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

Percentage Accurate: 77.1% → 88.9%

Time: 11.7s

Alternatives: 18

Speedup: 0.6×

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: 77.1% 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: 88.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+121}:\\ \;\;\;\;x + a \cdot \left(y \cdot \frac{z}{t \cdot a} - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.05e+121)
   (+ x (* a (- (* y (/ z (* t a))) (/ y t))))
   (if (<= t 1.6e+18)
     (fma (- z t) (/ y (- t a)) (+ x y))
     (+ x (* y (- (/ z t) (/ a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05e+121) {
		tmp = x + (a * ((y * (z / (t * a))) - (y / t)));
	} else if (t <= 1.6e+18) {
		tmp = fma((z - t), (y / (t - a)), (x + y));
	} else {
		tmp = x + (y * ((z / t) - (a / t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.05e+121)
		tmp = Float64(x + Float64(a * Float64(Float64(y * Float64(z / Float64(t * a))) - Float64(y / t))));
	elseif (t <= 1.6e+18)
		tmp = fma(Float64(z - t), Float64(y / Float64(t - a)), Float64(x + y));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.05e+121], N[(x + N[(a * N[(N[(y * N[(z / N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+18], N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.0500000000000001e121

   1. Initial program 63.0%

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

      1. sub-neg 63.0%

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

      2. +-commutative 63.0%

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

      3. distribute-frac-neg 63.0%

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

      4. distribute-rgt-neg-out 63.0%

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

      5. associate-/l* 65.5%

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

      6. fma-define 66.1%

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

      7. distribute-frac-neg 66.1%

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

      8. distribute-neg-frac2 66.1%

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

      9. sub-neg 66.1%

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

      10. distribute-neg-in 66.1%

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

      11. remove-double-neg 66.1%

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

      12. +-commutative 66.1%

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

      13. sub-neg 66.1%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in t around inf 66.4%

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

      1. associate--l+ 66.4%

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

      2. associate-+r+ 81.7%

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

      3. distribute-rgt1-in 81.7%

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

      4. metadata-eval 81.7%

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

      5. mul0-lft 81.7%

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

      6. associate-/l* 84.9%

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

      7. associate-/l* 92.5%

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

   7. Simplified 92.5%

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

   8. Taylor expanded in a around inf 86.5%

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

      1. associate-/l* 92.8%

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

      2. *-commutative 92.8%

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

   10. Simplified 92.8%

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

   if -1.0500000000000001e121 < t < 1.6e18

   1. Initial program 93.5%

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

      1. sub-neg 93.5%

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

      2. +-commutative 93.5%

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

      3. distribute-frac-neg 93.5%

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

      4. distribute-rgt-neg-out 93.5%

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

      5. associate-/l* 93.9%

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

      6. fma-define 94.0%

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

      7. distribute-frac-neg 94.0%

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

      8. distribute-neg-frac2 94.0%

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

      9. sub-neg 94.0%

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

      10. distribute-neg-in 94.0%

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

      11. remove-double-neg 94.0%

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

      12. +-commutative 94.0%

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

      13. sub-neg 94.0%

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

   3. Simplified 94.0%

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

   if 1.6e18 < t

   1. Initial program 53.9%

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

      1. sub-neg 53.9%

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

      2. +-commutative 53.9%

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

      3. distribute-frac-neg 53.9%

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

      4. distribute-rgt-neg-out 53.9%

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

      5. associate-/l* 66.4%

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

      6. fma-define 66.3%

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

      7. distribute-frac-neg 66.3%

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

      8. distribute-neg-frac2 66.3%

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

      9. sub-neg 66.3%

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

      10. distribute-neg-in 66.3%

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

      11. remove-double-neg 66.3%

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

      12. +-commutative 66.3%

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

      13. sub-neg 66.3%

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

   3. Simplified 66.3%

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

   5. Taylor expanded in t around inf 67.7%

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

      1. associate--l+ 67.7%

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

      2. associate-+r+ 76.5%

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

      3. distribute-rgt1-in 76.5%

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

      4. metadata-eval 76.5%

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

      5. mul0-lft 76.5%

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

      6. associate-/l* 84.0%

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

      7. associate-/l* 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in y around 0 90.5%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+121}:\\ \;\;\;\;x + a \cdot \left(y \cdot \frac{z}{t \cdot a} - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-83}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-103}:\\ \;\;\;\;\frac{z}{\frac{t - a}{y}}\\ \mathbf{elif}\;a \leq 1450000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* y (- a z)) t))))
   (if (<= a -1.8e+82)
     (+ x y)
     (if (<= a -7e-83)
       (* z (/ y (- t a)))
       (if (<= a 2.6e-142)
         t_1
         (if (<= a 2.6e-103)
           (/ z (/ (- t a) y))
           (if (<= a 1450000.0) t_1 (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y * (a - z)) / t);
	double tmp;
	if (a <= -1.8e+82) {
		tmp = x + y;
	} else if (a <= -7e-83) {
		tmp = z * (y / (t - a));
	} else if (a <= 2.6e-142) {
		tmp = t_1;
	} else if (a <= 2.6e-103) {
		tmp = z / ((t - a) / y);
	} else if (a <= 1450000.0) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y * (a - z)) / t)
    if (a <= (-1.8d+82)) then
        tmp = x + y
    else if (a <= (-7d-83)) then
        tmp = z * (y / (t - a))
    else if (a <= 2.6d-142) then
        tmp = t_1
    else if (a <= 2.6d-103) then
        tmp = z / ((t - a) / y)
    else if (a <= 1450000.0d0) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y * (a - z)) / t);
	double tmp;
	if (a <= -1.8e+82) {
		tmp = x + y;
	} else if (a <= -7e-83) {
		tmp = z * (y / (t - a));
	} else if (a <= 2.6e-142) {
		tmp = t_1;
	} else if (a <= 2.6e-103) {
		tmp = z / ((t - a) / y);
	} else if (a <= 1450000.0) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y * (a - z)) / t)
	tmp = 0
	if a <= -1.8e+82:
		tmp = x + y
	elif a <= -7e-83:
		tmp = z * (y / (t - a))
	elif a <= 2.6e-142:
		tmp = t_1
	elif a <= 2.6e-103:
		tmp = z / ((t - a) / y)
	elif a <= 1450000.0:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y * Float64(a - z)) / t))
	tmp = 0.0
	if (a <= -1.8e+82)
		tmp = Float64(x + y);
	elseif (a <= -7e-83)
		tmp = Float64(z * Float64(y / Float64(t - a)));
	elseif (a <= 2.6e-142)
		tmp = t_1;
	elseif (a <= 2.6e-103)
		tmp = Float64(z / Float64(Float64(t - a) / y));
	elseif (a <= 1450000.0)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y * (a - z)) / t);
	tmp = 0.0;
	if (a <= -1.8e+82)
		tmp = x + y;
	elseif (a <= -7e-83)
		tmp = z * (y / (t - a));
	elseif (a <= 2.6e-142)
		tmp = t_1;
	elseif (a <= 2.6e-103)
		tmp = z / ((t - a) / y);
	elseif (a <= 1450000.0)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+82], N[(x + y), $MachinePrecision], If[LessEqual[a, -7e-83], N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e-142], t$95$1, If[LessEqual[a, 2.6e-103], N[(z / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1450000.0], t$95$1, N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.80000000000000007e82 or 1.45e6 < a

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 78.5%

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

      1. +-commutative 78.5%

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

   5. Simplified 78.5%

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

   if -1.80000000000000007e82 < a < -7.00000000000000061e-83

   1. Initial program 76.6%

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

      1. sub-neg 76.6%

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

      2. +-commutative 76.6%

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

      3. distribute-frac-neg 76.6%

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

      4. distribute-rgt-neg-out 76.6%

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

      5. associate-/l* 81.1%

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

      6. fma-define 81.6%

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

      7. distribute-frac-neg 81.6%

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

      8. distribute-neg-frac2 81.6%

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

      9. sub-neg 81.6%

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

      10. distribute-neg-in 81.6%

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

      11. remove-double-neg 81.6%

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

      12. +-commutative 81.6%

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

      13. sub-neg 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in z around inf 50.7%

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

      1. *-commutative 50.7%

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

      2. *-un-lft-identity 50.7%

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

      3. times-frac 62.2%

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

   7. Applied egg-rr 62.2%

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

   if -7.00000000000000061e-83 < a < 2.6e-142 or 2.59999999999999996e-103 < a < 1.45e6

   1. Initial program 79.0%

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

   3. Taylor expanded in t around inf 83.1%

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

      1. associate--l+ 83.1%

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

      2. distribute-lft-out-- 83.1%

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

      3. div-sub 85.0%

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

      4. mul-1-neg 85.0%

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

      5. unsub-neg 85.0%

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

      6. *-commutative 85.0%

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

      7. distribute-lft-out-- 85.0%

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

   5. Simplified 85.0%

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

   if 2.6e-142 < a < 2.59999999999999996e-103

   1. Initial program 99.2%

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

      1. sub-neg 99.2%

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

      2. +-commutative 99.2%

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

      3. distribute-frac-neg 99.2%

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

      4. distribute-rgt-neg-out 99.2%

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

      5. associate-/l* 99.0%

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

      6. fma-define 99.0%

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

      7. distribute-frac-neg 99.0%

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

      8. distribute-neg-frac2 99.0%

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

      9. sub-neg 99.0%

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

      10. distribute-neg-in 99.0%

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

      11. remove-double-neg 99.0%

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

      12. +-commutative 99.0%

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

      13. sub-neg 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around inf 93.9%

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

      1. *-commutative 93.9%

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

      2. *-un-lft-identity 93.9%

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

      3. times-frac 93.7%

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

   7. Applied egg-rr 93.7%

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

   8. Taylor expanded in z around 0 93.9%

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

      1. *-commutative 93.9%

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

      2. *-rgt-identity 93.9%

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

      3. times-frac 83.9%

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

      4. /-rgt-identity 83.9%

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

      5. associate-/r/ 94.5%

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

   10. Simplified 94.5%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-83}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-142}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-103}:\\ \;\;\;\;\frac{z}{\frac{t - a}{y}}\\ \mathbf{elif}\;a \leq 1450000:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-103}:\\ \;\;\;\;\frac{z}{\frac{t - a}{y}}\\ \mathbf{elif}\;a \leq 0.21:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))))
   (if (<= a -1.8e+82)
     (+ x y)
     (if (<= a -8.5e-81)
       (* y (/ z (- t a)))
       (if (<= a 2.6e-142)
         t_1
         (if (<= a 2.6e-103)
           (/ z (/ (- t a) y))
           (if (<= a 0.21) t_1 (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * z) / t);
	double tmp;
	if (a <= -1.8e+82) {
		tmp = x + y;
	} else if (a <= -8.5e-81) {
		tmp = y * (z / (t - a));
	} else if (a <= 2.6e-142) {
		tmp = t_1;
	} else if (a <= 2.6e-103) {
		tmp = z / ((t - a) / y);
	} else if (a <= 0.21) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    if (a <= (-1.8d+82)) then
        tmp = x + y
    else if (a <= (-8.5d-81)) then
        tmp = y * (z / (t - a))
    else if (a <= 2.6d-142) then
        tmp = t_1
    else if (a <= 2.6d-103) then
        tmp = z / ((t - a) / y)
    else if (a <= 0.21d0) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * z) / t);
	double tmp;
	if (a <= -1.8e+82) {
		tmp = x + y;
	} else if (a <= -8.5e-81) {
		tmp = y * (z / (t - a));
	} else if (a <= 2.6e-142) {
		tmp = t_1;
	} else if (a <= 2.6e-103) {
		tmp = z / ((t - a) / y);
	} else if (a <= 0.21) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * z) / t)
	tmp = 0
	if a <= -1.8e+82:
		tmp = x + y
	elif a <= -8.5e-81:
		tmp = y * (z / (t - a))
	elif a <= 2.6e-142:
		tmp = t_1
	elif a <= 2.6e-103:
		tmp = z / ((t - a) / y)
	elif a <= 0.21:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (a <= -1.8e+82)
		tmp = Float64(x + y);
	elseif (a <= -8.5e-81)
		tmp = Float64(y * Float64(z / Float64(t - a)));
	elseif (a <= 2.6e-142)
		tmp = t_1;
	elseif (a <= 2.6e-103)
		tmp = Float64(z / Float64(Float64(t - a) / y));
	elseif (a <= 0.21)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * z) / t);
	tmp = 0.0;
	if (a <= -1.8e+82)
		tmp = x + y;
	elseif (a <= -8.5e-81)
		tmp = y * (z / (t - a));
	elseif (a <= 2.6e-142)
		tmp = t_1;
	elseif (a <= 2.6e-103)
		tmp = z / ((t - a) / y);
	elseif (a <= 0.21)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+82], N[(x + y), $MachinePrecision], If[LessEqual[a, -8.5e-81], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e-142], t$95$1, If[LessEqual[a, 2.6e-103], N[(z / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.21], t$95$1, N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.80000000000000007e82 or 0.209999999999999992 < a

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 78.5%

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

      1. +-commutative 78.5%

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

   5. Simplified 78.5%

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

   if -1.80000000000000007e82 < a < -8.5000000000000001e-81

   1. Initial program 76.6%

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

      1. sub-neg 76.6%

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

      2. +-commutative 76.6%

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

      3. distribute-frac-neg 76.6%

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

      4. distribute-rgt-neg-out 76.6%

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

      5. associate-/l* 81.1%

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

      6. fma-define 81.6%

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

      7. distribute-frac-neg 81.6%

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

      8. distribute-neg-frac2 81.6%

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

      9. sub-neg 81.6%

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

      10. distribute-neg-in 81.6%

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

      11. remove-double-neg 81.6%

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

      12. +-commutative 81.6%

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

      13. sub-neg 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in z around inf 50.7%

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

      1. associate-/l* 62.1%

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

   7. Simplified 62.1%

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

   if -8.5000000000000001e-81 < a < 2.6e-142 or 2.59999999999999996e-103 < a < 0.209999999999999992

   1. Initial program 79.0%

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

      1. sub-neg 79.0%

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

      2. +-commutative 79.0%

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

      3. distribute-frac-neg 79.0%

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

      4. distribute-rgt-neg-out 79.0%

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

      5. associate-/l* 78.3%

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

      6. fma-define 78.4%

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

      7. distribute-frac-neg 78.4%

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

      8. distribute-neg-frac2 78.4%

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

      9. sub-neg 78.4%

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

      10. distribute-neg-in 78.4%

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

      11. remove-double-neg 78.4%

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

      12. +-commutative 78.4%

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

      13. sub-neg 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in t around inf 74.2%

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

      1. associate--l+ 74.2%

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

      2. associate-+r+ 83.1%

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

      3. distribute-rgt1-in 83.1%

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

      4. metadata-eval 83.1%

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

      5. mul0-lft 83.1%

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

      6. associate-/l* 80.4%

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

      7. associate-/l* 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in a around 0 82.5%

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

   if 2.6e-142 < a < 2.59999999999999996e-103

   1. Initial program 99.2%

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

      1. sub-neg 99.2%

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

      2. +-commutative 99.2%

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

      3. distribute-frac-neg 99.2%

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

      4. distribute-rgt-neg-out 99.2%

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

      5. associate-/l* 99.0%

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

      6. fma-define 99.0%

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

      7. distribute-frac-neg 99.0%

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

      8. distribute-neg-frac2 99.0%

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

      9. sub-neg 99.0%

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

      10. distribute-neg-in 99.0%

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

      11. remove-double-neg 99.0%

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

      12. +-commutative 99.0%

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

      13. sub-neg 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around inf 93.9%

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

      1. *-commutative 93.9%

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

      2. *-un-lft-identity 93.9%

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

      3. times-frac 93.7%

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

   7. Applied egg-rr 93.7%

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

   8. Taylor expanded in z around 0 93.9%

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

      1. *-commutative 93.9%

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

      2. *-rgt-identity 93.9%

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

      3. times-frac 83.9%

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

      4. /-rgt-identity 83.9%

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

      5. associate-/r/ 94.5%

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

   10. Simplified 94.5%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-103}:\\ \;\;\;\;\frac{z}{\frac{t - a}{y}}\\ \mathbf{elif}\;a \leq 0.21:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-103}:\\ \;\;\;\;\frac{z}{\frac{t - a}{y}}\\ \mathbf{elif}\;a \leq 0.048:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))))
   (if (<= a -1.8e+82)
     (+ x y)
     (if (<= a -8.5e-81)
       (* z (/ y (- t a)))
       (if (<= a 2.6e-142)
         t_1
         (if (<= a 2.6e-103)
           (/ z (/ (- t a) y))
           (if (<= a 0.048) t_1 (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * z) / t);
	double tmp;
	if (a <= -1.8e+82) {
		tmp = x + y;
	} else if (a <= -8.5e-81) {
		tmp = z * (y / (t - a));
	} else if (a <= 2.6e-142) {
		tmp = t_1;
	} else if (a <= 2.6e-103) {
		tmp = z / ((t - a) / y);
	} else if (a <= 0.048) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    if (a <= (-1.8d+82)) then
        tmp = x + y
    else if (a <= (-8.5d-81)) then
        tmp = z * (y / (t - a))
    else if (a <= 2.6d-142) then
        tmp = t_1
    else if (a <= 2.6d-103) then
        tmp = z / ((t - a) / y)
    else if (a <= 0.048d0) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * z) / t);
	double tmp;
	if (a <= -1.8e+82) {
		tmp = x + y;
	} else if (a <= -8.5e-81) {
		tmp = z * (y / (t - a));
	} else if (a <= 2.6e-142) {
		tmp = t_1;
	} else if (a <= 2.6e-103) {
		tmp = z / ((t - a) / y);
	} else if (a <= 0.048) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * z) / t)
	tmp = 0
	if a <= -1.8e+82:
		tmp = x + y
	elif a <= -8.5e-81:
		tmp = z * (y / (t - a))
	elif a <= 2.6e-142:
		tmp = t_1
	elif a <= 2.6e-103:
		tmp = z / ((t - a) / y)
	elif a <= 0.048:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (a <= -1.8e+82)
		tmp = Float64(x + y);
	elseif (a <= -8.5e-81)
		tmp = Float64(z * Float64(y / Float64(t - a)));
	elseif (a <= 2.6e-142)
		tmp = t_1;
	elseif (a <= 2.6e-103)
		tmp = Float64(z / Float64(Float64(t - a) / y));
	elseif (a <= 0.048)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * z) / t);
	tmp = 0.0;
	if (a <= -1.8e+82)
		tmp = x + y;
	elseif (a <= -8.5e-81)
		tmp = z * (y / (t - a));
	elseif (a <= 2.6e-142)
		tmp = t_1;
	elseif (a <= 2.6e-103)
		tmp = z / ((t - a) / y);
	elseif (a <= 0.048)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+82], N[(x + y), $MachinePrecision], If[LessEqual[a, -8.5e-81], N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e-142], t$95$1, If[LessEqual[a, 2.6e-103], N[(z / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.048], t$95$1, N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.80000000000000007e82 or 0.048000000000000001 < a

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 78.5%

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

      1. +-commutative 78.5%

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

   5. Simplified 78.5%

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

   if -1.80000000000000007e82 < a < -8.5000000000000001e-81

   1. Initial program 76.6%

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

      1. sub-neg 76.6%

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

      2. +-commutative 76.6%

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

      3. distribute-frac-neg 76.6%

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

      4. distribute-rgt-neg-out 76.6%

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

      5. associate-/l* 81.1%

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

      6. fma-define 81.6%

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

      7. distribute-frac-neg 81.6%

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

      8. distribute-neg-frac2 81.6%

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

      9. sub-neg 81.6%

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

      10. distribute-neg-in 81.6%

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

      11. remove-double-neg 81.6%

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

      12. +-commutative 81.6%

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

      13. sub-neg 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in z around inf 50.7%

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

      1. *-commutative 50.7%

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

      2. *-un-lft-identity 50.7%

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

      3. times-frac 62.2%

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

   7. Applied egg-rr 62.2%

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

   if -8.5000000000000001e-81 < a < 2.6e-142 or 2.59999999999999996e-103 < a < 0.048000000000000001

   1. Initial program 79.0%

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

      1. sub-neg 79.0%

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

      2. +-commutative 79.0%

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

      3. distribute-frac-neg 79.0%

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

      4. distribute-rgt-neg-out 79.0%

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

      5. associate-/l* 78.3%

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

      6. fma-define 78.4%

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

      7. distribute-frac-neg 78.4%

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

      8. distribute-neg-frac2 78.4%

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

      9. sub-neg 78.4%

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

      10. distribute-neg-in 78.4%

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

      11. remove-double-neg 78.4%

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

      12. +-commutative 78.4%

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

      13. sub-neg 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in t around inf 74.2%

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

      1. associate--l+ 74.2%

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

      2. associate-+r+ 83.1%

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

      3. distribute-rgt1-in 83.1%

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

      4. metadata-eval 83.1%

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

      5. mul0-lft 83.1%

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

      6. associate-/l* 80.4%

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

      7. associate-/l* 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in a around 0 82.5%

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

   if 2.6e-142 < a < 2.59999999999999996e-103

   1. Initial program 99.2%

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

      1. sub-neg 99.2%

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

      2. +-commutative 99.2%

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

      3. distribute-frac-neg 99.2%

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

      4. distribute-rgt-neg-out 99.2%

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

      5. associate-/l* 99.0%

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

      6. fma-define 99.0%

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

      7. distribute-frac-neg 99.0%

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

      8. distribute-neg-frac2 99.0%

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

      9. sub-neg 99.0%

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

      10. distribute-neg-in 99.0%

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

      11. remove-double-neg 99.0%

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

      12. +-commutative 99.0%

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

      13. sub-neg 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around inf 93.9%

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

      1. *-commutative 93.9%

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

      2. *-un-lft-identity 93.9%

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

      3. times-frac 93.7%

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

   7. Applied egg-rr 93.7%

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

   8. Taylor expanded in z around 0 93.9%

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

      1. *-commutative 93.9%

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

      2. *-rgt-identity 93.9%

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

      3. times-frac 83.9%

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

      4. /-rgt-identity 83.9%

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

      5. associate-/r/ 94.5%

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

   10. Simplified 94.5%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-103}:\\ \;\;\;\;\frac{z}{\frac{t - a}{y}}\\ \mathbf{elif}\;a \leq 0.048:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -4.45 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-174}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-89} \lor \neg \left(a \leq 0.084\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (* y (/ z a)))))
   (if (<= a -4.45e-23)
     t_1
     (if (<= a 3.2e-174)
       (+ x (* z (/ y t)))
       (if (or (<= a 1.05e-89) (not (<= a 0.084)))
         t_1
         (- x (/ (* y (- a z)) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y * (z / a));
	double tmp;
	if (a <= -4.45e-23) {
		tmp = t_1;
	} else if (a <= 3.2e-174) {
		tmp = x + (z * (y / t));
	} else if ((a <= 1.05e-89) || !(a <= 0.084)) {
		tmp = t_1;
	} else {
		tmp = x - ((y * (a - 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) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - (y * (z / a))
    if (a <= (-4.45d-23)) then
        tmp = t_1
    else if (a <= 3.2d-174) then
        tmp = x + (z * (y / t))
    else if ((a <= 1.05d-89) .or. (.not. (a <= 0.084d0))) then
        tmp = t_1
    else
        tmp = x - ((y * (a - z)) / t)
    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) - (y * (z / a));
	double tmp;
	if (a <= -4.45e-23) {
		tmp = t_1;
	} else if (a <= 3.2e-174) {
		tmp = x + (z * (y / t));
	} else if ((a <= 1.05e-89) || !(a <= 0.084)) {
		tmp = t_1;
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (y * (z / a))
	tmp = 0
	if a <= -4.45e-23:
		tmp = t_1
	elif a <= 3.2e-174:
		tmp = x + (z * (y / t))
	elif (a <= 1.05e-89) or not (a <= 0.084):
		tmp = t_1
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -4.45e-23)
		tmp = t_1;
	elseif (a <= 3.2e-174)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif ((a <= 1.05e-89) || !(a <= 0.084))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (y * (z / a));
	tmp = 0.0;
	if (a <= -4.45e-23)
		tmp = t_1;
	elseif (a <= 3.2e-174)
		tmp = x + (z * (y / t));
	elseif ((a <= 1.05e-89) || ~((a <= 0.084)))
		tmp = t_1;
	else
		tmp = x - ((y * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.45e-23], t$95$1, If[LessEqual[a, 3.2e-174], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1.05e-89], N[Not[LessEqual[a, 0.084]], $MachinePrecision]], t$95$1, N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.45000000000000011e-23 or 3.2e-174 < a < 1.05e-89 or 0.0840000000000000052 < a

   1. Initial program 83.9%

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

   3. Taylor expanded in t around 0 84.0%

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

      1. +-commutative 84.0%

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

      2. associate-/l* 86.8%

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

   5. Simplified 86.8%

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

   if -4.45000000000000011e-23 < a < 3.2e-174

   1. Initial program 73.4%

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

      1. sub-neg 73.4%

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

      2. +-commutative 73.4%

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

      3. distribute-frac-neg 73.4%

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

      4. distribute-rgt-neg-out 73.4%

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

      5. associate-/l* 75.4%

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

      6. fma-define 75.6%

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

      7. distribute-frac-neg 75.6%

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

      8. distribute-neg-frac2 75.6%

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

      9. sub-neg 75.6%

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

      10. distribute-neg-in 75.6%

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

      11. remove-double-neg 75.6%

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

      12. +-commutative 75.6%

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

      13. sub-neg 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in t around inf 75.9%

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

      1. associate--l+ 75.9%

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

      2. associate-+r+ 86.2%

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

      3. distribute-rgt1-in 86.2%

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

      4. metadata-eval 86.2%

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

      5. mul0-lft 86.2%

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

      6. associate-/l* 86.2%

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

      7. associate-/l* 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in z around inf 85.6%

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

      1. +-commutative 85.6%

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

      2. mul-1-neg 85.6%

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

      3. sub-neg 85.6%

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

      4. *-commutative 85.6%

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

      5. *-commutative 85.6%

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

      6. times-frac 83.3%

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

   10. Simplified 83.3%

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

   11. Taylor expanded in z around inf 87.4%

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

   if 1.05e-89 < a < 0.0840000000000000052

   1. Initial program 78.2%

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

   3. Taylor expanded in t around inf 69.9%

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

      1. associate--l+ 69.9%

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

      2. distribute-lft-out-- 69.9%

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

      3. div-sub 81.0%

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

      4. mul-1-neg 81.0%

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

      5. unsub-neg 81.0%

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

      6. *-commutative 81.0%

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

      7. distribute-lft-out-- 81.0%

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

   5. Simplified 81.0%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.45 \cdot 10^{-23}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-174}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-89} \lor \neg \left(a \leq 0.084\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-174}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{t}{y}}{z - a}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-90} \lor \neg \left(a \leq 0.345\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (* y (/ z a)))))
   (if (<= a -6.2e-24)
     t_1
     (if (<= a 3.2e-174)
       (+ x (/ 1.0 (/ (/ t y) (- z a))))
       (if (or (<= a 6.5e-90) (not (<= a 0.345)))
         t_1
         (- x (/ (* y (- a z)) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y * (z / a));
	double tmp;
	if (a <= -6.2e-24) {
		tmp = t_1;
	} else if (a <= 3.2e-174) {
		tmp = x + (1.0 / ((t / y) / (z - a)));
	} else if ((a <= 6.5e-90) || !(a <= 0.345)) {
		tmp = t_1;
	} else {
		tmp = x - ((y * (a - 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) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - (y * (z / a))
    if (a <= (-6.2d-24)) then
        tmp = t_1
    else if (a <= 3.2d-174) then
        tmp = x + (1.0d0 / ((t / y) / (z - a)))
    else if ((a <= 6.5d-90) .or. (.not. (a <= 0.345d0))) then
        tmp = t_1
    else
        tmp = x - ((y * (a - z)) / t)
    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) - (y * (z / a));
	double tmp;
	if (a <= -6.2e-24) {
		tmp = t_1;
	} else if (a <= 3.2e-174) {
		tmp = x + (1.0 / ((t / y) / (z - a)));
	} else if ((a <= 6.5e-90) || !(a <= 0.345)) {
		tmp = t_1;
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (y * (z / a))
	tmp = 0
	if a <= -6.2e-24:
		tmp = t_1
	elif a <= 3.2e-174:
		tmp = x + (1.0 / ((t / y) / (z - a)))
	elif (a <= 6.5e-90) or not (a <= 0.345):
		tmp = t_1
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -6.2e-24)
		tmp = t_1;
	elseif (a <= 3.2e-174)
		tmp = Float64(x + Float64(1.0 / Float64(Float64(t / y) / Float64(z - a))));
	elseif ((a <= 6.5e-90) || !(a <= 0.345))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (y * (z / a));
	tmp = 0.0;
	if (a <= -6.2e-24)
		tmp = t_1;
	elseif (a <= 3.2e-174)
		tmp = x + (1.0 / ((t / y) / (z - a)));
	elseif ((a <= 6.5e-90) || ~((a <= 0.345)))
		tmp = t_1;
	else
		tmp = x - ((y * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e-24], t$95$1, If[LessEqual[a, 3.2e-174], N[(x + N[(1.0 / N[(N[(t / y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 6.5e-90], N[Not[LessEqual[a, 0.345]], $MachinePrecision]], t$95$1, N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.2000000000000001e-24 or 3.2e-174 < a < 6.4999999999999996e-90 or 0.34499999999999997 < a

   1. Initial program 83.9%

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

   3. Taylor expanded in t around 0 84.0%

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

      1. +-commutative 84.0%

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

      2. associate-/l* 86.8%

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

   5. Simplified 86.8%

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

   if -6.2000000000000001e-24 < a < 3.2e-174

   1. Initial program 73.4%

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

   3. Taylor expanded in t around inf 86.2%

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

      1. associate--l+ 86.2%

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

      2. distribute-lft-out-- 86.2%

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

      3. div-sub 86.3%

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

      4. mul-1-neg 86.3%

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

      5. unsub-neg 86.3%

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

      6. *-commutative 86.3%

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

      7. distribute-lft-out-- 86.3%

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

   5. Simplified 86.3%

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

      1. clear-num 86.3%

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

      2. inv-pow 86.3%

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

   7. Applied egg-rr 86.3%

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

      1. unpow-1 86.3%

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

      2. associate-/r* 88.4%

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

   9. Simplified 88.4%

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

   if 6.4999999999999996e-90 < a < 0.34499999999999997

   1. Initial program 78.2%

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

   3. Taylor expanded in t around inf 69.9%

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

      1. associate--l+ 69.9%

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

      2. distribute-lft-out-- 69.9%

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

      3. div-sub 81.0%

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

      4. mul-1-neg 81.0%

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

      5. unsub-neg 81.0%

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

      6. *-commutative 81.0%

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

      7. distribute-lft-out-- 81.0%

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

   5. Simplified 81.0%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-24}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-174}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{t}{y}}{z - a}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-90} \lor \neg \left(a \leq 0.345\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{-a}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+166}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+161} \lor \neg \left(z \leq 4.7 \cdot 10^{+154}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a)))))
   (if (<= z -8.5e+217)
     t_1
     (if (<= z -2.2e+166)
       (* y (/ z t))
       (if (or (<= z -1.45e+161) (not (<= z 4.7e+154))) t_1 (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / -a);
	double tmp;
	if (z <= -8.5e+217) {
		tmp = t_1;
	} else if (z <= -2.2e+166) {
		tmp = y * (z / t);
	} else if ((z <= -1.45e+161) || !(z <= 4.7e+154)) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y / -a)
    if (z <= (-8.5d+217)) then
        tmp = t_1
    else if (z <= (-2.2d+166)) then
        tmp = y * (z / t)
    else if ((z <= (-1.45d+161)) .or. (.not. (z <= 4.7d+154))) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / -a);
	double tmp;
	if (z <= -8.5e+217) {
		tmp = t_1;
	} else if (z <= -2.2e+166) {
		tmp = y * (z / t);
	} else if ((z <= -1.45e+161) || !(z <= 4.7e+154)) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / -a)
	tmp = 0
	if z <= -8.5e+217:
		tmp = t_1
	elif z <= -2.2e+166:
		tmp = y * (z / t)
	elif (z <= -1.45e+161) or not (z <= 4.7e+154):
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(-a)))
	tmp = 0.0
	if (z <= -8.5e+217)
		tmp = t_1;
	elseif (z <= -2.2e+166)
		tmp = Float64(y * Float64(z / t));
	elseif ((z <= -1.45e+161) || !(z <= 4.7e+154))
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / -a);
	tmp = 0.0;
	if (z <= -8.5e+217)
		tmp = t_1;
	elseif (z <= -2.2e+166)
		tmp = y * (z / t);
	elseif ((z <= -1.45e+161) || ~((z <= 4.7e+154)))
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+217], t$95$1, If[LessEqual[z, -2.2e+166], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.45e+161], N[Not[LessEqual[z, 4.7e+154]], $MachinePrecision]], t$95$1, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.50000000000000021e217 or -2.1999999999999999e166 < z < -1.45000000000000008e161 or 4.69999999999999983e154 < z

   1. Initial program 88.2%

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

      1. sub-neg 88.2%

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

      2. +-commutative 88.2%

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

      3. distribute-frac-neg 88.2%

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

      4. distribute-rgt-neg-out 88.2%

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

      5. associate-/l* 86.6%

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

      6. fma-define 86.8%

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

      7. distribute-frac-neg 86.8%

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

      8. distribute-neg-frac2 86.8%

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

      9. sub-neg 86.8%

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

      10. distribute-neg-in 86.8%

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

      11. remove-double-neg 86.8%

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

      12. +-commutative 86.8%

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

      13. sub-neg 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in z around inf 77.4%

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

   6. Taylor expanded in t around 0 66.3%

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

      1. associate-*r/ 66.3%

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

      2. neg-mul-1 66.3%

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

      3. distribute-rgt-neg-in 66.3%

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

   8. Simplified 66.3%

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

   9. Taylor expanded in y around 0 66.3%

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

       1. mul-1-neg 66.3%

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

       2. *-commutative 66.3%

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

       3. associate-*r/ 63.3%

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

       4. distribute-rgt-neg-in 63.3%

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

       5. distribute-neg-frac2 63.3%

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

   11. Simplified 63.3%

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

   if -8.50000000000000021e217 < z < -2.1999999999999999e166

   1. Initial program 71.5%

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

      1. sub-neg 71.5%

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

      2. +-commutative 71.5%

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

      3. distribute-frac-neg 71.5%

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

      4. distribute-rgt-neg-out 71.5%

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

      5. associate-/l* 88.3%

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

      6. fma-define 88.1%

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

      7. distribute-frac-neg 88.1%

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

      8. distribute-neg-frac2 88.1%

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

      9. sub-neg 88.1%

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

      10. distribute-neg-in 88.1%

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

      11. remove-double-neg 88.1%

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

      12. +-commutative 88.1%

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

      13. sub-neg 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in z around inf 43.2%

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

   6. Taylor expanded in t around inf 42.5%

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

      1. associate-*r/ 61.4%

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

   8. Simplified 61.4%

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

   if -1.45000000000000008e161 < z < 4.69999999999999983e154

   1. Initial program 78.7%

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

   3. Taylor expanded in a around inf 66.8%

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

      1. +-commutative 66.8%

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

   5. Simplified 66.8%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+217}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+166}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+161} \lor \neg \left(z \leq 4.7 \cdot 10^{+154}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+218}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+161} \lor \neg \left(z \leq 2.05 \cdot 10^{+154}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+218)
   (* y (/ z (- a)))
   (if (<= z -3.7e+168)
     (* y (/ z t))
     (if (or (<= z -2.1e+161) (not (<= z 2.05e+154)))
       (* z (/ y (- a)))
       (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+218) {
		tmp = y * (z / -a);
	} else if (z <= -3.7e+168) {
		tmp = y * (z / t);
	} else if ((z <= -2.1e+161) || !(z <= 2.05e+154)) {
		tmp = z * (y / -a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.1d+218)) then
        tmp = y * (z / -a)
    else if (z <= (-3.7d+168)) then
        tmp = y * (z / t)
    else if ((z <= (-2.1d+161)) .or. (.not. (z <= 2.05d+154))) then
        tmp = z * (y / -a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+218) {
		tmp = y * (z / -a);
	} else if (z <= -3.7e+168) {
		tmp = y * (z / t);
	} else if ((z <= -2.1e+161) || !(z <= 2.05e+154)) {
		tmp = z * (y / -a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.1e+218:
		tmp = y * (z / -a)
	elif z <= -3.7e+168:
		tmp = y * (z / t)
	elif (z <= -2.1e+161) or not (z <= 2.05e+154):
		tmp = z * (y / -a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e+218)
		tmp = Float64(y * Float64(z / Float64(-a)));
	elseif (z <= -3.7e+168)
		tmp = Float64(y * Float64(z / t));
	elseif ((z <= -2.1e+161) || !(z <= 2.05e+154))
		tmp = Float64(z * Float64(y / Float64(-a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.1e+218)
		tmp = y * (z / -a);
	elseif (z <= -3.7e+168)
		tmp = y * (z / t);
	elseif ((z <= -2.1e+161) || ~((z <= 2.05e+154)))
		tmp = z * (y / -a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e+218], N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.7e+168], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.1e+161], N[Not[LessEqual[z, 2.05e+154]], $MachinePrecision]], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1e218

   1. Initial program 75.6%

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

      1. sub-neg 75.6%

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

      2. +-commutative 75.6%

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

      3. distribute-frac-neg 75.6%

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

      4. distribute-rgt-neg-out 75.6%

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

      5. associate-/l* 87.8%

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

      6. fma-define 88.1%

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

      7. distribute-frac-neg 88.1%

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

      8. distribute-neg-frac2 88.1%

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

      9. sub-neg 88.1%

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

      10. distribute-neg-in 88.1%

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

      11. remove-double-neg 88.1%

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

      12. +-commutative 88.1%

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

      13. sub-neg 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in z around inf 75.3%

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

   6. Taylor expanded in t around 0 63.4%

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

      1. mul-1-neg 63.4%

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

      2. associate-/l* 69.2%

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

      3. distribute-lft-neg-in 69.2%

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

   8. Simplified 69.2%

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

   if -1.1e218 < z < -3.70000000000000009e168

   1. Initial program 71.5%

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

      1. sub-neg 71.5%

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

      2. +-commutative 71.5%

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

      3. distribute-frac-neg 71.5%

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

      4. distribute-rgt-neg-out 71.5%

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

      5. associate-/l* 88.3%

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

      6. fma-define 88.1%

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

      7. distribute-frac-neg 88.1%

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

      8. distribute-neg-frac2 88.1%

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

      9. sub-neg 88.1%

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

      10. distribute-neg-in 88.1%

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

      11. remove-double-neg 88.1%

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

      12. +-commutative 88.1%

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

      13. sub-neg 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in z around inf 43.2%

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

   6. Taylor expanded in t around inf 42.5%

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

      1. associate-*r/ 61.4%

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

   8. Simplified 61.4%

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

   if -3.70000000000000009e168 < z < -2.1e161 or 2.05e154 < z

   1. Initial program 95.3%

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

      1. sub-neg 95.3%

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

      2. +-commutative 95.3%

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

      3. distribute-frac-neg 95.3%

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

      4. distribute-rgt-neg-out 95.3%

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

      5. associate-/l* 86.0%

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

      6. fma-define 86.1%

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

      7. distribute-frac-neg 86.1%

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

      8. distribute-neg-frac2 86.1%

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

      9. sub-neg 86.1%

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

      10. distribute-neg-in 86.1%

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

      11. remove-double-neg 86.1%

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

      12. +-commutative 86.1%

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

      13. sub-neg 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in z around inf 78.5%

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

   6. Taylor expanded in t around 0 67.9%

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

      1. associate-*r/ 67.9%

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

      2. neg-mul-1 67.9%

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

      3. distribute-rgt-neg-in 67.9%

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

   8. Simplified 67.9%

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

   9. Taylor expanded in y around 0 67.9%

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

       1. mul-1-neg 67.9%

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

       2. *-commutative 67.9%

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

       3. associate-*r/ 63.3%

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

       4. distribute-rgt-neg-in 63.3%

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

       5. distribute-neg-frac2 63.3%

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

   11. Simplified 63.3%

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

   if -2.1e161 < z < 2.05e154

   1. Initial program 78.7%

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

   3. Taylor expanded in a around inf 66.8%

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

      1. +-commutative 66.8%

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

   5. Simplified 66.8%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+218}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+161} \lor \neg \left(z \leq 2.05 \cdot 10^{+154}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+160}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+154}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e+217)
   (* y (/ z (- a)))
   (if (<= z -8.5e+168)
     (* y (/ z t))
     (if (<= z -3e+160)
       (* z (/ y (- a)))
       (if (<= z 3.2e+154) (+ x y) (/ (* y z) (- a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+217) {
		tmp = y * (z / -a);
	} else if (z <= -8.5e+168) {
		tmp = y * (z / t);
	} else if (z <= -3e+160) {
		tmp = z * (y / -a);
	} else if (z <= 3.2e+154) {
		tmp = x + y;
	} else {
		tmp = (y * z) / -a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.5d+217)) then
        tmp = y * (z / -a)
    else if (z <= (-8.5d+168)) then
        tmp = y * (z / t)
    else if (z <= (-3d+160)) then
        tmp = z * (y / -a)
    else if (z <= 3.2d+154) then
        tmp = x + y
    else
        tmp = (y * z) / -a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+217) {
		tmp = y * (z / -a);
	} else if (z <= -8.5e+168) {
		tmp = y * (z / t);
	} else if (z <= -3e+160) {
		tmp = z * (y / -a);
	} else if (z <= 3.2e+154) {
		tmp = x + y;
	} else {
		tmp = (y * z) / -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.5e+217:
		tmp = y * (z / -a)
	elif z <= -8.5e+168:
		tmp = y * (z / t)
	elif z <= -3e+160:
		tmp = z * (y / -a)
	elif z <= 3.2e+154:
		tmp = x + y
	else:
		tmp = (y * z) / -a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e+217)
		tmp = Float64(y * Float64(z / Float64(-a)));
	elseif (z <= -8.5e+168)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= -3e+160)
		tmp = Float64(z * Float64(y / Float64(-a)));
	elseif (z <= 3.2e+154)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(y * z) / Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.5e+217)
		tmp = y * (z / -a);
	elseif (z <= -8.5e+168)
		tmp = y * (z / t);
	elseif (z <= -3e+160)
		tmp = z * (y / -a);
	elseif (z <= 3.2e+154)
		tmp = x + y;
	else
		tmp = (y * z) / -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e+217], N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.5e+168], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3e+160], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+154], N[(x + y), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / (-a)), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.5000000000000001e217

   1. Initial program 75.6%

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

      1. sub-neg 75.6%

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

      2. +-commutative 75.6%

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

      3. distribute-frac-neg 75.6%

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

      4. distribute-rgt-neg-out 75.6%

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

      5. associate-/l* 87.8%

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

      6. fma-define 88.1%

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

      7. distribute-frac-neg 88.1%

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

      8. distribute-neg-frac2 88.1%

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

      9. sub-neg 88.1%

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

      10. distribute-neg-in 88.1%

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

      11. remove-double-neg 88.1%

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

      12. +-commutative 88.1%

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

      13. sub-neg 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in z around inf 75.3%

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

   6. Taylor expanded in t around 0 63.4%

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

      1. mul-1-neg 63.4%

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

      2. associate-/l* 69.2%

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

      3. distribute-lft-neg-in 69.2%

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

   8. Simplified 69.2%

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

   if -7.5000000000000001e217 < z < -8.50000000000000069e168

   1. Initial program 71.5%

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

      1. sub-neg 71.5%

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

      2. +-commutative 71.5%

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

      3. distribute-frac-neg 71.5%

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

      4. distribute-rgt-neg-out 71.5%

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

      5. associate-/l* 88.3%

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

      6. fma-define 88.1%

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

      7. distribute-frac-neg 88.1%

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

      8. distribute-neg-frac2 88.1%

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

      9. sub-neg 88.1%

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

      10. distribute-neg-in 88.1%

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

      11. remove-double-neg 88.1%

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

      12. +-commutative 88.1%

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

      13. sub-neg 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in z around inf 43.2%

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

   6. Taylor expanded in t around inf 42.5%

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

      1. associate-*r/ 61.4%

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

   8. Simplified 61.4%

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

   if -8.50000000000000069e168 < z < -2.9999999999999999e160

   1. Initial program 99.2%

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

      1. sub-neg 99.2%

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

      2. +-commutative 99.2%

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

      3. distribute-frac-neg 99.2%

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

      4. distribute-rgt-neg-out 99.2%

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

      5. associate-/l* 100.0%

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

      6. fma-define 100.0%

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

      7. distribute-frac-neg 100.0%

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

      8. distribute-neg-frac2 100.0%

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

      9. sub-neg 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. remove-double-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 99.2%

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

   6. Taylor expanded in t around 0 99.2%

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

      1. associate-*r/ 99.2%

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

      2. neg-mul-1 99.2%

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

      3. distribute-rgt-neg-in 99.2%

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

   8. Simplified 99.2%

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

   9. Taylor expanded in y around 0 99.2%

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

       1. mul-1-neg 99.2%

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

       2. *-commutative 99.2%

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

       3. associate-*r/ 100.0%

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

       4. distribute-rgt-neg-in 100.0%

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

       5. distribute-neg-frac2 100.0%

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

   11. Simplified 100.0%

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

   if -2.9999999999999999e160 < z < 3.2e154

   1. Initial program 78.7%

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

   3. Taylor expanded in a around inf 66.8%

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

      1. +-commutative 66.8%

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

   5. Simplified 66.8%

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

   if 3.2e154 < z

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. +-commutative 95.0%

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

      3. distribute-frac-neg 95.0%

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

      4. distribute-rgt-neg-out 95.0%

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

      5. associate-/l* 84.9%

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

      6. fma-define 85.1%

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

      7. distribute-frac-neg 85.1%

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

      8. distribute-neg-frac2 85.1%

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

      9. sub-neg 85.1%

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

      10. distribute-neg-in 85.1%

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

      11. remove-double-neg 85.1%

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

      12. +-commutative 85.1%

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

      13. sub-neg 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in z around inf 76.9%

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

   6. Taylor expanded in t around 0 65.5%

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

      1. associate-*r/ 65.5%

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

      2. neg-mul-1 65.5%

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

      3. distribute-rgt-neg-in 65.5%

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

   8. Simplified 65.5%

      \[\leadsto \color{blue}{\frac{y \cdot \left(-z\right)}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+160}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+154}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+120} \lor \neg \left(t \leq 3.4 \cdot 10^{+16}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.85e+120) (not (<= t 3.4e+16)))
   (+ x (* y (- (/ z t) (/ a t))))
   (- (+ x y) (* (- z t) (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.85e+120) || !(t <= 3.4e+16)) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else {
		tmp = (x + y) - ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.85d+120)) .or. (.not. (t <= 3.4d+16))) then
        tmp = x + (y * ((z / t) - (a / t)))
    else
        tmp = (x + y) - ((z - t) * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.85e+120) || !(t <= 3.4e+16)) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else {
		tmp = (x + y) - ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.85e+120) or not (t <= 3.4e+16):
		tmp = x + (y * ((z / t) - (a / t)))
	else:
		tmp = (x + y) - ((z - t) * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.85e+120) || !(t <= 3.4e+16))
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	else
		tmp = Float64(Float64(x + y) - Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.85e+120) || ~((t <= 3.4e+16)))
		tmp = x + (y * ((z / t) - (a / t)));
	else
		tmp = (x + y) - ((z - t) * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.85e+120], N[Not[LessEqual[t, 3.4e+16]], $MachinePrecision]], N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.85000000000000012e120 or 3.4e16 < t

   1. Initial program 57.0%

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

      1. sub-neg 57.0%

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

      2. +-commutative 57.0%

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

      3. distribute-frac-neg 57.0%

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

      4. distribute-rgt-neg-out 57.0%

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

      5. associate-/l* 66.1%

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

      6. fma-define 66.2%

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

      7. distribute-frac-neg 66.2%

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

      8. distribute-neg-frac2 66.2%

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

      9. sub-neg 66.2%

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

      10. distribute-neg-in 66.2%

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

      11. remove-double-neg 66.2%

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

      12. +-commutative 66.2%

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

      13. sub-neg 66.2%

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

   3. Simplified 66.2%

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

   5. Taylor expanded in t around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. associate-+r+ 78.3%

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

      3. distribute-rgt1-in 78.3%

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

      4. metadata-eval 78.3%

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

      5. mul0-lft 78.3%

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

      6. associate-/l* 84.3%

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

      7. associate-/l* 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in y around 0 91.2%

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

   if -1.85000000000000012e120 < t < 3.4e16

   1. Initial program 93.5%

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

      1. associate-/l* 93.9%

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

      2. *-commutative 93.9%

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

   4. Applied egg-rr 93.9%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+120} \lor \neg \left(t \leq 3.4 \cdot 10^{+16}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 88.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+119} \lor \neg \left(t \leq 920\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5e+119) (not (<= t 920.0)))
   (+ x (* y (- (/ z t) (/ a t))))
   (- (+ x y) (/ (* y (- z t)) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5e+119) || !(t <= 920.0)) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else {
		tmp = (x + y) - ((y * (z - t)) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5d+119)) .or. (.not. (t <= 920.0d0))) then
        tmp = x + (y * ((z / t) - (a / t)))
    else
        tmp = (x + y) - ((y * (z - t)) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5e+119) || !(t <= 920.0)) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else {
		tmp = (x + y) - ((y * (z - t)) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5e+119) or not (t <= 920.0):
		tmp = x + (y * ((z / t) - (a / t)))
	else:
		tmp = (x + y) - ((y * (z - t)) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5e+119) || !(t <= 920.0))
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	else
		tmp = Float64(Float64(x + y) - Float64(Float64(y * Float64(z - t)) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5e+119) || ~((t <= 920.0)))
		tmp = x + (y * ((z / t) - (a / t)));
	else
		tmp = (x + y) - ((y * (z - t)) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5e+119], N[Not[LessEqual[t, 920.0]], $MachinePrecision]], N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.9999999999999999e119 or 920 < t

   1. Initial program 57.0%

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

      1. sub-neg 57.0%

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

      2. +-commutative 57.0%

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

      3. distribute-frac-neg 57.0%

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

      4. distribute-rgt-neg-out 57.0%

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

      5. associate-/l* 66.8%

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

      6. fma-define 66.9%

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

      7. distribute-frac-neg 66.9%

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

      8. distribute-neg-frac2 66.9%

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

      9. sub-neg 66.9%

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

      10. distribute-neg-in 66.9%

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

      11. remove-double-neg 66.9%

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

      12. +-commutative 66.9%

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

      13. sub-neg 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in t around inf 67.1%

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

      1. associate--l+ 67.1%

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

      2. associate-+r+ 77.9%

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

      3. distribute-rgt1-in 77.9%

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

      4. metadata-eval 77.9%

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

      5. mul0-lft 77.9%

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

      6. associate-/l* 84.6%

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

      7. associate-/l* 90.3%

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

   7. Simplified 90.3%

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

   8. Taylor expanded in y around 0 91.3%

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

   if -4.9999999999999999e119 < t < 920

   1. Initial program 93.9%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+119} \lor \neg \left(t \leq 920\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+120}:\\ \;\;\;\;x + a \cdot \left(y \cdot \frac{z}{t \cdot a} - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 920:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2e+120)
   (+ x (* a (- (* y (/ z (* t a))) (/ y t))))
   (if (<= t 920.0)
     (- (+ x y) (/ (* y (- z t)) (- a t)))
     (+ x (* y (- (/ z t) (/ a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2e+120) {
		tmp = x + (a * ((y * (z / (t * a))) - (y / t)));
	} else if (t <= 920.0) {
		tmp = (x + y) - ((y * (z - t)) / (a - t));
	} else {
		tmp = x + (y * ((z / t) - (a / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2d+120)) then
        tmp = x + (a * ((y * (z / (t * a))) - (y / t)))
    else if (t <= 920.0d0) then
        tmp = (x + y) - ((y * (z - t)) / (a - t))
    else
        tmp = x + (y * ((z / t) - (a / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2e+120) {
		tmp = x + (a * ((y * (z / (t * a))) - (y / t)));
	} else if (t <= 920.0) {
		tmp = (x + y) - ((y * (z - t)) / (a - t));
	} else {
		tmp = x + (y * ((z / t) - (a / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2e+120:
		tmp = x + (a * ((y * (z / (t * a))) - (y / t)))
	elif t <= 920.0:
		tmp = (x + y) - ((y * (z - t)) / (a - t))
	else:
		tmp = x + (y * ((z / t) - (a / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2e+120)
		tmp = Float64(x + Float64(a * Float64(Float64(y * Float64(z / Float64(t * a))) - Float64(y / t))));
	elseif (t <= 920.0)
		tmp = Float64(Float64(x + y) - Float64(Float64(y * Float64(z - t)) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2e+120)
		tmp = x + (a * ((y * (z / (t * a))) - (y / t)));
	elseif (t <= 920.0)
		tmp = (x + y) - ((y * (z - t)) / (a - t));
	else
		tmp = x + (y * ((z / t) - (a / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2e+120], N[(x + N[(a * N[(N[(y * N[(z / N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 920.0], N[(N[(x + y), $MachinePrecision] - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2e120

   1. Initial program 63.0%

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

      1. sub-neg 63.0%

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

      2. +-commutative 63.0%

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

      3. distribute-frac-neg 63.0%

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

      4. distribute-rgt-neg-out 63.0%

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

      5. associate-/l* 65.5%

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

      6. fma-define 66.1%

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

      7. distribute-frac-neg 66.1%

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

      8. distribute-neg-frac2 66.1%

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

      9. sub-neg 66.1%

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

      10. distribute-neg-in 66.1%

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

      11. remove-double-neg 66.1%

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

      12. +-commutative 66.1%

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

      13. sub-neg 66.1%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in t around inf 66.4%

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

      1. associate--l+ 66.4%

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

      2. associate-+r+ 81.7%

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

      3. distribute-rgt1-in 81.7%

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

      4. metadata-eval 81.7%

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

      5. mul0-lft 81.7%

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

      6. associate-/l* 84.9%

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

      7. associate-/l* 92.5%

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

   7. Simplified 92.5%

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

   8. Taylor expanded in a around inf 86.5%

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

      1. associate-/l* 92.8%

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

      2. *-commutative 92.8%

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

   10. Simplified 92.8%

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

   if -2e120 < t < 920

   1. Initial program 93.9%

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

   if 920 < t

   1. Initial program 54.0%

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

      1. sub-neg 54.0%

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

      2. +-commutative 54.0%

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

      3. distribute-frac-neg 54.0%

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

      4. distribute-rgt-neg-out 54.0%

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

      5. associate-/l* 67.5%

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

      6. fma-define 67.4%

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

      7. distribute-frac-neg 67.4%

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

      8. distribute-neg-frac2 67.4%

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

      9. sub-neg 67.4%

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

      10. distribute-neg-in 67.4%

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

      11. remove-double-neg 67.4%

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

      12. +-commutative 67.4%

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

      13. sub-neg 67.4%

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

   3. Simplified 67.4%

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

   5. Taylor expanded in t around inf 67.4%

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

      1. associate--l+ 67.4%

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

      2. associate-+r+ 76.0%

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

      3. distribute-rgt1-in 76.0%

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

      4. metadata-eval 76.0%

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

      5. mul0-lft 76.0%

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

      6. associate-/l* 84.5%

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

      7. associate-/l* 89.2%

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

   7. Simplified 89.2%

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

   8. Taylor expanded in y around 0 90.7%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+120}:\\ \;\;\;\;x + a \cdot \left(y \cdot \frac{z}{t \cdot a} - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 920:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 2600000:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.8e+82)
   (+ x y)
   (if (<= a -1.02e-57)
     (* y (/ z (- t a)))
     (if (<= a 2600000.0) (+ x (* z (/ y t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e+82) {
		tmp = x + y;
	} else if (a <= -1.02e-57) {
		tmp = y * (z / (t - a));
	} else if (a <= 2600000.0) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.8d+82)) then
        tmp = x + y
    else if (a <= (-1.02d-57)) then
        tmp = y * (z / (t - a))
    else if (a <= 2600000.0d0) then
        tmp = x + (z * (y / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e+82) {
		tmp = x + y;
	} else if (a <= -1.02e-57) {
		tmp = y * (z / (t - a));
	} else if (a <= 2600000.0) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.8e+82:
		tmp = x + y
	elif a <= -1.02e-57:
		tmp = y * (z / (t - a))
	elif a <= 2600000.0:
		tmp = x + (z * (y / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.8e+82)
		tmp = Float64(x + y);
	elseif (a <= -1.02e-57)
		tmp = Float64(y * Float64(z / Float64(t - a)));
	elseif (a <= 2600000.0)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.8e+82)
		tmp = x + y;
	elseif (a <= -1.02e-57)
		tmp = y * (z / (t - a));
	elseif (a <= 2600000.0)
		tmp = x + (z * (y / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.8e+82], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.02e-57], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2600000.0], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.80000000000000007e82 or 2.6e6 < a

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 78.5%

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

      1. +-commutative 78.5%

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

   5. Simplified 78.5%

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

   if -1.80000000000000007e82 < a < -1.02e-57

   1. Initial program 83.8%

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

      1. sub-neg 83.8%

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

      2. +-commutative 83.8%

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

      3. distribute-frac-neg 83.8%

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

      4. distribute-rgt-neg-out 83.8%

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

      5. associate-/l* 89.1%

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

      6. fma-define 89.4%

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

      7. distribute-frac-neg 89.4%

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

      8. distribute-neg-frac2 89.4%

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

      9. sub-neg 89.4%

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

      10. distribute-neg-in 89.4%

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

      11. remove-double-neg 89.4%

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

      12. +-commutative 89.4%

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

      13. sub-neg 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around inf 51.8%

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

      1. associate-/l* 59.5%

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

   7. Simplified 59.5%

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

   if -1.02e-57 < a < 2.6e6

   1. Initial program 78.1%

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

      1. sub-neg 78.1%

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

      2. +-commutative 78.1%

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

      3. distribute-frac-neg 78.1%

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

      4. distribute-rgt-neg-out 78.1%

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

      5. associate-/l* 77.4%

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

      6. fma-define 77.6%

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

      7. distribute-frac-neg 77.6%

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

      8. distribute-neg-frac2 77.6%

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

      9. sub-neg 77.6%

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

      10. distribute-neg-in 77.6%

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

      11. remove-double-neg 77.6%

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

      12. +-commutative 77.6%

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

      13. sub-neg 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in t around inf 70.2%

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

      1. associate--l+ 70.2%

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

      2. associate-+r+ 79.0%

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

      3. distribute-rgt1-in 79.0%

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

      4. metadata-eval 79.0%

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

      5. mul0-lft 79.0%

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

      6. associate-/l* 78.2%

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

      7. associate-/l* 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in z around inf 77.0%

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

      1. +-commutative 77.0%

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

      2. mul-1-neg 77.0%

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

      3. sub-neg 77.0%

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

      4. *-commutative 77.0%

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

      5. *-commutative 77.0%

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

      6. times-frac 76.1%

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

   10. Simplified 76.1%

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

   11. Taylor expanded in z around inf 78.9%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 2600000:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 71.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 236:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e+82)
   (+ x y)
   (if (<= a -8.5e-81)
     (* y (/ z (- t a)))
     (if (<= a 236.0) (+ x (/ (* y z) t)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e+82) {
		tmp = x + y;
	} else if (a <= -8.5e-81) {
		tmp = y * (z / (t - a));
	} else if (a <= 236.0) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.2d+82)) then
        tmp = x + y
    else if (a <= (-8.5d-81)) then
        tmp = y * (z / (t - a))
    else if (a <= 236.0d0) then
        tmp = x + ((y * z) / t)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e+82) {
		tmp = x + y;
	} else if (a <= -8.5e-81) {
		tmp = y * (z / (t - a));
	} else if (a <= 236.0) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e+82:
		tmp = x + y
	elif a <= -8.5e-81:
		tmp = y * (z / (t - a))
	elif a <= 236.0:
		tmp = x + ((y * z) / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e+82)
		tmp = Float64(x + y);
	elseif (a <= -8.5e-81)
		tmp = Float64(y * Float64(z / Float64(t - a)));
	elseif (a <= 236.0)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e+82)
		tmp = x + y;
	elseif (a <= -8.5e-81)
		tmp = y * (z / (t - a));
	elseif (a <= 236.0)
		tmp = x + ((y * z) / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e+82], N[(x + y), $MachinePrecision], If[LessEqual[a, -8.5e-81], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 236.0], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.19999999999999975e82 or 236 < a

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 78.5%

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

      1. +-commutative 78.5%

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

   5. Simplified 78.5%

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

   if -3.19999999999999975e82 < a < -8.5000000000000001e-81

   1. Initial program 76.6%

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

      1. sub-neg 76.6%

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

      2. +-commutative 76.6%

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

      3. distribute-frac-neg 76.6%

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

      4. distribute-rgt-neg-out 76.6%

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

      5. associate-/l* 81.1%

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

      6. fma-define 81.6%

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

      7. distribute-frac-neg 81.6%

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

      8. distribute-neg-frac2 81.6%

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

      9. sub-neg 81.6%

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

      10. distribute-neg-in 81.6%

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

      11. remove-double-neg 81.6%

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

      12. +-commutative 81.6%

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

      13. sub-neg 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in z around inf 50.7%

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

      1. associate-/l* 62.1%

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

   7. Simplified 62.1%

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

   if -8.5000000000000001e-81 < a < 236

   1. Initial program 80.4%

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

      1. sub-neg 80.4%

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

      2. +-commutative 80.4%

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

      3. distribute-frac-neg 80.4%

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

      4. distribute-rgt-neg-out 80.4%

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

      5. associate-/l* 79.7%

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

      6. fma-define 79.9%

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

      7. distribute-frac-neg 79.9%

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

      8. distribute-neg-frac2 79.9%

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

      9. sub-neg 79.9%

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

      10. distribute-neg-in 79.9%

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

      11. remove-double-neg 79.9%

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

      12. +-commutative 79.9%

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

      13. sub-neg 79.9%

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

   3. Simplified 79.9%

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

   5. Taylor expanded in t around inf 71.4%

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

      1. associate--l+ 71.4%

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

      2. associate-+r+ 79.7%

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

      3. distribute-rgt1-in 79.7%

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

      4. metadata-eval 79.7%

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

      5. mul0-lft 79.7%

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

      6. associate-/l* 77.2%

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

      7. associate-/l* 75.5%

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

   7. Simplified 75.5%

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

   8. Taylor expanded in a around 0 79.1%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 236:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+120} \lor \neg \left(z \leq 2 \cdot 10^{+108}\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.8e+120) (not (<= z 2e+108))) (* y (/ z (- t a))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+120) || !(z <= 2e+108)) {
		tmp = y * (z / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.8d+120)) .or. (.not. (z <= 2d+108))) then
        tmp = y * (z / (t - a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+120) || !(z <= 2e+108)) {
		tmp = y * (z / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.8e+120) or not (z <= 2e+108):
		tmp = y * (z / (t - a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.8e+120) || !(z <= 2e+108))
		tmp = Float64(y * Float64(z / Float64(t - a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.8e+120) || ~((z <= 2e+108)))
		tmp = y * (z / (t - a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.8e+120], N[Not[LessEqual[z, 2e+108]], $MachinePrecision]], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000005e120 or 2.0000000000000001e108 < z

   1. Initial program 83.2%

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

      1. sub-neg 83.2%

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

      2. +-commutative 83.2%

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

      3. distribute-frac-neg 83.2%

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

      4. distribute-rgt-neg-out 83.2%

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

      5. associate-/l* 85.9%

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

      6. fma-define 86.1%

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

      7. distribute-frac-neg 86.1%

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

      8. distribute-neg-frac2 86.1%

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

      9. sub-neg 86.1%

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

      10. distribute-neg-in 86.1%

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

      11. remove-double-neg 86.1%

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

      12. +-commutative 86.1%

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

      13. sub-neg 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in z around inf 67.1%

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

      1. associate-/l* 72.5%

         \[\leadsto \color{blue}{y \cdot \frac{z}{t - a}} \]

   7. Simplified 72.5%

      \[\leadsto \color{blue}{y \cdot \frac{z}{t - a}} \]

   if -8.8000000000000005e120 < z < 2.0000000000000001e108

   1. Initial program 78.9%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 69.5%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 69.5%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 69.5%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+120} \lor \neg \left(z \leq 2 \cdot 10^{+108}\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 60.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+153} \lor \neg \left(z \leq 2.4 \cdot 10^{+207}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.12e+153) (not (<= z 2.4e+207))) (* y (/ z t)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.12e+153) || !(z <= 2.4e+207)) {
		tmp = y * (z / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.12d+153)) .or. (.not. (z <= 2.4d+207))) then
        tmp = y * (z / t)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.12e+153) || !(z <= 2.4e+207)) {
		tmp = y * (z / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.12e+153) or not (z <= 2.4e+207):
		tmp = y * (z / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.12e+153) || !(z <= 2.4e+207))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.12e+153) || ~((z <= 2.4e+207)))
		tmp = y * (z / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.12e+153], N[Not[LessEqual[z, 2.4e+207]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1200000000000001e153 or 2.4000000000000001e207 < z

   1. Initial program 81.9%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   2. Step-by-step derivation

      1. sub-neg 81.9%

         \[\leadsto \color{blue}{\left(x + y\right) + \left(-\frac{\left(z - t\right) \cdot y}{a - t}\right)} \]

      2. +-commutative 81.9%

         \[\leadsto \color{blue}{\left(-\frac{\left(z - t\right) \cdot y}{a - t}\right) + \left(x + y\right)} \]

      3. distribute-frac-neg 81.9%

         \[\leadsto \color{blue}{\frac{-\left(z - t\right) \cdot y}{a - t}} + \left(x + y\right) \]

      4. distribute-rgt-neg-out 81.9%

         \[\leadsto \frac{\color{blue}{\left(z - t\right) \cdot \left(-y\right)}}{a - t} + \left(x + y\right) \]

      5. associate-/l* 84.0%

         \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{-y}{a - t}} + \left(x + y\right) \]

      6. fma-define 84.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{-y}{a - t}, x + y\right)} \]

      7. distribute-frac-neg 84.1%

         \[\leadsto \mathsf{fma}\left(z - t, \color{blue}{-\frac{y}{a - t}}, x + y\right) \]

      8. distribute-neg-frac2 84.1%

         \[\leadsto \mathsf{fma}\left(z - t, \color{blue}{\frac{y}{-\left(a - t\right)}}, x + y\right) \]

      9. sub-neg 84.1%

         \[\leadsto \mathsf{fma}\left(z - t, \frac{y}{-\color{blue}{\left(a + \left(-t\right)\right)}}, x + y\right) \]

      10. distribute-neg-in 84.1%

          \[\leadsto \mathsf{fma}\left(z - t, \frac{y}{\color{blue}{\left(-a\right) + \left(-\left(-t\right)\right)}}, x + y\right) \]

      11. remove-double-neg 84.1%

          \[\leadsto \mathsf{fma}\left(z - t, \frac{y}{\left(-a\right) + \color{blue}{t}}, x + y\right) \]

      12. +-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(z - t, \frac{y}{\color{blue}{t + \left(-a\right)}}, x + y\right) \]

      13. sub-neg 84.1%

          \[\leadsto \mathsf{fma}\left(z - t, \frac{y}{\color{blue}{t - a}}, x + y\right) \]

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 71.7%

      \[\leadsto \color{blue}{\frac{y \cdot z}{t - a}} \]

   6. Taylor expanded in t around inf 35.4%

      \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]
   7. Step-by-step derivation

      1. associate-*r/ 41.1%

         \[\leadsto \color{blue}{y \cdot \frac{z}{t}} \]

   8. Simplified 41.1%

      \[\leadsto \color{blue}{y \cdot \frac{z}{t}} \]

   if -1.1200000000000001e153 < z < 2.4000000000000001e207

   1. Initial program 79.6%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 66.1%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 66.1%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 66.1%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+153} \lor \neg \left(z \leq 2.4 \cdot 10^{+207}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 61.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.2 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t 2.2e+76) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.2e+76) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 2.2d+76) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.2e+76) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 2.2e+76:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2.2e+76)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 2.2e+76)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2.2e+76], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < 2.2e76

   1. Initial program 87.2%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 58.5%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 58.5%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 58.5%

      \[\leadsto \color{blue}{y + x} \]

   if 2.2e76 < t

   1. Initial program 45.7%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 66.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.2 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.6% 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 80.1%

   \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 48.2%

   \[\leadsto \color{blue}{x} \]

4. Final simplification 48.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 88.2% 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 2024130 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (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))))