmp = t_1;
	elseif (a <= -2.05e-78)
		tmp = Float64(x - Float64(Float64(Float64(y * a) - Float64(y * z)) / t));
	elseif (a <= 50000000000000.0)
		tmp = Float64(x - Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (y * (z / a));
	tmp = 0.0;
	if (a <= -4e+56)
		tmp = t_1;
	elseif (a <= -3.8e+35)
		tmp = x + (y / (t / (z - a)));
	elseif (a <= -1.8e-33)
		tmp = t_1;
	elseif (a <= -2.05e-78)
		tmp = x - (((y * a) - (y * z)) / t);
	elseif (a <= 50000000000000.0)
		tmp = x - ((y * z) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e+56], t$95$1, If[LessEqual[a, -3.8e+35], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.8e-33], t$95$1, If[LessEqual[a, -2.05e-78], N[(x - N[(N[(N[(y * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 50000000000000.0], N[(x - N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.00000000000000037e56 or -3.8e35 < a < -1.80000000000000017e-33 or 5e13 < a

   1. Initial program 81.3%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in t around 0 89.6%

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

   if -4.00000000000000037e56 < a < -3.8e35

   1. Initial program 41.4%

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

      1. sub-neg 41.4%

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

      2. distribute-frac-neg 41.4%

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

      3. distribute-rgt-neg-out 41.4%

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

      4. +-commutative 41.4%

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

      5. associate-*l/ 42.0%

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

      6. distribute-rgt-neg-in 42.0%

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

      7. distribute-lft-neg-in 42.0%

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

      8. distribute-frac-neg 42.0%

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

      9. fma-def 42.0%

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

      10. sub-neg 42.0%

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

      11. distribute-neg-in 42.0%

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

      12. remove-double-neg 42.0%

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

      13. +-commutative 42.0%

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

      14. sub-neg 42.0%

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

   3. Simplified 42.0%

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

      1. fma-udef 42.0%

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

      2. +-commutative 42.0%

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

      3. associate-+r+ 60.7%

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

      4. clear-num 60.4%

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

      5. associate-*l/ 60.4%

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

      6. *-un-lft-identity 60.4%

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

   6. Applied egg-rr 60.4%

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

   7. Taylor expanded in t around inf 80.3%

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

      1. neg-mul-1 80.3%

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

      2. associate-*l/ 61.5%

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

      3. associate-+r+ 61.5%

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

      4. neg-mul-1 61.5%

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

      5. distribute-rgt1-in 61.5%

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

      6. metadata-eval 61.5%

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

      7. mul0-lft 61.5%

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

      8. associate-*l/ 80.2%

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

      9. associate--l+ 80.2%

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

      10. associate-*l/ 99.1%

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

      11. associate-*l/ 80.3%

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

      12. div-sub 80.3%

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

      13. *-commutative 80.3%

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

      14. distribute-rgt-out-- 80.3%

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

      15. associate-*l/ 80.2%

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

      16. +-lft-identity 80.2%

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

      17. associate-*l/ 80.3%

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

      18. associate-/l* 99.4%

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

   9. Simplified 99.4%

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

   if -1.80000000000000017e-33 < a < -2.0499999999999999e-78

   1. Initial program 71.5%

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

      1. associate-*l/ 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in t around -inf 85.0%

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

      1. mul-1-neg 85.0%

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

      2. unsub-neg 85.0%

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

      3. *-commutative 85.0%

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

   7. Simplified 85.0%

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

   if -2.0499999999999999e-78 < a < 5e13

   1. Initial program 80.8%

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

      1. sub-neg 80.8%

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

      2. distribute-frac-neg 80.8%

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

      3. distribute-rgt-neg-out 80.8%

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

      4. +-commutative 80.8%

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

      5. associate-*l/ 78.4%

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

      6. distribute-rgt-neg-in 78.4%

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

      7. distribute-lft-neg-in 78.4%

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

      8. distribute-frac-neg 78.4%

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

      9. fma-def 78.4%

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

      10. sub-neg 78.4%

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

      11. distribute-neg-in 78.4%

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

      12. remove-double-neg 78.4%

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

      13. +-commutative 78.4%

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

      14. sub-neg 78.4%

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

   3. Simplified 78.4%

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

      1. fma-udef 78.4%

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

      2. +-commutative 78.4%

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

      3. associate-+r+ 84.8%

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

      4. clear-num 84.8%

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

      5. associate-*l/ 85.5%

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

      6. *-un-lft-identity 85.5%

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

   6. Applied egg-rr 85.5%

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

   7. Taylor expanded in z around inf 90.7%

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

      1. associate-*r/ 90.7%

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

      2. associate-*r* 90.7%

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

      3. neg-mul-1 90.7%

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

   9. Simplified 90.7%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+56}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-33}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-78}:\\ \;\;\;\;x - \frac{y \cdot a - y \cdot z}{t}\\ \mathbf{elif}\;a \leq 50000000000000:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{if}\;a \leq -4 \cdot 10^{+83}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7500000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-33}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ t (- z a))))))
   (if (<= a -4e+83)
     (+ y x)
     (if (<= a -6.8e+31)
       t_1
       (if (<= a -7500000000.0)
         (+ y x)
         (if (<= a -5.8e-33)
           (- x (/ y (/ a z)))
           (if (<= a 1.16e-36) t_1 (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (t / (z - a)));
	double tmp;
	if (a <= -4e+83) {
		tmp = y + x;
	} else if (a <= -6.8e+31) {
		tmp = t_1;
	} else if (a <= -7500000000.0) {
		tmp = y + x;
	} else if (a <= -5.8e-33) {
		tmp = x - (y / (a / z));
	} else if (a <= 1.16e-36) {
		tmp = t_1;
	} else {
		tmp = y + 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (t / (z - a)))
    if (a <= (-4d+83)) then
        tmp = y + x
    else if (a <= (-6.8d+31)) then
        tmp = t_1
    else if (a <= (-7500000000.0d0)) then
        tmp = y + x
    else if (a <= (-5.8d-33)) then
        tmp = x - (y / (a / z))
    else if (a <= 1.16d-36) then
        tmp = t_1
    else
        tmp = y + x
    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 / (t / (z - a)));
	double tmp;
	if (a <= -4e+83) {
		tmp = y + x;
	} else if (a <= -6.8e+31) {
		tmp = t_1;
	} else if (a <= -7500000000.0) {
		tmp = y + x;
	} else if (a <= -5.8e-33) {
		tmp = x - (y / (a / z));
	} else if (a <= 1.16e-36) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (t / (z - a)))
	tmp = 0
	if a <= -4e+83:
		tmp = y + x
	elif a <= -6.8e+31:
		tmp = t_1
	elif a <= -7500000000.0:
		tmp = y + x
	elif a <= -5.8e-33:
		tmp = x - (y / (a / z))
	elif a <= 1.16e-36:
		tmp = t_1
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(t / Float64(z - a))))
	tmp = 0.0
	if (a <= -4e+83)
		tmp = Float64(y + x);
	elseif (a <= -6.8e+31)
		tmp = t_1;
	elseif (a <= -7500000000.0)
		tmp = Float64(y + x);
	elseif (a <= -5.8e-33)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	elseif (a <= 1.16e-36)
		tmp = t_1;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (t / (z - a)));
	tmp = 0.0;
	if (a <= -4e+83)
		tmp = y + x;
	elseif (a <= -6.8e+31)
		tmp = t_1;
	elseif (a <= -7500000000.0)
		tmp = y + x;
	elseif (a <= -5.8e-33)
		tmp = x - (y / (a / z));
	elseif (a <= 1.16e-36)
		tmp = t_1;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e+83], N[(y + x), $MachinePrecision], If[LessEqual[a, -6.8e+31], t$95$1, If[LessEqual[a, -7500000000.0], N[(y + x), $MachinePrecision], If[LessEqual[a, -5.8e-33], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.16e-36], t$95$1, N[(y + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.00000000000000012e83 or -6.7999999999999996e31 < a < -7.5e9 or 1.16000000000000002e-36 < a

   1. Initial program 81.3%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in a around inf 81.6%

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

      1. +-commutative 81.6%

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

   7. Simplified 81.6%

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

   if -4.00000000000000012e83 < a < -6.7999999999999996e31 or -5.80000000000000005e-33 < a < 1.16000000000000002e-36

   1. Initial program 77.0%

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

      1. sub-neg 77.0%

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

      2. distribute-frac-neg 77.0%

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

      3. distribute-rgt-neg-out 77.0%

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

      4. +-commutative 77.0%

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

      5. associate-*l/ 74.8%

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

      6. distribute-rgt-neg-in 74.8%

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

      7. distribute-lft-neg-in 74.8%

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

      8. distribute-frac-neg 74.8%

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

      9. fma-def 74.8%

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

      10. sub-neg 74.8%

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

      11. distribute-neg-in 74.8%

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

      12. remove-double-neg 74.8%

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

      13. +-commutative 74.8%

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

      14. sub-neg 74.8%

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

   3. Simplified 74.8%

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

      1. fma-udef 74.8%

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

      2. +-commutative 74.8%

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

      3. associate-+r+ 81.6%

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

      4. clear-num 81.5%

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

      5. associate-*l/ 82.2%

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

      6. *-un-lft-identity 82.2%

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

   6. Applied egg-rr 82.2%

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

   7. Taylor expanded in t around inf 76.8%

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

      1. neg-mul-1 76.8%

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

      2. associate-*l/ 75.9%

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

      3. associate-+r+ 82.2%

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

      4. neg-mul-1 82.2%

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

      5. distribute-rgt1-in 82.2%

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

      6. metadata-eval 82.2%

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

      7. mul0-lft 82.2%

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

      8. associate-*l/ 82.2%

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

      9. associate--l+ 82.2%

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

      10. associate-*l/ 82.3%

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

      11. associate-*l/ 82.3%

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

      12. div-sub 82.3%

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

      13. *-commutative 82.3%

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

      14. distribute-rgt-out-- 82.3%

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

      15. associate-*l/ 82.9%

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

      16. +-lft-identity 82.9%

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

      17. associate-*l/ 82.3%

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

      18. associate-/l* 81.7%

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

   9. Simplified 81.7%

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

   if -7.5e9 < a < -5.80000000000000005e-33

   1. Initial program 96.3%

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

      1. sub-neg 96.3%

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

      2. distribute-frac-neg 96.3%

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

      3. distribute-rgt-neg-out 96.3%

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

      4. +-commutative 96.3%

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

      5. associate-*l/ 96.8%

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

      6. distribute-rgt-neg-in 96.8%

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

      7. distribute-lft-neg-in 96.8%

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

      8. distribute-frac-neg 96.8%

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

      9. fma-def 97.0%

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

      10. sub-neg 97.0%

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

      11. distribute-neg-in 97.0%

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

      12. remove-double-neg 97.0%

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

      13. +-commutative 97.0%

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

      14. sub-neg 97.0%

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

   3. Simplified 97.0%

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

      1. fma-udef 96.8%

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

      2. +-commutative 96.8%

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

      3. associate-+r+ 96.8%

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

      4. clear-num 96.8%

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

      5. associate-*l/ 96.7%

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

      6. *-un-lft-identity 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in z around inf 91.2%

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

      1. associate-*r/ 91.2%

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

      2. associate-*r* 91.2%

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

      3. neg-mul-1 91.2%

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

   9. Simplified 91.2%

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

   10. Taylor expanded in a around inf 81.6%

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

       1. mul-1-neg 81.6%

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

       2. associate-/l* 81.6%

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

   12. Simplified 81.6%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+83}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq -7500000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-33}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{t}{z - a}}\\ t_2 := \left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 22000000000000:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ t (- z a))))) (t_2 (- (+ y x) (* y (/ z a)))))
   (if (<= a -3.2e+56)
     t_2
     (if (<= a -3.8e+35)
       t_1
       (if (<= a -2.9e-32)
         t_2
         (if (<= a -3e-77)
           t_1
           (if (<= a 22000000000000.0) (- x (/ (* y z) (- a t))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (t / (z - a)));
	double t_2 = (y + x) - (y * (z / a));
	double tmp;
	if (a <= -3.2e+56) {
		tmp = t_2;
	} else if (a <= -3.8e+35) {
		tmp = t_1;
	} else if (a <= -2.9e-32) {
		tmp = t_2;
	} else if (a <= -3e-77) {
		tmp = t_1;
	} else if (a <= 22000000000000.0) {
		tmp = x - ((y * z) / (a - t));
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x + (y / (t / (z - a)))
    t_2 = (y + x) - (y * (z / a))
    if (a <= (-3.2d+56)) then
        tmp = t_2
    else if (a <= (-3.8d+35)) then
        tmp = t_1
    else if (a <= (-2.9d-32)) then
        tmp = t_2
    else if (a <= (-3d-77)) then
        tmp = t_1
    else if (a <= 22000000000000.0d0) then
        tmp = x - ((y * z) / (a - t))
    else
        tmp = t_2
    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 / (t / (z - a)));
	double t_2 = (y + x) - (y * (z / a));
	double tmp;
	if (a <= -3.2e+56) {
		tmp = t_2;
	} else if (a <= -3.8e+35) {
		tmp = t_1;
	} else if (a <= -2.9e-32) {
		tmp = t_2;
	} else if (a <= -3e-77) {
		tmp = t_1;
	} else if (a <= 22000000000000.0) {
		tmp = x - ((y * z) / (a - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (t / (z - a)))
	t_2 = (y + x) - (y * (z / a))
	tmp = 0
	if a <= -3.2e+56:
		tmp = t_2
	elif a <= -3.8e+35:
		tmp = t_1
	elif a <= -2.9e-32:
		tmp = t_2
	elif a <= -3e-77:
		tmp = t_1
	elif a <= 22000000000000.0:
		tmp = x - ((y * z) / (a - t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(t / Float64(z - a))))
	t_2 = Float64(Float64(y + x) - Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -3.2e+56)
		tmp = t_2;
	elseif (a <= -3.8e+35)
		tmp = t_1;
	elseif (a <= -2.9e-32)
		tmp = t_2;
	elseif (a <= -3e-77)
		tmp = t_1;
	elseif (a <= 22000000000000.0)
		tmp = Float64(x - Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (t / (z - a)));
	t_2 = (y + x) - (y * (z / a));
	tmp = 0.0;
	if (a <= -3.2e+56)
		tmp = t_2;
	elseif (a <= -3.8e+35)
		tmp = t_1;
	elseif (a <= -2.9e-32)
		tmp = t_2;
	elseif (a <= -3e-77)
		tmp = t_1;
	elseif (a <= 22000000000000.0)
		tmp = x - ((y * z) / (a - t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + x), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e+56], t$95$2, If[LessEqual[a, -3.8e+35], t$95$1, If[LessEqual[a, -2.9e-32], t$95$2, If[LessEqual[a, -3e-77], t$95$1, If[LessEqual[a, 22000000000000.0], N[(x - N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.20000000000000003e56 or -3.8e35 < a < -2.89999999999999996e-32 or 2.2e13 < a

   1. Initial program 81.3%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in t around 0 89.6%

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

   if -3.20000000000000003e56 < a < -3.8e35 or -2.89999999999999996e-32 < a < -3.00000000000000016e-77

   1. Initial program 63.2%

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

      1. sub-neg 63.2%

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

      2. distribute-frac-neg 63.2%

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

      3. distribute-rgt-neg-out 63.2%

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

      4. +-commutative 63.2%

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

      5. associate-*l/ 63.5%

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

      6. distribute-rgt-neg-in 63.5%

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

      7. distribute-lft-neg-in 63.5%

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

      8. distribute-frac-neg 63.5%

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

      9. fma-def 63.3%

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

      10. sub-neg 63.3%

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

      11. distribute-neg-in 63.3%

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

      12. remove-double-neg 63.3%

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

      13. +-commutative 63.3%

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

      14. sub-neg 63.3%

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

   3. Simplified 63.3%

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

      1. fma-udef 63.5%

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

      2. +-commutative 63.5%

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

      3. associate-+r+ 74.0%

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

      4. clear-num 74.0%

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

      5. associate-*l/ 74.0%

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

      6. *-un-lft-identity 74.0%

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

   6. Applied egg-rr 74.0%

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

   7. Taylor expanded in t around inf 78.2%

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

      1. neg-mul-1 78.2%

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

      2. associate-*l/ 73.0%

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

      3. associate-+r+ 78.4%

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

      4. neg-mul-1 78.4%

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

      5. distribute-rgt1-in 78.4%

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

      6. metadata-eval 78.4%

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

      7. mul0-lft 78.4%

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

      8. associate-*l/ 83.6%

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

      9. associate--l+ 83.6%

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

      10. associate-*l/ 88.9%

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

      11. associate-*l/ 83.7%

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

      12. div-sub 83.7%

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

      13. *-commutative 83.7%

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

      14. distribute-rgt-out-- 83.7%

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

      15. associate-*l/ 83.6%

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

      16. +-lft-identity 83.6%

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

      17. associate-*l/ 83.7%

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

      18. associate-/l* 88.8%

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

   9. Simplified 88.8%

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

   if -3.00000000000000016e-77 < a < 2.2e13

   1. Initial program 80.8%

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

      1. sub-neg 80.8%

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

      2. distribute-frac-neg 80.8%

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

      3. distribute-rgt-neg-out 80.8%

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

      4. +-commutative 80.8%

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

      5. associate-*l/ 78.4%

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

      6. distribute-rgt-neg-in 78.4%

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

      7. distribute-lft-neg-in 78.4%

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

      8. distribute-frac-neg 78.4%

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

      9. fma-def 78.4%

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

      10. sub-neg 78.4%

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

      11. distribute-neg-in 78.4%

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

      12. remove-double-neg 78.4%

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

      13. +-commutative 78.4%

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

      14. sub-neg 78.4%

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

   3. Simplified 78.4%

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

      1. fma-udef 78.4%

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

      2. +-commutative 78.4%

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

      3. associate-+r+ 84.8%

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

      4. clear-num 84.8%

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

      5. associate-*l/ 85.5%

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

      6. *-un-lft-identity 85.5%

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

   6. Applied egg-rr 85.5%

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

   7. Taylor expanded in z around inf 90.7%

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

      1. associate-*r/ 90.7%

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

      2. associate-*r* 90.7%

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

      3. neg-mul-1 90.7%

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

   9. Simplified 90.7%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+56}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-32}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-77}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 22000000000000:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+56} \lor \neg \left(a \leq -1.15 \cdot 10^{+35} \lor \neg \left(a \leq -3.2 \cdot 10^{-33}\right) \land a \leq 8.1 \cdot 10^{-41}\right):\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.2e+56)
         (not
          (or (<= a -1.15e+35) (and (not (<= a -3.2e-33)) (<= a 8.1e-41)))))
   (- (+ y x) (* y (/ z a)))
   (+ x (/ y (/ t (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.2e+56) || !((a <= -1.15e+35) || (!(a <= -3.2e-33) && (a <= 8.1e-41)))) {
		tmp = (y + x) - (y * (z / a));
	} else {
		tmp = x + (y / (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.2d+56)) .or. (.not. (a <= (-1.15d+35)) .or. (.not. (a <= (-3.2d-33))) .and. (a <= 8.1d-41))) then
        tmp = (y + x) - (y * (z / a))
    else
        tmp = x + (y / (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.2e+56) || !((a <= -1.15e+35) || (!(a <= -3.2e-33) && (a <= 8.1e-41)))) {
		tmp = (y + x) - (y * (z / a));
	} else {
		tmp = x + (y / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.2e+56) or not ((a <= -1.15e+35) or (not (a <= -3.2e-33) and (a <= 8.1e-41))):
		tmp = (y + x) - (y * (z / a))
	else:
		tmp = x + (y / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.2e+56) || !((a <= -1.15e+35) || (!(a <= -3.2e-33) && (a <= 8.1e-41))))
		tmp = Float64(Float64(y + x) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.2e+56) || ~(((a <= -1.15e+35) || (~((a <= -3.2e-33)) && (a <= 8.1e-41)))))
		tmp = (y + x) - (y * (z / a));
	else
		tmp = x + (y / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.2e+56], N[Not[Or[LessEqual[a, -1.15e+35], And[N[Not[LessEqual[a, -3.2e-33]], $MachinePrecision], LessEqual[a, 8.1e-41]]]], $MachinePrecision]], N[(N[(y + x), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.20000000000000003e56 or -1.1499999999999999e35 < a < -3.19999999999999977e-33 or 8.1e-41 < a

   1. Initial program 82.4%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in t around 0 88.5%

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

   if -3.20000000000000003e56 < a < -1.1499999999999999e35 or -3.19999999999999977e-33 < a < 8.1e-41

   1. Initial program 77.1%

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

      1. sub-neg 77.1%

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

      2. distribute-frac-neg 77.1%

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

      3. distribute-rgt-neg-out 77.1%

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

      4. +-commutative 77.1%

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

      5. associate-*l/ 74.8%

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

      6. distribute-rgt-neg-in 74.8%

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

      7. distribute-lft-neg-in 74.8%

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

      8. distribute-frac-neg 74.8%

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

      9. fma-def 74.8%

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

      10. sub-neg 74.8%

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

      11. distribute-neg-in 74.8%

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

      12. remove-double-neg 74.8%

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

      13. +-commutative 74.8%

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

      14. sub-neg 74.8%

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

   3. Simplified 74.8%

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

      1. fma-udef 74.8%

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

      2. +-commutative 74.8%

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

      3. associate-+r+ 81.7%

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

      4. clear-num 81.6%

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

      5. associate-*l/ 82.4%

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

      6. *-un-lft-identity 82.4%

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

   6. Applied egg-rr 82.4%

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

   7. Taylor expanded in t around inf 77.5%

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

      1. neg-mul-1 77.5%

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

      2. associate-*l/ 76.6%

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

      3. associate-+r+ 83.1%

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

      4. neg-mul-1 83.1%

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

      5. distribute-rgt1-in 83.1%

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

      6. metadata-eval 83.1%

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

      7. mul0-lft 83.1%

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

      8. associate-*l/ 83.1%

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

      9. associate--l+ 83.1%

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

      10. associate-*l/ 83.2%

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

      11. associate-*l/ 83.2%

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

      12. div-sub 83.2%

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

      13. *-commutative 83.2%

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

      14. distribute-rgt-out-- 83.2%

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

      15. associate-*l/ 83.8%

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

      16. +-lft-identity 83.8%

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

      17. associate-*l/ 83.2%

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

      18. associate-/l* 82.6%

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

   9. Simplified 82.6%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+56} \lor \neg \left(a \leq -1.15 \cdot 10^{+35} \lor \neg \left(a \leq -3.2 \cdot 10^{-33}\right) \land a \leq 8.1 \cdot 10^{-41}\right):\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+261}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+150}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+170}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.15e+261)
   (/ (- y) (/ a z))
   (if (<= z -3.3e+150)
     (+ y x)
     (if (<= z -2.3e+115)
       (* z (/ y t))
       (if (<= z 1.95e+170) (+ y x) (/ (* y z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.15e+261) {
		tmp = -y / (a / z);
	} else if (z <= -3.3e+150) {
		tmp = y + x;
	} else if (z <= -2.3e+115) {
		tmp = z * (y / t);
	} else if (z <= 1.95e+170) {
		tmp = y + x;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.15d+261)) then
        tmp = -y / (a / z)
    else if (z <= (-3.3d+150)) then
        tmp = y + x
    else if (z <= (-2.3d+115)) then
        tmp = z * (y / t)
    else if (z <= 1.95d+170) then
        tmp = y + x
    else
        tmp = (y * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.15e+261) {
		tmp = -y / (a / z);
	} else if (z <= -3.3e+150) {
		tmp = y + x;
	} else if (z <= -2.3e+115) {
		tmp = z * (y / t);
	} else if (z <= 1.95e+170) {
		tmp = y + x;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.15e+261:
		tmp = -y / (a / z)
	elif z <= -3.3e+150:
		tmp = y + x
	elif z <= -2.3e+115:
		tmp = z * (y / t)
	elif z <= 1.95e+170:
		tmp = y + x
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.15e+261)
		tmp = Float64(Float64(-y) / Float64(a / z));
	elseif (z <= -3.3e+150)
		tmp = Float64(y + x);
	elseif (z <= -2.3e+115)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 1.95e+170)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.15e+261)
		tmp = -y / (a / z);
	elseif (z <= -3.3e+150)
		tmp = y + x;
	elseif (z <= -2.3e+115)
		tmp = z * (y / t);
	elseif (z <= 1.95e+170)
		tmp = y + x;
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.15e+261], N[((-y) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e+150], N[(y + x), $MachinePrecision], If[LessEqual[z, -2.3e+115], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+170], N[(y + x), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1500000000000001e261

   1. Initial program 79.3%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 79.7%

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

   6. Taylor expanded in x around 0 59.1%

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

   7. Taylor expanded in z around inf 59.1%

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

      1. mul-1-neg 59.1%

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

      2. associate-/l* 66.2%

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

      3. distribute-frac-neg 66.2%

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

   9. Simplified 66.2%

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

   if -3.1500000000000001e261 < z < -3.29999999999999981e150 or -2.30000000000000004e115 < z < 1.9500000000000001e170

   1. Initial program 79.7%

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

      1. associate-*l/ 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in a around inf 71.4%

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

      1. +-commutative 71.4%

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

   7. Simplified 71.4%

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

   if -3.29999999999999981e150 < z < -2.30000000000000004e115

   1. Initial program 67.6%

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

      1. sub-neg 67.6%

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

      2. distribute-frac-neg 67.6%

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

      3. distribute-rgt-neg-out 67.6%

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

      4. +-commutative 67.6%

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

      5. associate-*l/ 51.7%

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

      6. distribute-rgt-neg-in 51.7%

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

      7. distribute-lft-neg-in 51.7%

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

      8. distribute-frac-neg 51.7%

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

      9. fma-def 51.7%

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

      10. sub-neg 51.7%

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

      11. distribute-neg-in 51.7%

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

      12. remove-double-neg 51.7%

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

      13. +-commutative 51.7%

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

      14. sub-neg 51.7%

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

   3. Simplified 51.7%

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

      1. fma-udef 51.7%

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

      2. +-commutative 51.7%

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

      3. associate-+r+ 51.6%

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

      4. clear-num 51.6%

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

      5. associate-*l/ 51.6%

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

      6. *-un-lft-identity 51.6%

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

   6. Applied egg-rr 51.6%

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

   7. Taylor expanded in z around inf 83.6%

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

      1. associate-*r/ 83.6%

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

      2. associate-*r* 83.6%

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

      3. neg-mul-1 83.6%

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

   9. Simplified 83.6%

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

   10. Taylor expanded in a around 0 61.8%

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

       1. associate-/l* 67.4%

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

   12. Simplified 67.4%

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

   13. Taylor expanded in y around inf 61.8%

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

       1. associate-*l/ 77.6%

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

       2. *-commutative 77.6%

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

   15. Simplified 77.6%

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

   if 1.9500000000000001e170 < z

   1. Initial program 84.2%

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

      1. sub-neg 84.2%

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

      2. distribute-frac-neg 84.2%

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

      3. distribute-rgt-neg-out 84.2%

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

      4. +-commutative 84.2%

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

      5. associate-*l/ 84.0%

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

      6. distribute-rgt-neg-in 84.0%

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

      7. distribute-lft-neg-in 84.0%

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

      8. distribute-frac-neg 84.0%

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

      9. fma-def 84.0%

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

      10. sub-neg 84.0%

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

      11. distribute-neg-in 84.0%

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

      12. remove-double-neg 84.0%

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

      13. +-commutative 84.0%

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

      14. sub-neg 84.0%

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

   3. Simplified 84.0%

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

      1. fma-udef 84.0%

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

      2. +-commutative 84.0%

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

      3. associate-+r+ 84.0%

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

      4. clear-num 83.8%

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

      5. associate-*l/ 87.4%

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

      6. *-un-lft-identity 87.4%

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

   6. Applied egg-rr 87.4%

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

   7. Taylor expanded in z around inf 80.1%

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

      1. associate-*r/ 80.1%

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

      2. associate-*r* 80.1%

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

      3. neg-mul-1 80.1%

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

   9. Simplified 80.1%

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

   10. Taylor expanded in a around 0 64.3%

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

       1. associate-/l* 63.8%

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

   12. Simplified 63.8%

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

   13. Taylor expanded in y around inf 48.8%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+261}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+150}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+170}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+150} \lor \neg \left(z \leq -2.75 \cdot 10^{+115}\right) \land z \leq 4.2 \cdot 10^{+167}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.3e+150) (and (not (<= z -2.75e+115)) (<= z 4.2e+167)))
   (+ y x)
   (* z (/ y t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+150) || (!(z <= -2.75e+115) && (z <= 4.2e+167))) {
		tmp = y + x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.3d+150)) .or. (.not. (z <= (-2.75d+115))) .and. (z <= 4.2d+167)) then
        tmp = y + x
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+150) || (!(z <= -2.75e+115) && (z <= 4.2e+167))) {
		tmp = y + x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.3e+150) or (not (z <= -2.75e+115) and (z <= 4.2e+167)):
		tmp = y + x
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.3e+150) || (!(z <= -2.75e+115) && (z <= 4.2e+167)))
		tmp = Float64(y + x);
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.3e+150) || (~((z <= -2.75e+115)) && (z <= 4.2e+167)))
		tmp = y + x;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.3e+150], And[N[Not[LessEqual[z, -2.75e+115]], $MachinePrecision], LessEqual[z, 4.2e+167]]], N[(y + x), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.30000000000000003e150 or -2.75e115 < z < 4.1999999999999998e167

   1. Initial program 79.6%

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

      1. associate-*l/ 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in a around inf 68.9%

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

      1. +-commutative 68.9%

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

   7. Simplified 68.9%

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

   if -1.30000000000000003e150 < z < -2.75e115 or 4.1999999999999998e167 < z

   1. Initial program 80.9%

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

      1. sub-neg 80.9%

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

      2. distribute-frac-neg 80.9%

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

      3. distribute-rgt-neg-out 80.9%

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

      4. +-commutative 80.9%

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

      5. associate-*l/ 77.5%

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

      6. distribute-rgt-neg-in 77.5%

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

      7. distribute-lft-neg-in 77.5%

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

      8. distribute-frac-neg 77.5%

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

      9. fma-def 77.5%

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

      10. sub-neg 77.5%

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

      11. distribute-neg-in 77.5%

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

      12. remove-double-neg 77.5%

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

      13. +-commutative 77.5%

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

      14. sub-neg 77.5%

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

   3. Simplified 77.5%

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

      1. fma-udef 77.5%

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

      2. +-commutative 77.5%

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

      3. associate-+r+ 77.5%

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

      4. clear-num 77.4%

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

      5. associate-*l/ 80.3%

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

      6. *-un-lft-identity 80.3%

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

   6. Applied egg-rr 80.3%

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

   7. Taylor expanded in z around inf 80.8%

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

      1. associate-*r/ 80.8%

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

      2. associate-*r* 80.8%

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

      3. neg-mul-1 80.8%

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

   9. Simplified 80.8%

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

   10. Taylor expanded in a around 0 63.8%

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

       1. associate-/l* 64.5%

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

   12. Simplified 64.5%

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

   13. Taylor expanded in y around inf 51.4%

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

       1. associate-*l/ 53.3%

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

       2. *-commutative 53.3%

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

   15. Simplified 53.3%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+150} \lor \neg \left(z \leq -2.75 \cdot 10^{+115}\right) \land z \leq 4.2 \cdot 10^{+167}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+150}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+170}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+150)
   (+ y x)
   (if (<= z -2.75e+115)
     (* z (/ y t))
     (if (<= z 1.25e+170) (+ y x) (/ (* y z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+150) {
		tmp = y + x;
	} else if (z <= -2.75e+115) {
		tmp = z * (y / t);
	} else if (z <= 1.25e+170) {
		tmp = y + x;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.05d+150)) then
        tmp = y + x
    else if (z <= (-2.75d+115)) then
        tmp = z * (y / t)
    else if (z <= 1.25d+170) then
        tmp = y + x
    else
        tmp = (y * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+150) {
		tmp = y + x;
	} else if (z <= -2.75e+115) {
		tmp = z * (y / t);
	} else if (z <= 1.25e+170) {
		tmp = y + x;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+150:
		tmp = y + x
	elif z <= -2.75e+115:
		tmp = z * (y / t)
	elif z <= 1.25e+170:
		tmp = y + x
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+150)
		tmp = Float64(y + x);
	elseif (z <= -2.75e+115)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 1.25e+170)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e+150)
		tmp = y + x;
	elseif (z <= -2.75e+115)
		tmp = z * (y / t);
	elseif (z <= 1.25e+170)
		tmp = y + x;
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+150], N[(y + x), $MachinePrecision], If[LessEqual[z, -2.75e+115], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+170], N[(y + x), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.04999999999999999e150 or -2.75e115 < z < 1.24999999999999994e170

   1. Initial program 79.6%

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

      1. associate-*l/ 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in a around inf 68.9%

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

      1. +-commutative 68.9%

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

   7. Simplified 68.9%

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

   if -1.04999999999999999e150 < z < -2.75e115

   1. Initial program 67.6%

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

      1. sub-neg 67.6%

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

      2. distribute-frac-neg 67.6%

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

      3. distribute-rgt-neg-out 67.6%

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

      4. +-commutative 67.6%

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

      5. associate-*l/ 51.7%

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

      6. distribute-rgt-neg-in 51.7%

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

      7. distribute-lft-neg-in 51.7%

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

      8. distribute-frac-neg 51.7%

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

      9. fma-def 51.7%

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

      10. sub-neg 51.7%

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

      11. distribute-neg-in 51.7%

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

      12. remove-double-neg 51.7%

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

      13. +-commutative 51.7%

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

      14. sub-neg 51.7%

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

   3. Simplified 51.7%

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

      1. fma-udef 51.7%

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

      2. +-commutative 51.7%

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

      3. associate-+r+ 51.6%

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

      4. clear-num 51.6%

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

      5. associate-*l/ 51.6%

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

      6. *-un-lft-identity 51.6%

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

   6. Applied egg-rr 51.6%

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

   7. Taylor expanded in z around inf 83.6%

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

      1. associate-*r/ 83.6%

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

      2. associate-*r* 83.6%

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

      3. neg-mul-1 83.6%

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

   9. Simplified 83.6%

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

   10. Taylor expanded in a around 0 61.8%

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

       1. associate-/l* 67.4%

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

   12. Simplified 67.4%

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

   13. Taylor expanded in y around inf 61.8%

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

       1. associate-*l/ 77.6%

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

       2. *-commutative 77.6%

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

   15. Simplified 77.6%

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

   if 1.24999999999999994e170 < z

   1. Initial program 84.2%

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

      1. sub-neg 84.2%

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

      2. distribute-frac-neg 84.2%

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

      3. distribute-rgt-neg-out 84.2%

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

      4. +-commutative 84.2%

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

      5. associate-*l/ 84.0%

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

      6. distribute-rgt-neg-in 84.0%

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

      7. distribute-lft-neg-in 84.0%

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

      8. distribute-frac-neg 84.0%

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

      9. fma-def 84.0%

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

      10. sub-neg 84.0%

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

      11. distribute-neg-in 84.0%

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

      12. remove-double-neg 84.0%

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

      13. +-commutative 84.0%

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

      14. sub-neg 84.0%

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

   3. Simplified 84.0%

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

      1. fma-udef 84.0%

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

      2. +-commutative 84.0%

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

      3. associate-+r+ 84.0%

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

      4. clear-num 83.8%

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

      5. associate-*l/ 87.4%

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

      6. *-un-lft-identity 87.4%

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

   6. Applied egg-rr 87.4%

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

   7. Taylor expanded in z around inf 80.1%

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

      1. associate-*r/ 80.1%

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

      2. associate-*r* 80.1%

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

      3. neg-mul-1 80.1%

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

   9. Simplified 80.1%

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

   10. Taylor expanded in a around 0 64.3%

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

       1. associate-/l* 63.8%

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

   12. Simplified 63.8%

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

   13. Taylor expanded in y around inf 48.8%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+150}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+170}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -820 \lor \neg \left(a \leq 4.5 \cdot 10^{-86}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -820.0) (not (<= a 4.5e-86))) (+ y x) (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -820.0) || !(a <= 4.5e-86)) {
		tmp = y + x;
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-820.0d0)) .or. (.not. (a <= 4.5d-86))) then
        tmp = y + x
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -820.0) || !(a <= 4.5e-86)) {
		tmp = y + x;
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -820.0) or not (a <= 4.5e-86):
		tmp = y + x
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -820.0) || !(a <= 4.5e-86))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -820.0) || ~((a <= 4.5e-86)))
		tmp = y + x;
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -820.0], N[Not[LessEqual[a, 4.5e-86]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -820 or 4.4999999999999998e-86 < a

   1. Initial program 79.5%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in a around inf 76.9%

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

      1. +-commutative 76.9%

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

   7. Simplified 76.9%

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

   if -820 < a < 4.4999999999999998e-86

   1. Initial program 80.2%

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

      1. sub-neg 80.2%

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

      2. distribute-frac-neg 80.2%

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

      3. distribute-rgt-neg-out 80.2%

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

      4. +-commutative 80.2%

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

      5. associate-*l/ 77.1%

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

      6. distribute-rgt-neg-in 77.1%

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

      7. distribute-lft-neg-in 77.1%

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

      8. distribute-frac-neg 77.1%

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

      9. fma-def 77.0%

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

      10. sub-neg 77.0%

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

      11. distribute-neg-in 77.0%

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

      12. remove-double-neg 77.0%

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

      13. +-commutative 77.0%

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

      14. sub-neg 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in t around inf 72.5%

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

      1. associate-+r+ 81.7%

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

      2. distribute-rgt1-in 81.7%

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

      3. metadata-eval 81.7%

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

      4. mul0-lft 81.7%

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

      5. associate-/l* 79.5%

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

   7. Simplified 79.5%

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

   8. Taylor expanded in a around 0 78.5%

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

      1. associate-*l/ 79.2%

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

      2. *-commutative 79.2%

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

   10. Simplified 79.2%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -820 \lor \neg \left(a \leq 4.5 \cdot 10^{-86}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.8%

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

   1. sub-neg 79.8%

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

   2. distribute-frac-neg 79.8%

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

   3. distribute-rgt-neg-out 79.8%

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

   4. +-commutative 79.8%

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

   5. associate-*l/ 85.4%

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

   6. distribute-rgt-neg-in 85.4%

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

   7. distribute-lft-neg-in 85.4%

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

   8. distribute-frac-neg 85.4%

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

   9. fma-def 85.4%

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

   10. sub-neg 85.4%

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

   11. distribute-neg-in 85.4%

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

   12. remove-double-neg 85.4%

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

   13. +-commutative 85.4%

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

   14. sub-neg 85.4%

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

3. Simplified 85.4%

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

   1. fma-udef 85.4%

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

   2. +-commutative 85.4%

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

   3. associate-+r+ 89.2%

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

   4. clear-num 89.2%

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

   5. associate-*l/ 89.5%

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

   6. *-un-lft-identity 89.5%

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

6. Applied egg-rr 89.5%

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

7. Final simplification 89.5%

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

Alternative 10: 54.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+115}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.15e+115) y (if (<= y 4.2e+174) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.15e+115) {
		tmp = y;
	} else if (y <= 4.2e+174) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-1.15d+115)) then
        tmp = y
    else if (y <= 4.2d+174) then
        tmp = x
    else
        tmp = 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 (y <= -1.15e+115) {
		tmp = y;
	} else if (y <= 4.2e+174) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.15e+115:
		tmp = y
	elif y <= 4.2e+174:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.15e+115)
		tmp = y;
	elseif (y <= 4.2e+174)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.15e+115)
		tmp = y;
	elseif (y <= 4.2e+174)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.15e+115], y, If[LessEqual[y, 4.2e+174], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15000000000000002e115 or 4.20000000000000033e174 < y

   1. Initial program 58.7%

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

      1. associate-*l/ 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in t around 0 60.5%

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

   6. Taylor expanded in x around 0 43.0%

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

   7. Taylor expanded in z around 0 39.1%

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

   if -1.15000000000000002e115 < y < 4.20000000000000033e174

   1. Initial program 88.4%

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

      1. associate-*l/ 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in x around inf 63.8%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+115}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.0% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ y + x \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(y + x), $MachinePrecision]

Derivation

1. Initial program 79.8%

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

   1. associate-*l/ 85.4%

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

3. Simplified 85.4%

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

5. Taylor expanded in a around inf 62.9%

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

   1. +-commutative 62.9%

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

7. Simplified 62.9%

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

8. Final simplification 62.9%

   \[\leadsto y + x \]
9. Add Preprocessing

Alternative 12: 51.8% accurate, 13.0× 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 79.8%

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

   1. associate-*l/ 85.4%

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

3. Simplified 85.4%

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

5. Taylor expanded in x around inf 49.1%

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

6. Final simplification 49.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (a - t)
    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 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024018 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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