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

Percentage Accurate: 77.6% → 91.3%

Time: 11.3s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.3 \cdot 10^{+205}:\\ \;\;\;\;y \cdot \left(\frac{t - z}{a - t} + 1\right) + x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 2.3e+205)
   (+ (* y (+ (/ (- t z) (- a t)) 1.0)) x)
   (- x (/ y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.3e+205) {
		tmp = (y * (((t - z) / (a - t)) + 1.0)) + x;
	} else {
		tmp = x - (y / (t / (a - 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 <= 2.3d+205) then
        tmp = (y * (((t - z) / (a - t)) + 1.0d0)) + x
    else
        tmp = x - (y / (t / (a - 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 <= 2.3e+205) {
		tmp = (y * (((t - z) / (a - t)) + 1.0)) + x;
	} else {
		tmp = x - (y / (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 2.3e+205:
		tmp = (y * (((t - z) / (a - t)) + 1.0)) + x
	else:
		tmp = x - (y / (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2.3e+205)
		tmp = Float64(Float64(y * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0)) + x);
	else
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 2.3e+205)
		tmp = (y * (((t - z) / (a - t)) + 1.0)) + x;
	else
		tmp = x - (y / (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2.3e+205], N[(N[(y * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.30000000000000007e205

   1. Initial program 81.7%

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

      1. +-commutative 81.7%

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

      2. associate--l+ 81.7%

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

      3. sub-neg 81.7%

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

      4. distribute-frac-neg 81.7%

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

      5. *-commutative 81.7%

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

      6. distribute-rgt-neg-in 81.7%

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

      7. associate-/l* 88.5%

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

      8. sub-neg 88.5%

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

      9. distribute-neg-in 88.5%

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

      10. remove-double-neg 88.5%

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

      11. +-commutative 88.5%

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

      12. sub-neg 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around 0 93.3%

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

      1. +-commutative 93.3%

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

      2. associate--l+ 91.7%

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

      3. div-sub 91.7%

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

   6. Simplified 91.7%

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

   if 2.30000000000000007e205 < t

   1. Initial program 53.5%

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

      1. +-commutative 53.5%

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

      2. associate--l+ 53.5%

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

      3. sub-neg 53.5%

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

      4. distribute-frac-neg 53.5%

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

      5. *-commutative 53.5%

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

      6. distribute-rgt-neg-in 53.5%

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

      7. associate-/l* 62.7%

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

      8. sub-neg 62.7%

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

      9. distribute-neg-in 62.7%

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

      10. remove-double-neg 62.7%

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

      11. +-commutative 62.7%

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

      12. sub-neg 62.7%

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

   3. Simplified 62.7%

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

   4. Taylor expanded in y around 0 81.9%

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

      1. +-commutative 81.9%

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

      2. associate--l+ 71.7%

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

      3. div-sub 71.7%

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

   6. Simplified 71.7%

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

   7. Taylor expanded in t around inf 81.7%

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

      1. mul-1-neg 81.7%

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

      2. associate-/l* 99.7%

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

      3. distribute-neg-frac 99.7%

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

      4. mul-1-neg 99.7%

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

      5. unsub-neg 99.7%

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

   9. Simplified 99.7%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.3 \cdot 10^{+205}:\\ \;\;\;\;y \cdot \left(\frac{t - z}{a - t} + 1\right) + x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \]

Alternative 2: 77.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+112}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-91}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-92}:\\ \;\;\;\;x + \left(y + \frac{t \cdot y}{a}\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.6e+112)
   (+ y x)
   (if (<= a -2.7e-91)
     (+ x (* y (/ z t)))
     (if (<= a -6e-92)
       (+ x (+ y (/ (* t y) a)))
       (if (<= a 1.7e-10) (+ x (/ (* y (- z a)) t)) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e+112) {
		tmp = y + x;
	} else if (a <= -2.7e-91) {
		tmp = x + (y * (z / t));
	} else if (a <= -6e-92) {
		tmp = x + (y + ((t * y) / a));
	} else if (a <= 1.7e-10) {
		tmp = x + ((y * (z - 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 <= (-2.6d+112)) then
        tmp = y + x
    else if (a <= (-2.7d-91)) then
        tmp = x + (y * (z / t))
    else if (a <= (-6d-92)) then
        tmp = x + (y + ((t * y) / a))
    else if (a <= 1.7d-10) then
        tmp = x + ((y * (z - 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 <= -2.6e+112) {
		tmp = y + x;
	} else if (a <= -2.7e-91) {
		tmp = x + (y * (z / t));
	} else if (a <= -6e-92) {
		tmp = x + (y + ((t * y) / a));
	} else if (a <= 1.7e-10) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.6e+112:
		tmp = y + x
	elif a <= -2.7e-91:
		tmp = x + (y * (z / t))
	elif a <= -6e-92:
		tmp = x + (y + ((t * y) / a))
	elif a <= 1.7e-10:
		tmp = x + ((y * (z - a)) / t)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.6e+112)
		tmp = Float64(y + x);
	elseif (a <= -2.7e-91)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (a <= -6e-92)
		tmp = Float64(x + Float64(y + Float64(Float64(t * y) / a)));
	elseif (a <= 1.7e-10)
		tmp = Float64(x + Float64(Float64(y * Float64(z - 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 <= -2.6e+112)
		tmp = y + x;
	elseif (a <= -2.7e-91)
		tmp = x + (y * (z / t));
	elseif (a <= -6e-92)
		tmp = x + (y + ((t * y) / a));
	elseif (a <= 1.7e-10)
		tmp = x + ((y * (z - a)) / t);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.6e+112], N[(y + x), $MachinePrecision], If[LessEqual[a, -2.7e-91], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6e-92], N[(x + N[(y + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-10], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.6000000000000001e112 or 1.70000000000000007e-10 < a

   1. Initial program 78.2%

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

      1. +-commutative 78.2%

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

      2. associate--l+ 78.2%

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

      3. sub-neg 78.2%

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

      4. distribute-frac-neg 78.2%

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

      5. *-commutative 78.2%

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

      6. distribute-rgt-neg-in 78.2%

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

      7. associate-/l* 91.0%

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

      8. sub-neg 91.0%

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

      9. distribute-neg-in 91.0%

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

      10. remove-double-neg 91.0%

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

      11. +-commutative 91.0%

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

      12. sub-neg 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in a around inf 85.1%

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

      1. +-commutative 85.1%

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

   6. Simplified 85.1%

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

   if -2.6000000000000001e112 < a < -2.6999999999999997e-91

   1. Initial program 82.6%

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

      1. +-commutative 82.6%

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

      2. associate--l+ 82.6%

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

      3. sub-neg 82.6%

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

      4. distribute-frac-neg 82.6%

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

      5. *-commutative 82.6%

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

      6. distribute-rgt-neg-in 82.6%

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

      7. associate-/l* 90.8%

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

      8. sub-neg 90.8%

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

      9. distribute-neg-in 90.8%

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

      10. remove-double-neg 90.8%

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

      11. +-commutative 90.8%

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

      12. sub-neg 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in y around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 96.8%

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

      3. div-sub 96.8%

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

   6. Simplified 96.8%

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

   7. Taylor expanded in a around 0 73.8%

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

   if -2.6999999999999997e-91 < a < -6.00000000000000027e-92

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. *-commutative 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. associate-/l* 100.0%

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

      8. sub-neg 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. remove-double-neg 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. div-sub 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around 0 100.0%

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

   8. Taylor expanded in t around 0 85.8%

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

   if -6.00000000000000027e-92 < a < 1.70000000000000007e-10

   1. Initial program 79.3%

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

      1. +-commutative 79.3%

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

      2. associate--l+ 79.3%

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

      3. sub-neg 79.3%

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

      4. distribute-frac-neg 79.3%

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

      5. *-commutative 79.3%

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

      6. distribute-rgt-neg-in 79.3%

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

      7. associate-/l* 80.3%

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

      8. sub-neg 80.3%

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

      9. distribute-neg-in 80.3%

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

      10. remove-double-neg 80.3%

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

      11. +-commutative 80.3%

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

      12. sub-neg 80.3%

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

   3. Simplified 80.3%

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

   4. Taylor expanded in y around 0 89.6%

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

      1. +-commutative 89.6%

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

      2. associate--l+ 86.1%

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

      3. div-sub 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in t around -inf 81.8%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+112}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-91}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-92}:\\ \;\;\;\;x + \left(y + \frac{t \cdot y}{a}\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 3: 75.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+112}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-108}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-11}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3e+112)
   (+ y x)
   (if (<= a 1.02e-168)
     (+ x (/ y (/ t z)))
     (if (<= a 2.3e-108)
       (- x (/ a (/ t y)))
       (if (<= a 1.95e-11) (+ x (* z (/ y t))) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3e+112) {
		tmp = y + x;
	} else if (a <= 1.02e-168) {
		tmp = x + (y / (t / z));
	} else if (a <= 2.3e-108) {
		tmp = x - (a / (t / y));
	} else if (a <= 1.95e-11) {
		tmp = x + (z * (y / 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 <= (-3d+112)) then
        tmp = y + x
    else if (a <= 1.02d-168) then
        tmp = x + (y / (t / z))
    else if (a <= 2.3d-108) then
        tmp = x - (a / (t / y))
    else if (a <= 1.95d-11) then
        tmp = x + (z * (y / 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 <= -3e+112) {
		tmp = y + x;
	} else if (a <= 1.02e-168) {
		tmp = x + (y / (t / z));
	} else if (a <= 2.3e-108) {
		tmp = x - (a / (t / y));
	} else if (a <= 1.95e-11) {
		tmp = x + (z * (y / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3e+112:
		tmp = y + x
	elif a <= 1.02e-168:
		tmp = x + (y / (t / z))
	elif a <= 2.3e-108:
		tmp = x - (a / (t / y))
	elif a <= 1.95e-11:
		tmp = x + (z * (y / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3e+112)
		tmp = Float64(y + x);
	elseif (a <= 1.02e-168)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (a <= 2.3e-108)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (a <= 1.95e-11)
		tmp = Float64(x + Float64(z * Float64(y / 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 <= -3e+112)
		tmp = y + x;
	elseif (a <= 1.02e-168)
		tmp = x + (y / (t / z));
	elseif (a <= 2.3e-108)
		tmp = x - (a / (t / y));
	elseif (a <= 1.95e-11)
		tmp = x + (z * (y / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3e+112], N[(y + x), $MachinePrecision], If[LessEqual[a, 1.02e-168], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e-108], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.95e-11], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.99999999999999979e112 or 1.95000000000000005e-11 < a

   1. Initial program 78.2%

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

      1. +-commutative 78.2%

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

      2. associate--l+ 78.2%

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

      3. sub-neg 78.2%

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

      4. distribute-frac-neg 78.2%

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

      5. *-commutative 78.2%

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

      6. distribute-rgt-neg-in 78.2%

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

      7. associate-/l* 91.0%

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

      8. sub-neg 91.0%

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

      9. distribute-neg-in 91.0%

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

      10. remove-double-neg 91.0%

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

      11. +-commutative 91.0%

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

      12. sub-neg 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in a around inf 85.1%

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

      1. +-commutative 85.1%

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

   6. Simplified 85.1%

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

   if -2.99999999999999979e112 < a < 1.01999999999999999e-168

   1. Initial program 80.2%

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

      1. +-commutative 80.2%

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

      2. associate--l+ 80.2%

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

      3. sub-neg 80.2%

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

      4. distribute-frac-neg 80.2%

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

      5. *-commutative 80.2%

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

      6. distribute-rgt-neg-in 80.2%

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

      7. associate-/l* 83.2%

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

      8. sub-neg 83.2%

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

      9. distribute-neg-in 83.2%

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

      10. remove-double-neg 83.2%

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

      11. +-commutative 83.2%

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

      12. sub-neg 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in y around 0 94.7%

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

      1. +-commutative 94.7%

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

      2. associate--l+ 90.3%

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

      3. div-sub 90.2%

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

   6. Simplified 90.2%

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

   7. Taylor expanded in a around 0 78.4%

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

      1. *-commutative 78.4%

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

   9. Simplified 78.4%

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

   10. Taylor expanded in z around 0 78.4%

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

       1. associate-/l* 80.0%

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

   12. Simplified 80.0%

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

   if 1.01999999999999999e-168 < a < 2.29999999999999996e-108

   1. Initial program 74.0%

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

      1. +-commutative 74.0%

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

      2. associate--l+ 74.0%

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

      3. sub-neg 74.0%

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

      4. distribute-frac-neg 74.0%

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

      5. *-commutative 74.0%

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

      6. distribute-rgt-neg-in 74.0%

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

      7. associate-/l* 74.1%

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

      8. sub-neg 74.1%

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

      9. distribute-neg-in 74.1%

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

      10. remove-double-neg 74.1%

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

      11. +-commutative 74.1%

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

      12. sub-neg 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in y around 0 80.7%

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

      1. +-commutative 80.7%

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

      2. associate--l+ 80.7%

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

      3. div-sub 80.7%

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

   6. Simplified 80.7%

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

   7. Taylor expanded in t around -inf 63.4%

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

   8. Taylor expanded in z around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. unsub-neg 67.8%

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

      3. associate-/l* 73.8%

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

   10. Simplified 73.8%

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

   if 2.29999999999999996e-108 < a < 1.95000000000000005e-11

   1. Initial program 85.4%

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

      1. +-commutative 85.4%

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

      2. associate--l+ 85.4%

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

      3. sub-neg 85.4%

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

      4. distribute-frac-neg 85.4%

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

      5. *-commutative 85.4%

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

      6. distribute-rgt-neg-in 85.4%

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

      7. associate-/l* 88.2%

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

      8. sub-neg 88.2%

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

      9. distribute-neg-in 88.2%

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

      10. remove-double-neg 88.2%

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

      11. +-commutative 88.2%

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

      12. sub-neg 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in y around 0 85.9%

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

      1. +-commutative 85.9%

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

      2. associate--l+ 85.9%

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

      3. div-sub 85.9%

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

   6. Simplified 85.9%

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

   7. Taylor expanded in a around 0 71.0%

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

      1. associate-/l* 76.0%

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

      2. associate-/r/ 76.1%

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

   9. Simplified 76.1%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+112}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-108}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-11}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4: 89.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6 \cdot 10^{+204}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 6e+204)
   (+ x (+ y (/ (- t z) (/ (- a t) y))))
   (- x (/ y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 6e+204) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x - (y / (t / (a - 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 <= 6d+204) then
        tmp = x + (y + ((t - z) / ((a - t) / y)))
    else
        tmp = x - (y / (t / (a - 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 <= 6e+204) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x - (y / (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 6e+204:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	else:
		tmp = x - (y / (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 6e+204)
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	else
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 6e+204)
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	else
		tmp = x - (y / (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 6e+204], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.99999999999999965e204

   1. Initial program 81.7%

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

      1. sub-neg 81.7%

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

      2. distribute-frac-neg 81.7%

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

      3. distribute-rgt-neg-out 81.7%

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

      4. associate-/l* 88.1%

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

      5. div-sub 88.0%

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

      6. associate-+r- 88.0%

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

      7. associate-/r/ 88.0%

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

      8. distribute-rgt-neg-out 88.0%

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

      9. associate-/r/ 88.0%

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

      10. distribute-frac-neg 88.0%

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

      11. associate-+l+ 88.0%

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

      12. associate-+r- 90.5%

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

      13. distribute-frac-neg 90.5%

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

   3. Simplified 90.5%

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

   if 5.99999999999999965e204 < t

   1. Initial program 53.5%

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

      1. +-commutative 53.5%

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

      2. associate--l+ 53.5%

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

      3. sub-neg 53.5%

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

      4. distribute-frac-neg 53.5%

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

      5. *-commutative 53.5%

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

      6. distribute-rgt-neg-in 53.5%

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

      7. associate-/l* 62.7%

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

      8. sub-neg 62.7%

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

      9. distribute-neg-in 62.7%

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

      10. remove-double-neg 62.7%

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

      11. +-commutative 62.7%

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

      12. sub-neg 62.7%

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

   3. Simplified 62.7%

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

   4. Taylor expanded in y around 0 81.9%

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

      1. +-commutative 81.9%

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

      2. associate--l+ 71.7%

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

      3. div-sub 71.7%

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

   6. Simplified 71.7%

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

   7. Taylor expanded in t around inf 81.7%

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

      1. mul-1-neg 81.7%

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

      2. associate-/l* 99.7%

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

      3. distribute-neg-frac 99.7%

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

      4. mul-1-neg 99.7%

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

      5. unsub-neg 99.7%

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

   9. Simplified 99.7%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6 \cdot 10^{+204}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \]

Alternative 5: 81.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-176} \lor \neg \left(a \leq 2.1 \cdot 10^{-9}\right):\\ \;\;\;\;\left(y + x\right) - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.8e-176) (not (<= a 2.1e-9)))
   (- (+ y x) (* z (/ y a)))
   (+ x (/ (* y (- z a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-176) || !(a <= 2.1e-9)) {
		tmp = (y + x) - (z * (y / a));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.8d-176)) .or. (.not. (a <= 2.1d-9))) then
        tmp = (y + x) - (z * (y / a))
    else
        tmp = x + ((y * (z - a)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-176) || !(a <= 2.1e-9)) {
		tmp = (y + x) - (z * (y / a));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.8e-176) or not (a <= 2.1e-9):
		tmp = (y + x) - (z * (y / a))
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.8e-176) || !(a <= 2.1e-9))
		tmp = Float64(Float64(y + x) - Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.8e-176) || ~((a <= 2.1e-9)))
		tmp = (y + x) - (z * (y / a));
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.8e-176], N[Not[LessEqual[a, 2.1e-9]], $MachinePrecision]], N[(N[(y + x), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.80000000000000012e-176 or 2.10000000000000019e-9 < a

   1. Initial program 80.8%

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

      1. associate-*l/ 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in t around 0 79.4%

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

      1. expm1-log1p-u 72.6%

         \[\leadsto \left(x + y\right) - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot z}{a}\right)\right)} \]

      2. expm1-udef 72.0%

         \[\leadsto \left(x + y\right) - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot z}{a}\right)} - 1\right)} \]

      3. *-commutative 72.0%

         \[\leadsto \left(x + y\right) - \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{z \cdot y}}{a}\right)} - 1\right) \]

   6. Applied egg-rr 72.0%

      \[\leadsto \left(x + y\right) - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{z \cdot y}{a}\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 72.6%

         \[\leadsto \left(x + y\right) - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{z \cdot y}{a}\right)\right)} \]

      2. expm1-log1p 79.4%

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

      3. *-rgt-identity 79.4%

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

      4. associate-*r/ 79.4%

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

      5. associate-*l* 83.4%

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

      6. associate-*r/ 83.5%

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

      7. *-rgt-identity 83.5%

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

   8. Simplified 83.5%

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

   if -4.80000000000000012e-176 < a < 2.10000000000000019e-9

   1. Initial program 77.0%

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

      1. +-commutative 77.0%

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

      2. associate--l+ 77.0%

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

      3. sub-neg 77.0%

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

      4. distribute-frac-neg 77.0%

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

      5. *-commutative 77.0%

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

      6. distribute-rgt-neg-in 77.0%

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

      7. associate-/l* 78.5%

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

      8. sub-neg 78.5%

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

      9. distribute-neg-in 78.5%

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

      10. remove-double-neg 78.5%

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

      11. +-commutative 78.5%

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

      12. sub-neg 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in y around 0 90.9%

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

      1. +-commutative 90.9%

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

      2. associate--l+ 86.9%

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

      3. div-sub 86.8%

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

   6. Simplified 86.8%

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

   7. Taylor expanded in t around -inf 84.1%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-176} \lor \neg \left(a \leq 2.1 \cdot 10^{-9}\right):\\ \;\;\;\;\left(y + x\right) - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]

Alternative 6: 86.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+79} \lor \neg \left(a \leq 1.4 \cdot 10^{-9}\right):\\ \;\;\;\;\left(y + x\right) - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.2e+79) (not (<= a 1.4e-9)))
   (- (+ y x) (* z (/ y a)))
   (- x (/ (* y z) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.2e+79) || !(a <= 1.4e-9)) {
		tmp = (y + x) - (z * (y / a));
	} else {
		tmp = x - ((y * z) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-6.2d+79)) .or. (.not. (a <= 1.4d-9))) then
        tmp = (y + x) - (z * (y / a))
    else
        tmp = x - ((y * z) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.2e+79) || !(a <= 1.4e-9)) {
		tmp = (y + x) - (z * (y / a));
	} else {
		tmp = x - ((y * z) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6.2e+79) or not (a <= 1.4e-9):
		tmp = (y + x) - (z * (y / a))
	else:
		tmp = x - ((y * z) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.2e+79) || !(a <= 1.4e-9))
		tmp = Float64(Float64(y + x) - Float64(z * Float64(y / a)));
	else
		tmp = Float64(x - Float64(Float64(y * z) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6.2e+79) || ~((a <= 1.4e-9)))
		tmp = (y + x) - (z * (y / a));
	else
		tmp = x - ((y * z) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6.2e+79], N[Not[LessEqual[a, 1.4e-9]], $MachinePrecision]], N[(N[(y + x), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.1999999999999998e79 or 1.39999999999999992e-9 < a

   1. Initial program 78.3%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in t around 0 82.5%

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

      1. expm1-log1p-u 77.8%

         \[\leadsto \left(x + y\right) - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot z}{a}\right)\right)} \]

      2. expm1-udef 77.8%

         \[\leadsto \left(x + y\right) - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot z}{a}\right)} - 1\right)} \]

      3. *-commutative 77.8%

         \[\leadsto \left(x + y\right) - \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{z \cdot y}}{a}\right)} - 1\right) \]

   6. Applied egg-rr 77.8%

      \[\leadsto \left(x + y\right) - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{z \cdot y}{a}\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 77.8%

         \[\leadsto \left(x + y\right) - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{z \cdot y}{a}\right)\right)} \]

      2. expm1-log1p 82.5%

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

      3. *-rgt-identity 82.5%

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

      4. associate-*r/ 82.5%

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

      5. associate-*l* 89.1%

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

      6. associate-*r/ 89.1%

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

      7. *-rgt-identity 89.1%

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

   8. Simplified 89.1%

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

   if -6.1999999999999998e79 < a < 1.39999999999999992e-9

   1. Initial program 80.3%

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

      1. sub-neg 80.3%

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

      2. distribute-frac-neg 80.3%

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

      3. distribute-rgt-neg-out 80.3%

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

      4. associate-/l* 81.6%

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

      5. div-sub 81.5%

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

      6. associate-+r- 81.5%

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

      7. associate-/r/ 81.6%

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

      8. distribute-rgt-neg-out 81.6%

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

      9. associate-/r/ 81.5%

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

      10. distribute-frac-neg 81.5%

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

      11. associate-+l+ 81.5%

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

      12. associate-+r- 86.4%

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

      13. distribute-frac-neg 86.4%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in z around inf 87.8%

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

      1. associate-*r/ 87.8%

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

      2. associate-*r* 87.8%

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

      3. neg-mul-1 87.8%

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

   6. Simplified 87.8%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+79} \lor \neg \left(a \leq 1.4 \cdot 10^{-9}\right):\\ \;\;\;\;\left(y + x\right) - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \end{array} \]

Alternative 7: 87.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+113} \lor \neg \left(a \leq 4.8 \cdot 10^{-9}\right):\\ \;\;\;\;\left(y + x\right) - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7e+113) (not (<= a 4.8e-9)))
   (- (+ y x) (* z (/ y a)))
   (- x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7e+113) || !(a <= 4.8e-9)) {
		tmp = (y + x) - (z * (y / a));
	} else {
		tmp = x - (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 ((a <= (-7d+113)) .or. (.not. (a <= 4.8d-9))) then
        tmp = (y + x) - (z * (y / a))
    else
        tmp = x - (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 ((a <= -7e+113) || !(a <= 4.8e-9)) {
		tmp = (y + x) - (z * (y / a));
	} else {
		tmp = x - (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7e+113) or not (a <= 4.8e-9):
		tmp = (y + x) - (z * (y / a))
	else:
		tmp = x - (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7e+113) || !(a <= 4.8e-9))
		tmp = Float64(Float64(y + x) - Float64(z * Float64(y / a)));
	else
		tmp = Float64(x - 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 ((a <= -7e+113) || ~((a <= 4.8e-9)))
		tmp = (y + x) - (z * (y / a));
	else
		tmp = x - (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7e+113], N[Not[LessEqual[a, 4.8e-9]], $MachinePrecision]], N[(N[(y + x), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.0000000000000001e113 or 4.8e-9 < a

   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/ 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in t around 0 82.3%

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

      1. expm1-log1p-u 78.2%

         \[\leadsto \left(x + y\right) - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot z}{a}\right)\right)} \]

      2. expm1-udef 78.2%

         \[\leadsto \left(x + y\right) - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot z}{a}\right)} - 1\right)} \]

      3. *-commutative 78.2%

         \[\leadsto \left(x + y\right) - \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{z \cdot y}}{a}\right)} - 1\right) \]

   6. Applied egg-rr 78.2%

      \[\leadsto \left(x + y\right) - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{z \cdot y}{a}\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 78.2%

         \[\leadsto \left(x + y\right) - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{z \cdot y}{a}\right)\right)} \]

      2. expm1-log1p 82.3%

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

      3. *-rgt-identity 82.3%

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

      4. associate-*r/ 82.3%

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

      5. associate-*l* 89.3%

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

      6. associate-*r/ 89.3%

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

      7. *-rgt-identity 89.3%

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

   8. Simplified 89.3%

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

   if -7.0000000000000001e113 < a < 4.8e-9

   1. Initial program 80.6%

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

      1. +-commutative 80.6%

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

      2. associate--l+ 80.6%

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

      3. sub-neg 80.6%

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

      4. distribute-frac-neg 80.6%

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

      5. *-commutative 80.6%

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

      6. distribute-rgt-neg-in 80.6%

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

      7. associate-/l* 83.2%

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

      8. sub-neg 83.2%

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

      9. distribute-neg-in 83.2%

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

      10. remove-double-neg 83.2%

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

      11. +-commutative 83.2%

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

      12. sub-neg 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in y around 0 92.2%

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

      1. +-commutative 92.2%

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

      2. associate--l+ 88.8%

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

      3. div-sub 88.8%

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

   6. Simplified 88.8%

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

   7. Taylor expanded in z around inf 87.1%

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

      1. mul-1-neg 87.1%

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

      2. associate-/l* 89.2%

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

      3. distribute-neg-frac 89.2%

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

   9. Simplified 89.2%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+113} \lor \neg \left(a \leq 4.8 \cdot 10^{-9}\right):\\ \;\;\;\;\left(y + x\right) - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 8: 76.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+112} \lor \neg \left(a \leq 4.1 \cdot 10^{-10}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.6e+112) (not (<= a 4.1e-10))) (+ y x) (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.6e+112) || !(a <= 4.1e-10)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.6d+112)) .or. (.not. (a <= 4.1d-10))) then
        tmp = y + x
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.6e+112) || !(a <= 4.1e-10)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.6e+112) or not (a <= 4.1e-10):
		tmp = y + x
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.6e+112) || !(a <= 4.1e-10))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.6e+112) || ~((a <= 4.1e-10)))
		tmp = y + x;
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.6e+112], N[Not[LessEqual[a, 4.1e-10]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.6000000000000001e112 or 4.0999999999999998e-10 < a

   1. Initial program 78.2%

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

      1. +-commutative 78.2%

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

      2. associate--l+ 78.2%

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

      3. sub-neg 78.2%

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

      4. distribute-frac-neg 78.2%

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

      5. *-commutative 78.2%

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

      6. distribute-rgt-neg-in 78.2%

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

      7. associate-/l* 91.0%

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

      8. sub-neg 91.0%

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

      9. distribute-neg-in 91.0%

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

      10. remove-double-neg 91.0%

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

      11. +-commutative 91.0%

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

      12. sub-neg 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in a around inf 85.1%

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

      1. +-commutative 85.1%

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

   6. Simplified 85.1%

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

   if -2.6000000000000001e112 < a < 4.0999999999999998e-10

   1. Initial program 80.3%

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

      1. +-commutative 80.3%

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

      2. associate--l+ 80.3%

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

      3. sub-neg 80.3%

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

      4. distribute-frac-neg 80.3%

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

      5. *-commutative 80.3%

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

      6. distribute-rgt-neg-in 80.3%

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

      7. associate-/l* 82.9%

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

      8. sub-neg 82.9%

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

      9. distribute-neg-in 82.9%

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

      10. remove-double-neg 82.9%

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

      11. +-commutative 82.9%

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

      12. sub-neg 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in y around 0 92.0%

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

      1. +-commutative 92.0%

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

      2. associate--l+ 88.7%

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

      3. div-sub 88.7%

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

   6. Simplified 88.7%

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

   7. Taylor expanded in a around 0 73.9%

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

      1. *-commutative 73.9%

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

   9. Simplified 73.9%

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

   10. Taylor expanded in z around 0 73.9%

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

       1. associate-/l* 75.8%

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

   12. Simplified 75.8%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+112} \lor \neg \left(a \leq 4.1 \cdot 10^{-10}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 9: 76.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+112}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.6e+112) (+ y x) (if (<= a 1.8e-11) (+ x (* y (/ z t))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e+112) {
		tmp = y + x;
	} else if (a <= 1.8e-11) {
		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 <= (-2.6d+112)) then
        tmp = y + x
    else if (a <= 1.8d-11) 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 <= -2.6e+112) {
		tmp = y + x;
	} else if (a <= 1.8e-11) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.6e+112:
		tmp = y + x
	elif a <= 1.8e-11:
		tmp = x + (y * (z / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.6e+112)
		tmp = Float64(y + x);
	elseif (a <= 1.8e-11)
		tmp = Float64(x + Float64(y * Float64(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 <= -2.6e+112)
		tmp = y + x;
	elseif (a <= 1.8e-11)
		tmp = x + (y * (z / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.6e+112], N[(y + x), $MachinePrecision], If[LessEqual[a, 1.8e-11], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.6000000000000001e112 or 1.79999999999999992e-11 < a

   1. Initial program 78.2%

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

      1. +-commutative 78.2%

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

      2. associate--l+ 78.2%

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

      3. sub-neg 78.2%

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

      4. distribute-frac-neg 78.2%

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

      5. *-commutative 78.2%

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

      6. distribute-rgt-neg-in 78.2%

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

      7. associate-/l* 91.0%

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

      8. sub-neg 91.0%

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

      9. distribute-neg-in 91.0%

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

      10. remove-double-neg 91.0%

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

      11. +-commutative 91.0%

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

      12. sub-neg 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in a around inf 85.1%

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

      1. +-commutative 85.1%

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

   6. Simplified 85.1%

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

   if -2.6000000000000001e112 < a < 1.79999999999999992e-11

   1. Initial program 80.3%

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

      1. +-commutative 80.3%

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

      2. associate--l+ 80.3%

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

      3. sub-neg 80.3%

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

      4. distribute-frac-neg 80.3%

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

      5. *-commutative 80.3%

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

      6. distribute-rgt-neg-in 80.3%

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

      7. associate-/l* 82.9%

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

      8. sub-neg 82.9%

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

      9. distribute-neg-in 82.9%

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

      10. remove-double-neg 82.9%

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

      11. +-commutative 82.9%

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

      12. sub-neg 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in y around 0 92.0%

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

      1. +-commutative 92.0%

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

      2. associate--l+ 88.7%

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

      3. div-sub 88.7%

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

   6. Simplified 88.7%

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

   7. Taylor expanded in a around 0 74.4%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+112}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10: 64.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-174}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1e-174) (+ y x) (if (<= a 9e-18) x (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e-174) {
		tmp = y + x;
	} else if (a <= 9e-18) {
		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 <= (-1d-174)) then
        tmp = y + x
    else if (a <= 9d-18) 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 <= -1e-174) {
		tmp = y + x;
	} else if (a <= 9e-18) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1e-174:
		tmp = y + x
	elif a <= 9e-18:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1e-174)
		tmp = Float64(y + x);
	elseif (a <= 9e-18)
		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 <= -1e-174)
		tmp = y + x;
	elseif (a <= 9e-18)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1e-174], N[(y + x), $MachinePrecision], If[LessEqual[a, 9e-18], x, N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1e-174 or 8.99999999999999987e-18 < a

   1. Initial program 80.8%

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

      1. +-commutative 80.8%

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

      2. associate--l+ 80.8%

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

      3. sub-neg 80.8%

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

      4. distribute-frac-neg 80.8%

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

      5. *-commutative 80.8%

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

      6. distribute-rgt-neg-in 80.8%

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

      7. associate-/l* 91.2%

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

      8. sub-neg 91.2%

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

      9. distribute-neg-in 91.2%

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

      10. remove-double-neg 91.2%

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

      11. +-commutative 91.2%

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

      12. sub-neg 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in a around inf 78.1%

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

      1. +-commutative 78.1%

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

   6. Simplified 78.1%

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

   if -1e-174 < a < 8.99999999999999987e-18

   1. Initial program 77.0%

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

      1. +-commutative 77.0%

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

      2. associate--l+ 77.0%

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

      3. sub-neg 77.0%

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

      4. distribute-frac-neg 77.0%

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

      5. *-commutative 77.0%

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

      6. distribute-rgt-neg-in 77.0%

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

      7. associate-/l* 78.5%

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

      8. sub-neg 78.5%

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

      9. distribute-neg-in 78.5%

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

      10. remove-double-neg 78.5%

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

      11. +-commutative 78.5%

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

      12. sub-neg 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in y around 0 55.5%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-174}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 11: 51.7% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 79.4%

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

   1. +-commutative 79.4%

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

   2. associate--l+ 79.4%

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

   3. sub-neg 79.4%

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

   4. distribute-frac-neg 79.4%

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

   5. *-commutative 79.4%

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

   6. distribute-rgt-neg-in 79.4%

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

   7. associate-/l* 86.4%

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

   8. sub-neg 86.4%

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

   9. distribute-neg-in 86.4%

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

   10. remove-double-neg 86.4%

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

   11. +-commutative 86.4%

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

   12. sub-neg 86.4%

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

3. Simplified 86.4%

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

4. Taylor expanded in y around 0 52.8%

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

5. Final simplification 52.8%

   \[\leadsto x \]

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 2023293 
(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))))