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

Percentage Accurate: 77.0% → 91.2%

Time: 15.3s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.0% 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: 91.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+145} \lor \neg \left(t \leq 1.9 \cdot 10^{+91}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.5e+145) (not (<= t 1.9e+91)))
   (+ x (/ y (/ t (- z a))))
   (+ x (fma (/ (- t z) (- a t)) y y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e+145) || !(t <= 1.9e+91)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = x + fma(((t - z) / (a - t)), y, y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.5e+145) || !(t <= 1.9e+91))
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + fma(Float64(Float64(t - z) / Float64(a - t)), y, y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.5e+145], N[Not[LessEqual[t, 1.9e+91]], $MachinePrecision]], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * y + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.49999999999999983e145 or 1.8999999999999999e91 < t

   1. Initial program 42.9%

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

      1. sub-neg 42.9%

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

      2. associate-+l+ 53.1%

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

      3. distribute-frac-neg 53.1%

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

      4. distribute-rgt-neg-out 53.1%

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

      5. +-commutative 53.1%

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

      6. distribute-rgt-neg-out 53.1%

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

      7. distribute-lft-neg-in 53.1%

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

      8. associate-*l/ 73.3%

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

      9. fma-def 73.3%

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

      10. neg-sub0 73.3%

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

      11. associate-+l- 73.3%

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

      12. neg-sub0 73.3%

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

      13. +-commutative 73.3%

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

      14. sub-neg 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in t around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. associate-+r+ 73.3%

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

      3. mul-1-neg 73.3%

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

      4. distribute-rgt1-in 73.3%

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

      5. metadata-eval 73.3%

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

      6. div0 73.3%

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

      7. associate-/r/ 73.3%

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

      8. div0 73.3%

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

      9. associate-/l* 93.9%

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

   6. Simplified 93.9%

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

   if -2.49999999999999983e145 < t < 1.8999999999999999e91

   1. Initial program 87.6%

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

      1. sub-neg 87.6%

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

      2. associate-+l+ 90.7%

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

      3. distribute-frac-neg 90.7%

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

      4. distribute-rgt-neg-out 90.7%

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

      5. +-commutative 90.7%

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

      6. distribute-rgt-neg-out 90.7%

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

      7. distribute-lft-neg-in 90.7%

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

      8. associate-*l/ 93.6%

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

      9. fma-def 93.6%

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

      10. neg-sub0 93.6%

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

      11. associate-+l- 93.6%

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

      12. neg-sub0 93.6%

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

      13. +-commutative 93.6%

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

      14. sub-neg 93.6%

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

   3. Simplified 93.6%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+145} \lor \neg \left(t \leq 1.9 \cdot 10^{+91}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)\\ \end{array} \]

Alternative 2: 89.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.25 \cdot 10^{+99} \lor \neg \left(t \leq 2.3 \cdot 10^{+89}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{y \cdot \left(t - z\right)}{a - t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.25e+99) (not (<= t 2.3e+89)))
   (+ x (/ y (/ t (- z a))))
   (+ x (+ y (/ (* y (- t z)) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.25e+99) || !(t <= 2.3e+89)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = x + (y + ((y * (t - 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 ((t <= (-4.25d+99)) .or. (.not. (t <= 2.3d+89))) then
        tmp = x + (y / (t / (z - a)))
    else
        tmp = x + (y + ((y * (t - 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 ((t <= -4.25e+99) || !(t <= 2.3e+89)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = x + (y + ((y * (t - z)) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.25e+99) or not (t <= 2.3e+89):
		tmp = x + (y / (t / (z - a)))
	else:
		tmp = x + (y + ((y * (t - z)) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.25e+99) || !(t <= 2.3e+89))
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(y * Float64(t - z)) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.25e+99) || ~((t <= 2.3e+89)))
		tmp = x + (y / (t / (z - a)));
	else
		tmp = x + (y + ((y * (t - z)) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.25e+99], N[Not[LessEqual[t, 2.3e+89]], $MachinePrecision]], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.24999999999999992e99 or 2.2999999999999999e89 < t

   1. Initial program 43.0%

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

      1. sub-neg 43.0%

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

      2. associate-+l+ 54.6%

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

      3. distribute-frac-neg 54.6%

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

      4. distribute-rgt-neg-out 54.6%

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

      5. +-commutative 54.6%

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

      6. distribute-rgt-neg-out 54.6%

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

      7. distribute-lft-neg-in 54.6%

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

      8. associate-*l/ 74.3%

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

      9. fma-def 74.3%

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

      10. neg-sub0 74.3%

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

      11. associate-+l- 74.3%

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

      12. neg-sub0 74.3%

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

      13. +-commutative 74.3%

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

      14. sub-neg 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in t around inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. associate-+r+ 74.3%

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

      3. mul-1-neg 74.3%

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

      4. distribute-rgt1-in 74.3%

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

      5. metadata-eval 74.3%

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

      6. div0 74.3%

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

      7. associate-/r/ 74.3%

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

      8. div0 74.3%

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

      9. associate-/l* 93.3%

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

   6. Simplified 93.3%

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

   if -4.24999999999999992e99 < t < 2.2999999999999999e89

   1. Initial program 89.4%

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

      1. associate--l+ 91.5%

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

      2. sub-neg 91.5%

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

      3. distribute-frac-neg 91.5%

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

      4. distribute-rgt-neg-out 91.5%

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

      5. distribute-rgt-neg-out 91.5%

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

      6. distribute-lft-neg-in 91.5%

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

      7. *-commutative 91.5%

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

      8. neg-sub0 91.5%

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

      9. associate-+l- 91.5%

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

      10. neg-sub0 91.5%

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

      11. +-commutative 91.5%

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

      12. sub-neg 91.5%

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

   3. Simplified 91.5%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.25 \cdot 10^{+99} \lor \neg \left(t \leq 2.3 \cdot 10^{+89}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{y \cdot \left(t - z\right)}{a - t}\right)\\ \end{array} \]

Alternative 3: 90.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+99} \lor \neg \left(t \leq 3.1 \cdot 10^{+90}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{t - z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.8e+99) (not (<= t 3.1e+90)))
   (+ x (/ y (/ t (- z a))))
   (+ (+ x y) (* y (/ (- t z) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.8e+99) || !(t <= 3.1e+90)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = (x + y) + (y * ((t - 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 ((t <= (-3.8d+99)) .or. (.not. (t <= 3.1d+90))) then
        tmp = x + (y / (t / (z - a)))
    else
        tmp = (x + y) + (y * ((t - 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 ((t <= -3.8e+99) || !(t <= 3.1e+90)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = (x + y) + (y * ((t - z) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.8e+99) or not (t <= 3.1e+90):
		tmp = x + (y / (t / (z - a)))
	else:
		tmp = (x + y) + (y * ((t - z) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.8e+99) || !(t <= 3.1e+90))
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	else
		tmp = Float64(Float64(x + y) + Float64(y * Float64(Float64(t - z) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.8e+99) || ~((t <= 3.1e+90)))
		tmp = x + (y / (t / (z - a)));
	else
		tmp = (x + y) + (y * ((t - z) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.8e+99], N[Not[LessEqual[t, 3.1e+90]], $MachinePrecision]], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(y * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.8e99 or 3.09999999999999988e90 < t

   1. Initial program 43.0%

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

      1. sub-neg 43.0%

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

      2. associate-+l+ 54.6%

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

      3. distribute-frac-neg 54.6%

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

      4. distribute-rgt-neg-out 54.6%

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

      5. +-commutative 54.6%

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

      6. distribute-rgt-neg-out 54.6%

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

      7. distribute-lft-neg-in 54.6%

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

      8. associate-*l/ 74.3%

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

      9. fma-def 74.3%

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

      10. neg-sub0 74.3%

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

      11. associate-+l- 74.3%

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

      12. neg-sub0 74.3%

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

      13. +-commutative 74.3%

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

      14. sub-neg 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in t around inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. associate-+r+ 74.3%

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

      3. mul-1-neg 74.3%

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

      4. distribute-rgt1-in 74.3%

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

      5. metadata-eval 74.3%

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

      6. div0 74.3%

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

      7. associate-/r/ 74.3%

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

      8. div0 74.3%

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

      9. associate-/l* 93.3%

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

   6. Simplified 93.3%

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

   if -3.8e99 < t < 3.09999999999999988e90

   1. Initial program 89.4%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+99} \lor \neg \left(t \leq 3.1 \cdot 10^{+90}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{t - z}{a - t}\\ \end{array} \]

Alternative 4: 75.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{-32}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-55}:\\ \;\;\;\;\frac{z}{a - t} \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-80}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.25e-32)
   (+ x y)
   (if (<= a -6.2e-55)
     (* (/ z (- a t)) (- y))
     (if (<= a -2.4e-80)
       (+ x y)
       (if (<= a 9e-19) (+ x (/ (* y z) t)) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.25e-32) {
		tmp = x + y;
	} else if (a <= -6.2e-55) {
		tmp = (z / (a - t)) * -y;
	} else if (a <= -2.4e-80) {
		tmp = x + y;
	} else if (a <= 9e-19) {
		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 <= (-2.25d-32)) then
        tmp = x + y
    else if (a <= (-6.2d-55)) then
        tmp = (z / (a - t)) * -y
    else if (a <= (-2.4d-80)) then
        tmp = x + y
    else if (a <= 9d-19) 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 <= -2.25e-32) {
		tmp = x + y;
	} else if (a <= -6.2e-55) {
		tmp = (z / (a - t)) * -y;
	} else if (a <= -2.4e-80) {
		tmp = x + y;
	} else if (a <= 9e-19) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.25e-32:
		tmp = x + y
	elif a <= -6.2e-55:
		tmp = (z / (a - t)) * -y
	elif a <= -2.4e-80:
		tmp = x + y
	elif a <= 9e-19:
		tmp = x + ((y * z) / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.25e-32)
		tmp = Float64(x + y);
	elseif (a <= -6.2e-55)
		tmp = Float64(Float64(z / Float64(a - t)) * Float64(-y));
	elseif (a <= -2.4e-80)
		tmp = Float64(x + y);
	elseif (a <= 9e-19)
		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 <= -2.25e-32)
		tmp = x + y;
	elseif (a <= -6.2e-55)
		tmp = (z / (a - t)) * -y;
	elseif (a <= -2.4e-80)
		tmp = x + y;
	elseif (a <= 9e-19)
		tmp = x + ((y * z) / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.25e-32], N[(x + y), $MachinePrecision], If[LessEqual[a, -6.2e-55], N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[a, -2.4e-80], N[(x + y), $MachinePrecision], If[LessEqual[a, 9e-19], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.25000000000000002e-32 or -6.19999999999999993e-55 < a < -2.3999999999999999e-80 or 9.00000000000000026e-19 < a

   1. Initial program 79.5%

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

      1. associate--l+ 80.4%

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

      2. sub-neg 80.4%

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

      3. distribute-frac-neg 80.4%

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

      4. distribute-rgt-neg-out 80.4%

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

      5. distribute-rgt-neg-out 80.4%

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

      6. distribute-lft-neg-in 80.4%

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

      7. *-commutative 80.4%

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

      8. neg-sub0 80.4%

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

      9. associate-+l- 80.4%

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

      10. neg-sub0 80.4%

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

      11. +-commutative 80.4%

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

      12. sub-neg 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in a around inf 74.8%

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

      1. +-commutative 74.8%

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

   6. Simplified 74.8%

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

   if -2.25000000000000002e-32 < a < -6.19999999999999993e-55

   1. Initial program 67.4%

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

      1. associate-*l/ 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in y around -inf 67.7%

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

      1. mul-1-neg 67.7%

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

      2. distribute-neg-frac 67.7%

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

   6. Simplified 67.7%

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

   7. Taylor expanded in z around inf 83.8%

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

      1. associate-*r/ 83.8%

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

      2. mul-1-neg 83.8%

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

   9. Simplified 83.8%

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

   if -2.3999999999999999e-80 < a < 9.00000000000000026e-19

   1. Initial program 64.2%

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

      1. sub-neg 64.2%

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

      2. associate-+l+ 76.5%

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

      3. distribute-frac-neg 76.5%

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

      4. distribute-rgt-neg-out 76.5%

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

      5. +-commutative 76.5%

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

      6. distribute-rgt-neg-out 76.5%

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

      7. distribute-lft-neg-in 76.5%

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

      8. associate-*l/ 81.3%

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

      9. fma-def 81.3%

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

      10. neg-sub0 81.3%

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

      11. associate-+l- 81.3%

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

      12. neg-sub0 81.3%

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

      13. +-commutative 81.3%

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

      14. sub-neg 81.3%

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

   3. Simplified 81.3%

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

      1. add-cube-cbrt_binary64 81.2%

         \[\leadsto \color{blue}{x + \left(\sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)}} \]

   5. Applied rewrite-once 81.2%

      \[\leadsto x + \color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)}} \]

   6. Taylor expanded in z around inf 86.5%

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

      1. associate-*r/ 86.5%

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

      2. associate-*r* 86.5%

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

      3. mul-1-neg 86.5%

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

      4. *-commutative 86.5%

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

   8. Simplified 86.5%

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

   9. Taylor expanded in a around 0 77.0%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{-32}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-55}:\\ \;\;\;\;\frac{z}{a - t} \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-80}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 84.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-30}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-266}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.4e-30)
   (- (+ x y) (* z (/ y a)))
   (if (<= a -3e-266)
     (- x (/ (* y z) (- a t)))
     (if (<= a 3.4e+38) (+ x (/ y (/ t (- z a)))) (- (+ x y) (* y (/ z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.4e-30) {
		tmp = (x + y) - (z * (y / a));
	} else if (a <= -3e-266) {
		tmp = x - ((y * z) / (a - t));
	} else if (a <= 3.4e+38) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = (x + y) - (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 (a <= (-4.4d-30)) then
        tmp = (x + y) - (z * (y / a))
    else if (a <= (-3d-266)) then
        tmp = x - ((y * z) / (a - t))
    else if (a <= 3.4d+38) then
        tmp = x + (y / (t / (z - a)))
    else
        tmp = (x + y) - (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 (a <= -4.4e-30) {
		tmp = (x + y) - (z * (y / a));
	} else if (a <= -3e-266) {
		tmp = x - ((y * z) / (a - t));
	} else if (a <= 3.4e+38) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = (x + y) - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.4e-30:
		tmp = (x + y) - (z * (y / a))
	elif a <= -3e-266:
		tmp = x - ((y * z) / (a - t))
	elif a <= 3.4e+38:
		tmp = x + (y / (t / (z - a)))
	else:
		tmp = (x + y) - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.4e-30)
		tmp = Float64(Float64(x + y) - Float64(z * Float64(y / a)));
	elseif (a <= -3e-266)
		tmp = Float64(x - Float64(Float64(y * z) / Float64(a - t)));
	elseif (a <= 3.4e+38)
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	else
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.4e-30)
		tmp = (x + y) - (z * (y / a));
	elseif (a <= -3e-266)
		tmp = x - ((y * z) / (a - t));
	elseif (a <= 3.4e+38)
		tmp = x + (y / (t / (z - a)));
	else
		tmp = (x + y) - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.4e-30], N[(N[(x + y), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3e-266], N[(x - N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e+38], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.39999999999999967e-30

   1. Initial program 75.8%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in t around 0 79.3%

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

      1. associate-/l* 86.5%

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

      2. associate-/r/ 86.5%

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

   6. Applied egg-rr 86.5%

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

   if -4.39999999999999967e-30 < a < -3e-266

   1. Initial program 80.1%

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

      1. associate--l+ 85.0%

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

      2. sub-neg 85.0%

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

      3. distribute-frac-neg 85.0%

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

      4. distribute-rgt-neg-out 85.0%

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

      5. distribute-rgt-neg-out 85.0%

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

      6. distribute-lft-neg-in 85.0%

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

      7. *-commutative 85.0%

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

      8. neg-sub0 85.0%

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

      9. associate-+l- 85.0%

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

      10. neg-sub0 85.0%

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

      11. +-commutative 85.0%

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

      12. sub-neg 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in z around inf 88.2%

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

      1. associate-*r/ 88.2%

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

      2. mul-1-neg 88.2%

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

      3. distribute-rgt-neg-out 88.2%

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

   6. Simplified 88.2%

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

   if -3e-266 < a < 3.39999999999999996e38

   1. Initial program 58.7%

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

      1. sub-neg 58.7%

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

      2. associate-+l+ 72.0%

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

      3. distribute-frac-neg 72.0%

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

      4. distribute-rgt-neg-out 72.0%

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

      5. +-commutative 72.0%

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

      6. distribute-rgt-neg-out 72.0%

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

      7. distribute-lft-neg-in 72.0%

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

      8. associate-*l/ 78.8%

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

      9. fma-def 78.8%

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

      10. neg-sub0 78.8%

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

      11. associate-+l- 78.8%

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

      12. neg-sub0 78.8%

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

      13. +-commutative 78.8%

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

      14. sub-neg 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in t around inf 66.2%

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

      1. mul-1-neg 66.2%

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

      2. associate-+r+ 84.5%

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

      3. mul-1-neg 84.5%

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

      4. distribute-rgt1-in 84.5%

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

      5. metadata-eval 84.5%

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

      6. div0 84.5%

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

      7. associate-/r/ 80.0%

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

      8. div0 84.5%

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

      9. associate-/l* 89.8%

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

   6. Simplified 89.8%

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

   if 3.39999999999999996e38 < a

   1. Initial program 81.2%

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

      1. associate-*l/ 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in t around 0 88.2%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-30}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-266}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 6: 89.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+100} \lor \neg \left(t \leq 3.9 \cdot 10^{+90}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.2e+100) (not (<= t 3.9e+90)))
   (+ x (/ y (/ t (- z a))))
   (- (+ x y) (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e+100) || !(t <= 3.9e+90)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = (x + y) - (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 ((t <= (-1.2d+100)) .or. (.not. (t <= 3.9d+90))) then
        tmp = x + (y / (t / (z - a)))
    else
        tmp = (x + y) - (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 ((t <= -1.2e+100) || !(t <= 3.9e+90)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = (x + y) - (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.2e+100) or not (t <= 3.9e+90):
		tmp = x + (y / (t / (z - a)))
	else:
		tmp = (x + y) - (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.2e+100) || !(t <= 3.9e+90))
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	else
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.2e+100) || ~((t <= 3.9e+90)))
		tmp = x + (y / (t / (z - a)));
	else
		tmp = (x + y) - (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.2e+100], N[Not[LessEqual[t, 3.9e+90]], $MachinePrecision]], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.20000000000000006e100 or 3.9000000000000002e90 < t

   1. Initial program 43.0%

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

      1. sub-neg 43.0%

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

      2. associate-+l+ 54.6%

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

      3. distribute-frac-neg 54.6%

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

      4. distribute-rgt-neg-out 54.6%

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

      5. +-commutative 54.6%

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

      6. distribute-rgt-neg-out 54.6%

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

      7. distribute-lft-neg-in 54.6%

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

      8. associate-*l/ 74.3%

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

      9. fma-def 74.3%

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

      10. neg-sub0 74.3%

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

      11. associate-+l- 74.3%

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

      12. neg-sub0 74.3%

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

      13. +-commutative 74.3%

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

      14. sub-neg 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in t around inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. associate-+r+ 74.3%

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

      3. mul-1-neg 74.3%

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

      4. distribute-rgt1-in 74.3%

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

      5. metadata-eval 74.3%

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

      6. div0 74.3%

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

      7. associate-/r/ 74.3%

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

      8. div0 74.3%

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

      9. associate-/l* 93.3%

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

   6. Simplified 93.3%

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

   if -1.20000000000000006e100 < t < 3.9000000000000002e90

   1. Initial program 89.4%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in z around inf 91.1%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+100} \lor \neg \left(t \leq 3.9 \cdot 10^{+90}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 7: 80.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-144} \lor \neg \left(a \leq 9 \cdot 10^{-22}\right):\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.2e-144) (not (<= a 9e-22)))
   (- (+ x y) (* z (/ y a)))
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.2e-144) || !(a <= 9e-22)) {
		tmp = (x + y) - (z * (y / a));
	} 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 <= (-6.2d-144)) .or. (.not. (a <= 9d-22))) then
        tmp = (x + y) - (z * (y / a))
    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 <= -6.2e-144) || !(a <= 9e-22)) {
		tmp = (x + y) - (z * (y / a));
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6.2e-144) or not (a <= 9e-22):
		tmp = (x + y) - (z * (y / a))
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.2e-144) || !(a <= 9e-22))
		tmp = Float64(Float64(x + y) - Float64(z * Float64(y / a)));
	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 <= -6.2e-144) || ~((a <= 9e-22)))
		tmp = (x + y) - (z * (y / a));
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6.2e-144], N[Not[LessEqual[a, 9e-22]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.2000000000000001e-144 or 8.99999999999999973e-22 < a

   1. Initial program 79.7%

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

      1. associate-*l/ 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in t around 0 78.3%

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

      1. associate-/l* 82.5%

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

      2. associate-/r/ 81.3%

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

   6. Applied egg-rr 81.3%

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

   if -6.2000000000000001e-144 < a < 8.99999999999999973e-22

   1. Initial program 60.7%

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

      1. sub-neg 60.7%

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

      2. associate-+l+ 73.8%

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

      3. distribute-frac-neg 73.8%

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

      4. distribute-rgt-neg-out 73.8%

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

      5. +-commutative 73.8%

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

      6. distribute-rgt-neg-out 73.8%

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

      7. distribute-lft-neg-in 73.8%

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

      8. associate-*l/ 79.4%

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

      9. fma-def 79.4%

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

      10. neg-sub0 79.4%

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

      11. associate-+l- 79.4%

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

      12. neg-sub0 79.4%

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

      13. +-commutative 79.4%

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

      14. sub-neg 79.4%

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

   3. Simplified 79.4%

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

      1. add-cube-cbrt_binary64 79.2%

         \[\leadsto \color{blue}{x + \left(\sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)}} \]

   5. Applied rewrite-once 79.2%

      \[\leadsto x + \color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)}} \]

   6. Taylor expanded in z around inf 86.4%

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

      1. associate-*r/ 86.4%

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

      2. associate-*r* 86.4%

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

      3. mul-1-neg 86.4%

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

      4. *-commutative 86.4%

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

   8. Simplified 86.4%

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

   9. Taylor expanded in a around 0 81.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-144} \lor \neg \left(a \leq 9 \cdot 10^{-22}\right):\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]

Alternative 8: 80.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-144} \lor \neg \left(a \leq 1.32 \cdot 10^{-21}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.7e-144) (not (<= a 1.32e-21)))
   (- (+ x y) (* y (/ z a)))
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.7e-144) || !(a <= 1.32e-21)) {
		tmp = (x + y) - (y * (z / a));
	} 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 <= (-4.7d-144)) .or. (.not. (a <= 1.32d-21))) then
        tmp = (x + y) - (y * (z / a))
    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 <= -4.7e-144) || !(a <= 1.32e-21)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.7e-144) or not (a <= 1.32e-21):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.7e-144) || !(a <= 1.32e-21))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	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 <= -4.7e-144) || ~((a <= 1.32e-21)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.7e-144], N[Not[LessEqual[a, 1.32e-21]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.7000000000000002e-144 or 1.32e-21 < a

   1. Initial program 79.7%

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

      1. associate-*l/ 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in t around 0 82.5%

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

   if -4.7000000000000002e-144 < a < 1.32e-21

   1. Initial program 60.7%

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

      1. sub-neg 60.7%

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

      2. associate-+l+ 73.8%

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

      3. distribute-frac-neg 73.8%

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

      4. distribute-rgt-neg-out 73.8%

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

      5. +-commutative 73.8%

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

      6. distribute-rgt-neg-out 73.8%

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

      7. distribute-lft-neg-in 73.8%

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

      8. associate-*l/ 79.4%

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

      9. fma-def 79.4%

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

      10. neg-sub0 79.4%

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

      11. associate-+l- 79.4%

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

      12. neg-sub0 79.4%

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

      13. +-commutative 79.4%

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

      14. sub-neg 79.4%

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

   3. Simplified 79.4%

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

      1. add-cube-cbrt_binary64 79.2%

         \[\leadsto \color{blue}{x + \left(\sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)}} \]

   5. Applied rewrite-once 79.2%

      \[\leadsto x + \color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)}} \]

   6. Taylor expanded in z around inf 86.4%

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

      1. associate-*r/ 86.4%

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

      2. associate-*r* 86.4%

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

      3. mul-1-neg 86.4%

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

      4. *-commutative 86.4%

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

   8. Simplified 86.4%

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

   9. Taylor expanded in a around 0 81.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-144} \lor \neg \left(a \leq 1.32 \cdot 10^{-21}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]

Alternative 9: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.56 \cdot 10^{-30}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+39}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.56e-30)
   (- (+ x y) (* z (/ y a)))
   (if (<= a 6e+39) (- x (/ (* y z) (- a t))) (- (+ x y) (* y (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.56e-30) {
		tmp = (x + y) - (z * (y / a));
	} else if (a <= 6e+39) {
		tmp = x - ((y * z) / (a - t));
	} else {
		tmp = (x + y) - (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 (a <= (-1.56d-30)) then
        tmp = (x + y) - (z * (y / a))
    else if (a <= 6d+39) then
        tmp = x - ((y * z) / (a - t))
    else
        tmp = (x + y) - (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 (a <= -1.56e-30) {
		tmp = (x + y) - (z * (y / a));
	} else if (a <= 6e+39) {
		tmp = x - ((y * z) / (a - t));
	} else {
		tmp = (x + y) - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.56e-30:
		tmp = (x + y) - (z * (y / a))
	elif a <= 6e+39:
		tmp = x - ((y * z) / (a - t))
	else:
		tmp = (x + y) - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.56e-30)
		tmp = Float64(Float64(x + y) - Float64(z * Float64(y / a)));
	elseif (a <= 6e+39)
		tmp = Float64(x - Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.56e-30)
		tmp = (x + y) - (z * (y / a));
	elseif (a <= 6e+39)
		tmp = x - ((y * z) / (a - t));
	else
		tmp = (x + y) - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.56e-30], N[(N[(x + y), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+39], N[(x - N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5600000000000001e-30

   1. Initial program 75.8%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in t around 0 79.3%

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

      1. associate-/l* 86.5%

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

      2. associate-/r/ 86.5%

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

   6. Applied egg-rr 86.5%

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

   if -1.5600000000000001e-30 < a < 5.9999999999999999e39

   1. Initial program 68.2%

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

      1. associate--l+ 77.8%

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

      2. sub-neg 77.8%

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

      3. distribute-frac-neg 77.8%

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

      4. distribute-rgt-neg-out 77.8%

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

      5. distribute-rgt-neg-out 77.8%

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

      6. distribute-lft-neg-in 77.8%

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

      7. *-commutative 77.8%

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

      8. neg-sub0 77.8%

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

      9. associate-+l- 77.8%

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

      10. neg-sub0 77.8%

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

      11. +-commutative 77.8%

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

      12. sub-neg 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in z around inf 84.9%

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

      1. associate-*r/ 84.9%

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

      2. mul-1-neg 84.9%

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

      3. distribute-rgt-neg-out 84.9%

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

   6. Simplified 84.9%

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

   if 5.9999999999999999e39 < a

   1. Initial program 81.2%

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

      1. associate-*l/ 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in t around 0 88.2%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.56 \cdot 10^{-30}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+39}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 10: 76.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-31}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8e-31) (+ x y) (if (<= a 1.7e-18) (+ x (/ (* y z) t)) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8e-31) {
		tmp = x + y;
	} else if (a <= 1.7e-18) {
		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 <= (-8d-31)) then
        tmp = x + y
    else if (a <= 1.7d-18) 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 <= -8e-31) {
		tmp = x + y;
	} else if (a <= 1.7e-18) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8e-31:
		tmp = x + y
	elif a <= 1.7e-18:
		tmp = x + ((y * z) / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8e-31)
		tmp = Float64(x + y);
	elseif (a <= 1.7e-18)
		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 <= -8e-31)
		tmp = x + y;
	elseif (a <= 1.7e-18)
		tmp = x + ((y * z) / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8e-31], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.7e-18], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.000000000000001e-31 or 1.70000000000000001e-18 < a

   1. Initial program 78.0%

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

      1. associate--l+ 79.0%

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

      2. sub-neg 79.0%

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

      3. distribute-frac-neg 79.0%

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

      4. distribute-rgt-neg-out 79.0%

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

      5. distribute-rgt-neg-out 79.0%

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

      6. distribute-lft-neg-in 79.0%

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

      7. *-commutative 79.0%

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

      8. neg-sub0 79.0%

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

      9. associate-+l- 79.0%

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

      10. neg-sub0 79.0%

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

      11. +-commutative 79.0%

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

      12. sub-neg 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in a around inf 75.0%

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

      1. +-commutative 75.0%

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

   6. Simplified 75.0%

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

   if -8.000000000000001e-31 < a < 1.70000000000000001e-18

   1. Initial program 67.4%

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

      1. sub-neg 67.4%

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

      2. associate-+l+ 78.0%

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

      3. distribute-frac-neg 78.0%

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

      4. distribute-rgt-neg-out 78.0%

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

      5. +-commutative 78.0%

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

      6. distribute-rgt-neg-out 78.0%

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

      7. distribute-lft-neg-in 78.0%

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

      8. associate-*l/ 82.2%

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

      9. fma-def 82.2%

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

      10. neg-sub0 82.2%

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

      11. associate-+l- 82.2%

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

      12. neg-sub0 82.2%

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

      13. +-commutative 82.2%

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

      14. sub-neg 82.2%

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

   3. Simplified 82.2%

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

      1. add-cube-cbrt_binary64 82.0%

         \[\leadsto \color{blue}{x + \left(\sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)}} \]

   5. Applied rewrite-once 82.0%

      \[\leadsto x + \color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)}} \]

   6. Taylor expanded in z around inf 85.9%

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

      1. associate-*r/ 85.9%

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

      2. associate-*r* 85.9%

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

      3. mul-1-neg 85.9%

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

      4. *-commutative 85.9%

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

   8. Simplified 85.9%

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

   9. Taylor expanded in a around 0 73.3%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-31}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 63.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{-144}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.9e-144) (+ x y) (if (<= a 2.4e+38) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.9e-144) {
		tmp = x + y;
	} else if (a <= 2.4e+38) {
		tmp = x;
	} 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 <= (-4.9d-144)) then
        tmp = x + y
    else if (a <= 2.4d+38) then
        tmp = x
    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 <= -4.9e-144) {
		tmp = x + y;
	} else if (a <= 2.4e+38) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.9e-144:
		tmp = x + y
	elif a <= 2.4e+38:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.9e-144)
		tmp = Float64(x + y);
	elseif (a <= 2.4e+38)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.9e-144)
		tmp = x + y;
	elseif (a <= 2.4e+38)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.9e-144], N[(x + y), $MachinePrecision], If[LessEqual[a, 2.4e+38], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.9000000000000001e-144 or 2.40000000000000017e38 < a

   1. Initial program 80.3%

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

      1. associate--l+ 81.2%

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

      2. sub-neg 81.2%

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

      3. distribute-frac-neg 81.2%

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

      4. distribute-rgt-neg-out 81.2%

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

      5. distribute-rgt-neg-out 81.2%

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

      6. distribute-lft-neg-in 81.2%

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

      7. *-commutative 81.2%

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

      8. neg-sub0 81.2%

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

      9. associate-+l- 81.2%

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

      10. neg-sub0 81.2%

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

      11. +-commutative 81.2%

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

      12. sub-neg 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in a around inf 70.1%

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

      1. +-commutative 70.1%

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

   6. Simplified 70.1%

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

   if -4.9000000000000001e-144 < a < 2.40000000000000017e38

   1. Initial program 62.3%

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

      1. associate--l+ 74.5%

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

      2. sub-neg 74.5%

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

      3. distribute-frac-neg 74.5%

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

      4. distribute-rgt-neg-out 74.5%

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

      5. distribute-rgt-neg-out 74.5%

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

      6. distribute-lft-neg-in 74.5%

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

      7. *-commutative 74.5%

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

      8. neg-sub0 74.5%

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

      9. associate-+l- 74.5%

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

      10. neg-sub0 74.5%

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

      11. +-commutative 74.5%

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

      12. sub-neg 74.5%

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

   3. Simplified 74.5%

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

   4. Taylor expanded in x around inf 54.6%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{-144}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12: 52.4% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= y 3.1e+116) x y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 3.1e+116) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 3.1d+116) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 3.1e+116) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 3.1e+116:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 3.1e+116)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 3.1e+116)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 3.1e+116], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 3.09999999999999996e116

   1. Initial program 78.3%

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

      1. associate--l+ 84.2%

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

      2. sub-neg 84.2%

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

      3. distribute-frac-neg 84.2%

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

      4. distribute-rgt-neg-out 84.2%

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

      5. distribute-rgt-neg-out 84.2%

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

      6. distribute-lft-neg-in 84.2%

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

      7. *-commutative 84.2%

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

      8. neg-sub0 84.2%

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

      9. associate-+l- 84.2%

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

      10. neg-sub0 84.2%

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

      11. +-commutative 84.2%

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

      12. sub-neg 84.2%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in x around inf 60.9%

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

   if 3.09999999999999996e116 < y

   1. Initial program 48.4%

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

      1. associate-*l/ 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in x around 0 48.2%

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

   5. Taylor expanded in z around inf 49.7%

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

      1. associate-/l* 62.4%

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

   7. Simplified 62.4%

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

   8. Taylor expanded in a around inf 32.9%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 13: 50.9% 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 73.1%

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

   1. associate--l+ 78.5%

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

   2. sub-neg 78.5%

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

   3. distribute-frac-neg 78.5%

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

   4. distribute-rgt-neg-out 78.5%

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

   5. distribute-rgt-neg-out 78.5%

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

   6. distribute-lft-neg-in 78.5%

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

   7. *-commutative 78.5%

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

   8. neg-sub0 78.5%

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

   9. associate-+l- 78.5%

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

   10. neg-sub0 78.5%

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

   11. +-commutative 78.5%

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

   12. sub-neg 78.5%

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

3. Simplified 78.5%

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

4. Taylor expanded in x around inf 52.2%

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

5. Final simplification 52.2%

   \[\leadsto x \]

Developer target: 88.1% 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 2023297 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

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

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