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

Percentage Accurate: 76.5% → 91.4%

Time: 11.1s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-246}:\\ \;\;\;\;\left(y + x\right) + y \cdot \frac{t - z}{a - t}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ y x) (/ (* y (- t z)) (- a t)))))
   (if (<= t_1 -5e-246)
     (+ (+ y x) (* y (/ (- t z) (- a t))))
     (if (<= t_1 0.0)
       (+ x (/ (* y (- z a)) t))
       (if (<= t_1 5e+305) t_1 (- x (* z (/ y (- a t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) + ((y * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -5e-246) {
		tmp = (y + x) + (y * ((t - z) / (a - t)));
	} else if (t_1 <= 0.0) {
		tmp = x + ((y * (z - a)) / t);
	} else if (t_1 <= 5e+305) {
		tmp = t_1;
	} else {
		tmp = x - (z * (y / (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 * (t - z)) / (a - t))
    if (t_1 <= (-5d-246)) then
        tmp = (y + x) + (y * ((t - z) / (a - t)))
    else if (t_1 <= 0.0d0) then
        tmp = x + ((y * (z - a)) / t)
    else if (t_1 <= 5d+305) then
        tmp = t_1
    else
        tmp = x - (z * (y / (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 * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -5e-246) {
		tmp = (y + x) + (y * ((t - z) / (a - t)));
	} else if (t_1 <= 0.0) {
		tmp = x + ((y * (z - a)) / t);
	} else if (t_1 <= 5e+305) {
		tmp = t_1;
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) + ((y * (t - z)) / (a - t))
	tmp = 0
	if t_1 <= -5e-246:
		tmp = (y + x) + (y * ((t - z) / (a - t)))
	elif t_1 <= 0.0:
		tmp = x + ((y * (z - a)) / t)
	elif t_1 <= 5e+305:
		tmp = t_1
	else:
		tmp = x - (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) + Float64(Float64(y * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -5e-246)
		tmp = Float64(Float64(y + x) + Float64(y * Float64(Float64(t - z) / Float64(a - t))));
	elseif (t_1 <= 0.0)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	elseif (t_1 <= 5e+305)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) + ((y * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -5e-246)
		tmp = (y + x) + (y * ((t - z) / (a - t)));
	elseif (t_1 <= 0.0)
		tmp = x + ((y * (z - a)) / t);
	elseif (t_1 <= 5e+305)
		tmp = t_1;
	else
		tmp = x - (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-246], N[(N[(y + x), $MachinePrecision] + N[(y * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], t$95$1, N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -4.9999999999999997e-246

   1. Initial program 88.5%

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

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

   if -4.9999999999999997e-246 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 9.1%

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

      1. associate--l+ 47.9%

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

      2. associate-/l* 24.5%

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

   3. Simplified 24.5%

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

   4. Taylor expanded in t around -inf 99.6%

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

      1. +-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. mul-1-neg 99.6%

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

      4. +-commutative 99.6%

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

      5. *-commutative 99.6%

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

      6. +-commutative 99.6%

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

      7. *-commutative 99.6%

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

      8. mul-1-neg 99.6%

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

      9. unsub-neg 99.6%

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

      10. mul-1-neg 99.6%

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

      11. sub-neg 99.6%

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

      12. distribute-lft-out-- 99.6%

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

   6. Simplified 99.6%

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

   if 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 5.00000000000000009e305

   1. Initial program 97.4%

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

   if 5.00000000000000009e305 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 42.5%

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

      1. associate--l+ 42.5%

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

      2. sub-neg 42.5%

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

      3. +-commutative 42.5%

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

      4. associate-/l* 78.8%

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

      5. distribute-neg-frac 78.8%

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

      6. associate-/r/ 82.2%

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

      7. fma-def 82.2%

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

      8. sub-neg 82.2%

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

      9. +-commutative 82.2%

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

      10. distribute-neg-in 82.2%

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

      11. unsub-neg 82.2%

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

      12. remove-double-neg 82.2%

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

   3. Simplified 82.2%

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

   4. Taylor expanded in y around 0 92.5%

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

   5. Taylor expanded in z around inf 60.2%

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

      1. associate-*r/ 60.2%

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

      2. mul-1-neg 60.2%

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

      3. distribute-rgt-neg-in 60.2%

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

   7. Simplified 60.2%

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

   8. Taylor expanded in y around 0 60.2%

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

      1. +-commutative 60.2%

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

      2. neg-mul-1 60.2%

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

      3. sub-neg 60.2%

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

      4. *-commutative 60.2%

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

      5. associate-*r/ 90.8%

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

   10. Simplified 90.8%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -5 \cdot 10^{-246}:\\ \;\;\;\;\left(y + x\right) + y \cdot \frac{t - z}{a - t}\\ \mathbf{elif}\;\left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;\left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 2: 93.1% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.0%

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

   1. associate--l+ 83.3%

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

   2. sub-neg 83.3%

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

   3. +-commutative 83.3%

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

   4. associate-/l* 86.6%

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

   5. distribute-neg-frac 86.6%

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

   6. associate-/r/ 90.5%

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

   7. fma-def 90.5%

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

   8. sub-neg 90.5%

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

   9. +-commutative 90.5%

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

   10. distribute-neg-in 90.5%

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

   11. unsub-neg 90.5%

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

   12. remove-double-neg 90.5%

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

3. Simplified 90.5%

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

4. Taylor expanded in y around 0 95.1%

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

   1. clear-num 95.1%

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

   2. inv-pow 95.1%

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

6. Applied egg-rr 95.1%

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

   1. unpow-1 95.1%

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

   2. div-sub 95.1%

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

   3. sub-neg 95.1%

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

   4. *-inverses 95.1%

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

   5. metadata-eval 95.1%

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

8. Simplified 95.1%

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

9. Final simplification 95.1%

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

Alternative 3: 89.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+136} \lor \neg \left(t \leq 3.7 \cdot 10^{+132}\right):\\ \;\;\;\;x + \frac{z - a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) + y \cdot \frac{t - z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8e+136) (not (<= t 3.7e+132)))
   (+ x (/ (- z a) (/ t y)))
   (+ (+ y x) (* y (/ (- t z) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e+136) || !(t <= 3.7e+132)) {
		tmp = x + ((z - a) / (t / y));
	} else {
		tmp = (y + x) + (y * ((t - z) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8d+136)) .or. (.not. (t <= 3.7d+132))) then
        tmp = x + ((z - a) / (t / y))
    else
        tmp = (y + x) + (y * ((t - z) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e+136) || !(t <= 3.7e+132)) {
		tmp = x + ((z - a) / (t / y));
	} else {
		tmp = (y + x) + (y * ((t - z) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8e+136) or not (t <= 3.7e+132):
		tmp = x + ((z - a) / (t / y))
	else:
		tmp = (y + x) + (y * ((t - z) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8e+136) || !(t <= 3.7e+132))
		tmp = Float64(x + Float64(Float64(z - a) / Float64(t / y)));
	else
		tmp = Float64(Float64(y + x) + Float64(y * Float64(Float64(t - z) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8e+136) || ~((t <= 3.7e+132)))
		tmp = x + ((z - a) / (t / y));
	else
		tmp = (y + x) + (y * ((t - z) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8e+136], N[Not[LessEqual[t, 3.7e+132]], $MachinePrecision]], N[(x + N[(N[(z - a), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + x), $MachinePrecision] + N[(y * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.00000000000000047e136 or 3.70000000000000011e132 < t

   1. Initial program 55.8%

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

      1. associate--l+ 66.1%

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

      2. associate-/l* 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in t around -inf 75.1%

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

      1. +-commutative 75.1%

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

      2. sub-neg 75.1%

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

      3. mul-1-neg 75.1%

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

      4. +-commutative 75.1%

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

      5. *-commutative 75.1%

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

      6. +-commutative 75.1%

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

      7. *-commutative 75.1%

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

      8. mul-1-neg 75.1%

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

      9. unsub-neg 75.1%

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

      10. mul-1-neg 75.1%

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

      11. sub-neg 75.1%

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

      12. distribute-lft-out-- 75.2%

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

   6. Simplified 75.2%

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

   7. Taylor expanded in x around 0 75.2%

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

      1. neg-mul-1 75.2%

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

      2. +-commutative 75.2%

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

      3. sub-neg 75.2%

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

      4. sub-neg 75.2%

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

      5. mul-1-neg 75.2%

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

      6. +-commutative 75.2%

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

      7. *-commutative 75.2%

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

      8. associate-/l* 87.8%

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

      9. +-commutative 87.8%

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

      10. mul-1-neg 87.8%

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

      11. sub-neg 87.8%

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

   9. Simplified 87.8%

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

   if -8.00000000000000047e136 < t < 3.70000000000000011e132

   1. Initial program 87.6%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+136} \lor \neg \left(t \leq 3.7 \cdot 10^{+132}\right):\\ \;\;\;\;x + \frac{z - a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) + y \cdot \frac{t - z}{a - t}\\ \end{array} \]

Alternative 4: 93.1% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * (((t / (a - t)) + 1.0) - (z / (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 * (((t / (a - t)) + 1.0d0) - (z / (a - t))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.0%

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

   1. associate--l+ 83.3%

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

   2. sub-neg 83.3%

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

   3. +-commutative 83.3%

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

   4. associate-/l* 86.6%

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

   5. distribute-neg-frac 86.6%

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

   6. associate-/r/ 90.5%

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

   7. fma-def 90.5%

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

   8. sub-neg 90.5%

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

   9. +-commutative 90.5%

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

   10. distribute-neg-in 90.5%

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

   11. unsub-neg 90.5%

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

   12. remove-double-neg 90.5%

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

3. Simplified 90.5%

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

4. Taylor expanded in y around 0 95.1%

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

5. Final simplification 95.1%

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

Alternative 5: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 4.3 \cdot 10^{+130}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - a}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 4.3e+130)
   (+ x (+ y (/ (- t z) (/ (- a t) y))))
   (+ x (/ (- z a) (/ t y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 4.3e+130) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x + ((z - a) / (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 4.3d+130) then
        tmp = x + (y + ((t - z) / ((a - t) / y)))
    else
        tmp = x + ((z - a) / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 4.3e+130) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x + ((z - a) / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 4.3e+130:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	else:
		tmp = x + ((z - a) / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 4.3e+130)
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	else
		tmp = Float64(x + Float64(Float64(z - a) / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 4.3e+130)
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	else
		tmp = x + ((z - a) / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 4.3e+130], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - a), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 4.29999999999999984e130

   1. Initial program 83.8%

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

      1. associate--l+ 86.3%

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

      2. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   if 4.29999999999999984e130 < t

   1. Initial program 54.1%

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

      1. associate--l+ 62.9%

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

      2. associate-/l* 66.9%

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

   3. Simplified 66.9%

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

   4. Taylor expanded in t around -inf 70.6%

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

      1. +-commutative 70.6%

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

      2. sub-neg 70.6%

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

      3. mul-1-neg 70.6%

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

      4. +-commutative 70.6%

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

      5. *-commutative 70.6%

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

      6. +-commutative 70.6%

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

      7. *-commutative 70.6%

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

      8. mul-1-neg 70.6%

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

      9. unsub-neg 70.6%

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

      10. mul-1-neg 70.6%

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

      11. sub-neg 70.6%

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

      12. distribute-lft-out-- 70.8%

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

   6. Simplified 70.8%

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

   7. Taylor expanded in x around 0 70.8%

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

      1. neg-mul-1 70.8%

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

      2. +-commutative 70.8%

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

      3. sub-neg 70.8%

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

      4. sub-neg 70.8%

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

      5. mul-1-neg 70.8%

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

      6. +-commutative 70.8%

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

      7. *-commutative 70.8%

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

      8. associate-/l* 88.8%

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

      9. +-commutative 88.8%

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

      10. mul-1-neg 88.8%

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

      11. sub-neg 88.8%

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

   9. Simplified 88.8%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.3 \cdot 10^{+130}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - a}{\frac{t}{y}}\\ \end{array} \]

Alternative 6: 75.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+153}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -85:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6e+153)
   (+ y x)
   (if (<= a -85.0)
     (- x (* y (/ z a)))
     (if (<= a 4.2e-13) (+ x (* y (/ z t))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e+153) {
		tmp = y + x;
	} else if (a <= -85.0) {
		tmp = x - (y * (z / a));
	} else if (a <= 4.2e-13) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6d+153)) then
        tmp = y + x
    else if (a <= (-85.0d0)) then
        tmp = x - (y * (z / a))
    else if (a <= 4.2d-13) then
        tmp = x + (y * (z / t))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e+153) {
		tmp = y + x;
	} else if (a <= -85.0) {
		tmp = x - (y * (z / a));
	} else if (a <= 4.2e-13) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6e+153:
		tmp = y + x
	elif a <= -85.0:
		tmp = x - (y * (z / a))
	elif a <= 4.2e-13:
		tmp = x + (y * (z / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6e+153)
		tmp = Float64(y + x);
	elseif (a <= -85.0)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	elseif (a <= 4.2e-13)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6e+153)
		tmp = y + x;
	elseif (a <= -85.0)
		tmp = x - (y * (z / a));
	elseif (a <= 4.2e-13)
		tmp = x + (y * (z / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6e+153], N[(y + x), $MachinePrecision], If[LessEqual[a, -85.0], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e-13], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.00000000000000037e153 or 4.19999999999999977e-13 < a

   1. Initial program 82.5%

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

      1. associate--l+ 83.4%

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

      2. sub-neg 83.4%

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

      3. +-commutative 83.4%

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

      4. associate-/l* 92.5%

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

      5. distribute-neg-frac 92.5%

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

      6. associate-/r/ 94.9%

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

      7. fma-def 94.9%

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

      8. sub-neg 94.9%

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

      9. +-commutative 94.9%

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

      10. distribute-neg-in 94.9%

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

      11. unsub-neg 94.9%

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

      12. remove-double-neg 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in a around inf 79.1%

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

   if -6.00000000000000037e153 < a < -85

   1. Initial program 81.0%

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

      1. associate--l+ 88.1%

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

      2. sub-neg 88.1%

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

      3. +-commutative 88.1%

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

      4. associate-/l* 85.1%

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

      5. distribute-neg-frac 85.1%

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

      6. associate-/r/ 94.5%

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

      7. fma-def 94.5%

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

      8. sub-neg 94.5%

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

      9. +-commutative 94.5%

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

      10. distribute-neg-in 94.5%

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

      11. unsub-neg 94.5%

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

      12. remove-double-neg 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in y around 0 95.1%

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

   5. Taylor expanded in z around inf 81.0%

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

      1. associate-*r/ 81.0%

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

      2. mul-1-neg 81.0%

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

      3. distribute-rgt-neg-in 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in a around inf 80.9%

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

      1. +-commutative 80.9%

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

      2. mul-1-neg 80.9%

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

      3. associate-/l* 85.5%

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

      4. unsub-neg 85.5%

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

      5. associate-/l* 80.9%

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

      6. associate-*r/ 85.4%

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

   10. Simplified 85.4%

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

   if -85 < a < 4.19999999999999977e-13

   1. Initial program 77.4%

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

      1. associate--l+ 81.6%

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

      2. sub-neg 81.6%

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

      3. +-commutative 81.6%

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

      4. associate-/l* 81.7%

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

      5. distribute-neg-frac 81.7%

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

      6. associate-/r/ 85.0%

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

      7. fma-def 85.0%

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

      8. sub-neg 85.0%

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

      9. +-commutative 85.0%

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

      10. distribute-neg-in 85.0%

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

      11. unsub-neg 85.0%

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

      12. remove-double-neg 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in y around 0 92.7%

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

   5. Taylor expanded in a around 0 79.1%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+153}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -85:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7: 75.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+153}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -1.75:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.05e+153)
   (+ y x)
   (if (<= a -1.75)
     (- x (/ y (/ a z)))
     (if (<= a 1.25e-6) (+ x (* y (/ z t))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e+153) {
		tmp = y + x;
	} else if (a <= -1.75) {
		tmp = x - (y / (a / z));
	} else if (a <= 1.25e-6) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.05d+153)) then
        tmp = y + x
    else if (a <= (-1.75d0)) then
        tmp = x - (y / (a / z))
    else if (a <= 1.25d-6) then
        tmp = x + (y * (z / t))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e+153) {
		tmp = y + x;
	} else if (a <= -1.75) {
		tmp = x - (y / (a / z));
	} else if (a <= 1.25e-6) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.05e+153:
		tmp = y + x
	elif a <= -1.75:
		tmp = x - (y / (a / z))
	elif a <= 1.25e-6:
		tmp = x + (y * (z / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.05e+153)
		tmp = Float64(y + x);
	elseif (a <= -1.75)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	elseif (a <= 1.25e-6)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.05e+153)
		tmp = y + x;
	elseif (a <= -1.75)
		tmp = x - (y / (a / z));
	elseif (a <= 1.25e-6)
		tmp = x + (y * (z / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.05e+153], N[(y + x), $MachinePrecision], If[LessEqual[a, -1.75], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e-6], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.05000000000000008e153 or 1.2500000000000001e-6 < a

   1. Initial program 82.5%

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

      1. associate--l+ 83.4%

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

      2. sub-neg 83.4%

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

      3. +-commutative 83.4%

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

      4. associate-/l* 92.5%

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

      5. distribute-neg-frac 92.5%

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

      6. associate-/r/ 94.9%

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

      7. fma-def 94.9%

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

      8. sub-neg 94.9%

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

      9. +-commutative 94.9%

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

      10. distribute-neg-in 94.9%

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

      11. unsub-neg 94.9%

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

      12. remove-double-neg 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in a around inf 79.1%

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

   if -2.05000000000000008e153 < a < -1.75

   1. Initial program 81.0%

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

      1. associate--l+ 88.1%

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

      2. associate-/l* 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in a around inf 78.2%

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

   5. Taylor expanded in z around inf 80.9%

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

      1. mul-1-neg 80.9%

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

      2. associate-/l* 85.5%

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

   7. Simplified 85.5%

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

   if -1.75 < a < 1.2500000000000001e-6

   1. Initial program 77.4%

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

      1. associate--l+ 81.6%

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

      2. sub-neg 81.6%

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

      3. +-commutative 81.6%

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

      4. associate-/l* 81.7%

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

      5. distribute-neg-frac 81.7%

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

      6. associate-/r/ 85.0%

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

      7. fma-def 85.0%

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

      8. sub-neg 85.0%

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

      9. +-commutative 85.0%

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

      10. distribute-neg-in 85.0%

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

      11. unsub-neg 85.0%

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

      12. remove-double-neg 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in y around 0 92.7%

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

   5. Taylor expanded in a around 0 79.1%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+153}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -1.75:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8: 81.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -460 \lor \neg \left(a \leq 1.1 \cdot 10^{-34}\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -460.0) (not (<= a 1.1e-34)))
   (+ y (- x (/ y (/ a z))))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -460.0) || !(a <= 1.1e-34)) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-460.0d0)) .or. (.not. (a <= 1.1d-34))) then
        tmp = y + (x - (y / (a / z)))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -460.0) || !(a <= 1.1e-34)) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -460.0) or not (a <= 1.1e-34):
		tmp = y + (x - (y / (a / z)))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -460.0) || !(a <= 1.1e-34))
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -460.0) || ~((a <= 1.1e-34)))
		tmp = y + (x - (y / (a / z)));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -460.0], N[Not[LessEqual[a, 1.1e-34]], $MachinePrecision]], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -460 or 1.0999999999999999e-34 < a

   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+ 84.7%

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

      2. sub-neg 84.7%

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

      3. +-commutative 84.7%

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

      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/ 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 82.8%

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

      1. mul-1-neg 82.8%

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

      2. sub-neg 82.8%

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

      3. associate-/l* 89.9%

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

   6. Simplified 89.9%

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

   if -460 < a < 1.0999999999999999e-34

   1. Initial program 77.4%

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

      1. associate--l+ 81.6%

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

      2. sub-neg 81.6%

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

      3. +-commutative 81.6%

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

      4. associate-/l* 81.7%

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

      5. distribute-neg-frac 81.7%

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

      6. associate-/r/ 85.0%

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

      7. fma-def 85.0%

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

      8. sub-neg 85.0%

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

      9. +-commutative 85.0%

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

      10. distribute-neg-in 85.0%

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

      11. unsub-neg 85.0%

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

      12. remove-double-neg 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in y around 0 92.7%

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

   5. Taylor expanded in a around 0 79.1%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -460 \lor \neg \left(a \leq 1.1 \cdot 10^{-34}\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 9: 87.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+58} \lor \neg \left(a \leq 0.45\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.8e+58) (not (<= a 0.45)))
   (+ y (- x (/ y (/ a z))))
   (- x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.8e+58) || !(a <= 0.45)) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x - (z * (y / (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 <= (-3.8d+58)) .or. (.not. (a <= 0.45d0))) then
        tmp = y + (x - (y / (a / z)))
    else
        tmp = x - (z * (y / (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 <= -3.8e+58) || !(a <= 0.45)) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.8e+58) or not (a <= 0.45):
		tmp = y + (x - (y / (a / z)))
	else:
		tmp = x - (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.8e+58) || !(a <= 0.45))
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	else
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.8e+58) || ~((a <= 0.45)))
		tmp = y + (x - (y / (a / z)));
	else
		tmp = x - (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.8e+58], N[Not[LessEqual[a, 0.45]], $MachinePrecision]], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.7999999999999999e58 or 0.450000000000000011 < a

   1. Initial program 81.6%

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

      1. associate--l+ 83.8%

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

      2. sub-neg 83.8%

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

      3. +-commutative 83.8%

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

      4. associate-/l* 90.1%

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

      5. distribute-neg-frac 90.1%

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

      6. associate-/r/ 95.0%

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

      7. fma-def 95.0%

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

      8. sub-neg 95.0%

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

      9. +-commutative 95.0%

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

      10. distribute-neg-in 95.0%

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

      11. unsub-neg 95.0%

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

      12. remove-double-neg 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in t around 0 82.5%

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

      1. mul-1-neg 82.5%

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

      2. sub-neg 82.5%

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

      3. associate-/l* 90.3%

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

   6. Simplified 90.3%

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

   if -3.7999999999999999e58 < a < 0.450000000000000011

   1. Initial program 78.4%

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

      1. associate--l+ 82.9%

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

      2. sub-neg 82.9%

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

      3. +-commutative 82.9%

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

      4. associate-/l* 83.0%

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

      5. distribute-neg-frac 83.0%

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

      6. associate-/r/ 85.9%

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

      7. fma-def 85.9%

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

      8. sub-neg 85.9%

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

      9. +-commutative 85.9%

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

      10. distribute-neg-in 85.9%

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

      11. unsub-neg 85.9%

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

      12. remove-double-neg 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in y around 0 92.7%

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

   5. Taylor expanded in z around inf 86.6%

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

      1. associate-*r/ 86.6%

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

      2. mul-1-neg 86.6%

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

      3. distribute-rgt-neg-in 86.6%

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

   7. Simplified 86.6%

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

   8. Taylor expanded in y around 0 86.6%

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

      1. +-commutative 86.6%

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

      2. neg-mul-1 86.6%

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

      3. sub-neg 86.6%

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

      4. *-commutative 86.6%

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

      5. associate-*r/ 88.8%

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

   10. Simplified 88.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+58} \lor \neg \left(a \leq 0.45\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 10: 76.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.6:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-12}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.6) (+ y x) (if (<= a 6.3e-12) (+ x (* y (/ z t))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.6) {
		tmp = y + x;
	} else if (a <= 6.3e-12) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-0.6d0)) then
        tmp = y + x
    else if (a <= 6.3d-12) then
        tmp = x + (y * (z / t))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.6) {
		tmp = y + x;
	} else if (a <= 6.3e-12) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.6:
		tmp = y + x
	elif a <= 6.3e-12:
		tmp = x + (y * (z / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.6)
		tmp = Float64(y + x);
	elseif (a <= 6.3e-12)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.6)
		tmp = y + x;
	elseif (a <= 6.3e-12)
		tmp = x + (y * (z / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.6], N[(y + x), $MachinePrecision], If[LessEqual[a, 6.3e-12], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -0.599999999999999978 or 6.3000000000000002e-12 < a

   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+ 84.7%

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

      2. sub-neg 84.7%

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

      3. +-commutative 84.7%

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

      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/ 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 a around inf 74.4%

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

   if -0.599999999999999978 < a < 6.3000000000000002e-12

   1. Initial program 77.4%

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

      1. associate--l+ 81.6%

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

      2. sub-neg 81.6%

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

      3. +-commutative 81.6%

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

      4. associate-/l* 81.7%

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

      5. distribute-neg-frac 81.7%

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

      6. associate-/r/ 85.0%

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

      7. fma-def 85.0%

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

      8. sub-neg 85.0%

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

      9. +-commutative 85.0%

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

      10. distribute-neg-in 85.0%

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

      11. unsub-neg 85.0%

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

      12. remove-double-neg 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in y around 0 92.7%

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

   5. Taylor expanded in a around 0 79.1%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.6:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-12}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 11: 59.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+131}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.55e+131) (* z (/ y t)) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.55e+131) {
		tmp = z * (y / t);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.55d+131)) then
        tmp = z * (y / t)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.55e+131) {
		tmp = z * (y / t);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.55e+131:
		tmp = z * (y / t)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.55e+131)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.55e+131)
		tmp = z * (y / t);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.55e+131], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.54999999999999971e131

   1. Initial program 79.9%

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

      1. associate--l+ 79.9%

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

      2. sub-neg 79.9%

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

      3. +-commutative 79.9%

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

      4. associate-/l* 85.4%

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

      5. distribute-neg-frac 85.4%

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

      6. associate-/r/ 93.0%

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

      7. fma-def 93.0%

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

      8. sub-neg 93.0%

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

      9. +-commutative 93.0%

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

      10. distribute-neg-in 93.0%

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

      11. unsub-neg 93.0%

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

      12. remove-double-neg 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in y around 0 96.9%

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

   5. Taylor expanded in a around 0 45.7%

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

   6. Taylor expanded in y around inf 35.1%

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

      1. *-commutative 35.1%

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

      2. associate-*r/ 40.6%

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

   8. Simplified 40.6%

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

   if -3.54999999999999971e131 < z

   1. Initial program 80.1%

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

      1. associate--l+ 83.9%

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

      2. sub-neg 83.9%

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

      3. +-commutative 83.9%

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

      4. associate-/l* 86.8%

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

      5. distribute-neg-frac 86.8%

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

      6. associate-/r/ 90.1%

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

      7. fma-def 90.1%

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

      8. sub-neg 90.1%

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

      9. +-commutative 90.1%

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

      10. distribute-neg-in 90.1%

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

      11. unsub-neg 90.1%

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

      12. remove-double-neg 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in a around inf 66.3%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+131}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 12: 60.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+151}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t -6.6e+151) x (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.6e+151) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.6d+151)) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.6e+151) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.6e+151:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.6e+151)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.6e+151)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.6e+151], x, N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.60000000000000049e151

   1. Initial program 61.8%

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

      1. associate--l+ 74.7%

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

      2. sub-neg 74.7%

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

      3. +-commutative 74.7%

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

      4. associate-/l* 84.2%

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

      5. distribute-neg-frac 84.2%

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

      6. associate-/r/ 94.0%

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

      7. fma-def 94.1%

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

      8. sub-neg 94.1%

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

      9. +-commutative 94.1%

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

      10. distribute-neg-in 94.1%

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

      11. unsub-neg 94.1%

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

      12. remove-double-neg 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in x around inf 80.8%

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

   if -6.60000000000000049e151 < t

   1. Initial program 82.2%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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* 86.9%

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

      5. distribute-neg-frac 86.9%

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

      6. associate-/r/ 90.1%

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

      7. fma-def 90.1%

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

      8. sub-neg 90.1%

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

      9. +-commutative 90.1%

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

      10. distribute-neg-in 90.1%

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

      11. unsub-neg 90.1%

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

      12. remove-double-neg 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in a around inf 60.0%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+151}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 13: 49.9% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.0%

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

   1. associate--l+ 83.3%

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

   2. sub-neg 83.3%

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

   3. +-commutative 83.3%

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

   4. associate-/l* 86.6%

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

   5. distribute-neg-frac 86.6%

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

   6. associate-/r/ 90.5%

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

   7. fma-def 90.5%

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

   8. sub-neg 90.5%

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

   9. +-commutative 90.5%

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

   10. distribute-neg-in 90.5%

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

   11. unsub-neg 90.5%

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

   12. remove-double-neg 90.5%

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

3. Simplified 90.5%

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

4. Taylor expanded in x around inf 49.4%

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

5. Final simplification 49.4%

   \[\leadsto x \]

Developer target: 88.1% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023230 
(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))))