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

Percentage Accurate: 76.8% → 90.2%

Time: 12.7s

Alternatives: 14

Speedup: 0.7×

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: 76.8% 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: 90.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+182}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{z}{t} - a \cdot \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6e+182)
   (+ x (* y (/ (- z a) t)))
   (if (<= t 1.95e+136)
     (fma (- z t) (/ y (- t a)) (+ x y))
     (+ x (- (* y (/ z t)) (* a (/ y t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6e+182) {
		tmp = x + (y * ((z - a) / t));
	} else if (t <= 1.95e+136) {
		tmp = fma((z - t), (y / (t - a)), (x + y));
	} else {
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6e+182)
		tmp = Float64(x + Float64(y * Float64(Float64(z - a) / t)));
	elseif (t <= 1.95e+136)
		tmp = fma(Float64(z - t), Float64(y / Float64(t - a)), Float64(x + y));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z / t)) - Float64(a * Float64(y / t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6e+182], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+136], N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.0000000000000004e182

   1. Initial program 46.7%

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

      1. associate-/l* 61.3%

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

      2. *-commutative 61.3%

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

   4. Applied egg-rr 61.3%

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

   5. Taylor expanded in t around -inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. sub-neg 85.7%

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

      3. distribute-rgt-neg-out 85.7%

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

      4. *-commutative 85.7%

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

      5. distribute-lft-out 85.7%

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

      6. sub-neg 85.7%

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

      7. unsub-neg 85.7%

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

      8. associate-/l* 93.1%

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

   7. Simplified 93.1%

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

   if -6.0000000000000004e182 < t < 1.9500000000000001e136

   1. Initial program 85.2%

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

      1. sub-neg 85.2%

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

      2. +-commutative 85.2%

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

      3. distribute-frac-neg 85.2%

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

      4. distribute-rgt-neg-out 85.2%

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

      5. associate-/l* 91.0%

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

      6. fma-define 91.0%

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

      7. distribute-frac-neg 91.0%

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

      8. distribute-neg-frac2 91.0%

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

      9. sub-neg 91.0%

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

      10. distribute-neg-in 91.0%

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

      11. remove-double-neg 91.0%

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

      12. +-commutative 91.0%

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

      13. sub-neg 91.0%

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

   3. Simplified 91.0%

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

   if 1.9500000000000001e136 < t

   1. Initial program 40.9%

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

      1. sub-neg 40.9%

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

      2. +-commutative 40.9%

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

      3. distribute-frac-neg 40.9%

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

      4. distribute-rgt-neg-out 40.9%

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

      5. associate-/l* 49.4%

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

      6. fma-define 49.5%

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

      7. distribute-frac-neg 49.5%

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

      8. distribute-neg-frac2 49.5%

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

      9. sub-neg 49.5%

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

      10. distribute-neg-in 49.5%

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

      11. remove-double-neg 49.5%

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

      12. +-commutative 49.5%

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

      13. sub-neg 49.5%

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

   3. Simplified 49.5%

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

   5. Taylor expanded in t around inf 55.1%

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

      1. associate--l+ 55.1%

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

      2. associate-+r+ 72.1%

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

      3. distribute-rgt1-in 72.1%

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

      4. metadata-eval 72.1%

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

      5. mul0-lft 72.1%

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

      6. associate-/l* 81.4%

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

      7. associate-/l* 95.2%

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

   7. Simplified 95.2%

      \[\leadsto \color{blue}{x + \left(\left(0 + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+182}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{z}{t} - a \cdot \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+180} \lor \neg \left(t \leq 6.8 \cdot 10^{+137}\right):\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.5e+180) (not (<= t 6.8e+137)))
   (+ x (* y (/ (- z 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 <= -1.5e+180) || !(t <= 6.8e+137)) {
		tmp = x + (y * ((z - 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 <= (-1.5d+180)) .or. (.not. (t <= 6.8d+137))) then
        tmp = x + (y * ((z - 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 <= -1.5e+180) || !(t <= 6.8e+137)) {
		tmp = x + (y * ((z - 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 <= -1.5e+180) or not (t <= 6.8e+137):
		tmp = x + (y * ((z - 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 <= -1.5e+180) || !(t <= 6.8e+137))
		tmp = Float64(x + Float64(y * Float64(Float64(z - 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 <= -1.5e+180) || ~((t <= 6.8e+137)))
		tmp = x + (y * ((z - 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, -1.5e+180], N[Not[LessEqual[t, 6.8e+137]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $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 < -1.50000000000000001e180 or 6.79999999999999973e137 < t

   1. Initial program 43.2%

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

      1. associate-/l* 54.1%

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

      2. *-commutative 54.1%

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

   4. Applied egg-rr 54.1%

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

   5. Taylor expanded in t around -inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. sub-neg 77.4%

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

      3. distribute-rgt-neg-out 77.4%

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

      4. *-commutative 77.4%

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

      5. distribute-lft-out 79.1%

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

      6. sub-neg 79.1%

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

      7. unsub-neg 79.1%

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

      8. associate-/l* 93.8%

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

   7. Simplified 93.8%

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

   if -1.50000000000000001e180 < t < 6.79999999999999973e137

   1. Initial program 85.2%

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

      1. associate-/l* 91.0%

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

      2. *-commutative 91.0%

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

   4. Applied egg-rr 91.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+180} \lor \neg \left(t \leq 6.8 \cdot 10^{+137}\right):\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+181}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+135}:\\ \;\;\;\;\left(x + y\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{z}{t} - a \cdot \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6e+181)
   (+ x (* y (/ (- z a) t)))
   (if (<= t 5.5e+135)
     (- (+ x y) (* (- z t) (/ y (- a t))))
     (+ x (- (* y (/ z t)) (* a (/ y t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6e+181) {
		tmp = x + (y * ((z - a) / t));
	} else if (t <= 5.5e+135) {
		tmp = (x + y) - ((z - t) * (y / (a - t)));
	} else {
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6d+181)) then
        tmp = x + (y * ((z - a) / t))
    else if (t <= 5.5d+135) then
        tmp = (x + y) - ((z - t) * (y / (a - t)))
    else
        tmp = x + ((y * (z / t)) - (a * (y / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6e+181) {
		tmp = x + (y * ((z - a) / t));
	} else if (t <= 5.5e+135) {
		tmp = (x + y) - ((z - t) * (y / (a - t)));
	} else {
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6e+181:
		tmp = x + (y * ((z - a) / t))
	elif t <= 5.5e+135:
		tmp = (x + y) - ((z - t) * (y / (a - t)))
	else:
		tmp = x + ((y * (z / t)) - (a * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6e+181)
		tmp = Float64(x + Float64(y * Float64(Float64(z - a) / t)));
	elseif (t <= 5.5e+135)
		tmp = Float64(Float64(x + y) - Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z / t)) - Float64(a * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6e+181)
		tmp = x + (y * ((z - a) / t));
	elseif (t <= 5.5e+135)
		tmp = (x + y) - ((z - t) * (y / (a - t)));
	else
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6e+181], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+135], N[(N[(x + y), $MachinePrecision] - N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.00000000000000024e181

   1. Initial program 46.7%

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

      1. associate-/l* 61.3%

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

      2. *-commutative 61.3%

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

   4. Applied egg-rr 61.3%

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

   5. Taylor expanded in t around -inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. sub-neg 85.7%

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

      3. distribute-rgt-neg-out 85.7%

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

      4. *-commutative 85.7%

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

      5. distribute-lft-out 85.7%

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

      6. sub-neg 85.7%

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

      7. unsub-neg 85.7%

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

      8. associate-/l* 93.1%

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

   7. Simplified 93.1%

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

   if -6.00000000000000024e181 < t < 5.4999999999999999e135

   1. Initial program 85.2%

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

      1. associate-/l* 91.0%

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

      2. *-commutative 91.0%

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

   4. Applied egg-rr 91.0%

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

   if 5.4999999999999999e135 < t

   1. Initial program 40.9%

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

      1. sub-neg 40.9%

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

      2. +-commutative 40.9%

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

      3. distribute-frac-neg 40.9%

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

      4. distribute-rgt-neg-out 40.9%

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

      5. associate-/l* 49.4%

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

      6. fma-define 49.5%

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

      7. distribute-frac-neg 49.5%

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

      8. distribute-neg-frac2 49.5%

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

      9. sub-neg 49.5%

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

      10. distribute-neg-in 49.5%

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

      11. remove-double-neg 49.5%

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

      12. +-commutative 49.5%

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

      13. sub-neg 49.5%

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

   3. Simplified 49.5%

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

   5. Taylor expanded in t around inf 55.1%

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

      1. associate--l+ 55.1%

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

      2. associate-+r+ 72.1%

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

      3. distribute-rgt1-in 72.1%

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

      4. metadata-eval 72.1%

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

      5. mul0-lft 72.1%

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

      6. associate-/l* 81.4%

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

      7. associate-/l* 95.2%

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

   7. Simplified 95.2%

      \[\leadsto \color{blue}{x + \left(\left(0 + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+181}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+135}:\\ \;\;\;\;\left(x + y\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{z}{t} - a \cdot \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+255} \lor \neg \left(y \leq -5.2 \cdot 10^{+124}\right) \land y \leq 8.2 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.05e+255) (and (not (<= y -5.2e+124)) (<= y 8.2e+122)))
   (+ x y)
   (* y (/ z t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.05e+255) || (!(y <= -5.2e+124) && (y <= 8.2e+122))) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.05d+255)) .or. (.not. (y <= (-5.2d+124))) .and. (y <= 8.2d+122)) then
        tmp = x + y
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.05e+255) || (!(y <= -5.2e+124) && (y <= 8.2e+122))) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.05e+255) or (not (y <= -5.2e+124) and (y <= 8.2e+122)):
		tmp = x + y
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.05e+255) || (!(y <= -5.2e+124) && (y <= 8.2e+122)))
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.05e+255) || (~((y <= -5.2e+124)) && (y <= 8.2e+122)))
		tmp = x + y;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.05e+255], And[N[Not[LessEqual[y, -5.2e+124]], $MachinePrecision], LessEqual[y, 8.2e+122]]], N[(x + y), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e255 or -5.2000000000000001e124 < y < 8.2000000000000004e122

   1. Initial program 82.5%

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

   3. Taylor expanded in a around inf 68.5%

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

      1. +-commutative 68.5%

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

   5. Simplified 68.5%

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

   if -1.05e255 < y < -5.2000000000000001e124 or 8.2000000000000004e122 < y

   1. Initial program 44.4%

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

      1. sub-neg 44.4%

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

      2. +-commutative 44.4%

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

      3. distribute-frac-neg 44.4%

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

      4. distribute-rgt-neg-out 44.4%

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

      5. associate-/l* 61.3%

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

      6. fma-define 61.4%

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

      7. distribute-frac-neg 61.4%

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

      8. distribute-neg-frac2 61.4%

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

      9. sub-neg 61.4%

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

      10. distribute-neg-in 61.4%

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

      11. remove-double-neg 61.4%

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

      12. +-commutative 61.4%

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

      13. sub-neg 61.4%

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

   3. Simplified 61.4%

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

   5. Taylor expanded in z around inf 46.1%

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

   6. Taylor expanded in t around inf 41.0%

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

      1. associate-/l* 52.2%

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

   8. Simplified 52.2%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+255} \lor \neg \left(y \leq -5.2 \cdot 10^{+124}\right) \land y \leq 8.2 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+109} \lor \neg \left(a \leq 1.9 \cdot 10^{+24}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.2e+109) (not (<= a 1.9e+24)))
   (+ x y)
   (+ x (* y (/ (- z a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.2e+109) || !(a <= 1.9e+24)) {
		tmp = x + y;
	} else {
		tmp = x + (y * ((z - 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 ((a <= (-7.2d+109)) .or. (.not. (a <= 1.9d+24))) then
        tmp = x + y
    else
        tmp = x + (y * ((z - 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 ((a <= -7.2e+109) || !(a <= 1.9e+24)) {
		tmp = x + y;
	} else {
		tmp = x + (y * ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.2e+109) or not (a <= 1.9e+24):
		tmp = x + y
	else:
		tmp = x + (y * ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.2e+109) || !(a <= 1.9e+24))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7.2e+109) || ~((a <= 1.9e+24)))
		tmp = x + y;
	else
		tmp = x + (y * ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.2e+109], N[Not[LessEqual[a, 1.9e+24]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.2e109 or 1.90000000000000008e24 < a

   1. Initial program 77.9%

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

   3. Taylor expanded in a around inf 79.1%

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

      1. +-commutative 79.1%

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

   5. Simplified 79.1%

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

   if -7.2e109 < a < 1.90000000000000008e24

   1. Initial program 71.1%

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

      1. associate-/l* 73.7%

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

      2. *-commutative 73.7%

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

   4. Applied egg-rr 73.7%

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

   5. Taylor expanded in t around -inf 78.0%

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

      1. mul-1-neg 78.0%

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

      2. sub-neg 78.0%

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

      3. distribute-rgt-neg-out 78.0%

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

      4. *-commutative 78.0%

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

      5. distribute-lft-out 78.7%

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

      6. sub-neg 78.7%

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

      7. unsub-neg 78.7%

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

      8. associate-/l* 81.5%

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

   7. Simplified 81.5%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+109} \lor \neg \left(a \leq 1.9 \cdot 10^{+24}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+70} \lor \neg \left(a \leq 8500000\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.4e+70) (not (<= a 8500000.0)))
   (- (+ x y) (* y (/ z a)))
   (+ x (* y (/ (- z a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.4e+70) || !(a <= 8500000.0)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + (y * ((z - 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 ((a <= (-1.4d+70)) .or. (.not. (a <= 8500000.0d0))) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = x + (y * ((z - 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 ((a <= -1.4e+70) || !(a <= 8500000.0)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + (y * ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.4e+70) or not (a <= 8500000.0):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x + (y * ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.4e+70) || !(a <= 8500000.0))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.4e+70) || ~((a <= 8500000.0)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x + (y * ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.4e+70], N[Not[LessEqual[a, 8500000.0]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.39999999999999995e70 or 8.5e6 < a

   1. Initial program 77.3%

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

   3. Taylor expanded in t around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. associate-/l* 87.6%

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

   5. Simplified 87.6%

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

   if -1.39999999999999995e70 < a < 8.5e6

   1. Initial program 71.1%

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

      1. associate-/l* 72.5%

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

      2. *-commutative 72.5%

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

   4. Applied egg-rr 72.5%

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

   5. Taylor expanded in t around -inf 82.0%

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

      1. mul-1-neg 82.0%

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

      2. sub-neg 82.0%

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

      3. distribute-rgt-neg-out 82.0%

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

      4. *-commutative 82.0%

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

      5. distribute-lft-out 82.0%

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

      6. sub-neg 82.0%

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

      7. unsub-neg 82.0%

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

      8. associate-/l* 83.7%

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

   7. Simplified 83.7%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+70} \lor \neg \left(a \leq 8500000\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+77} \lor \neg \left(z \leq 5 \cdot 10^{+212}\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+77) (not (<= z 5e+212))) (* y (/ z (- t a))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+77) || !(z <= 5e+212)) {
		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 <= (-1.35d+77)) .or. (.not. (z <= 5d+212))) 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 <= -1.35e+77) || !(z <= 5e+212)) {
		tmp = y * (z / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e+77) or not (z <= 5e+212):
		tmp = y * (z / (t - a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e+77) || !(z <= 5e+212))
		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 <= -1.35e+77) || ~((z <= 5e+212)))
		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, -1.35e+77], N[Not[LessEqual[z, 5e+212]], $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 < -1.3499999999999999e77 or 4.99999999999999992e212 < z

   1. Initial program 69.6%

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

      1. sub-neg 69.6%

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

      2. +-commutative 69.6%

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

      3. distribute-frac-neg 69.6%

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

      4. distribute-rgt-neg-out 69.6%

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

      5. associate-/l* 86.7%

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

      6. fma-define 86.7%

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

      7. distribute-frac-neg 86.7%

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

      8. distribute-neg-frac2 86.7%

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

      9. sub-neg 86.7%

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

      10. distribute-neg-in 86.7%

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

      11. remove-double-neg 86.7%

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

      12. +-commutative 86.7%

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

      13. sub-neg 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in z around inf 55.0%

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

      1. associate-/l* 67.3%

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

   7. Simplified 67.3%

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

   if -1.3499999999999999e77 < z < 4.99999999999999992e212

   1. Initial program 75.4%

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

   3. Taylor expanded in a around inf 68.9%

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

      1. +-commutative 68.9%

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

   5. Simplified 68.9%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+77} \lor \neg \left(z \leq 5 \cdot 10^{+212}\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+74} \lor \neg \left(z \leq 3.9 \cdot 10^{+207}\right):\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+74) (not (<= z 3.9e+207))) (* z (/ y (- t a))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+74) || !(z <= 3.9e+207)) {
		tmp = z * (y / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.5d+74)) .or. (.not. (z <= 3.9d+207))) then
        tmp = z * (y / (t - a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+74) || !(z <= 3.9e+207)) {
		tmp = z * (y / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.5e+74) or not (z <= 3.9e+207):
		tmp = z * (y / (t - a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e+74) || !(z <= 3.9e+207))
		tmp = Float64(z * Float64(y / Float64(t - a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.5e+74) || ~((z <= 3.9e+207)))
		tmp = z * (y / (t - a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e+74], N[Not[LessEqual[z, 3.9e+207]], $MachinePrecision]], N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5000000000000006e74 or 3.89999999999999972e207 < z

   1. Initial program 70.9%

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

      1. sub-neg 70.9%

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

      2. +-commutative 70.9%

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

      3. distribute-frac-neg 70.9%

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

      4. distribute-rgt-neg-out 70.9%

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

      5. associate-/l* 87.3%

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

      6. fma-define 87.3%

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

      7. distribute-frac-neg 87.3%

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

      8. distribute-neg-frac2 87.3%

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

      9. sub-neg 87.3%

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

      10. distribute-neg-in 87.3%

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

      11. remove-double-neg 87.3%

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

      12. +-commutative 87.3%

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

      13. sub-neg 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in z around inf 55.5%

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

      1. clear-num 55.5%

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

      2. inv-pow 55.5%

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

   7. Applied egg-rr 55.5%

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

      1. unpow-1 55.5%

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

   9. Simplified 55.5%

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

       1. clear-num 55.5%

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

       2. *-commutative 55.5%

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

       3. associate-/l* 69.0%

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

   11. Applied egg-rr 69.0%

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

   if -9.5000000000000006e74 < z < 3.89999999999999972e207

   1. Initial program 75.0%

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

   3. Taylor expanded in a around inf 69.4%

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

      1. +-commutative 69.4%

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

   5. Simplified 69.4%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+74} \lor \neg \left(z \leq 3.9 \cdot 10^{+207}\right):\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+102} \lor \neg \left(a \leq 460000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.1e+102) (not (<= a 460000000000.0)))
   (+ x y)
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.1e+102) || !(a <= 460000000000.0)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.1d+102)) .or. (.not. (a <= 460000000000.0d0))) then
        tmp = x + y
    else
        tmp = x + ((y * z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.1e+102) || !(a <= 460000000000.0)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.1e+102) or not (a <= 460000000000.0):
		tmp = x + y
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.1e+102) || !(a <= 460000000000.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.1e+102) || ~((a <= 460000000000.0)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.1e+102], N[Not[LessEqual[a, 460000000000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.10000000000000004e102 or 4.6e11 < a

   1. Initial program 77.8%

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

   3. Taylor expanded in a around inf 78.1%

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

      1. +-commutative 78.1%

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

   5. Simplified 78.1%

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

   if -1.10000000000000004e102 < a < 4.6e11

   1. Initial program 71.0%

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

      1. associate-/l* 73.0%

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

      2. *-commutative 73.0%

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

   4. Applied egg-rr 73.0%

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

   5. Taylor expanded in t around -inf 79.4%

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

      1. mul-1-neg 79.4%

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

      2. sub-neg 79.4%

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

      3. distribute-rgt-neg-out 79.4%

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

      4. *-commutative 79.4%

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

      5. distribute-lft-out 80.1%

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

      6. sub-neg 80.1%

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

      7. unsub-neg 80.1%

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

      8. associate-/l* 82.3%

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

   7. Simplified 82.3%

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

   8. Taylor expanded in a around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. associate-/l* 80.7%

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

      3. distribute-lft-neg-in 80.7%

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

   10. Simplified 80.7%

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

   11. Taylor expanded in y around 0 78.1%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+102} \lor \neg \left(a \leq 460000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+112} \lor \neg \left(a \leq 1.5 \cdot 10^{+14}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.8e+112) (not (<= a 1.5e+14))) (+ x y) (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e+112) || !(a <= 1.5e+14)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.8d+112)) .or. (.not. (a <= 1.5d+14))) then
        tmp = x + y
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e+112) || !(a <= 1.5e+14)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.8e+112) or not (a <= 1.5e+14):
		tmp = x + y
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.8e+112) || !(a <= 1.5e+14))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.8e+112) || ~((a <= 1.5e+14)))
		tmp = x + y;
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.8e+112], N[Not[LessEqual[a, 1.5e+14]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8e112 or 1.5e14 < a

   1. Initial program 77.9%

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

   3. Taylor expanded in a around inf 79.1%

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

      1. +-commutative 79.1%

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

   5. Simplified 79.1%

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

   if -1.8e112 < a < 1.5e14

   1. Initial program 71.1%

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

      1. associate-/l* 73.7%

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

      2. *-commutative 73.7%

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

   4. Applied egg-rr 73.7%

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

   5. Taylor expanded in t around -inf 78.0%

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

      1. mul-1-neg 78.0%

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

      2. sub-neg 78.0%

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

      3. distribute-rgt-neg-out 78.0%

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

      4. *-commutative 78.0%

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

      5. distribute-lft-out 78.7%

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

      6. sub-neg 78.7%

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

      7. unsub-neg 78.7%

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

      8. associate-/l* 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in a around 0 76.8%

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

      1. mul-1-neg 76.8%

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

      2. associate-/l* 79.9%

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

      3. distribute-lft-neg-in 79.9%

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

   10. Simplified 79.9%

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

       1. cancel-sign-sub 79.9%

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

       2. +-commutative 79.9%

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

   12. Applied egg-rr 79.9%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+112} \lor \neg \left(a \leq 1.5 \cdot 10^{+14}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+110} \lor \neg \left(a \leq 2.5 \cdot 10^{+18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.9e+110) (not (<= a 2.5e+18))) (+ x y) (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.9e+110) || !(a <= 2.5e+18)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.9d+110)) .or. (.not. (a <= 2.5d+18))) then
        tmp = x + y
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.9e+110) || !(a <= 2.5e+18)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.9e+110) or not (a <= 2.5e+18):
		tmp = x + y
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.9e+110) || !(a <= 2.5e+18))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.9e+110) || ~((a <= 2.5e+18)))
		tmp = x + y;
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.9e+110], N[Not[LessEqual[a, 2.5e+18]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.89999999999999994e110 or 2.5e18 < a

   1. Initial program 77.9%

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

   3. Taylor expanded in a around inf 79.1%

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

      1. +-commutative 79.1%

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

   5. Simplified 79.1%

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

   if -1.89999999999999994e110 < a < 2.5e18

   1. Initial program 71.1%

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

      1. associate-/l* 73.7%

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

      2. *-commutative 73.7%

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

   4. Applied egg-rr 73.7%

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

   5. Taylor expanded in t around -inf 78.0%

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

      1. mul-1-neg 78.0%

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

      2. sub-neg 78.0%

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

      3. distribute-rgt-neg-out 78.0%

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

      4. *-commutative 78.0%

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

      5. distribute-lft-out 78.7%

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

      6. sub-neg 78.7%

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

      7. unsub-neg 78.7%

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

      8. associate-/l* 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in a around 0 76.8%

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

      1. mul-1-neg 76.8%

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

      2. associate-/l* 79.9%

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

      3. distribute-lft-neg-in 79.9%

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

   10. Simplified 79.9%

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

   11. Taylor expanded in y around 0 76.8%

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

       1. mul-1-neg 76.8%

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

       2. associate-*l/ 77.3%

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

       3. associate-/r/ 80.3%

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

   13. Simplified 80.3%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+110} \lor \neg \left(a \leq 2.5 \cdot 10^{+18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+76} \lor \neg \left(z \leq 2 \cdot 10^{+202}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e+76) (not (<= z 2e+202))) (/ y (/ t z)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+76) || !(z <= 2e+202)) {
		tmp = y / (t / z);
	} 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 <= (-9d+76)) .or. (.not. (z <= 2d+202))) then
        tmp = y / (t / z)
    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 <= -9e+76) || !(z <= 2e+202)) {
		tmp = y / (t / z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e+76) or not (z <= 2e+202):
		tmp = y / (t / z)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e+76) || !(z <= 2e+202))
		tmp = Float64(y / Float64(t / z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9e+76) || ~((z <= 2e+202)))
		tmp = y / (t / z);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9e+76], N[Not[LessEqual[z, 2e+202]], $MachinePrecision]], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.9999999999999995e76 or 1.9999999999999998e202 < z

   1. Initial program 70.9%

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

      1. associate-/l* 87.3%

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

      2. *-commutative 87.3%

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

   4. Applied egg-rr 87.3%

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

   5. Taylor expanded in t around -inf 48.5%

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

      1. mul-1-neg 48.5%

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

      2. sub-neg 48.5%

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

      3. distribute-rgt-neg-out 48.5%

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

      4. *-commutative 48.5%

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

      5. distribute-lft-out 51.9%

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

      6. sub-neg 51.9%

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

      7. unsub-neg 51.9%

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

      8. associate-/l* 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in a around 0 53.2%

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

      1. mul-1-neg 53.2%

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

      2. associate-/l* 60.2%

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

      3. distribute-lft-neg-in 60.2%

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

   10. Simplified 60.2%

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

   11. Taylor expanded in x around 0 40.0%

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

       1. associate-*l/ 47.7%

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

       2. associate-/r/ 46.7%

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

   13. Simplified 46.7%

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

   if -8.9999999999999995e76 < z < 1.9999999999999998e202

   1. Initial program 75.0%

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

   3. Taylor expanded in a around inf 69.4%

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

      1. +-commutative 69.4%

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

   5. Simplified 69.4%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+76} \lor \neg \left(z \leq 2 \cdot 10^{+202}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-34} \lor \neg \left(a \leq 2 \cdot 10^{-51}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.5e-34) (not (<= a 2e-51))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e-34) || !(a <= 2e-51)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-8.5d-34)) .or. (.not. (a <= 2d-51))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e-34) || !(a <= 2e-51)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.5e-34) or not (a <= 2e-51):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.5e-34) || !(a <= 2e-51))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8.5e-34) || ~((a <= 2e-51)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.5e-34], N[Not[LessEqual[a, 2e-51]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -8.5000000000000001e-34 or 2e-51 < a

   1. Initial program 75.7%

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

   3. Taylor expanded in a around inf 70.9%

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

      1. +-commutative 70.9%

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

   5. Simplified 70.9%

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

   if -8.5000000000000001e-34 < a < 2e-51

   1. Initial program 71.6%

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

   3. Taylor expanded in x around inf 49.2%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-34} \lor \neg \left(a \leq 2 \cdot 10^{-51}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.3% 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 73.9%

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

3. Taylor expanded in x around inf 45.8%

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

4. Final simplification 45.8%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 87.9% 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 2024079 
(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))))