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

Percentage Accurate: 77.6% → 86.2%

Time: 15.8s

Alternatives: 17

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: 86.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;x + \left(y - \frac{z - t}{\frac{a - t}{y}}\right)\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-124}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-123}:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.7e+53)
   (+ x (- y (/ (- z t) (/ (- a t) y))))
   (if (<= a -3.4e+42)
     (* y (- (/ z t) (/ a t)))
     (if (<= a -3e-124)
       (- x (/ (* y z) (- a t)))
       (if (<= a 2.7e-123)
         (+ (- x (/ y (/ t a))) (/ y (/ t z)))
         (+ x (- y (/ y (/ (- a t) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e+53) {
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	} else if (a <= -3.4e+42) {
		tmp = y * ((z / t) - (a / t));
	} else if (a <= -3e-124) {
		tmp = x - ((y * z) / (a - t));
	} else if (a <= 2.7e-123) {
		tmp = (x - (y / (t / a))) + (y / (t / z));
	} else {
		tmp = x + (y - (y / ((a - t) / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.7d+53)) then
        tmp = x + (y - ((z - t) / ((a - t) / y)))
    else if (a <= (-3.4d+42)) then
        tmp = y * ((z / t) - (a / t))
    else if (a <= (-3d-124)) then
        tmp = x - ((y * z) / (a - t))
    else if (a <= 2.7d-123) then
        tmp = (x - (y / (t / a))) + (y / (t / z))
    else
        tmp = x + (y - (y / ((a - t) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e+53) {
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	} else if (a <= -3.4e+42) {
		tmp = y * ((z / t) - (a / t));
	} else if (a <= -3e-124) {
		tmp = x - ((y * z) / (a - t));
	} else if (a <= 2.7e-123) {
		tmp = (x - (y / (t / a))) + (y / (t / z));
	} else {
		tmp = x + (y - (y / ((a - t) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.7e+53:
		tmp = x + (y - ((z - t) / ((a - t) / y)))
	elif a <= -3.4e+42:
		tmp = y * ((z / t) - (a / t))
	elif a <= -3e-124:
		tmp = x - ((y * z) / (a - t))
	elif a <= 2.7e-123:
		tmp = (x - (y / (t / a))) + (y / (t / z))
	else:
		tmp = x + (y - (y / ((a - t) / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.7e+53)
		tmp = Float64(x + Float64(y - Float64(Float64(z - t) / Float64(Float64(a - t) / y))));
	elseif (a <= -3.4e+42)
		tmp = Float64(y * Float64(Float64(z / t) - Float64(a / t)));
	elseif (a <= -3e-124)
		tmp = Float64(x - Float64(Float64(y * z) / Float64(a - t)));
	elseif (a <= 2.7e-123)
		tmp = Float64(Float64(x - Float64(y / Float64(t / a))) + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + Float64(y - Float64(y / Float64(Float64(a - t) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.7e+53)
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	elseif (a <= -3.4e+42)
		tmp = y * ((z / t) - (a / t));
	elseif (a <= -3e-124)
		tmp = x - ((y * z) / (a - t));
	elseif (a <= 2.7e-123)
		tmp = (x - (y / (t / a))) + (y / (t / z));
	else
		tmp = x + (y - (y / ((a - t) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.7e+53], N[(x + N[(y - N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.4e+42], N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3e-124], N[(x - N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-123], N[(N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.7e53

   1. Initial program 83.5%

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

      1. associate--l+ 83.6%

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

      2. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   if -3.7e53 < a < -3.39999999999999975e42

   1. Initial program 34.5%

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

      1. associate--l+ 34.3%

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

      2. associate-/l* 19.9%

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

   3. Simplified 19.9%

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

   4. Taylor expanded in t around -inf 83.1%

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

      1. +-commutative 83.1%

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

      2. sub-neg 83.1%

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

      3. mul-1-neg 83.1%

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

      4. +-commutative 83.1%

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

      5. *-commutative 83.1%

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

      6. +-commutative 83.1%

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

      7. *-commutative 83.1%

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

      8. mul-1-neg 83.1%

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

      9. unsub-neg 83.1%

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

      10. mul-1-neg 83.1%

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

      11. sub-neg 83.1%

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

      12. distribute-lft-out-- 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around inf 100.0%

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

   if -3.39999999999999975e42 < a < -3e-124

   1. Initial program 78.9%

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

      1. associate--l+ 83.6%

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

      2. sub-neg 83.6%

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

      3. +-commutative 83.6%

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

      4. associate-/l* 83.8%

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

      5. distribute-neg-frac 83.8%

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

      6. associate-/r/ 88.2%

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

      7. fma-def 88.1%

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

      8. sub-neg 88.1%

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

      9. +-commutative 88.1%

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

      10. distribute-neg-in 88.1%

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

      11. unsub-neg 88.1%

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

      12. remove-double-neg 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in z around inf 90.2%

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

      1. associate-*r/ 90.2%

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

      2. associate-*r* 90.2%

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

      3. neg-mul-1 90.2%

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

   6. Simplified 90.2%

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

   if -3e-124 < a < 2.7000000000000001e-123

   1. Initial program 58.3%

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

      1. associate--l+ 62.6%

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

      2. associate-/l* 68.5%

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

   3. Simplified 68.5%

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

   4. Taylor expanded in t around inf 87.8%

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

      1. sub-neg 87.8%

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

      2. +-commutative 87.8%

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

      3. mul-1-neg 87.8%

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

      4. unsub-neg 87.8%

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

      5. associate-/l* 87.9%

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

      6. mul-1-neg 87.9%

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

      7. remove-double-neg 87.9%

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

      8. associate-/l* 91.7%

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

   6. Simplified 91.7%

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

   if 2.7000000000000001e-123 < a

   1. Initial program 85.6%

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

      1. associate--l+ 85.7%

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

      2. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around inf 86.9%

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

      1. associate-/l* 94.8%

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

   6. Simplified 94.8%

      \[\leadsto x + \left(y - \color{blue}{\frac{y}{\frac{a - t}{z}}}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;x + \left(y - \frac{z - t}{\frac{a - t}{y}}\right)\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-124}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-123}:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \end{array} \]

Alternative 2: 92.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-231} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (/ (* y (- t z)) (- a t)))))
   (if (or (<= t_1 -2e-231) (not (<= t_1 0.0)))
     (+ x (fma (/ (- t z) (- a t)) y y))
     (+ (- x (/ y (/ t a))) (/ y (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((y * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-231) || !(t_1 <= 0.0)) {
		tmp = x + fma(((t - z) / (a - t)), y, y);
	} else {
		tmp = (x - (y / (t / a))) + (y / (t / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) + Float64(Float64(y * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -2e-231) || !(t_1 <= 0.0))
		tmp = Float64(x + fma(Float64(Float64(t - z) / Float64(a - t)), y, y));
	else
		tmp = Float64(Float64(x - Float64(y / Float64(t / a))) + Float64(y / Float64(t / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-231], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * y + y), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -2e-231 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   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+ 82.1%

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

      2. sub-neg 82.1%

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

      3. +-commutative 82.1%

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

      4. associate-/l* 89.7%

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

      5. distribute-neg-frac 89.7%

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

      6. associate-/r/ 92.5%

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

      7. fma-def 92.4%

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

      8. sub-neg 92.4%

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

      9. +-commutative 92.4%

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

      10. distribute-neg-in 92.4%

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

      11. unsub-neg 92.4%

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

      12. remove-double-neg 92.4%

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

   3. Simplified 92.4%

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

   if -2e-231 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 8.3%

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

      1. associate--l+ 30.6%

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

      2. associate-/l* 22.3%

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

   3. Simplified 22.3%

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

   4. Taylor expanded in t around inf 96.7%

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

      1. sub-neg 96.7%

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

      2. +-commutative 96.7%

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

      3. mul-1-neg 96.7%

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

      4. unsub-neg 96.7%

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

      5. associate-/l* 96.7%

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

      6. mul-1-neg 96.7%

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

      7. remove-double-neg 96.7%

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

      8. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-231} \lor \neg \left(\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 3: 86.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;x + \left(y - \frac{z - t}{\frac{a - t}{y}}\right)\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-124}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.7e+53)
   (+ x (- y (/ (- z t) (/ (- a t) y))))
   (if (<= a -3.4e+42)
     (* y (- (/ z t) (/ a t)))
     (if (<= a -2.8e-124)
       (- x (/ (* y z) (- a t)))
       (if (<= a 4.1e-123)
         (+ x (/ (* y (- z a)) t))
         (+ x (- y (/ y (/ (- a t) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e+53) {
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	} else if (a <= -3.4e+42) {
		tmp = y * ((z / t) - (a / t));
	} else if (a <= -2.8e-124) {
		tmp = x - ((y * z) / (a - t));
	} else if (a <= 4.1e-123) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = x + (y - (y / ((a - t) / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.7d+53)) then
        tmp = x + (y - ((z - t) / ((a - t) / y)))
    else if (a <= (-3.4d+42)) then
        tmp = y * ((z / t) - (a / t))
    else if (a <= (-2.8d-124)) then
        tmp = x - ((y * z) / (a - t))
    else if (a <= 4.1d-123) then
        tmp = x + ((y * (z - a)) / t)
    else
        tmp = x + (y - (y / ((a - t) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e+53) {
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	} else if (a <= -3.4e+42) {
		tmp = y * ((z / t) - (a / t));
	} else if (a <= -2.8e-124) {
		tmp = x - ((y * z) / (a - t));
	} else if (a <= 4.1e-123) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = x + (y - (y / ((a - t) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.7e+53:
		tmp = x + (y - ((z - t) / ((a - t) / y)))
	elif a <= -3.4e+42:
		tmp = y * ((z / t) - (a / t))
	elif a <= -2.8e-124:
		tmp = x - ((y * z) / (a - t))
	elif a <= 4.1e-123:
		tmp = x + ((y * (z - a)) / t)
	else:
		tmp = x + (y - (y / ((a - t) / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.7e+53)
		tmp = Float64(x + Float64(y - Float64(Float64(z - t) / Float64(Float64(a - t) / y))));
	elseif (a <= -3.4e+42)
		tmp = Float64(y * Float64(Float64(z / t) - Float64(a / t)));
	elseif (a <= -2.8e-124)
		tmp = Float64(x - Float64(Float64(y * z) / Float64(a - t)));
	elseif (a <= 4.1e-123)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	else
		tmp = Float64(x + Float64(y - Float64(y / Float64(Float64(a - t) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.7e+53)
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	elseif (a <= -3.4e+42)
		tmp = y * ((z / t) - (a / t));
	elseif (a <= -2.8e-124)
		tmp = x - ((y * z) / (a - t));
	elseif (a <= 4.1e-123)
		tmp = x + ((y * (z - a)) / t);
	else
		tmp = x + (y - (y / ((a - t) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.7e+53], N[(x + N[(y - N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.4e+42], N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.8e-124], N[(x - N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.1e-123], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.7e53

   1. Initial program 83.5%

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

      1. associate--l+ 83.6%

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

      2. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   if -3.7e53 < a < -3.39999999999999975e42

   1. Initial program 34.5%

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

      1. associate--l+ 34.3%

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

      2. associate-/l* 19.9%

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

   3. Simplified 19.9%

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

   4. Taylor expanded in t around -inf 83.1%

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

      1. +-commutative 83.1%

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

      2. sub-neg 83.1%

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

      3. mul-1-neg 83.1%

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

      4. +-commutative 83.1%

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

      5. *-commutative 83.1%

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

      6. +-commutative 83.1%

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

      7. *-commutative 83.1%

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

      8. mul-1-neg 83.1%

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

      9. unsub-neg 83.1%

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

      10. mul-1-neg 83.1%

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

      11. sub-neg 83.1%

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

      12. distribute-lft-out-- 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around inf 100.0%

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

   if -3.39999999999999975e42 < a < -2.79999999999999998e-124

   1. Initial program 78.9%

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

      1. associate--l+ 83.6%

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

      2. sub-neg 83.6%

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

      3. +-commutative 83.6%

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

      4. associate-/l* 83.8%

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

      5. distribute-neg-frac 83.8%

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

      6. associate-/r/ 88.2%

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

      7. fma-def 88.1%

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

      8. sub-neg 88.1%

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

      9. +-commutative 88.1%

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

      10. distribute-neg-in 88.1%

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

      11. unsub-neg 88.1%

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

      12. remove-double-neg 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in z around inf 90.2%

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

      1. associate-*r/ 90.2%

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

      2. associate-*r* 90.2%

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

      3. neg-mul-1 90.2%

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

   6. Simplified 90.2%

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

   if -2.79999999999999998e-124 < a < 4.1e-123

   1. Initial program 58.3%

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

      1. associate--l+ 62.6%

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

      2. associate-/l* 68.5%

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

   3. Simplified 68.5%

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

   4. Taylor expanded in t around -inf 87.8%

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

      1. +-commutative 87.8%

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

      2. sub-neg 87.8%

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

      3. mul-1-neg 87.8%

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

      4. +-commutative 87.8%

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

      5. *-commutative 87.8%

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

      6. +-commutative 87.8%

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

      7. *-commutative 87.8%

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

      8. mul-1-neg 87.8%

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

      9. unsub-neg 87.8%

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

      10. mul-1-neg 87.8%

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

      11. sub-neg 87.8%

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

      12. distribute-lft-out-- 87.8%

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

   6. Simplified 87.8%

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

   if 4.1e-123 < a

   1. Initial program 85.6%

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

      1. associate--l+ 85.7%

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

      2. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around inf 86.9%

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

      1. associate-/l* 94.8%

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

   6. Simplified 94.8%

      \[\leadsto x + \left(y - \color{blue}{\frac{y}{\frac{a - t}{z}}}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;x + \left(y - \frac{z - t}{\frac{a - t}{y}}\right)\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-124}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \end{array} \]

Alternative 4: 80.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-84} \lor \neg \left(a \leq 1.45 \cdot 10^{-143}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (- x (/ y (/ a z))))))
   (if (<= a -3.7e+53)
     t_1
     (if (<= a -3.4e+42)
       (* y (- (/ z t) (/ a t)))
       (if (or (<= a -7.2e-84) (not (<= a 1.45e-143)))
         t_1
         (+ x (/ y (/ t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x - (y / (a / z)));
	double tmp;
	if (a <= -3.7e+53) {
		tmp = t_1;
	} else if (a <= -3.4e+42) {
		tmp = y * ((z / t) - (a / t));
	} else if ((a <= -7.2e-84) || !(a <= 1.45e-143)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y + (x - (y / (a / z)))
    if (a <= (-3.7d+53)) then
        tmp = t_1
    else if (a <= (-3.4d+42)) then
        tmp = y * ((z / t) - (a / t))
    else if ((a <= (-7.2d-84)) .or. (.not. (a <= 1.45d-143))) then
        tmp = t_1
    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 t_1 = y + (x - (y / (a / z)));
	double tmp;
	if (a <= -3.7e+53) {
		tmp = t_1;
	} else if (a <= -3.4e+42) {
		tmp = y * ((z / t) - (a / t));
	} else if ((a <= -7.2e-84) || !(a <= 1.45e-143)) {
		tmp = t_1;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (x - (y / (a / z)))
	tmp = 0
	if a <= -3.7e+53:
		tmp = t_1
	elif a <= -3.4e+42:
		tmp = y * ((z / t) - (a / t))
	elif (a <= -7.2e-84) or not (a <= 1.45e-143):
		tmp = t_1
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(x - Float64(y / Float64(a / z))))
	tmp = 0.0
	if (a <= -3.7e+53)
		tmp = t_1;
	elseif (a <= -3.4e+42)
		tmp = Float64(y * Float64(Float64(z / t) - Float64(a / t)));
	elseif ((a <= -7.2e-84) || !(a <= 1.45e-143))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (x - (y / (a / z)));
	tmp = 0.0;
	if (a <= -3.7e+53)
		tmp = t_1;
	elseif (a <= -3.4e+42)
		tmp = y * ((z / t) - (a / t));
	elseif ((a <= -7.2e-84) || ~((a <= 1.45e-143)))
		tmp = t_1;
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.7e+53], t$95$1, If[LessEqual[a, -3.4e+42], N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -7.2e-84], N[Not[LessEqual[a, 1.45e-143]], $MachinePrecision]], t$95$1, N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.7e53 or -3.39999999999999975e42 < a < -7.20000000000000007e-84 or 1.45e-143 < a

   1. Initial program 83.2%

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

      1. associate--l+ 84.3%

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

      2. sub-neg 84.3%

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

      3. +-commutative 84.3%

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

      4. associate-/l* 90.9%

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

      5. distribute-neg-frac 90.9%

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

      6. associate-/r/ 92.9%

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

      7. fma-def 92.9%

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

      8. sub-neg 92.9%

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

      9. +-commutative 92.9%

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

      10. distribute-neg-in 92.9%

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

      11. unsub-neg 92.9%

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

      12. remove-double-neg 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in t around 0 81.6%

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

      1. mul-1-neg 81.6%

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

      2. sub-neg 81.6%

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

      3. associate-/l* 85.7%

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

   6. Simplified 85.7%

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

   if -3.7e53 < a < -3.39999999999999975e42

   1. Initial program 34.5%

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

      1. associate--l+ 34.3%

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

      2. associate-/l* 19.9%

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

   3. Simplified 19.9%

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

   4. Taylor expanded in t around -inf 83.1%

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

      1. +-commutative 83.1%

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

      2. sub-neg 83.1%

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

      3. mul-1-neg 83.1%

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

      4. +-commutative 83.1%

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

      5. *-commutative 83.1%

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

      6. +-commutative 83.1%

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

      7. *-commutative 83.1%

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

      8. mul-1-neg 83.1%

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

      9. unsub-neg 83.1%

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

      10. mul-1-neg 83.1%

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

      11. sub-neg 83.1%

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

      12. distribute-lft-out-- 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around inf 100.0%

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

   if -7.20000000000000007e-84 < a < 1.45e-143

   1. Initial program 60.6%

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

      1. associate--l+ 64.8%

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

      2. sub-neg 64.8%

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

      3. +-commutative 64.8%

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

      4. associate-/l* 71.9%

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

      5. distribute-neg-frac 71.9%

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

      6. associate-/r/ 76.9%

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

      7. fma-def 76.9%

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

      8. sub-neg 76.9%

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

      9. +-commutative 76.9%

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

      10. distribute-neg-in 76.9%

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

      11. unsub-neg 76.9%

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

      12. remove-double-neg 76.9%

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

   3. Simplified 76.9%

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

      1. add-cube-cbrt 75.7%

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

      2. pow3 75.7%

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

      3. +-commutative 75.7%

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

   5. Applied egg-rr 75.7%

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

   6. Taylor expanded in y around 0 95.5%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right)} + x}\right)}^{3} \]
   7. Step-by-step derivation

      1. associate--l+ 75.7%

         \[\leadsto {\left(\sqrt[3]{y \cdot \color{blue}{\left(1 + \left(\frac{t}{a - t} - \frac{z}{a - t}\right)\right)} + x}\right)}^{3} \]

      2. div-sub 75.7%

         \[\leadsto {\left(\sqrt[3]{y \cdot \left(1 + \color{blue}{\frac{t - z}{a - t}}\right) + x}\right)}^{3} \]

   8. Simplified 75.7%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \left(1 + \frac{t - z}{a - t}\right)} + x}\right)}^{3} \]

   9. Taylor expanded in a around 0 84.9%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(\frac{y \cdot z}{t} + x\right)} \]
   10. Step-by-step derivation

       1. pow-base-1 84.9%

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

       2. *-lft-identity 84.9%

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

       3. +-commutative 84.9%

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

       4. associate-/l* 89.9%

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

   11. Simplified 89.9%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-84} \lor \neg \left(a \leq 1.45 \cdot 10^{-143}\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 5: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-82} \lor \neg \left(a \leq 4.1 \cdot 10^{-123}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (- x (/ y (/ a z))))))
   (if (<= a -3.7e+53)
     t_1
     (if (<= a -3.4e+42)
       (* y (- (/ z t) (/ a t)))
       (if (or (<= a -1.12e-82) (not (<= a 4.1e-123)))
         t_1
         (+ x (/ (* y (- z a)) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x - (y / (a / z)));
	double tmp;
	if (a <= -3.7e+53) {
		tmp = t_1;
	} else if (a <= -3.4e+42) {
		tmp = y * ((z / t) - (a / t));
	} else if ((a <= -1.12e-82) || !(a <= 4.1e-123)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y + (x - (y / (a / z)))
    if (a <= (-3.7d+53)) then
        tmp = t_1
    else if (a <= (-3.4d+42)) then
        tmp = y * ((z / t) - (a / t))
    else if ((a <= (-1.12d-82)) .or. (.not. (a <= 4.1d-123))) then
        tmp = t_1
    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 t_1 = y + (x - (y / (a / z)));
	double tmp;
	if (a <= -3.7e+53) {
		tmp = t_1;
	} else if (a <= -3.4e+42) {
		tmp = y * ((z / t) - (a / t));
	} else if ((a <= -1.12e-82) || !(a <= 4.1e-123)) {
		tmp = t_1;
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (x - (y / (a / z)))
	tmp = 0
	if a <= -3.7e+53:
		tmp = t_1
	elif a <= -3.4e+42:
		tmp = y * ((z / t) - (a / t))
	elif (a <= -1.12e-82) or not (a <= 4.1e-123):
		tmp = t_1
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(x - Float64(y / Float64(a / z))))
	tmp = 0.0
	if (a <= -3.7e+53)
		tmp = t_1;
	elseif (a <= -3.4e+42)
		tmp = Float64(y * Float64(Float64(z / t) - Float64(a / t)));
	elseif ((a <= -1.12e-82) || !(a <= 4.1e-123))
		tmp = t_1;
	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)
	t_1 = y + (x - (y / (a / z)));
	tmp = 0.0;
	if (a <= -3.7e+53)
		tmp = t_1;
	elseif (a <= -3.4e+42)
		tmp = y * ((z / t) - (a / t));
	elseif ((a <= -1.12e-82) || ~((a <= 4.1e-123)))
		tmp = t_1;
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.7e+53], t$95$1, If[LessEqual[a, -3.4e+42], N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -1.12e-82], N[Not[LessEqual[a, 4.1e-123]], $MachinePrecision]], t$95$1, N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.7e53 or -3.39999999999999975e42 < a < -1.12e-82 or 4.1e-123 < a

   1. Initial program 84.2%

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

      1. associate--l+ 85.3%

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

      2. sub-neg 85.3%

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

      3. +-commutative 85.3%

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

      4. associate-/l* 92.2%

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

      5. distribute-neg-frac 92.2%

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

      6. associate-/r/ 94.8%

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

      7. fma-def 94.8%

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

      8. sub-neg 94.8%

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

      9. +-commutative 94.8%

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

      10. distribute-neg-in 94.8%

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

      11. unsub-neg 94.8%

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

      12. remove-double-neg 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in t around 0 83.1%

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

      1. mul-1-neg 83.1%

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

      2. sub-neg 83.1%

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

      3. associate-/l* 87.4%

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

   6. Simplified 87.4%

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

   if -3.7e53 < a < -3.39999999999999975e42

   1. Initial program 34.5%

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

      1. associate--l+ 34.3%

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

      2. associate-/l* 19.9%

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

   3. Simplified 19.9%

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

   4. Taylor expanded in t around -inf 83.1%

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

      1. +-commutative 83.1%

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

      2. sub-neg 83.1%

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

      3. mul-1-neg 83.1%

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

      4. +-commutative 83.1%

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

      5. *-commutative 83.1%

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

      6. +-commutative 83.1%

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

      7. *-commutative 83.1%

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

      8. mul-1-neg 83.1%

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

      9. unsub-neg 83.1%

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

      10. mul-1-neg 83.1%

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

      11. sub-neg 83.1%

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

      12. distribute-lft-out-- 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around inf 100.0%

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

   if -1.12e-82 < a < 4.1e-123

   1. Initial program 60.4%

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

      1. associate--l+ 64.2%

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

      2. associate-/l* 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in t around -inf 87.5%

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

      1. +-commutative 87.5%

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

      2. sub-neg 87.5%

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

      3. mul-1-neg 87.5%

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

      4. +-commutative 87.5%

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

      5. *-commutative 87.5%

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

      6. +-commutative 87.5%

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

      7. *-commutative 87.5%

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

      8. mul-1-neg 87.5%

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

      9. unsub-neg 87.5%

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

      10. mul-1-neg 87.5%

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

      11. sub-neg 87.5%

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

      12. distribute-lft-out-- 87.5%

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

   6. Simplified 87.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-82} \lor \neg \left(a \leq 4.1 \cdot 10^{-123}\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]

Alternative 6: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-83}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (- x (/ y (/ a z))))))
   (if (<= a -3.7e+53)
     t_1
     (if (<= a -3.4e+42)
       (* y (- (/ z t) (/ a t)))
       (if (<= a -6.2e-83)
         (- (+ x y) (* y (/ z a)))
         (if (<= a 4.1e-123) (+ x (/ (* y (- z a)) t)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x - (y / (a / z)));
	double tmp;
	if (a <= -3.7e+53) {
		tmp = t_1;
	} else if (a <= -3.4e+42) {
		tmp = y * ((z / t) - (a / t));
	} else if (a <= -6.2e-83) {
		tmp = (x + y) - (y * (z / a));
	} else if (a <= 4.1e-123) {
		tmp = x + ((y * (z - 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) :: tmp
    t_1 = y + (x - (y / (a / z)))
    if (a <= (-3.7d+53)) then
        tmp = t_1
    else if (a <= (-3.4d+42)) then
        tmp = y * ((z / t) - (a / t))
    else if (a <= (-6.2d-83)) then
        tmp = (x + y) - (y * (z / a))
    else if (a <= 4.1d-123) then
        tmp = x + ((y * (z - 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 - (y / (a / z)));
	double tmp;
	if (a <= -3.7e+53) {
		tmp = t_1;
	} else if (a <= -3.4e+42) {
		tmp = y * ((z / t) - (a / t));
	} else if (a <= -6.2e-83) {
		tmp = (x + y) - (y * (z / a));
	} else if (a <= 4.1e-123) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (x - (y / (a / z)))
	tmp = 0
	if a <= -3.7e+53:
		tmp = t_1
	elif a <= -3.4e+42:
		tmp = y * ((z / t) - (a / t))
	elif a <= -6.2e-83:
		tmp = (x + y) - (y * (z / a))
	elif a <= 4.1e-123:
		tmp = x + ((y * (z - a)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(x - Float64(y / Float64(a / z))))
	tmp = 0.0
	if (a <= -3.7e+53)
		tmp = t_1;
	elseif (a <= -3.4e+42)
		tmp = Float64(y * Float64(Float64(z / t) - Float64(a / t)));
	elseif (a <= -6.2e-83)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	elseif (a <= 4.1e-123)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (x - (y / (a / z)));
	tmp = 0.0;
	if (a <= -3.7e+53)
		tmp = t_1;
	elseif (a <= -3.4e+42)
		tmp = y * ((z / t) - (a / t));
	elseif (a <= -6.2e-83)
		tmp = (x + y) - (y * (z / a));
	elseif (a <= 4.1e-123)
		tmp = x + ((y * (z - a)) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.7e+53], t$95$1, If[LessEqual[a, -3.4e+42], N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.2e-83], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.1e-123], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.7e53 or 4.1e-123 < a

   1. Initial program 84.9%

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

      1. associate--l+ 85.0%

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

      2. sub-neg 85.0%

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

      3. +-commutative 85.0%

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

      4. associate-/l* 94.0%

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

      5. distribute-neg-frac 94.0%

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

      6. associate-/r/ 96.5%

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

      7. fma-def 96.5%

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

      8. sub-neg 96.5%

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

      9. +-commutative 96.5%

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

      10. distribute-neg-in 96.5%

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

      11. unsub-neg 96.5%

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

      12. remove-double-neg 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in t around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. sub-neg 84.6%

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

      3. associate-/l* 90.5%

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

   6. Simplified 90.5%

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

   if -3.7e53 < a < -3.39999999999999975e42

   1. Initial program 34.5%

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

      1. associate--l+ 34.3%

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

      2. associate-/l* 19.9%

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

   3. Simplified 19.9%

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

   4. Taylor expanded in t around -inf 83.1%

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

      1. +-commutative 83.1%

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

      2. sub-neg 83.1%

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

      3. mul-1-neg 83.1%

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

      4. +-commutative 83.1%

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

      5. *-commutative 83.1%

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

      6. +-commutative 83.1%

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

      7. *-commutative 83.1%

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

      8. mul-1-neg 83.1%

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

      9. unsub-neg 83.1%

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

      10. mul-1-neg 83.1%

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

      11. sub-neg 83.1%

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

      12. distribute-lft-out-- 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around inf 100.0%

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

   if -3.39999999999999975e42 < a < -6.19999999999999985e-83

   1. Initial program 80.9%

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

      1. associate-*l/ 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in t around 0 72.8%

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

   if -6.19999999999999985e-83 < a < 4.1e-123

   1. Initial program 60.4%

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

      1. associate--l+ 64.2%

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

      2. associate-/l* 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in t around -inf 87.5%

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

      1. +-commutative 87.5%

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

      2. sub-neg 87.5%

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

      3. mul-1-neg 87.5%

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

      4. +-commutative 87.5%

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

      5. *-commutative 87.5%

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

      6. +-commutative 87.5%

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

      7. *-commutative 87.5%

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

      8. mul-1-neg 87.5%

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

      9. unsub-neg 87.5%

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

      10. mul-1-neg 87.5%

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

      11. sub-neg 87.5%

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

      12. distribute-lft-out-- 87.5%

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

   6. Simplified 87.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-83}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \end{array} \]

Alternative 7: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-82}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (- x (/ y (/ a z))))))
   (if (<= a -3.7e+53)
     t_1
     (if (<= a -3.4e+42)
       (* y (- (/ z t) (/ a t)))
       (if (<= a -1.22e-82)
         (- (+ x y) (/ (* y z) a))
         (if (<= a 4.1e-123) (+ x (/ (* y (- z a)) t)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x - (y / (a / z)));
	double tmp;
	if (a <= -3.7e+53) {
		tmp = t_1;
	} else if (a <= -3.4e+42) {
		tmp = y * ((z / t) - (a / t));
	} else if (a <= -1.22e-82) {
		tmp = (x + y) - ((y * z) / a);
	} else if (a <= 4.1e-123) {
		tmp = x + ((y * (z - 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) :: tmp
    t_1 = y + (x - (y / (a / z)))
    if (a <= (-3.7d+53)) then
        tmp = t_1
    else if (a <= (-3.4d+42)) then
        tmp = y * ((z / t) - (a / t))
    else if (a <= (-1.22d-82)) then
        tmp = (x + y) - ((y * z) / a)
    else if (a <= 4.1d-123) then
        tmp = x + ((y * (z - 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 - (y / (a / z)));
	double tmp;
	if (a <= -3.7e+53) {
		tmp = t_1;
	} else if (a <= -3.4e+42) {
		tmp = y * ((z / t) - (a / t));
	} else if (a <= -1.22e-82) {
		tmp = (x + y) - ((y * z) / a);
	} else if (a <= 4.1e-123) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (x - (y / (a / z)))
	tmp = 0
	if a <= -3.7e+53:
		tmp = t_1
	elif a <= -3.4e+42:
		tmp = y * ((z / t) - (a / t))
	elif a <= -1.22e-82:
		tmp = (x + y) - ((y * z) / a)
	elif a <= 4.1e-123:
		tmp = x + ((y * (z - a)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(x - Float64(y / Float64(a / z))))
	tmp = 0.0
	if (a <= -3.7e+53)
		tmp = t_1;
	elseif (a <= -3.4e+42)
		tmp = Float64(y * Float64(Float64(z / t) - Float64(a / t)));
	elseif (a <= -1.22e-82)
		tmp = Float64(Float64(x + y) - Float64(Float64(y * z) / a));
	elseif (a <= 4.1e-123)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (x - (y / (a / z)));
	tmp = 0.0;
	if (a <= -3.7e+53)
		tmp = t_1;
	elseif (a <= -3.4e+42)
		tmp = y * ((z / t) - (a / t));
	elseif (a <= -1.22e-82)
		tmp = (x + y) - ((y * z) / a);
	elseif (a <= 4.1e-123)
		tmp = x + ((y * (z - a)) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.7e+53], t$95$1, If[LessEqual[a, -3.4e+42], N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.22e-82], N[(N[(x + y), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.1e-123], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.7e53 or 4.1e-123 < a

   1. Initial program 84.9%

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

      1. associate--l+ 85.0%

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

      2. sub-neg 85.0%

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

      3. +-commutative 85.0%

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

      4. associate-/l* 94.0%

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

      5. distribute-neg-frac 94.0%

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

      6. associate-/r/ 96.5%

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

      7. fma-def 96.5%

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

      8. sub-neg 96.5%

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

      9. +-commutative 96.5%

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

      10. distribute-neg-in 96.5%

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

      11. unsub-neg 96.5%

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

      12. remove-double-neg 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in t around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. sub-neg 84.6%

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

      3. associate-/l* 90.5%

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

   6. Simplified 90.5%

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

   if -3.7e53 < a < -3.39999999999999975e42

   1. Initial program 34.5%

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

      1. associate--l+ 34.3%

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

      2. associate-/l* 19.9%

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

   3. Simplified 19.9%

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

   4. Taylor expanded in t around -inf 83.1%

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

      1. +-commutative 83.1%

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

      2. sub-neg 83.1%

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

      3. mul-1-neg 83.1%

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

      4. +-commutative 83.1%

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

      5. *-commutative 83.1%

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

      6. +-commutative 83.1%

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

      7. *-commutative 83.1%

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

      8. mul-1-neg 83.1%

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

      9. unsub-neg 83.1%

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

      10. mul-1-neg 83.1%

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

      11. sub-neg 83.1%

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

      12. distribute-lft-out-- 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around inf 100.0%

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

   if -3.39999999999999975e42 < a < -1.22000000000000001e-82

   1. Initial program 80.9%

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

      1. associate--l+ 87.1%

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

      2. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in t around 0 75.9%

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

   if -1.22000000000000001e-82 < a < 4.1e-123

   1. Initial program 60.4%

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

      1. associate--l+ 64.2%

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

      2. associate-/l* 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in t around -inf 87.5%

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

      1. +-commutative 87.5%

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

      2. sub-neg 87.5%

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

      3. mul-1-neg 87.5%

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

      4. +-commutative 87.5%

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

      5. *-commutative 87.5%

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

      6. +-commutative 87.5%

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

      7. *-commutative 87.5%

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

      8. mul-1-neg 87.5%

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

      9. unsub-neg 87.5%

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

      10. mul-1-neg 87.5%

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

      11. sub-neg 87.5%

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

      12. distribute-lft-out-- 87.5%

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

   6. Simplified 87.5%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-82}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \end{array} \]

Alternative 8: 89.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -850000000000 \lor \neg \left(a \leq 3.8 \cdot 10^{-139}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -850000000000.0) (not (<= a 3.8e-139)))
   (- (+ x y) (* y (/ (- z t) (- a t))))
   (- x (/ (* y z) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -850000000000.0) || !(a <= 3.8e-139)) {
		tmp = (x + y) - (y * ((z - t) / (a - t)));
	} 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 <= (-850000000000.0d0)) .or. (.not. (a <= 3.8d-139))) then
        tmp = (x + y) - (y * ((z - t) / (a - t)))
    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 <= -850000000000.0) || !(a <= 3.8e-139)) {
		tmp = (x + y) - (y * ((z - t) / (a - t)));
	} else {
		tmp = x - ((y * z) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -850000000000.0) or not (a <= 3.8e-139):
		tmp = (x + y) - (y * ((z - t) / (a - t)))
	else:
		tmp = x - ((y * z) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -850000000000.0) || !(a <= 3.8e-139))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	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 <= -850000000000.0) || ~((a <= 3.8e-139)))
		tmp = (x + y) - (y * ((z - t) / (a - t)));
	else
		tmp = x - ((y * z) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -850000000000.0], N[Not[LessEqual[a, 3.8e-139]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $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 < -8.5e11 or 3.80000000000000008e-139 < a

   1. Initial program 82.7%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

   if -8.5e11 < a < 3.80000000000000008e-139

   1. Initial program 64.9%

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

      1. associate--l+ 68.9%

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

      2. sub-neg 68.9%

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

      3. +-commutative 68.9%

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

      4. associate-/l* 73.9%

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

      5. distribute-neg-frac 73.9%

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

      6. associate-/r/ 76.5%

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

      7. fma-def 76.5%

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

      8. sub-neg 76.5%

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

      9. +-commutative 76.5%

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

      10. distribute-neg-in 76.5%

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

      11. unsub-neg 76.5%

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

      12. remove-double-neg 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in z around inf 89.4%

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

      1. associate-*r/ 89.4%

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

      2. associate-*r* 89.4%

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

      3. neg-mul-1 89.4%

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

   6. Simplified 89.4%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -850000000000 \lor \neg \left(a \leq 3.8 \cdot 10^{-139}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \end{array} \]

Alternative 9: 75.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;a \leq -0.0115 \lor \neg \left(a \leq 4.1 \cdot 10^{-123}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.7e+53)
   (+ x y)
   (if (<= a -3.4e+42)
     (* y (- (/ z t) (/ a t)))
     (if (or (<= a -0.0115) (not (<= a 4.1e-123)))
       (+ x y)
       (+ x (/ y (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e+53) {
		tmp = x + y;
	} else if (a <= -3.4e+42) {
		tmp = y * ((z / t) - (a / t));
	} else if ((a <= -0.0115) || !(a <= 4.1e-123)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.7d+53)) then
        tmp = x + y
    else if (a <= (-3.4d+42)) then
        tmp = y * ((z / t) - (a / t))
    else if ((a <= (-0.0115d0)) .or. (.not. (a <= 4.1d-123))) then
        tmp = x + y
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e+53) {
		tmp = x + y;
	} else if (a <= -3.4e+42) {
		tmp = y * ((z / t) - (a / t));
	} else if ((a <= -0.0115) || !(a <= 4.1e-123)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.7e+53:
		tmp = x + y
	elif a <= -3.4e+42:
		tmp = y * ((z / t) - (a / t))
	elif (a <= -0.0115) or not (a <= 4.1e-123):
		tmp = x + y
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.7e+53)
		tmp = Float64(x + y);
	elseif (a <= -3.4e+42)
		tmp = Float64(y * Float64(Float64(z / t) - Float64(a / t)));
	elseif ((a <= -0.0115) || !(a <= 4.1e-123))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.7e+53)
		tmp = x + y;
	elseif (a <= -3.4e+42)
		tmp = y * ((z / t) - (a / t));
	elseif ((a <= -0.0115) || ~((a <= 4.1e-123)))
		tmp = x + y;
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.7e+53], N[(x + y), $MachinePrecision], If[LessEqual[a, -3.4e+42], N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -0.0115], N[Not[LessEqual[a, 4.1e-123]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.7e53 or -3.39999999999999975e42 < a < -0.0115 or 4.1e-123 < a

   1. Initial program 85.0%

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

      1. associate--l+ 85.7%

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

      2. sub-neg 85.7%

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

      3. +-commutative 85.7%

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

      4. associate-/l* 93.7%

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

      5. distribute-neg-frac 93.7%

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

      6. associate-/r/ 96.7%

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

      7. fma-def 96.7%

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

      8. sub-neg 96.7%

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

      9. +-commutative 96.7%

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

      10. distribute-neg-in 96.7%

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

      11. unsub-neg 96.7%

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

      12. remove-double-neg 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in a around inf 81.1%

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

   if -3.7e53 < a < -3.39999999999999975e42

   1. Initial program 34.5%

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

      1. associate--l+ 34.3%

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

      2. associate-/l* 19.9%

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

   3. Simplified 19.9%

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

   4. Taylor expanded in t around -inf 83.1%

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

      1. +-commutative 83.1%

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

      2. sub-neg 83.1%

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

      3. mul-1-neg 83.1%

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

      4. +-commutative 83.1%

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

      5. *-commutative 83.1%

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

      6. +-commutative 83.1%

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

      7. *-commutative 83.1%

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

      8. mul-1-neg 83.1%

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

      9. unsub-neg 83.1%

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

      10. mul-1-neg 83.1%

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

      11. sub-neg 83.1%

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

      12. distribute-lft-out-- 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around inf 100.0%

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

   if -0.0115 < a < 4.1e-123

   1. Initial program 64.7%

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

      1. associate--l+ 68.5%

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

      2. sub-neg 68.5%

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

      3. +-commutative 68.5%

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

      4. associate-/l* 73.4%

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

      5. distribute-neg-frac 73.4%

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

      6. associate-/r/ 76.1%

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

      7. fma-def 76.0%

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

      8. sub-neg 76.0%

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

      9. +-commutative 76.0%

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

      10. distribute-neg-in 76.0%

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

      11. unsub-neg 76.0%

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

      12. remove-double-neg 76.0%

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

   3. Simplified 76.0%

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

      1. add-cube-cbrt 74.8%

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

      2. pow3 74.9%

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

      3. +-commutative 74.9%

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

   5. Applied egg-rr 74.9%

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

   6. Taylor expanded in y around 0 89.8%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right)} + x}\right)}^{3} \]
   7. Step-by-step derivation

      1. associate--l+ 74.9%

         \[\leadsto {\left(\sqrt[3]{y \cdot \color{blue}{\left(1 + \left(\frac{t}{a - t} - \frac{z}{a - t}\right)\right)} + x}\right)}^{3} \]

      2. div-sub 74.9%

         \[\leadsto {\left(\sqrt[3]{y \cdot \left(1 + \color{blue}{\frac{t - z}{a - t}}\right) + x}\right)}^{3} \]

   8. Simplified 74.9%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \left(1 + \frac{t - z}{a - t}\right)} + x}\right)}^{3} \]

   9. Taylor expanded in a around 0 75.0%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(\frac{y \cdot z}{t} + x\right)} \]
   10. Step-by-step derivation

       1. pow-base-1 75.0%

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

       2. *-lft-identity 75.0%

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

       3. +-commutative 75.0%

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

       4. associate-/l* 77.5%

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

   11. Simplified 77.5%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;a \leq -0.0115 \lor \neg \left(a \leq 4.1 \cdot 10^{-123}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 10: 74.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;y + \left(x + \frac{y}{\frac{a}{t}}\right)\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;a \leq -260000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.7e+53)
   (+ y (+ x (/ y (/ a t))))
   (if (<= a -3.4e+42)
     (* y (- (/ z t) (/ a t)))
     (if (<= a -260000.0)
       (+ x y)
       (if (<= a 4.1e-123) (+ x (/ y (/ t z))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e+53) {
		tmp = y + (x + (y / (a / t)));
	} else if (a <= -3.4e+42) {
		tmp = y * ((z / t) - (a / t));
	} else if (a <= -260000.0) {
		tmp = x + y;
	} else if (a <= 4.1e-123) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.7d+53)) then
        tmp = y + (x + (y / (a / t)))
    else if (a <= (-3.4d+42)) then
        tmp = y * ((z / t) - (a / t))
    else if (a <= (-260000.0d0)) then
        tmp = x + y
    else if (a <= 4.1d-123) then
        tmp = x + (y / (t / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e+53) {
		tmp = y + (x + (y / (a / t)));
	} else if (a <= -3.4e+42) {
		tmp = y * ((z / t) - (a / t));
	} else if (a <= -260000.0) {
		tmp = x + y;
	} else if (a <= 4.1e-123) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.7e+53:
		tmp = y + (x + (y / (a / t)))
	elif a <= -3.4e+42:
		tmp = y * ((z / t) - (a / t))
	elif a <= -260000.0:
		tmp = x + y
	elif a <= 4.1e-123:
		tmp = x + (y / (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.7e+53)
		tmp = Float64(y + Float64(x + Float64(y / Float64(a / t))));
	elseif (a <= -3.4e+42)
		tmp = Float64(y * Float64(Float64(z / t) - Float64(a / t)));
	elseif (a <= -260000.0)
		tmp = Float64(x + y);
	elseif (a <= 4.1e-123)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.7e+53)
		tmp = y + (x + (y / (a / t)));
	elseif (a <= -3.4e+42)
		tmp = y * ((z / t) - (a / t));
	elseif (a <= -260000.0)
		tmp = x + y;
	elseif (a <= 4.1e-123)
		tmp = x + (y / (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.7e+53], N[(y + N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.4e+42], N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -260000.0], N[(x + y), $MachinePrecision], If[LessEqual[a, 4.1e-123], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.7e53

   1. Initial program 83.5%

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

      1. associate--l+ 83.6%

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

      2. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in a around inf 91.4%

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

   5. Taylor expanded in z around 0 80.0%

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

      1. associate--l+ 80.0%

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

      2. sub-neg 80.0%

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

      3. mul-1-neg 80.0%

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

      4. remove-double-neg 80.0%

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

      5. associate-/l* 84.8%

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

   7. Simplified 84.8%

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

   if -3.7e53 < a < -3.39999999999999975e42

   1. Initial program 34.5%

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

      1. associate--l+ 34.3%

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

      2. associate-/l* 19.9%

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

   3. Simplified 19.9%

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

   4. Taylor expanded in t around -inf 83.1%

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

      1. +-commutative 83.1%

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

      2. sub-neg 83.1%

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

      3. mul-1-neg 83.1%

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

      4. +-commutative 83.1%

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

      5. *-commutative 83.1%

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

      6. +-commutative 83.1%

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

      7. *-commutative 83.1%

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

      8. mul-1-neg 83.1%

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

      9. unsub-neg 83.1%

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

      10. mul-1-neg 83.1%

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

      11. sub-neg 83.1%

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

      12. distribute-lft-out-- 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around inf 100.0%

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

   if -3.39999999999999975e42 < a < -2.6e5 or 4.1e-123 < a

   1. Initial program 85.7%

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

      1. associate--l+ 86.6%

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

      2. sub-neg 86.6%

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

      3. +-commutative 86.6%

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

      4. associate-/l* 93.2%

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

      5. distribute-neg-frac 93.2%

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

      6. associate-/r/ 97.1%

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

      7. fma-def 97.1%

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

      8. sub-neg 97.1%

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

      9. +-commutative 97.1%

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

      10. distribute-neg-in 97.1%

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

      11. unsub-neg 97.1%

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

      12. remove-double-neg 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in a around inf 79.6%

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

   if -2.6e5 < a < 4.1e-123

   1. Initial program 64.7%

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

      1. associate--l+ 68.5%

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

      2. sub-neg 68.5%

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

      3. +-commutative 68.5%

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

      4. associate-/l* 73.4%

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

      5. distribute-neg-frac 73.4%

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

      6. associate-/r/ 76.1%

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

      7. fma-def 76.0%

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

      8. sub-neg 76.0%

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

      9. +-commutative 76.0%

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

      10. distribute-neg-in 76.0%

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

      11. unsub-neg 76.0%

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

      12. remove-double-neg 76.0%

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

   3. Simplified 76.0%

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

      1. add-cube-cbrt 74.8%

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

      2. pow3 74.9%

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

      3. +-commutative 74.9%

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

   5. Applied egg-rr 74.9%

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

   6. Taylor expanded in y around 0 89.8%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right)} + x}\right)}^{3} \]
   7. Step-by-step derivation

      1. associate--l+ 74.9%

         \[\leadsto {\left(\sqrt[3]{y \cdot \color{blue}{\left(1 + \left(\frac{t}{a - t} - \frac{z}{a - t}\right)\right)} + x}\right)}^{3} \]

      2. div-sub 74.9%

         \[\leadsto {\left(\sqrt[3]{y \cdot \left(1 + \color{blue}{\frac{t - z}{a - t}}\right) + x}\right)}^{3} \]

   8. Simplified 74.9%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \left(1 + \frac{t - z}{a - t}\right)} + x}\right)}^{3} \]

   9. Taylor expanded in a around 0 75.0%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(\frac{y \cdot z}{t} + x\right)} \]
   10. Step-by-step derivation

       1. pow-base-1 75.0%

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

       2. *-lft-identity 75.0%

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

       3. +-commutative 75.0%

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

       4. associate-/l* 77.5%

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

   11. Simplified 77.5%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;y + \left(x + \frac{y}{\frac{a}{t}}\right)\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;a \leq -260000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 88.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -900000000000 \lor \neg \left(a \leq 4.1 \cdot 10^{-123}\right):\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -900000000000.0) (not (<= a 4.1e-123)))
   (+ x (- y (/ y (/ (- a t) z))))
   (- x (/ (* y z) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -900000000000.0) || !(a <= 4.1e-123)) {
		tmp = x + (y - (y / ((a - t) / z)));
	} 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 <= (-900000000000.0d0)) .or. (.not. (a <= 4.1d-123))) then
        tmp = x + (y - (y / ((a - t) / z)))
    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 <= -900000000000.0) || !(a <= 4.1e-123)) {
		tmp = x + (y - (y / ((a - t) / z)));
	} else {
		tmp = x - ((y * z) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -900000000000.0) or not (a <= 4.1e-123):
		tmp = x + (y - (y / ((a - t) / z)))
	else:
		tmp = x - ((y * z) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -900000000000.0) || !(a <= 4.1e-123))
		tmp = Float64(x + Float64(y - Float64(y / Float64(Float64(a - t) / z))));
	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 <= -900000000000.0) || ~((a <= 4.1e-123)))
		tmp = x + (y - (y / ((a - t) / z)));
	else
		tmp = x - ((y * z) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -900000000000.0], N[Not[LessEqual[a, 4.1e-123]], $MachinePrecision]], N[(x + N[(y - N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $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 < -9e11 or 4.1e-123 < a

   1. Initial program 82.9%

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

      1. associate--l+ 83.6%

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

      2. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in z around inf 84.0%

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

      1. associate-/l* 91.8%

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

   6. Simplified 91.8%

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

   if -9e11 < a < 4.1e-123

   1. Initial program 65.0%

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

      1. associate--l+ 68.8%

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

      2. sub-neg 68.8%

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

      3. +-commutative 68.8%

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

      4. associate-/l* 73.7%

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

      5. distribute-neg-frac 73.7%

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

      6. associate-/r/ 76.3%

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

      7. fma-def 76.3%

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

      8. sub-neg 76.3%

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

      9. +-commutative 76.3%

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

      10. distribute-neg-in 76.3%

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

      11. unsub-neg 76.3%

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

      12. remove-double-neg 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in z around inf 88.7%

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

      1. associate-*r/ 88.7%

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

      2. associate-*r* 88.7%

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

      3. neg-mul-1 88.7%

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

   6. Simplified 88.7%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -900000000000 \lor \neg \left(a \leq 4.1 \cdot 10^{-123}\right):\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \end{array} \]

Alternative 12: 88.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1800000000000:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-123}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1800000000000.0)
   (- (+ x y) (* y (/ z (- a t))))
   (if (<= a 4.1e-123)
     (- x (/ (* y z) (- a t)))
     (+ x (- y (/ y (/ (- a t) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1800000000000.0) {
		tmp = (x + y) - (y * (z / (a - t)));
	} else if (a <= 4.1e-123) {
		tmp = x - ((y * z) / (a - t));
	} else {
		tmp = x + (y - (y / ((a - t) / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1800000000000.0d0)) then
        tmp = (x + y) - (y * (z / (a - t)))
    else if (a <= 4.1d-123) then
        tmp = x - ((y * z) / (a - t))
    else
        tmp = x + (y - (y / ((a - t) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1800000000000.0) {
		tmp = (x + y) - (y * (z / (a - t)));
	} else if (a <= 4.1e-123) {
		tmp = x - ((y * z) / (a - t));
	} else {
		tmp = x + (y - (y / ((a - t) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1800000000000.0:
		tmp = (x + y) - (y * (z / (a - t)))
	elif a <= 4.1e-123:
		tmp = x - ((y * z) / (a - t))
	else:
		tmp = x + (y - (y / ((a - t) / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1800000000000.0)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / Float64(a - t))));
	elseif (a <= 4.1e-123)
		tmp = Float64(x - Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y - Float64(y / Float64(Float64(a - t) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1800000000000.0)
		tmp = (x + y) - (y * (z / (a - t)));
	elseif (a <= 4.1e-123)
		tmp = x - ((y * z) / (a - t));
	else
		tmp = x + (y - (y / ((a - t) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1800000000000.0], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.1e-123], N[(x - N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8e12

   1. Initial program 78.6%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in z around inf 86.9%

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

   if -1.8e12 < a < 4.1e-123

   1. Initial program 65.0%

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

      1. associate--l+ 68.8%

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

      2. sub-neg 68.8%

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

      3. +-commutative 68.8%

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

      4. associate-/l* 73.7%

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

      5. distribute-neg-frac 73.7%

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

      6. associate-/r/ 76.3%

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

      7. fma-def 76.3%

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

      8. sub-neg 76.3%

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

      9. +-commutative 76.3%

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

      10. distribute-neg-in 76.3%

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

      11. unsub-neg 76.3%

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

      12. remove-double-neg 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in z around inf 88.7%

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

      1. associate-*r/ 88.7%

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

      2. associate-*r* 88.7%

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

      3. neg-mul-1 88.7%

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

   6. Simplified 88.7%

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

   if 4.1e-123 < a

   1. Initial program 85.6%

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

      1. associate--l+ 85.7%

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

      2. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around inf 86.9%

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

      1. associate-/l* 94.8%

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

   6. Simplified 94.8%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1800000000000:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-123}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \end{array} \]

Alternative 13: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+55} \lor \neg \left(a \leq 2 \cdot 10^{-104}\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.5e+55) (not (<= a 2e-104)))
   (+ y (- x (/ y (/ a z))))
   (- x (/ (* y z) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.5e+55) || !(a <= 2e-104)) {
		tmp = y + (x - (y / (a / z)));
	} 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 <= (-5.5d+55)) .or. (.not. (a <= 2d-104))) then
        tmp = y + (x - (y / (a / z)))
    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 <= -5.5e+55) || !(a <= 2e-104)) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x - ((y * z) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.5e+55) or not (a <= 2e-104):
		tmp = y + (x - (y / (a / z)))
	else:
		tmp = x - ((y * z) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.5e+55) || !(a <= 2e-104))
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	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 <= -5.5e+55) || ~((a <= 2e-104)))
		tmp = y + (x - (y / (a / z)));
	else
		tmp = x - ((y * z) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.5e+55], N[Not[LessEqual[a, 2e-104]], $MachinePrecision]], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $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 < -5.5000000000000004e55 or 1.99999999999999985e-104 < a

   1. Initial program 84.4%

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

      1. associate--l+ 84.4%

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

      2. sub-neg 84.4%

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

      3. +-commutative 84.4%

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

      4. associate-/l* 93.8%

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

      5. distribute-neg-frac 93.8%

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

      6. associate-/r/ 96.4%

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

      7. fma-def 96.4%

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

      8. sub-neg 96.4%

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

      9. +-commutative 96.4%

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

      10. distribute-neg-in 96.4%

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

      11. unsub-neg 96.4%

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

      12. remove-double-neg 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. sub-neg 84.8%

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

      3. associate-/l* 90.8%

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

   6. Simplified 90.8%

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

   if -5.5000000000000004e55 < a < 1.99999999999999985e-104

   1. Initial program 65.9%

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

      1. associate--l+ 70.0%

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

      2. sub-neg 70.0%

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

      3. +-commutative 70.0%

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

      4. associate-/l* 72.6%

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

      5. distribute-neg-frac 72.6%

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

      6. associate-/r/ 76.5%

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

      7. fma-def 76.5%

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

      8. sub-neg 76.5%

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

      9. +-commutative 76.5%

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

      10. distribute-neg-in 76.5%

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

      11. unsub-neg 76.5%

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

      12. remove-double-neg 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in z around inf 86.3%

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

      1. associate-*r/ 86.3%

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

      2. associate-*r* 86.3%

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

      3. neg-mul-1 86.3%

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

   6. Simplified 86.3%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+55} \lor \neg \left(a \leq 2 \cdot 10^{-104}\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \end{array} \]

Alternative 14: 60.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-11}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-163}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-137}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.02e-11)
   (+ x y)
   (if (<= a -2.5e-163) x (if (<= a 9.6e-137) (/ (* y z) t) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.02e-11) {
		tmp = x + y;
	} else if (a <= -2.5e-163) {
		tmp = x;
	} else if (a <= 9.6e-137) {
		tmp = (y * z) / t;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.02d-11)) then
        tmp = x + y
    else if (a <= (-2.5d-163)) then
        tmp = x
    else if (a <= 9.6d-137) then
        tmp = (y * z) / t
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.02e-11) {
		tmp = x + y;
	} else if (a <= -2.5e-163) {
		tmp = x;
	} else if (a <= 9.6e-137) {
		tmp = (y * z) / t;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.02e-11:
		tmp = x + y
	elif a <= -2.5e-163:
		tmp = x
	elif a <= 9.6e-137:
		tmp = (y * z) / t
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.02e-11)
		tmp = Float64(x + y);
	elseif (a <= -2.5e-163)
		tmp = x;
	elseif (a <= 9.6e-137)
		tmp = Float64(Float64(y * z) / t);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.02e-11)
		tmp = x + y;
	elseif (a <= -2.5e-163)
		tmp = x;
	elseif (a <= 9.6e-137)
		tmp = (y * z) / t;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.02e-11], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.5e-163], x, If[LessEqual[a, 9.6e-137], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.01999999999999994e-11 or 9.6000000000000002e-137 < a

   1. Initial program 82.9%

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

      1. associate--l+ 83.5%

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

      2. sub-neg 83.5%

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

      3. +-commutative 83.5%

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

      4. associate-/l* 90.4%

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

      5. distribute-neg-frac 90.4%

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

      6. associate-/r/ 93.9%

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

      7. fma-def 93.9%

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

      8. sub-neg 93.9%

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

      9. +-commutative 93.9%

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

      10. distribute-neg-in 93.9%

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

      11. unsub-neg 93.9%

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

      12. remove-double-neg 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in a around inf 77.4%

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

   if -1.01999999999999994e-11 < a < -2.49999999999999989e-163

   1. Initial program 70.3%

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

      1. associate--l+ 75.2%

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

      2. sub-neg 75.2%

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

      3. +-commutative 75.2%

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

      4. associate-/l* 78.1%

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

      5. distribute-neg-frac 78.1%

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

      6. associate-/r/ 82.5%

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

      7. fma-def 82.5%

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

      8. sub-neg 82.5%

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

      9. +-commutative 82.5%

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

      10. distribute-neg-in 82.5%

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

      11. unsub-neg 82.5%

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

      12. remove-double-neg 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in x around inf 57.6%

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

   if -2.49999999999999989e-163 < a < 9.6000000000000002e-137

   1. Initial program 60.1%

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

      1. associate--l+ 63.5%

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

      2. associate-/l* 70.1%

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

   3. Simplified 70.1%

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

   4. Taylor expanded in t around -inf 86.0%

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

      1. +-commutative 86.0%

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

      2. sub-neg 86.0%

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

      3. mul-1-neg 86.0%

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

      4. +-commutative 86.0%

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

      5. *-commutative 86.0%

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

      6. +-commutative 86.0%

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

      7. *-commutative 86.0%

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

      8. mul-1-neg 86.0%

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

      9. unsub-neg 86.0%

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

      10. mul-1-neg 86.0%

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

      11. sub-neg 86.0%

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

      12. distribute-lft-out-- 86.0%

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

   6. Simplified 86.0%

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

   7. Taylor expanded in z around inf 50.5%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-11}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-163}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-137}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 15: 75.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.45 \cdot 10^{+56} \lor \neg \left(a \leq 4.1 \cdot 10^{-123}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.45e+56) (not (<= a 4.1e-123))) (+ x y) (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.45e+56) || !(a <= 4.1e-123)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.45d+56)) .or. (.not. (a <= 4.1d-123))) then
        tmp = x + y
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.45e+56) || !(a <= 4.1e-123)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.45e+56) or not (a <= 4.1e-123):
		tmp = x + y
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.45e+56) || !(a <= 4.1e-123))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.45e+56) || ~((a <= 4.1e-123)))
		tmp = x + y;
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.45e+56], N[Not[LessEqual[a, 4.1e-123]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.45e56 or 4.1e-123 < a

   1. Initial program 84.8%

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

      1. associate--l+ 84.9%

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

      2. sub-neg 84.9%

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

      3. +-commutative 84.9%

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

      4. associate-/l* 94.0%

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

      5. distribute-neg-frac 94.0%

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

      6. associate-/r/ 96.5%

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

      7. fma-def 96.5%

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

      8. sub-neg 96.5%

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

      9. +-commutative 96.5%

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

      10. distribute-neg-in 96.5%

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

      11. unsub-neg 96.5%

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

      12. remove-double-neg 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in a around inf 81.3%

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

   if -3.45e56 < a < 4.1e-123

   1. Initial program 64.7%

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

      1. associate--l+ 68.9%

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

      2. sub-neg 68.9%

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

      3. +-commutative 68.9%

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

      4. associate-/l* 71.7%

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

      5. distribute-neg-frac 71.7%

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

      6. associate-/r/ 75.7%

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

      7. fma-def 75.6%

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

      8. sub-neg 75.6%

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

      9. +-commutative 75.6%

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

      10. distribute-neg-in 75.6%

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

      11. unsub-neg 75.6%

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

      12. remove-double-neg 75.6%

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

   3. Simplified 75.6%

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

      1. add-cube-cbrt 74.4%

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

      2. pow3 74.5%

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

      3. +-commutative 74.5%

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

   5. Applied egg-rr 74.5%

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

   6. Taylor expanded in y around 0 87.5%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right)} + x}\right)}^{3} \]
   7. Step-by-step derivation

      1. associate--l+ 74.5%

         \[\leadsto {\left(\sqrt[3]{y \cdot \color{blue}{\left(1 + \left(\frac{t}{a - t} - \frac{z}{a - t}\right)\right)} + x}\right)}^{3} \]

      2. div-sub 74.5%

         \[\leadsto {\left(\sqrt[3]{y \cdot \left(1 + \color{blue}{\frac{t - z}{a - t}}\right) + x}\right)}^{3} \]

   8. Simplified 74.5%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \left(1 + \frac{t - z}{a - t}\right)} + x}\right)}^{3} \]

   9. Taylor expanded in a around 0 72.1%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(\frac{y \cdot z}{t} + x\right)} \]
   10. Step-by-step derivation

       1. pow-base-1 72.1%

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

       2. *-lft-identity 72.1%

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

       3. +-commutative 72.1%

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

       4. associate-/l* 74.4%

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

   11. Simplified 74.4%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.45 \cdot 10^{+56} \lor \neg \left(a \leq 4.1 \cdot 10^{-123}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 16: 64.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.9e-10) (+ x y) (if (<= a 3.9e-142) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e-10) {
		tmp = x + y;
	} else if (a <= 3.9e-142) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.9d-10)) then
        tmp = x + y
    else if (a <= 3.9d-142) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e-10) {
		tmp = x + y;
	} else if (a <= 3.9e-142) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.9e-10:
		tmp = x + y
	elif a <= 3.9e-142:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.9e-10)
		tmp = Float64(x + y);
	elseif (a <= 3.9e-142)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.9e-10)
		tmp = x + y;
	elseif (a <= 3.9e-142)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.9e-10], N[(x + y), $MachinePrecision], If[LessEqual[a, 3.9e-142], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.9e-10 or 3.9000000000000003e-142 < a

   1. Initial program 83.1%

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

      1. associate--l+ 83.7%

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

      2. sub-neg 83.7%

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

      3. +-commutative 83.7%

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

      4. associate-/l* 90.5%

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

      5. distribute-neg-frac 90.5%

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

      6. associate-/r/ 93.4%

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

      7. fma-def 93.4%

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

      8. sub-neg 93.4%

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

      9. +-commutative 93.4%

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

      10. distribute-neg-in 93.4%

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

      11. unsub-neg 93.4%

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

      12. remove-double-neg 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in a around inf 76.5%

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

   if -3.9e-10 < a < 3.9000000000000003e-142

   1. Initial program 63.5%

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

      1. associate--l+ 67.5%

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

      2. sub-neg 67.5%

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

      3. +-commutative 67.5%

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

      4. associate-/l* 72.8%

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

      5. distribute-neg-frac 72.8%

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

      6. associate-/r/ 76.6%

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

      7. fma-def 76.6%

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

      8. sub-neg 76.6%

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

      9. +-commutative 76.6%

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

      10. distribute-neg-in 76.6%

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

      11. unsub-neg 76.6%

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

      12. remove-double-neg 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in x around inf 44.7%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 17: 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 75.8%

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

   1. associate--l+ 77.7%

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

   2. sub-neg 77.7%

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

   3. +-commutative 77.7%

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

   4. associate-/l* 84.0%

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

   5. distribute-neg-frac 84.0%

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

   6. associate-/r/ 87.1%

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

   7. fma-def 87.1%

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

   8. sub-neg 87.1%

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

   9. +-commutative 87.1%

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

   10. distribute-neg-in 87.1%

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

   11. unsub-neg 87.1%

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

   12. remove-double-neg 87.1%

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

3. Simplified 87.1%

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

4. Taylor expanded in x around inf 47.4%

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

5. Final simplification 47.4%

   \[\leadsto x \]

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 2023238 
(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))))