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

Percentage Accurate: 77.0% → 90.2%

Time: 9.7s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+77}:\\ \;\;\;\;\left(x - \frac{a}{\frac{t}{y}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+176}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - z}{a - t}, y, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.1e+77)
   (+ (- x (/ a (/ t y))) (/ y (/ t z)))
   (if (<= t 3.4e+176)
     (fma (/ (- t z) (- a t)) y (+ x y))
     (+ x (/ y (/ t (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+77) {
		tmp = (x - (a / (t / y))) + (y / (t / z));
	} else if (t <= 3.4e+176) {
		tmp = fma(((t - z) / (a - t)), y, (x + y));
	} else {
		tmp = x + (y / (t / (z - a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.1e+77)
		tmp = Float64(Float64(x - Float64(a / Float64(t / y))) + Float64(y / Float64(t / z)));
	elseif (t <= 3.4e+176)
		tmp = fma(Float64(Float64(t - z) / Float64(a - t)), y, Float64(x + y));
	else
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.1e+77], N[(N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+176], N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * y + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0999999999999999e77

   1. Initial program 53.7%

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

      1. associate-*l/ 62.1%

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

   3. Simplified 62.1%

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

   4. Taylor expanded in t around inf 82.9%

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

      1. sub-neg 82.9%

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

      2. mul-1-neg 82.9%

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

      3. unsub-neg 82.9%

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

      4. associate-/l* 87.2%

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

      5. mul-1-neg 87.2%

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

      6. remove-double-neg 87.2%

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

      7. associate-/l* 89.2%

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

   6. Simplified 89.2%

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

   if -2.0999999999999999e77 < t < 3.40000000000000014e176

   1. Initial program 88.8%

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

      1. sub-neg 88.8%

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

      2. distribute-frac-neg 88.8%

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

      3. distribute-rgt-neg-out 88.8%

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

      4. +-commutative 88.8%

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

      5. distribute-rgt-neg-out 88.8%

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

      6. distribute-lft-neg-in 88.8%

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

      7. associate-/l* 90.8%

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

      8. associate-/r/ 90.9%

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

      9. fma-def 90.9%

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

      10. sub-neg 90.9%

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

      11. distribute-neg-in 90.9%

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

      12. remove-double-neg 90.9%

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

      13. +-commutative 90.9%

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

      14. sub-neg 90.9%

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

   3. Simplified 90.9%

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

   if 3.40000000000000014e176 < t

   1. Initial program 44.6%

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

      1. sub-neg 44.6%

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

      2. distribute-frac-neg 44.6%

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

      3. distribute-rgt-neg-out 44.6%

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

      4. +-commutative 44.6%

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

      5. distribute-rgt-neg-out 44.6%

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

      6. distribute-lft-neg-in 44.6%

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

      7. associate-/l* 55.7%

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

      8. associate-/r/ 58.9%

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

      9. fma-def 58.9%

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

      10. sub-neg 58.9%

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

      11. distribute-neg-in 58.9%

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

      12. remove-double-neg 58.9%

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

      13. +-commutative 58.9%

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

      14. sub-neg 58.9%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in t around inf 59.0%

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

      1. associate-+r+ 75.7%

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

      2. distribute-rgt1-in 75.7%

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

      3. metadata-eval 75.7%

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

      4. mul0-lft 75.7%

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

      5. associate-/l* 92.6%

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

   6. Simplified 92.6%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+77}:\\ \;\;\;\;\left(x - \frac{a}{\frac{t}{y}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+176}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - z}{a - t}, y, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 2: 90.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+77}:\\ \;\;\;\;\left(x - \frac{a}{\frac{t}{y}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+176}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{t - z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4e+77)
   (+ (- x (/ a (/ t y))) (/ y (/ t z)))
   (if (<= t 2.8e+176)
     (+ (+ x y) (* y (/ (- t z) (- a t))))
     (+ x (/ y (/ t (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+77) {
		tmp = (x - (a / (t / y))) + (y / (t / z));
	} else if (t <= 2.8e+176) {
		tmp = (x + y) + (y * ((t - z) / (a - t)));
	} else {
		tmp = x + (y / (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4d+77)) then
        tmp = (x - (a / (t / y))) + (y / (t / z))
    else if (t <= 2.8d+176) then
        tmp = (x + y) + (y * ((t - z) / (a - t)))
    else
        tmp = x + (y / (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+77) {
		tmp = (x - (a / (t / y))) + (y / (t / z));
	} else if (t <= 2.8e+176) {
		tmp = (x + y) + (y * ((t - z) / (a - t)));
	} else {
		tmp = x + (y / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4e+77:
		tmp = (x - (a / (t / y))) + (y / (t / z))
	elif t <= 2.8e+176:
		tmp = (x + y) + (y * ((t - z) / (a - t)))
	else:
		tmp = x + (y / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4e+77)
		tmp = Float64(Float64(x - Float64(a / Float64(t / y))) + Float64(y / Float64(t / z)));
	elseif (t <= 2.8e+176)
		tmp = Float64(Float64(x + y) + Float64(y * Float64(Float64(t - z) / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4e+77)
		tmp = (x - (a / (t / y))) + (y / (t / z));
	elseif (t <= 2.8e+176)
		tmp = (x + y) + (y * ((t - z) / (a - t)));
	else
		tmp = x + (y / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4e+77], N[(N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+176], N[(N[(x + y), $MachinePrecision] + N[(y * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.99999999999999993e77

   1. Initial program 53.7%

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

      1. associate-*l/ 62.1%

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

   3. Simplified 62.1%

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

   4. Taylor expanded in t around inf 82.9%

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

      1. sub-neg 82.9%

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

      2. mul-1-neg 82.9%

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

      3. unsub-neg 82.9%

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

      4. associate-/l* 87.2%

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

      5. mul-1-neg 87.2%

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

      6. remove-double-neg 87.2%

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

      7. associate-/l* 89.2%

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

   6. Simplified 89.2%

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

   if -3.99999999999999993e77 < t < 2.8000000000000002e176

   1. Initial program 88.8%

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

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

   if 2.8000000000000002e176 < t

   1. Initial program 44.6%

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

      1. sub-neg 44.6%

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

      2. distribute-frac-neg 44.6%

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

      3. distribute-rgt-neg-out 44.6%

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

      4. +-commutative 44.6%

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

      5. distribute-rgt-neg-out 44.6%

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

      6. distribute-lft-neg-in 44.6%

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

      7. associate-/l* 55.7%

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

      8. associate-/r/ 58.9%

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

      9. fma-def 58.9%

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

      10. sub-neg 58.9%

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

      11. distribute-neg-in 58.9%

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

      12. remove-double-neg 58.9%

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

      13. +-commutative 58.9%

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

      14. sub-neg 58.9%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in t around inf 59.0%

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

      1. associate-+r+ 75.7%

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

      2. distribute-rgt1-in 75.7%

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

      3. metadata-eval 75.7%

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

      4. mul0-lft 75.7%

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

      5. associate-/l* 92.6%

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

   6. Simplified 92.6%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+77}:\\ \;\;\;\;\left(x - \frac{a}{\frac{t}{y}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+176}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{t - z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 3: 81.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.00115 \lor \neg \left(a \leq 9.2 \cdot 10^{-69}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.00115) (not (<= a 9.2e-69)))
   (- (+ x y) (/ y (/ a z)))
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.00115) || !(a <= 9.2e-69)) {
		tmp = (x + y) - (y / (a / z));
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-0.00115d0)) .or. (.not. (a <= 9.2d-69))) then
        tmp = (x + y) - (y / (a / z))
    else
        tmp = x + ((y * z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.00115) || !(a <= 9.2e-69)) {
		tmp = (x + y) - (y / (a / z));
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -0.00115) or not (a <= 9.2e-69):
		tmp = (x + y) - (y / (a / z))
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.00115) || !(a <= 9.2e-69))
		tmp = Float64(Float64(x + y) - Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -0.00115) || ~((a <= 9.2e-69)))
		tmp = (x + y) - (y / (a / z));
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.00115], N[Not[LessEqual[a, 9.2e-69]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.00115 or 9.2000000000000003e-69 < a

   1. Initial program 85.9%

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

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in t around 0 86.0%

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

      1. associate-/l* 89.2%

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

   6. Simplified 89.2%

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

   if -0.00115 < a < 9.2000000000000003e-69

   1. Initial program 64.8%

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

      1. sub-neg 64.8%

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

      2. distribute-frac-neg 64.8%

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

      3. distribute-rgt-neg-out 64.8%

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

      4. +-commutative 64.8%

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

      5. distribute-rgt-neg-out 64.8%

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

      6. distribute-lft-neg-in 64.8%

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

      7. associate-/l* 64.4%

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

      8. associate-/r/ 65.9%

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

      9. fma-def 65.9%

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

      10. sub-neg 65.9%

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

      11. distribute-neg-in 65.9%

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

      12. remove-double-neg 65.9%

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

      13. +-commutative 65.9%

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

      14. sub-neg 65.9%

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

   3. Simplified 65.9%

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

   4. Taylor expanded in t around inf 70.0%

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

      1. associate-+r+ 84.2%

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

      2. distribute-rgt1-in 84.2%

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

      3. metadata-eval 84.2%

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

      4. mul0-lft 84.2%

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

      5. associate-/l* 84.3%

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

   6. Simplified 84.3%

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

   7. Taylor expanded in a around 0 81.2%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00115 \lor \neg \left(a \leq 9.2 \cdot 10^{-69}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]

Alternative 4: 83.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.00105 \lor \neg \left(a \leq 2.7 \cdot 10^{+48}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.00105) (not (<= a 2.7e+48)))
   (- (+ x y) (/ y (/ a z)))
   (+ x (/ y (/ t (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.00105) || !(a <= 2.7e+48)) {
		tmp = (x + y) - (y / (a / z));
	} else {
		tmp = x + (y / (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-0.00105d0)) .or. (.not. (a <= 2.7d+48))) then
        tmp = (x + y) - (y / (a / z))
    else
        tmp = x + (y / (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.00105) || !(a <= 2.7e+48)) {
		tmp = (x + y) - (y / (a / z));
	} else {
		tmp = x + (y / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -0.00105) or not (a <= 2.7e+48):
		tmp = (x + y) - (y / (a / z))
	else:
		tmp = x + (y / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.00105) || !(a <= 2.7e+48))
		tmp = Float64(Float64(x + y) - Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -0.00105) || ~((a <= 2.7e+48)))
		tmp = (x + y) - (y / (a / z));
	else
		tmp = x + (y / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.00105], N[Not[LessEqual[a, 2.7e+48]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.00104999999999999994 or 2.70000000000000004e48 < a

   1. Initial program 87.6%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in t around 0 87.8%

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

      1. associate-/l* 91.2%

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

   6. Simplified 91.2%

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

   if -0.00104999999999999994 < a < 2.70000000000000004e48

   1. Initial program 64.8%

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

      1. sub-neg 64.8%

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

      2. distribute-frac-neg 64.8%

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

      3. distribute-rgt-neg-out 64.8%

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

      4. +-commutative 64.8%

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

      5. distribute-rgt-neg-out 64.8%

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

      6. distribute-lft-neg-in 64.8%

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

      7. associate-/l* 65.3%

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

      8. associate-/r/ 65.7%

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

      9. fma-def 65.8%

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

      10. sub-neg 65.8%

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

      11. distribute-neg-in 65.8%

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

      12. remove-double-neg 65.8%

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

      13. +-commutative 65.8%

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

      14. sub-neg 65.8%

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

   3. Simplified 65.8%

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

   4. Taylor expanded in t around inf 67.8%

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

      1. associate-+r+ 80.6%

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

      2. distribute-rgt1-in 80.6%

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

      3. metadata-eval 80.6%

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

      4. mul0-lft 80.6%

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

      5. associate-/l* 83.2%

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

   6. Simplified 83.2%

      \[\leadsto \color{blue}{x + \left(0 + \frac{y}{\frac{t}{z - a}}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00105 \lor \neg \left(a \leq 2.7 \cdot 10^{+48}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 5: 76.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+26} \lor \neg \left(a \leq 1.9 \cdot 10^{+80}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.6e+26) (not (<= a 1.9e+80))) (+ x y) (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.6e+26) || !(a <= 1.9e+80)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.6d+26)) .or. (.not. (a <= 1.9d+80))) then
        tmp = x + y
    else
        tmp = x + ((y * z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.6e+26) || !(a <= 1.9e+80)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.6e+26) or not (a <= 1.9e+80):
		tmp = x + y
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.6e+26) || !(a <= 1.9e+80))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.6e+26) || ~((a <= 1.9e+80)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.6e+26], N[Not[LessEqual[a, 1.9e+80]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.6000000000000001e26 or 1.89999999999999999e80 < a

   1. Initial program 89.2%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in a around inf 86.9%

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

      1. +-commutative 86.9%

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

   6. Simplified 86.9%

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

   if -4.6000000000000001e26 < a < 1.89999999999999999e80

   1. Initial program 66.4%

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

      1. sub-neg 66.4%

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

      2. distribute-frac-neg 66.4%

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

      3. distribute-rgt-neg-out 66.4%

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

      4. +-commutative 66.4%

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

      5. distribute-rgt-neg-out 66.4%

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

      6. distribute-lft-neg-in 66.4%

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

      7. associate-/l* 67.6%

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

      8. associate-/r/ 68.0%

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

      9. fma-def 68.0%

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

      10. sub-neg 68.0%

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

      11. distribute-neg-in 68.0%

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

      12. remove-double-neg 68.0%

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

      13. +-commutative 68.0%

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

      14. sub-neg 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in t around inf 64.0%

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

      1. associate-+r+ 75.9%

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

      2. distribute-rgt1-in 75.9%

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

      3. metadata-eval 75.9%

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

      4. mul0-lft 75.9%

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

      5. associate-/l* 78.1%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in a around 0 74.2%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+26} \lor \neg \left(a \leq 1.9 \cdot 10^{+80}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]

Alternative 6: 63.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-15} \lor \neg \left(a \leq 1.16 \cdot 10^{+80}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.6e-15) (not (<= a 1.16e+80))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.6e-15) || !(a <= 1.16e+80)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.6d-15)) .or. (.not. (a <= 1.16d+80))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.6e-15) || !(a <= 1.16e+80)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.6e-15) or not (a <= 1.16e+80):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.6e-15) || !(a <= 1.16e+80))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.6e-15) || ~((a <= 1.16e+80)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.6e-15], N[Not[LessEqual[a, 1.16e+80]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -3.6000000000000001e-15 or 1.15999999999999997e80 < a

   1. Initial program 89.0%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in a around inf 83.0%

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

      1. +-commutative 83.0%

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

   6. Simplified 83.0%

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

   if -3.6000000000000001e-15 < a < 1.15999999999999997e80

   1. Initial program 64.5%

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

      1. associate-*l/ 66.2%

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

   3. Simplified 66.2%

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

   4. Taylor expanded in x around inf 56.5%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-15} \lor \neg \left(a \leq 1.16 \cdot 10^{+80}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 52.1% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.2 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= y 7.2e+89) x y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 7.2e+89) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 7.2d+89) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 7.2e+89) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 7.2e+89:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 7.2e+89)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 7.2e+89)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 7.2e+89], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 7.2e89

   1. Initial program 82.1%

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

      1. associate-*l/ 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in x around inf 65.4%

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

   if 7.2e89 < y

   1. Initial program 57.7%

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

      1. associate-*l/ 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in x around 0 53.8%

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

      1. sub-neg 53.8%

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

      2. associate-*r/ 65.6%

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

      3. *-rgt-identity 65.6%

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

      4. distribute-rgt-neg-in 65.6%

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

      5. distribute-frac-neg 65.6%

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

      6. distribute-lft-in 65.6%

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

      7. distribute-frac-neg 65.6%

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

      8. sub-neg 65.6%

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

   6. Simplified 65.6%

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

   7. Taylor expanded in a around inf 39.9%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.2 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 2.7% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 77.5%

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

   1. sub-neg 77.5%

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

   2. distribute-frac-neg 77.5%

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

   3. distribute-rgt-neg-out 77.5%

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

   4. +-commutative 77.5%

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

   5. distribute-rgt-neg-out 77.5%

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

   6. distribute-lft-neg-in 77.5%

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

   7. associate-/l* 81.7%

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

   8. associate-/r/ 82.1%

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

   9. fma-def 82.1%

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

   10. sub-neg 82.1%

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

   11. distribute-neg-in 82.1%

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

   12. remove-double-neg 82.1%

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

   13. +-commutative 82.1%

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

   14. sub-neg 82.1%

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

3. Simplified 82.1%

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

4. Taylor expanded in x around 0 33.1%

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

   1. associate-/l* 36.6%

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

   2. +-commutative 36.6%

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

   3. associate-/r/ 36.0%

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

   4. fma-def 36.3%

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

6. Simplified 36.3%

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

7. Taylor expanded in t around inf 2.7%

   \[\leadsto \color{blue}{y + -1 \cdot y} \]
8. Step-by-step derivation

   1. distribute-rgt1-in 2.7%

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

   2. metadata-eval 2.7%

      \[\leadsto \color{blue}{0} \cdot y \]

   3. mul0-lft 2.7%

      \[\leadsto \color{blue}{0} \]

9. Simplified 2.7%

   \[\leadsto \color{blue}{0} \]

10. Final simplification 2.7%

    \[\leadsto 0 \]

Alternative 9: 51.3% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.5%

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

   1. associate-*l/ 82.1%

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

3. Simplified 82.1%

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

4. Taylor expanded in x around inf 57.1%

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

5. Final simplification 57.1%

   \[\leadsto x \]

Developer target: 88.3% 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 2023322 
(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))))