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

Percentage Accurate: 76.7% → 90.3%

Time: 12.4s

Alternatives: 16

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+137}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{t}{y}}{a - z}}\\ \mathbf{elif}\;t \leq 0.00015:\\ \;\;\;\;x + \left(y - \frac{z - t}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{a - t} + \frac{a}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.75e+137)
   (- x (/ 1.0 (/ (/ t y) (- a z))))
   (if (<= t 0.00015)
     (+ x (- y (/ (- z t) (/ (- a t) y))))
     (- x (* y (+ (/ z (- a t)) (/ a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.75e+137) {
		tmp = x - (1.0 / ((t / y) / (a - z)));
	} else if (t <= 0.00015) {
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	} else {
		tmp = x - (y * ((z / (a - t)) + (a / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.75d+137)) then
        tmp = x - (1.0d0 / ((t / y) / (a - z)))
    else if (t <= 0.00015d0) then
        tmp = x + (y - ((z - t) / ((a - t) / y)))
    else
        tmp = x - (y * ((z / (a - t)) + (a / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.75e+137) {
		tmp = x - (1.0 / ((t / y) / (a - z)));
	} else if (t <= 0.00015) {
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	} else {
		tmp = x - (y * ((z / (a - t)) + (a / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.75e+137:
		tmp = x - (1.0 / ((t / y) / (a - z)))
	elif t <= 0.00015:
		tmp = x + (y - ((z - t) / ((a - t) / y)))
	else:
		tmp = x - (y * ((z / (a - t)) + (a / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.75e+137)
		tmp = Float64(x - Float64(1.0 / Float64(Float64(t / y) / Float64(a - z))));
	elseif (t <= 0.00015)
		tmp = Float64(x + Float64(y - Float64(Float64(z - t) / Float64(Float64(a - t) / y))));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(z / Float64(a - t)) + Float64(a / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.75e+137)
		tmp = x - (1.0 / ((t / y) / (a - z)));
	elseif (t <= 0.00015)
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	else
		tmp = x - (y * ((z / (a - t)) + (a / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.75e+137], N[(x - N[(1.0 / N[(N[(t / y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00015], N[(x + N[(y - N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7500000000000001e137

   1. Initial program 56.8%

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

      1. associate--l+ 70.3%

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

      2. associate-/l* 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in t around -inf 82.5%

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

      1. +-commutative 82.5%

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

      2. sub-neg 82.5%

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

      3. mul-1-neg 82.5%

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

      4. mul-1-neg 82.5%

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

      5. unsub-neg 82.5%

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

      6. mul-1-neg 82.5%

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

      7. sub-neg 82.5%

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

      8. distribute-lft-out-- 82.7%

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

   6. Simplified 82.7%

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

      1. clear-num 82.6%

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

      2. inv-pow 82.6%

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

   8. Applied egg-rr 82.6%

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

      1. unpow-1 82.6%

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

      2. associate-/r* 97.3%

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

   10. Simplified 97.3%

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

   if -1.7500000000000001e137 < t < 1.49999999999999987e-4

   1. Initial program 90.9%

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

      1. associate--l+ 91.7%

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

      2. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   if 1.49999999999999987e-4 < t

   1. Initial program 56.1%

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

      1. associate--l+ 61.7%

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

      2. sub-neg 61.7%

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

      3. +-commutative 61.7%

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

      4. associate-/l* 74.3%

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

      5. distribute-neg-frac 74.3%

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

      6. associate-/r/ 78.1%

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

      7. fma-def 78.3%

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

      8. sub-neg 78.3%

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

      9. +-commutative 78.3%

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

      10. distribute-neg-in 78.3%

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

      11. unsub-neg 78.3%

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

      12. remove-double-neg 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in y around 0 89.8%

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

   5. Taylor expanded in t around inf 90.2%

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

      1. associate-*r/ 90.2%

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

      2. neg-mul-1 90.2%

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

   7. Simplified 90.2%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+137}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{t}{y}}{a - z}}\\ \mathbf{elif}\;t \leq 0.00015:\\ \;\;\;\;x + \left(y - \frac{z - t}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{a - t} + \frac{a}{t}\right)\\ \end{array} \]

Alternative 2: 89.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+136} \lor \neg \left(t \leq 8 \cdot 10^{-7}\right):\\ \;\;\;\;x + \frac{-1}{\frac{\frac{t}{y}}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.2e+136) (not (<= t 8e-7)))
   (+ x (/ -1.0 (/ (/ t y) (- a z))))
   (+ x (+ y (/ (- t z) (/ (- a t) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.2e+136) || !(t <= 8e-7)) {
		tmp = x + (-1.0 / ((t / y) / (a - z)));
	} else {
		tmp = x + (y + ((t - z) / ((a - t) / 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 ((t <= (-5.2d+136)) .or. (.not. (t <= 8d-7))) then
        tmp = x + ((-1.0d0) / ((t / y) / (a - z)))
    else
        tmp = x + (y + ((t - z) / ((a - t) / 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 ((t <= -5.2e+136) || !(t <= 8e-7)) {
		tmp = x + (-1.0 / ((t / y) / (a - z)));
	} else {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.2e+136) or not (t <= 8e-7):
		tmp = x + (-1.0 / ((t / y) / (a - z)))
	else:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.2e+136) || !(t <= 8e-7))
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(t / y) / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.2e+136) || ~((t <= 8e-7)))
		tmp = x + (-1.0 / ((t / y) / (a - z)));
	else
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.2e+136], N[Not[LessEqual[t, 8e-7]], $MachinePrecision]], N[(x + N[(-1.0 / N[(N[(t / y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.2000000000000003e136 or 7.9999999999999996e-7 < t

   1. Initial program 56.3%

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

      1. associate--l+ 64.8%

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

      2. associate-/l* 72.0%

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

   3. Simplified 72.0%

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

   4. Taylor expanded in t around -inf 82.2%

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

      1. +-commutative 82.2%

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

      2. sub-neg 82.2%

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

      3. mul-1-neg 82.2%

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

      4. mul-1-neg 82.2%

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

      5. unsub-neg 82.2%

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

      6. mul-1-neg 82.2%

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

      7. sub-neg 82.2%

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

      8. distribute-lft-out-- 82.3%

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

   6. Simplified 82.3%

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

      1. clear-num 82.2%

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

      2. inv-pow 82.2%

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

   8. Applied egg-rr 82.2%

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

      1. unpow-1 82.2%

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

      2. associate-/r* 92.5%

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

   10. Simplified 92.5%

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

   if -5.2000000000000003e136 < t < 7.9999999999999996e-7

   1. Initial program 90.9%

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

      1. associate--l+ 91.7%

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

      2. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+136} \lor \neg \left(t \leq 8 \cdot 10^{-7}\right):\\ \;\;\;\;x + \frac{-1}{\frac{\frac{t}{y}}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \end{array} \]

Alternative 3: 93.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) + x \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (* y (- (+ 1.0 (/ t (- a t))) (/ z (- a t)))) x))

C

double code(double x, double y, double z, double t, double a) {
	return (y * ((1.0 + (t / (a - t))) - (z / (a - t)))) + x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (y * ((1.0d0 + (t / (a - t))) - (z / (a - t)))) + x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (y * ((1.0 + (t / (a - t))) - (z / (a - t)))) + x;
}

Python

def code(x, y, z, t, a):
	return (y * ((1.0 + (t / (a - t))) - (z / (a - t)))) + x

Julia

function code(x, y, z, t, a)
	return Float64(Float64(y * Float64(Float64(1.0 + Float64(t / Float64(a - t))) - Float64(z / Float64(a - t)))) + x)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (y * ((1.0 + (t / (a - t))) - (z / (a - t)))) + x;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(y * N[(N[(1.0 + N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 76.0%

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

   1. associate--l+ 80.1%

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

   2. sub-neg 80.1%

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

   3. +-commutative 80.1%

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

   4. associate-/l* 85.0%

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

   5. distribute-neg-frac 85.0%

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

   6. associate-/r/ 85.8%

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

   7. fma-def 85.9%

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

   8. sub-neg 85.9%

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

   9. +-commutative 85.9%

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

   10. distribute-neg-in 85.9%

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

   11. unsub-neg 85.9%

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

   12. remove-double-neg 85.9%

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

3. Simplified 85.9%

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

4. Taylor expanded in y around 0 90.4%

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

5. Final simplification 90.4%

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

Alternative 4: 88.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+136} \lor \neg \left(t \leq 0.00015\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.4e+136) (not (<= t 0.00015)))
   (- x (/ y (/ t (- a z))))
   (+ x (- y (/ y (/ (- a t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.4e+136) || !(t <= 0.00015)) {
		tmp = x - (y / (t / (a - z)));
	} else {
		tmp = x + (y - (y / ((a - t) / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5.4d+136)) .or. (.not. (t <= 0.00015d0))) then
        tmp = x - (y / (t / (a - z)))
    else
        tmp = x + (y - (y / ((a - t) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.4e+136) || !(t <= 0.00015)) {
		tmp = x - (y / (t / (a - z)));
	} else {
		tmp = x + (y - (y / ((a - t) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.4e+136) or not (t <= 0.00015):
		tmp = x - (y / (t / (a - z)))
	else:
		tmp = x + (y - (y / ((a - t) / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.4e+136) || !(t <= 0.00015))
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y - Float64(y / Float64(Float64(a - t) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.4e+136) || ~((t <= 0.00015)))
		tmp = x - (y / (t / (a - z)));
	else
		tmp = x + (y - (y / ((a - t) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.4e+136], N[Not[LessEqual[t, 0.00015]], $MachinePrecision]], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.4000000000000003e136 or 1.49999999999999987e-4 < t

   1. Initial program 56.3%

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

      1. associate--l+ 64.8%

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

      2. sub-neg 64.8%

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

      3. +-commutative 64.8%

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

      4. associate-/l* 72.0%

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

      5. distribute-neg-frac 72.0%

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

      6. associate-/r/ 78.0%

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

      7. fma-def 78.1%

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

      8. sub-neg 78.1%

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

      9. +-commutative 78.1%

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

      10. distribute-neg-in 78.1%

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

      11. unsub-neg 78.1%

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

      12. remove-double-neg 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in y around 0 87.3%

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

   5. Taylor expanded in t around inf 82.3%

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

      1. fma-def 82.3%

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

      2. +-commutative 82.3%

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

      3. mul-1-neg 82.3%

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

      4. sub-neg 82.3%

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

      5. *-commutative 82.3%

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

      6. fma-def 82.3%

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

      7. +-commutative 82.3%

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

      8. mul-1-neg 82.3%

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

      9. unsub-neg 82.3%

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

      10. associate-/l* 90.0%

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

   7. Simplified 90.0%

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

   if -5.4000000000000003e136 < t < 1.49999999999999987e-4

   1. Initial program 90.9%

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

      1. associate--l+ 91.7%

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

      2. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around inf 89.5%

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

      1. associate-/l* 90.2%

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

   6. Simplified 90.2%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+136} \lor \neg \left(t \leq 0.00015\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \end{array} \]

Alternative 5: 88.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+136} \lor \neg \left(t \leq 0.00015\right):\\ \;\;\;\;x + \frac{-1}{\frac{\frac{t}{y}}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.9e+136) (not (<= t 0.00015)))
   (+ x (/ -1.0 (/ (/ t y) (- a z))))
   (+ x (- y (/ y (/ (- a t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.9e+136) || !(t <= 0.00015)) {
		tmp = x + (-1.0 / ((t / y) / (a - z)));
	} else {
		tmp = x + (y - (y / ((a - t) / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.9d+136)) .or. (.not. (t <= 0.00015d0))) then
        tmp = x + ((-1.0d0) / ((t / y) / (a - z)))
    else
        tmp = x + (y - (y / ((a - t) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.9e+136) || !(t <= 0.00015)) {
		tmp = x + (-1.0 / ((t / y) / (a - z)));
	} else {
		tmp = x + (y - (y / ((a - t) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.9e+136) or not (t <= 0.00015):
		tmp = x + (-1.0 / ((t / y) / (a - z)))
	else:
		tmp = x + (y - (y / ((a - t) / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.9e+136) || !(t <= 0.00015))
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(t / y) / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y - Float64(y / Float64(Float64(a - t) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.9e+136) || ~((t <= 0.00015)))
		tmp = x + (-1.0 / ((t / y) / (a - z)));
	else
		tmp = x + (y - (y / ((a - t) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.9e+136], N[Not[LessEqual[t, 0.00015]], $MachinePrecision]], N[(x + N[(-1.0 / N[(N[(t / y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.89999999999999974e136 or 1.49999999999999987e-4 < t

   1. Initial program 56.3%

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

      1. associate--l+ 64.8%

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

      2. associate-/l* 72.0%

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

   3. Simplified 72.0%

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

   4. Taylor expanded in t around -inf 82.2%

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

      1. +-commutative 82.2%

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

      2. sub-neg 82.2%

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

      3. mul-1-neg 82.2%

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

      4. mul-1-neg 82.2%

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

      5. unsub-neg 82.2%

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

      6. mul-1-neg 82.2%

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

      7. sub-neg 82.2%

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

      8. distribute-lft-out-- 82.3%

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

   6. Simplified 82.3%

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

      1. clear-num 82.2%

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

      2. inv-pow 82.2%

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

   8. Applied egg-rr 82.2%

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

      1. unpow-1 82.2%

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

      2. associate-/r* 92.5%

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

   10. Simplified 92.5%

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

   if -2.89999999999999974e136 < t < 1.49999999999999987e-4

   1. Initial program 90.9%

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

      1. associate--l+ 91.7%

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

      2. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around inf 89.5%

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

      1. associate-/l* 90.2%

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

   6. Simplified 90.2%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+136} \lor \neg \left(t \leq 0.00015\right):\\ \;\;\;\;x + \frac{-1}{\frac{\frac{t}{y}}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \end{array} \]

Alternative 6: 63.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{t}\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{-192}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-221}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.65 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y t))))
   (if (<= a -1.9e-192)
     (+ y x)
     (if (<= a 1.22e-287)
       t_1
       (if (<= a 3e-221)
         x
         (if (<= a 2.3e-200) t_1 (if (<= a 3.65e+50) x (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / t);
	double tmp;
	if (a <= -1.9e-192) {
		tmp = y + x;
	} else if (a <= 1.22e-287) {
		tmp = t_1;
	} else if (a <= 3e-221) {
		tmp = x;
	} else if (a <= 2.3e-200) {
		tmp = t_1;
	} else if (a <= 3.65e+50) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y / t)
    if (a <= (-1.9d-192)) then
        tmp = y + x
    else if (a <= 1.22d-287) then
        tmp = t_1
    else if (a <= 3d-221) then
        tmp = x
    else if (a <= 2.3d-200) then
        tmp = t_1
    else if (a <= 3.65d+50) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / t);
	double tmp;
	if (a <= -1.9e-192) {
		tmp = y + x;
	} else if (a <= 1.22e-287) {
		tmp = t_1;
	} else if (a <= 3e-221) {
		tmp = x;
	} else if (a <= 2.3e-200) {
		tmp = t_1;
	} else if (a <= 3.65e+50) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / t)
	tmp = 0
	if a <= -1.9e-192:
		tmp = y + x
	elif a <= 1.22e-287:
		tmp = t_1
	elif a <= 3e-221:
		tmp = x
	elif a <= 2.3e-200:
		tmp = t_1
	elif a <= 3.65e+50:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / t))
	tmp = 0.0
	if (a <= -1.9e-192)
		tmp = Float64(y + x);
	elseif (a <= 1.22e-287)
		tmp = t_1;
	elseif (a <= 3e-221)
		tmp = x;
	elseif (a <= 2.3e-200)
		tmp = t_1;
	elseif (a <= 3.65e+50)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / t);
	tmp = 0.0;
	if (a <= -1.9e-192)
		tmp = y + x;
	elseif (a <= 1.22e-287)
		tmp = t_1;
	elseif (a <= 3e-221)
		tmp = x;
	elseif (a <= 2.3e-200)
		tmp = t_1;
	elseif (a <= 3.65e+50)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e-192], N[(y + x), $MachinePrecision], If[LessEqual[a, 1.22e-287], t$95$1, If[LessEqual[a, 3e-221], x, If[LessEqual[a, 2.3e-200], t$95$1, If[LessEqual[a, 3.65e+50], x, N[(y + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9000000000000001e-192 or 3.6500000000000002e50 < a

   1. Initial program 76.1%

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

      1. associate--l+ 77.6%

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

      2. sub-neg 77.6%

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

      3. +-commutative 77.6%

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

      4. associate-/l* 87.7%

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

      5. distribute-neg-frac 87.7%

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

      6. associate-/r/ 89.1%

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

      7. fma-def 89.1%

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

      8. sub-neg 89.1%

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

      9. +-commutative 89.1%

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

      10. distribute-neg-in 89.1%

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

      11. unsub-neg 89.1%

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

      12. remove-double-neg 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in a around inf 67.3%

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

   if -1.9000000000000001e-192 < a < 1.21999999999999996e-287 or 3.0000000000000002e-221 < a < 2.30000000000000007e-200

   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+ 73.2%

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

      2. associate-/l* 68.8%

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

   3. Simplified 68.8%

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

   4. Taylor expanded in t around -inf 89.6%

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

      1. +-commutative 89.6%

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

      2. sub-neg 89.6%

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

      3. mul-1-neg 89.6%

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

      4. mul-1-neg 89.6%

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

      5. unsub-neg 89.6%

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

      6. mul-1-neg 89.6%

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

      7. sub-neg 89.6%

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

      8. distribute-lft-out-- 89.7%

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

   6. Simplified 89.7%

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

   7. Taylor expanded in z around inf 68.3%

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

      1. associate-/l* 58.7%

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

   9. Simplified 58.7%

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

       1. associate-/r/ 68.3%

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

   11. Applied egg-rr 68.3%

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

   if 1.21999999999999996e-287 < a < 3.0000000000000002e-221 or 2.30000000000000007e-200 < a < 3.6500000000000002e50

   1. Initial program 80.0%

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

      1. associate--l+ 88.5%

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

      2. sub-neg 88.5%

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

      3. +-commutative 88.5%

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

      4. associate-/l* 88.5%

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

      5. distribute-neg-frac 88.5%

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

      6. associate-/r/ 92.2%

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

      7. fma-def 92.2%

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

      8. sub-neg 92.2%

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

      9. +-commutative 92.2%

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

      10. distribute-neg-in 92.2%

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

      11. unsub-neg 92.2%

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

      12. remove-double-neg 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in x around inf 64.6%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-192}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-287}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-221}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 3.65 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7: 62.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-193}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-289}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-223}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-196}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 3.65 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.4e-193)
   (+ y x)
   (if (<= a 1.3e-289)
     (* z (/ y t))
     (if (<= a 1.55e-223)
       x
       (if (<= a 2.3e-196) (/ (* y z) t) (if (<= a 3.65e+50) x (+ y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e-193) {
		tmp = y + x;
	} else if (a <= 1.3e-289) {
		tmp = z * (y / t);
	} else if (a <= 1.55e-223) {
		tmp = x;
	} else if (a <= 2.3e-196) {
		tmp = (y * z) / t;
	} else if (a <= 3.65e+50) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.4d-193)) then
        tmp = y + x
    else if (a <= 1.3d-289) then
        tmp = z * (y / t)
    else if (a <= 1.55d-223) then
        tmp = x
    else if (a <= 2.3d-196) then
        tmp = (y * z) / t
    else if (a <= 3.65d+50) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e-193) {
		tmp = y + x;
	} else if (a <= 1.3e-289) {
		tmp = z * (y / t);
	} else if (a <= 1.55e-223) {
		tmp = x;
	} else if (a <= 2.3e-196) {
		tmp = (y * z) / t;
	} else if (a <= 3.65e+50) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.4e-193:
		tmp = y + x
	elif a <= 1.3e-289:
		tmp = z * (y / t)
	elif a <= 1.55e-223:
		tmp = x
	elif a <= 2.3e-196:
		tmp = (y * z) / t
	elif a <= 3.65e+50:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.4e-193)
		tmp = Float64(y + x);
	elseif (a <= 1.3e-289)
		tmp = Float64(z * Float64(y / t));
	elseif (a <= 1.55e-223)
		tmp = x;
	elseif (a <= 2.3e-196)
		tmp = Float64(Float64(y * z) / t);
	elseif (a <= 3.65e+50)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.4e-193)
		tmp = y + x;
	elseif (a <= 1.3e-289)
		tmp = z * (y / t);
	elseif (a <= 1.55e-223)
		tmp = x;
	elseif (a <= 2.3e-196)
		tmp = (y * z) / t;
	elseif (a <= 3.65e+50)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.4e-193], N[(y + x), $MachinePrecision], If[LessEqual[a, 1.3e-289], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e-223], x, If[LessEqual[a, 2.3e-196], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 3.65e+50], x, N[(y + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.4e-193 or 3.6500000000000002e50 < a

   1. Initial program 76.1%

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

      1. associate--l+ 77.6%

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

      2. sub-neg 77.6%

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

      3. +-commutative 77.6%

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

      4. associate-/l* 87.7%

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

      5. distribute-neg-frac 87.7%

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

      6. associate-/r/ 89.1%

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

      7. fma-def 89.1%

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

      8. sub-neg 89.1%

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

      9. +-commutative 89.1%

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

      10. distribute-neg-in 89.1%

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

      11. unsub-neg 89.1%

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

      12. remove-double-neg 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in a around inf 67.3%

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

   if -2.4e-193 < a < 1.2999999999999999e-289

   1. Initial program 68.3%

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

      1. associate--l+ 73.9%

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

      2. associate-/l* 68.8%

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

   3. Simplified 68.8%

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

   4. Taylor expanded in t around -inf 88.2%

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

      1. +-commutative 88.2%

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

      2. sub-neg 88.2%

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

      3. mul-1-neg 88.2%

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

      4. mul-1-neg 88.2%

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

      5. unsub-neg 88.2%

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

      6. mul-1-neg 88.2%

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

      7. sub-neg 88.2%

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

      8. distribute-lft-out-- 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in z around inf 63.6%

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

      1. associate-/l* 55.2%

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

   9. Simplified 55.2%

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

       1. associate-/r/ 63.8%

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

   11. Applied egg-rr 63.8%

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

   if 1.2999999999999999e-289 < a < 1.55000000000000009e-223 or 2.3000000000000002e-196 < a < 3.6500000000000002e50

   1. Initial program 80.0%

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

      1. associate--l+ 88.5%

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

      2. sub-neg 88.5%

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

      3. +-commutative 88.5%

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

      4. associate-/l* 88.5%

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

      5. distribute-neg-frac 88.5%

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

      6. associate-/r/ 92.2%

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

      7. fma-def 92.2%

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

      8. sub-neg 92.2%

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

      9. +-commutative 92.2%

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

      10. distribute-neg-in 92.2%

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

      11. unsub-neg 92.2%

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

      12. remove-double-neg 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in x around inf 64.6%

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

   if 1.55000000000000009e-223 < a < 2.3000000000000002e-196

   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+ 68.2%

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

      2. associate-/l* 68.8%

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

   3. Simplified 68.8%

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

   4. Taylor expanded in t around -inf 99.7%

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

      1. +-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. mul-1-neg 99.7%

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

      4. mul-1-neg 99.7%

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

      5. unsub-neg 99.7%

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

      6. mul-1-neg 99.7%

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

      7. sub-neg 99.7%

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

      8. distribute-lft-out-- 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in z around inf 99.7%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-193}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-289}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-223}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-196}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 3.65 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8: 75.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-38}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+161}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.7e-38)
   (+ y x)
   (if (<= a 2.3e-38)
     (+ x (/ (* y z) t))
     (if (<= a 1.55e+161) (- x (* z (/ y a))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e-38) {
		tmp = y + x;
	} else if (a <= 2.3e-38) {
		tmp = x + ((y * z) / t);
	} else if (a <= 1.55e+161) {
		tmp = x - (z * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.7d-38)) then
        tmp = y + x
    else if (a <= 2.3d-38) then
        tmp = x + ((y * z) / t)
    else if (a <= 1.55d+161) then
        tmp = x - (z * (y / a))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e-38) {
		tmp = y + x;
	} else if (a <= 2.3e-38) {
		tmp = x + ((y * z) / t);
	} else if (a <= 1.55e+161) {
		tmp = x - (z * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.7e-38:
		tmp = y + x
	elif a <= 2.3e-38:
		tmp = x + ((y * z) / t)
	elif a <= 1.55e+161:
		tmp = x - (z * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.7e-38)
		tmp = Float64(y + x);
	elseif (a <= 2.3e-38)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (a <= 1.55e+161)
		tmp = Float64(x - Float64(z * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.7e-38)
		tmp = y + x;
	elseif (a <= 2.3e-38)
		tmp = x + ((y * z) / t);
	elseif (a <= 1.55e+161)
		tmp = x - (z * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.7e-38], N[(y + x), $MachinePrecision], If[LessEqual[a, 2.3e-38], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+161], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.7e-38 or 1.55000000000000003e161 < a

   1. Initial program 73.3%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. +-commutative 74.5%

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

      4. associate-/l* 88.1%

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

      5. distribute-neg-frac 88.1%

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

      6. associate-/r/ 89.1%

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

      7. fma-def 89.1%

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

      8. sub-neg 89.1%

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

      9. +-commutative 89.1%

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

      10. distribute-neg-in 89.1%

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

      11. unsub-neg 89.1%

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

      12. remove-double-neg 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in a around inf 73.2%

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

   if -3.7e-38 < a < 2.30000000000000002e-38

   1. Initial program 75.1%

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

      1. associate--l+ 81.4%

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

      2. sub-neg 81.4%

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

      3. +-commutative 81.4%

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

      4. associate-/l* 80.8%

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

      5. distribute-neg-frac 80.8%

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

      6. associate-/r/ 80.1%

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

      7. fma-def 80.2%

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

      8. sub-neg 80.2%

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

      9. +-commutative 80.2%

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

      10. distribute-neg-in 80.2%

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

      11. unsub-neg 80.2%

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

      12. remove-double-neg 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in y around 0 88.4%

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

   5. Taylor expanded in a around 0 83.2%

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

   if 2.30000000000000002e-38 < a < 1.55000000000000003e161

   1. Initial program 85.1%

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

      1. associate--l+ 89.6%

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

      2. sub-neg 89.6%

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

      3. +-commutative 89.6%

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

      4. associate-/l* 89.7%

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

      5. distribute-neg-frac 89.7%

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

      6. associate-/r/ 94.1%

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

      7. fma-def 94.1%

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

      8. sub-neg 94.1%

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

      9. +-commutative 94.1%

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

      10. distribute-neg-in 94.1%

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

      11. unsub-neg 94.1%

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

      12. remove-double-neg 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around 0 94.1%

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

   5. Taylor expanded in t around inf 85.8%

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

   6. Taylor expanded in a around inf 79.0%

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

      1. +-commutative 79.0%

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

      2. mul-1-neg 79.0%

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

      3. associate-/l* 79.0%

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

      4. sub-neg 79.0%

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

      5. associate-/r/ 79.0%

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

      6. *-commutative 79.0%

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

   8. Simplified 79.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-38}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+161}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9: 85.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-38}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{+162}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.7e-38)
   (- (+ y x) (* y (/ z a)))
   (if (<= a 1.42e+162) (- x (* z (/ y (- a t)))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e-38) {
		tmp = (y + x) - (y * (z / a));
	} else if (a <= 1.42e+162) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.7d-38)) then
        tmp = (y + x) - (y * (z / a))
    else if (a <= 1.42d+162) then
        tmp = x - (z * (y / (a - t)))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e-38) {
		tmp = (y + x) - (y * (z / a));
	} else if (a <= 1.42e+162) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.7e-38:
		tmp = (y + x) - (y * (z / a))
	elif a <= 1.42e+162:
		tmp = x - (z * (y / (a - t)))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.7e-38)
		tmp = Float64(Float64(y + x) - Float64(y * Float64(z / a)));
	elseif (a <= 1.42e+162)
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.7e-38)
		tmp = (y + x) - (y * (z / a));
	elseif (a <= 1.42e+162)
		tmp = x - (z * (y / (a - t)));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.7e-38], N[(N[(y + x), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.42e+162], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.7e-38

   1. Initial program 70.3%

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

      1. associate-*l/ 84.7%

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

   3. Simplified 84.7%

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

   4. Taylor expanded in t around 0 75.9%

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

   if -3.7e-38 < a < 1.4199999999999999e162

   1. Initial program 77.8%

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

      1. associate--l+ 83.6%

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

      2. sub-neg 83.6%

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

      3. +-commutative 83.6%

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

      4. associate-/l* 83.2%

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

      5. distribute-neg-frac 83.2%

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

      6. associate-/r/ 83.8%

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

      7. fma-def 83.9%

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

      8. sub-neg 83.9%

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

      9. +-commutative 83.9%

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

      10. distribute-neg-in 83.9%

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

      11. unsub-neg 83.9%

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

      12. remove-double-neg 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in y around 0 89.9%

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

   5. Taylor expanded in t around inf 86.0%

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

   6. Taylor expanded in y around 0 89.5%

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

      1. +-commutative 89.5%

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

      2. mul-1-neg 89.5%

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

      3. associate-*r/ 86.0%

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

      4. sub-neg 86.0%

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

      5. associate-*r/ 89.5%

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

      6. associate-/l* 86.5%

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

   8. Simplified 86.5%

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

      1. associate-/r/ 90.7%

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

   10. Applied egg-rr 90.7%

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

   if 1.4199999999999999e162 < a

   1. Initial program 81.6%

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

      1. associate--l+ 81.6%

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

      2. sub-neg 81.6%

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

      3. +-commutative 81.6%

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

      4. associate-/l* 96.2%

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

      5. distribute-neg-frac 96.2%

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

      6. associate-/r/ 96.2%

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

      7. fma-def 96.2%

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

      8. sub-neg 96.2%

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

      9. +-commutative 96.2%

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

      10. distribute-neg-in 96.2%

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

      11. unsub-neg 96.2%

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

      12. remove-double-neg 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in a around inf 92.7%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-38}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{+162}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10: 75.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.3 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+161}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.3e-41)
   (+ y x)
   (if (<= a 1.55e+161) (+ x (/ y (/ t z))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.3e-41) {
		tmp = y + x;
	} else if (a <= 1.55e+161) {
		tmp = x + (y / (t / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7.3d-41)) then
        tmp = y + x
    else if (a <= 1.55d+161) then
        tmp = x + (y / (t / z))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.3e-41) {
		tmp = y + x;
	} else if (a <= 1.55e+161) {
		tmp = x + (y / (t / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.3e-41:
		tmp = y + x
	elif a <= 1.55e+161:
		tmp = x + (y / (t / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.3e-41)
		tmp = Float64(y + x);
	elseif (a <= 1.55e+161)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.3e-41)
		tmp = y + x;
	elseif (a <= 1.55e+161)
		tmp = x + (y / (t / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.3e-41], N[(y + x), $MachinePrecision], If[LessEqual[a, 1.55e+161], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.30000000000000026e-41 or 1.55000000000000003e161 < a

   1. Initial program 73.3%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. +-commutative 74.5%

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

      4. associate-/l* 88.1%

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

      5. distribute-neg-frac 88.1%

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

      6. associate-/r/ 89.1%

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

      7. fma-def 89.1%

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

      8. sub-neg 89.1%

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

      9. +-commutative 89.1%

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

      10. distribute-neg-in 89.1%

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

      11. unsub-neg 89.1%

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

      12. remove-double-neg 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in a around inf 73.2%

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

   if -7.30000000000000026e-41 < a < 1.55000000000000003e161

   1. Initial program 77.8%

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

      1. associate--l+ 83.6%

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

      2. sub-neg 83.6%

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

      3. +-commutative 83.6%

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

      4. associate-/l* 83.2%

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

      5. distribute-neg-frac 83.2%

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

      6. associate-/r/ 83.8%

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

      7. fma-def 83.9%

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

      8. sub-neg 83.9%

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

      9. +-commutative 83.9%

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

      10. distribute-neg-in 83.9%

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

      11. unsub-neg 83.9%

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

      12. remove-double-neg 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in y around 0 89.9%

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

   5. Taylor expanded in a around 0 78.4%

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

      1. associate-/l* 76.0%

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

   7. Simplified 76.0%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.3 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+161}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 11: 74.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-46}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+161}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.8e-46)
   (+ y x)
   (if (<= a 1.55e+161) (+ x (/ (* y z) t)) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e-46) {
		tmp = y + x;
	} else if (a <= 1.55e+161) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.8d-46)) then
        tmp = y + x
    else if (a <= 1.55d+161) then
        tmp = x + ((y * z) / t)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e-46) {
		tmp = y + x;
	} else if (a <= 1.55e+161) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.8e-46:
		tmp = y + x
	elif a <= 1.55e+161:
		tmp = x + ((y * z) / t)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.8e-46)
		tmp = Float64(y + x);
	elseif (a <= 1.55e+161)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.8e-46)
		tmp = y + x;
	elseif (a <= 1.55e+161)
		tmp = x + ((y * z) / t);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.8e-46], N[(y + x), $MachinePrecision], If[LessEqual[a, 1.55e+161], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.80000000000000009e-46 or 1.55000000000000003e161 < a

   1. Initial program 73.3%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. +-commutative 74.5%

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

      4. associate-/l* 88.1%

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

      5. distribute-neg-frac 88.1%

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

      6. associate-/r/ 89.1%

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

      7. fma-def 89.1%

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

      8. sub-neg 89.1%

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

      9. +-commutative 89.1%

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

      10. distribute-neg-in 89.1%

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

      11. unsub-neg 89.1%

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

      12. remove-double-neg 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in a around inf 73.2%

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

   if -5.80000000000000009e-46 < a < 1.55000000000000003e161

   1. Initial program 77.8%

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

      1. associate--l+ 83.6%

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

      2. sub-neg 83.6%

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

      3. +-commutative 83.6%

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

      4. associate-/l* 83.2%

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

      5. distribute-neg-frac 83.2%

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

      6. associate-/r/ 83.8%

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

      7. fma-def 83.9%

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

      8. sub-neg 83.9%

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

      9. +-commutative 83.9%

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

      10. distribute-neg-in 83.9%

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

      11. unsub-neg 83.9%

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

      12. remove-double-neg 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in y around 0 89.9%

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

   5. Taylor expanded in a around 0 78.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-46}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+161}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 12: 80.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 9.5 \cdot 10^{+166}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a 9.5e+166) (- x (* z (/ y (- a t)))) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 9.5e+166) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= 9.5d+166) then
        tmp = x - (z * (y / (a - t)))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 9.5e+166) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 9.5e+166:
		tmp = x - (z * (y / (a - t)))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 9.5e+166)
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 9.5e+166)
		tmp = x - (z * (y / (a - t)));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 9.5e+166], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 9.49999999999999984e166

   1. Initial program 75.4%

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

      1. associate--l+ 80.0%

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

      2. sub-neg 80.0%

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

      3. +-commutative 80.0%

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

      4. associate-/l* 83.8%

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

      5. distribute-neg-frac 83.8%

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

      6. associate-/r/ 84.6%

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

      7. fma-def 84.7%

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

      8. sub-neg 84.7%

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

      9. +-commutative 84.7%

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

      10. distribute-neg-in 84.7%

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

      11. unsub-neg 84.7%

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

      12. remove-double-neg 84.7%

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

   3. Simplified 84.7%

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

   4. Taylor expanded in y around 0 89.7%

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

   5. Taylor expanded in t around inf 79.5%

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

   6. Taylor expanded in y around 0 79.0%

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

      1. +-commutative 79.0%

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

      2. mul-1-neg 79.0%

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

      3. associate-*r/ 79.5%

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

      4. sub-neg 79.5%

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

      5. associate-*r/ 79.0%

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

      6. associate-/l* 79.9%

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

   8. Simplified 79.9%

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

      1. associate-/r/ 82.7%

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

   10. Applied egg-rr 82.7%

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

   if 9.49999999999999984e166 < a

   1. Initial program 81.6%

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

      1. associate--l+ 81.6%

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

      2. sub-neg 81.6%

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

      3. +-commutative 81.6%

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

      4. associate-/l* 96.2%

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

      5. distribute-neg-frac 96.2%

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

      6. associate-/r/ 96.2%

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

      7. fma-def 96.2%

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

      8. sub-neg 96.2%

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

      9. +-commutative 96.2%

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

      10. distribute-neg-in 96.2%

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

      11. unsub-neg 96.2%

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

      12. remove-double-neg 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in a around inf 92.7%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 9.5 \cdot 10^{+166}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 13: 60.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-236} \lor \neg \left(x \leq 2.5 \cdot 10^{-184}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -8e-236) (not (<= x 2.5e-184))) (+ y x) (* y (/ z t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -8e-236) || !(x <= 2.5e-184)) {
		tmp = y + x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-8d-236)) .or. (.not. (x <= 2.5d-184))) then
        tmp = y + x
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -8e-236) || !(x <= 2.5e-184)) {
		tmp = y + x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -8e-236) or not (x <= 2.5e-184):
		tmp = y + x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -8e-236) || !(x <= 2.5e-184))
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -8e-236) || ~((x <= 2.5e-184)))
		tmp = y + x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -8e-236], N[Not[LessEqual[x, 2.5e-184]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.0000000000000004e-236 or 2.50000000000000001e-184 < x

   1. Initial program 80.2%

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

      1. associate--l+ 83.7%

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

      2. sub-neg 83.7%

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

      3. +-commutative 83.7%

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

      4. associate-/l* 90.2%

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

      5. distribute-neg-frac 90.2%

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

      6. associate-/r/ 88.9%

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

      7. fma-def 88.9%

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

      8. sub-neg 88.9%

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

      9. +-commutative 88.9%

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

      10. distribute-neg-in 88.9%

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

      11. unsub-neg 88.9%

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

      12. remove-double-neg 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in a around inf 63.2%

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

   if -8.0000000000000004e-236 < x < 2.50000000000000001e-184

   1. Initial program 47.7%

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

      1. associate--l+ 55.9%

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

      2. associate-/l* 50.5%

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

   3. Simplified 50.5%

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

   4. Taylor expanded in t around -inf 72.8%

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

      1. +-commutative 72.8%

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

      2. sub-neg 72.8%

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

      3. mul-1-neg 72.8%

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

      4. mul-1-neg 72.8%

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

      5. unsub-neg 72.8%

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

      6. mul-1-neg 72.8%

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

      7. sub-neg 72.8%

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

      8. distribute-lft-out-- 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in z around inf 54.5%

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

      1. associate-/l* 51.6%

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

   9. Simplified 51.6%

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

   10. Taylor expanded in y around 0 54.5%

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

       1. associate-*r/ 51.8%

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

   12. Simplified 51.8%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-236} \lor \neg \left(x \leq 2.5 \cdot 10^{-184}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 14: 53.4% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.25 \cdot 10^{+174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= y 2.25e+174) x y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 2.25e+174) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 2.25d+174) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 2.25e+174) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 2.25e+174:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 2.25e+174)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 2.25e+174)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 2.25e+174], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 2.25000000000000021e174

   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+ 84.3%

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

      2. sub-neg 84.3%

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

      3. +-commutative 84.3%

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

      4. associate-/l* 87.8%

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

      5. distribute-neg-frac 87.8%

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

      6. associate-/r/ 88.3%

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

      7. fma-def 88.4%

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

      8. sub-neg 88.4%

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

      9. +-commutative 88.4%

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

      10. distribute-neg-in 88.4%

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

      11. unsub-neg 88.4%

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

      12. remove-double-neg 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in x around inf 57.9%

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

   if 2.25000000000000021e174 < y

   1. Initial program 56.1%

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

      1. associate-*l/ 71.2%

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

   3. Simplified 71.2%

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

   4. Taylor expanded in t around 0 55.1%

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

   5. Taylor expanded in x around 0 45.2%

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

   6. Taylor expanded in z around 0 28.2%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.25 \cdot 10^{+174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 15: 61.6% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.0%

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

   1. associate--l+ 80.1%

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

   2. sub-neg 80.1%

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

   3. +-commutative 80.1%

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

   4. associate-/l* 85.0%

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

   5. distribute-neg-frac 85.0%

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

   6. associate-/r/ 85.8%

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

   7. fma-def 85.9%

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

   8. sub-neg 85.9%

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

   9. +-commutative 85.9%

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

   10. distribute-neg-in 85.9%

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

   11. unsub-neg 85.9%

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

   12. remove-double-neg 85.9%

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

3. Simplified 85.9%

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

4. Taylor expanded in a around inf 56.7%

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

5. Final simplification 56.7%

   \[\leadsto y + x \]

Alternative 16: 51.9% 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 76.0%

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

   1. associate--l+ 80.1%

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

   2. sub-neg 80.1%

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

   3. +-commutative 80.1%

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

   4. associate-/l* 85.0%

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

   5. distribute-neg-frac 85.0%

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

   6. associate-/r/ 85.8%

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

   7. fma-def 85.9%

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

   8. sub-neg 85.9%

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

   9. +-commutative 85.9%

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

   10. distribute-neg-in 85.9%

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

   11. unsub-neg 85.9%

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

   12. remove-double-neg 85.9%

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

3. Simplified 85.9%

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

4. Taylor expanded in x around inf 50.8%

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

5. Final simplification 50.8%

   \[\leadsto x \]

Developer target: 87.9% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (a - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023224 
(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))))