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

Percentage Accurate: 77.6% → 90.8%

Time: 12.8s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-292}:\\ \;\;\;\;\left(x + y\right) + \frac{-1}{\frac{a - t}{y \cdot \left(z - t\right)}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (/ (* y (- t z)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (+ (- x (/ y (/ t a))) (/ y (/ t z)))
     (if (<= t_1 -5e-292)
       (+ (+ x y) (/ -1.0 (/ (- a t) (* y (- z t)))))
       (if (<= t_1 0.0)
         (+ x (/ (* y (- z a)) t))
         (if (<= t_1 5e+305)
           (- (+ x y) (* y (/ (- z t) (- a t))))
           (- x (* z (/ y (- a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((y * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x - (y / (t / a))) + (y / (t / z));
	} else if (t_1 <= -5e-292) {
		tmp = (x + y) + (-1.0 / ((a - t) / (y * (z - t))));
	} else if (t_1 <= 0.0) {
		tmp = x + ((y * (z - a)) / t);
	} else if (t_1 <= 5e+305) {
		tmp = (x + y) - (y * ((z - t) / (a - t)));
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((y * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x - (y / (t / a))) + (y / (t / z));
	} else if (t_1 <= -5e-292) {
		tmp = (x + y) + (-1.0 / ((a - t) / (y * (z - t))));
	} else if (t_1 <= 0.0) {
		tmp = x + ((y * (z - a)) / t);
	} else if (t_1 <= 5e+305) {
		tmp = (x + y) - (y * ((z - t) / (a - t)));
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) + ((y * (t - z)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x - (y / (t / a))) + (y / (t / z))
	elif t_1 <= -5e-292:
		tmp = (x + y) + (-1.0 / ((a - t) / (y * (z - t))))
	elif t_1 <= 0.0:
		tmp = x + ((y * (z - a)) / t)
	elif t_1 <= 5e+305:
		tmp = (x + y) - (y * ((z - t) / (a - t)))
	else:
		tmp = x - (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) + Float64(Float64(y * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x - Float64(y / Float64(t / a))) + Float64(y / Float64(t / z)));
	elseif (t_1 <= -5e-292)
		tmp = Float64(Float64(x + y) + Float64(-1.0 / Float64(Float64(a - t) / Float64(y * Float64(z - t)))));
	elseif (t_1 <= 0.0)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	elseif (t_1 <= 5e+305)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	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 = (x + y) + ((y * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x - (y / (t / a))) + (y / (t / z));
	elseif (t_1 <= -5e-292)
		tmp = (x + y) + (-1.0 / ((a - t) / (y * (z - t))));
	elseif (t_1 <= 0.0)
		tmp = x + ((y * (z - a)) / t);
	elseif (t_1 <= 5e+305)
		tmp = (x + y) - (y * ((z - t) / (a - t)));
	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[(x + y), $MachinePrecision] + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-292], N[(N[(x + y), $MachinePrecision] + N[(-1.0 / N[(N[(a - t), $MachinePrecision] / N[(y * N[(z - t), $MachinePrecision]), $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], N[(N[(x + y), $MachinePrecision] - N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0

   1. Initial program 32.2%

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

      1. associate-*l/ 56.1%

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

   3. Simplified 56.1%

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

   4. Taylor expanded in t around inf 63.4%

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

      1. sub-neg 63.4%

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

      2. +-commutative 63.4%

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

      3. mul-1-neg 63.4%

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

      4. unsub-neg 63.4%

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

      5. associate-/l* 70.6%

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

      6. mul-1-neg 70.6%

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

      7. remove-double-neg 70.6%

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

      8. associate-/l* 85.0%

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

   6. Simplified 85.0%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -4.99999999999999981e-292

   1. Initial program 97.9%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

      1. associate-*l/ 97.9%

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

      2. clear-num 97.9%

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

      3. *-commutative 97.9%

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

   5. Applied egg-rr 97.9%

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

   if -4.99999999999999981e-292 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 5.5%

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

      1. associate-*l/ 5.5%

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

   3. Simplified 5.5%

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

   4. Taylor expanded in t around -inf 99.8%

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

      1. +-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

      4. distribute-lft-out-- 99.8%

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

   6. Simplified 99.8%

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

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

   1. Initial program 96.4%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

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

   1. Initial program 38.6%

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

      1. associate--l+ 38.6%

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

      2. sub-neg 38.6%

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

      3. +-commutative 38.6%

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

      4. associate-/l* 74.9%

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

      5. distribute-neg-frac 74.9%

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

      6. associate-/r/ 74.9%

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

      7. fma-def 74.9%

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

      8. sub-neg 74.9%

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

      9. +-commutative 74.9%

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

      10. distribute-neg-in 74.9%

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

      11. unsub-neg 74.9%

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

      12. remove-double-neg 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in z around inf 65.3%

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

      1. mul-1-neg 65.3%

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

      2. *-commutative 65.3%

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

      3. associate-*r/ 79.8%

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

      4. distribute-lft-neg-in 79.8%

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

   6. Simplified 79.8%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -5 \cdot 10^{-292}:\\ \;\;\;\;\left(x + y\right) + \frac{-1}{\frac{a - t}{y \cdot \left(z - t\right)}}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 2: 91.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+190} \lor \neg \left(t \leq 10^{+61}\right):\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.9e+190) (not (<= t 1e+61)))
   (+ (- x (/ y (/ t a))) (/ y (/ t z)))
   (+ x (fma (/ (- t z) (- a t)) y y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.9e+190) || !(t <= 1e+61)) {
		tmp = (x - (y / (t / a))) + (y / (t / z));
	} else {
		tmp = x + fma(((t - z) / (a - t)), y, y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.9e+190) || !(t <= 1e+61))
		tmp = Float64(Float64(x - Float64(y / Float64(t / a))) + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + fma(Float64(Float64(t - z) / Float64(a - t)), y, y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.9e+190], N[Not[LessEqual[t, 1e+61]], $MachinePrecision]], N[(N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * y + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.89999999999999989e190 or 9.99999999999999949e60 < t

   1. Initial program 53.8%

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

      1. associate-*l/ 60.7%

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

   3. Simplified 60.7%

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

   4. Taylor expanded in t around inf 85.3%

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

      1. sub-neg 85.3%

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

      2. +-commutative 85.3%

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

      3. mul-1-neg 85.3%

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

      4. unsub-neg 85.3%

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

      5. associate-/l* 87.6%

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

      6. mul-1-neg 87.6%

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

      7. remove-double-neg 87.6%

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

      8. associate-/l* 94.4%

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

   6. Simplified 94.4%

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

   if -2.89999999999999989e190 < t < 9.99999999999999949e60

   1. Initial program 86.8%

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

      1. associate--l+ 87.9%

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

      2. sub-neg 87.9%

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

      3. +-commutative 87.9%

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

      4. associate-/l* 91.1%

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

      5. distribute-neg-frac 91.1%

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

      6. associate-/r/ 92.8%

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

      7. fma-def 92.9%

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

      8. sub-neg 92.9%

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

      9. +-commutative 92.9%

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

      10. distribute-neg-in 92.9%

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

      11. unsub-neg 92.9%

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

      12. remove-double-neg 92.9%

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

   3. Simplified 92.9%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+190} \lor \neg \left(t \leq 10^{+61}\right):\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)\\ \end{array} \]

Alternative 3: 90.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (/ (* y (- t z)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (+ (- x (/ y (/ t a))) (/ y (/ t z)))
     (if (<= t_1 -5e-292)
       t_1
       (if (<= t_1 0.0)
         (+ x (/ (* y (- z a)) t))
         (if (<= t_1 5e+305)
           (- (+ x y) (* y (/ (- z t) (- a t))))
           (- x (* z (/ y (- a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((y * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x - (y / (t / a))) + (y / (t / z));
	} else if (t_1 <= -5e-292) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = x + ((y * (z - a)) / t);
	} else if (t_1 <= 5e+305) {
		tmp = (x + y) - (y * ((z - t) / (a - t)));
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((y * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x - (y / (t / a))) + (y / (t / z));
	} else if (t_1 <= -5e-292) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = x + ((y * (z - a)) / t);
	} else if (t_1 <= 5e+305) {
		tmp = (x + y) - (y * ((z - t) / (a - t)));
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) + ((y * (t - z)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x - (y / (t / a))) + (y / (t / z))
	elif t_1 <= -5e-292:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = x + ((y * (z - a)) / t)
	elif t_1 <= 5e+305:
		tmp = (x + y) - (y * ((z - t) / (a - t)))
	else:
		tmp = x - (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) + Float64(Float64(y * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x - Float64(y / Float64(t / a))) + Float64(y / Float64(t / z)));
	elseif (t_1 <= -5e-292)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	elseif (t_1 <= 5e+305)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	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 = (x + y) + ((y * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x - (y / (t / a))) + (y / (t / z));
	elseif (t_1 <= -5e-292)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = x + ((y * (z - a)) / t);
	elseif (t_1 <= 5e+305)
		tmp = (x + y) - (y * ((z - t) / (a - t)));
	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[(x + y), $MachinePrecision] + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-292], t$95$1, 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], N[(N[(x + y), $MachinePrecision] - N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0

   1. Initial program 32.2%

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

      1. associate-*l/ 56.1%

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

   3. Simplified 56.1%

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

   4. Taylor expanded in t around inf 63.4%

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

      1. sub-neg 63.4%

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

      2. +-commutative 63.4%

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

      3. mul-1-neg 63.4%

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

      4. unsub-neg 63.4%

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

      5. associate-/l* 70.6%

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

      6. mul-1-neg 70.6%

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

      7. remove-double-neg 70.6%

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

      8. associate-/l* 85.0%

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

   6. Simplified 85.0%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -4.99999999999999981e-292

   1. Initial program 97.9%

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

   if -4.99999999999999981e-292 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 5.5%

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

      1. associate-*l/ 5.5%

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

   3. Simplified 5.5%

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

   4. Taylor expanded in t around -inf 99.8%

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

      1. +-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

      4. distribute-lft-out-- 99.8%

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

   6. Simplified 99.8%

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

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

   1. Initial program 96.4%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

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

   1. Initial program 38.6%

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

      1. associate--l+ 38.6%

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

      2. sub-neg 38.6%

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

      3. +-commutative 38.6%

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

      4. associate-/l* 74.9%

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

      5. distribute-neg-frac 74.9%

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

      6. associate-/r/ 74.9%

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

      7. fma-def 74.9%

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

      8. sub-neg 74.9%

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

      9. +-commutative 74.9%

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

      10. distribute-neg-in 74.9%

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

      11. unsub-neg 74.9%

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

      12. remove-double-neg 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in z around inf 65.3%

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

      1. mul-1-neg 65.3%

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

      2. *-commutative 65.3%

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

      3. associate-*r/ 79.8%

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

      4. distribute-lft-neg-in 79.8%

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

   6. Simplified 79.8%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -5 \cdot 10^{-292}:\\ \;\;\;\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 4: 89.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -8 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+77}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+49}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+58}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (- x (/ y (/ t a))) (/ y (/ t z)))))
   (if (<= t -8e+190)
     t_1
     (if (<= t -1.05e+77)
       (+ x (+ y (/ (- t z) (/ (- a t) y))))
       (if (<= t -1.9e+49)
         (- x (* z (/ y (- a t))))
         (if (<= t 8.5e+58) (- (+ x y) (* y (/ z (- a t)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y / (t / a))) + (y / (t / z));
	double tmp;
	if (t <= -8e+190) {
		tmp = t_1;
	} else if (t <= -1.05e+77) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else if (t <= -1.9e+49) {
		tmp = x - (z * (y / (a - t)));
	} else if (t <= 8.5e+58) {
		tmp = (x + y) - (y * (z / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (y / (t / a))) + (y / (t / z))
    if (t <= (-8d+190)) then
        tmp = t_1
    else if (t <= (-1.05d+77)) then
        tmp = x + (y + ((t - z) / ((a - t) / y)))
    else if (t <= (-1.9d+49)) then
        tmp = x - (z * (y / (a - t)))
    else if (t <= 8.5d+58) then
        tmp = (x + y) - (y * (z / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y / (t / a))) + (y / (t / z));
	double tmp;
	if (t <= -8e+190) {
		tmp = t_1;
	} else if (t <= -1.05e+77) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else if (t <= -1.9e+49) {
		tmp = x - (z * (y / (a - t)));
	} else if (t <= 8.5e+58) {
		tmp = (x + y) - (y * (z / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y / (t / a))) + (y / (t / z))
	tmp = 0
	if t <= -8e+190:
		tmp = t_1
	elif t <= -1.05e+77:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	elif t <= -1.9e+49:
		tmp = x - (z * (y / (a - t)))
	elif t <= 8.5e+58:
		tmp = (x + y) - (y * (z / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y / Float64(t / a))) + Float64(y / Float64(t / z)))
	tmp = 0.0
	if (t <= -8e+190)
		tmp = t_1;
	elseif (t <= -1.05e+77)
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	elseif (t <= -1.9e+49)
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	elseif (t <= 8.5e+58)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y / (t / a))) + (y / (t / z));
	tmp = 0.0;
	if (t <= -8e+190)
		tmp = t_1;
	elseif (t <= -1.05e+77)
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	elseif (t <= -1.9e+49)
		tmp = x - (z * (y / (a - t)));
	elseif (t <= 8.5e+58)
		tmp = (x + y) - (y * (z / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e+190], t$95$1, If[LessEqual[t, -1.05e+77], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.9e+49], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+58], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.0000000000000006e190 or 8.50000000000000015e58 < t

   1. Initial program 53.8%

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

      1. associate-*l/ 60.7%

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

   3. Simplified 60.7%

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

   4. Taylor expanded in t around inf 85.3%

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

      1. sub-neg 85.3%

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

      2. +-commutative 85.3%

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

      3. mul-1-neg 85.3%

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

      4. unsub-neg 85.3%

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

      5. associate-/l* 87.6%

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

      6. mul-1-neg 87.6%

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

      7. remove-double-neg 87.6%

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

      8. associate-/l* 94.4%

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

   6. Simplified 94.4%

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

   if -8.0000000000000006e190 < t < -1.0499999999999999e77

   1. Initial program 70.8%

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

      1. associate--l+ 75.0%

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

      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 -1.0499999999999999e77 < t < -1.8999999999999999e49

   1. Initial program 52.7%

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

      1. associate--l+ 52.8%

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

      2. sub-neg 52.8%

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

      3. +-commutative 52.8%

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

      4. associate-/l* 62.6%

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

      5. distribute-neg-frac 62.6%

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

      6. associate-/r/ 62.8%

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

      7. fma-def 63.2%

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

      8. sub-neg 63.2%

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

      9. +-commutative 63.2%

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

      10. distribute-neg-in 63.2%

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

      11. unsub-neg 63.2%

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

      12. remove-double-neg 63.2%

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

   3. Simplified 63.2%

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

   4. Taylor expanded in z around inf 88.6%

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

      1. mul-1-neg 88.6%

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

      2. *-commutative 88.6%

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

      3. associate-*r/ 99.6%

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

      4. distribute-lft-neg-in 99.6%

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

   6. Simplified 99.6%

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

   if -1.8999999999999999e49 < t < 8.50000000000000015e58

   1. Initial program 91.9%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in z around inf 93.9%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+190}:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+77}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+49}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+58}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 5: 89.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+77}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+34}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+55}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (- x (/ y (/ t a))) (/ y (/ t z)))))
   (if (<= t -2.8e+190)
     t_1
     (if (<= t -1.05e+77)
       (+ x (+ y (/ (- t z) (/ (- a t) y))))
       (if (<= t -9e+34)
         (- x (* z (/ y (- a t))))
         (if (<= t 3.6e+55) (- (+ x y) (* y (/ (- z t) (- a t)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y / (t / a))) + (y / (t / z));
	double tmp;
	if (t <= -2.8e+190) {
		tmp = t_1;
	} else if (t <= -1.05e+77) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else if (t <= -9e+34) {
		tmp = x - (z * (y / (a - t)));
	} else if (t <= 3.6e+55) {
		tmp = (x + y) - (y * ((z - 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) :: tmp
    t_1 = (x - (y / (t / a))) + (y / (t / z))
    if (t <= (-2.8d+190)) then
        tmp = t_1
    else if (t <= (-1.05d+77)) then
        tmp = x + (y + ((t - z) / ((a - t) / y)))
    else if (t <= (-9d+34)) then
        tmp = x - (z * (y / (a - t)))
    else if (t <= 3.6d+55) then
        tmp = (x + y) - (y * ((z - 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 = (x - (y / (t / a))) + (y / (t / z));
	double tmp;
	if (t <= -2.8e+190) {
		tmp = t_1;
	} else if (t <= -1.05e+77) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else if (t <= -9e+34) {
		tmp = x - (z * (y / (a - t)));
	} else if (t <= 3.6e+55) {
		tmp = (x + y) - (y * ((z - t) / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y / (t / a))) + (y / (t / z))
	tmp = 0
	if t <= -2.8e+190:
		tmp = t_1
	elif t <= -1.05e+77:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	elif t <= -9e+34:
		tmp = x - (z * (y / (a - t)))
	elif t <= 3.6e+55:
		tmp = (x + y) - (y * ((z - t) / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y / Float64(t / a))) + Float64(y / Float64(t / z)))
	tmp = 0.0
	if (t <= -2.8e+190)
		tmp = t_1;
	elseif (t <= -1.05e+77)
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	elseif (t <= -9e+34)
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	elseif (t <= 3.6e+55)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y / (t / a))) + (y / (t / z));
	tmp = 0.0;
	if (t <= -2.8e+190)
		tmp = t_1;
	elseif (t <= -1.05e+77)
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	elseif (t <= -9e+34)
		tmp = x - (z * (y / (a - t)));
	elseif (t <= 3.6e+55)
		tmp = (x + y) - (y * ((z - 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[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+190], t$95$1, If[LessEqual[t, -1.05e+77], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e+34], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+55], N[(N[(x + y), $MachinePrecision] - N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.79999999999999997e190 or 3.59999999999999987e55 < t

   1. Initial program 53.8%

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

      1. associate-*l/ 60.7%

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

   3. Simplified 60.7%

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

   4. Taylor expanded in t around inf 85.3%

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

      1. sub-neg 85.3%

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

      2. +-commutative 85.3%

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

      3. mul-1-neg 85.3%

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

      4. unsub-neg 85.3%

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

      5. associate-/l* 87.6%

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

      6. mul-1-neg 87.6%

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

      7. remove-double-neg 87.6%

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

      8. associate-/l* 94.4%

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

   6. Simplified 94.4%

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

   if -2.79999999999999997e190 < t < -1.0499999999999999e77

   1. Initial program 70.8%

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

      1. associate--l+ 75.0%

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

      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 -1.0499999999999999e77 < t < -9.0000000000000001e34

   1. Initial program 52.2%

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

      1. associate--l+ 52.3%

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

      2. sub-neg 52.3%

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

      3. +-commutative 52.3%

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

      4. associate-/l* 60.3%

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

      5. distribute-neg-frac 60.3%

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

      6. associate-/r/ 60.4%

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

      7. fma-def 60.7%

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

      8. sub-neg 60.7%

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

      9. +-commutative 60.7%

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

      10. distribute-neg-in 60.7%

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

      11. unsub-neg 60.7%

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

      12. remove-double-neg 60.7%

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

   3. Simplified 60.7%

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

   4. Taylor expanded in z around inf 81.6%

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

      1. mul-1-neg 81.6%

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

      2. *-commutative 81.6%

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

      3. associate-*r/ 90.2%

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

      4. distribute-lft-neg-in 90.2%

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

   6. Simplified 90.2%

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

   if -9.0000000000000001e34 < t < 3.59999999999999987e55

   1. Initial program 92.5%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+190}:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+77}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+34}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+55}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 6: 89.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-171} \lor \neg \left(a \leq 10^{+23}\right):\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.02e-171) (not (<= a 1e+23)))
   (+ x (+ y (/ (- t z) (/ (- a t) y))))
   (- x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.02e-171) || !(a <= 1e+23)) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} 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 <= (-1.02d-171)) .or. (.not. (a <= 1d+23))) then
        tmp = x + (y + ((t - z) / ((a - t) / y)))
    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 <= -1.02e-171) || !(a <= 1e+23)) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.02e-171) or not (a <= 1e+23):
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	else:
		tmp = x - (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.02e-171) || !(a <= 1e+23))
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	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 <= -1.02e-171) || ~((a <= 1e+23)))
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	else
		tmp = x - (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.02e-171], N[Not[LessEqual[a, 1e+23]], $MachinePrecision]], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $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 < -1.02e-171 or 9.9999999999999992e22 < a

   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+ 84.1%

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

      2. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   if -1.02e-171 < a < 9.9999999999999992e22

   1. Initial program 67.3%

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

      1. associate--l+ 72.6%

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

      2. sub-neg 72.6%

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

      3. +-commutative 72.6%

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

      4. associate-/l* 77.0%

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

      5. distribute-neg-frac 77.0%

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

      6. associate-/r/ 81.0%

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

      7. fma-def 81.0%

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

      8. sub-neg 81.0%

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

      9. +-commutative 81.0%

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

      10. distribute-neg-in 81.0%

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

      11. unsub-neg 81.0%

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

      12. remove-double-neg 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in z around inf 87.5%

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

      1. mul-1-neg 87.5%

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

      2. *-commutative 87.5%

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

      3. associate-*r/ 90.4%

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

      4. distribute-lft-neg-in 90.4%

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

   6. Simplified 90.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-171} \lor \neg \left(a \leq 10^{+23}\right):\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 7: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+41} \lor \neg \left(a \leq 10^{+23}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.7e+41) (not (<= a 1e+23)))
   (- (+ x y) (* y (/ z (- a t))))
   (- x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.7e+41) || !(a <= 1e+23)) {
		tmp = (x + y) - (y * (z / (a - t)));
	} 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 <= (-1.7d+41)) .or. (.not. (a <= 1d+23))) then
        tmp = (x + y) - (y * (z / (a - t)))
    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 <= -1.7e+41) || !(a <= 1e+23)) {
		tmp = (x + y) - (y * (z / (a - t)));
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.7e+41) or not (a <= 1e+23):
		tmp = (x + y) - (y * (z / (a - t)))
	else:
		tmp = x - (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.7e+41) || !(a <= 1e+23))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / Float64(a - t))));
	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 <= -1.7e+41) || ~((a <= 1e+23)))
		tmp = (x + y) - (y * (z / (a - t)));
	else
		tmp = x - (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.7e+41], N[Not[LessEqual[a, 1e+23]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / N[(a - t), $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 < -1.69999999999999999e41 or 9.9999999999999992e22 < a

   1. Initial program 84.2%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around inf 90.7%

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

   if -1.69999999999999999e41 < a < 9.9999999999999992e22

   1. Initial program 70.2%

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

      1. associate--l+ 74.5%

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

      2. sub-neg 74.5%

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

      3. +-commutative 74.5%

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

      4. associate-/l* 78.4%

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

      5. distribute-neg-frac 78.4%

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

      6. associate-/r/ 81.9%

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

      7. fma-def 81.9%

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

      8. sub-neg 81.9%

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

      9. +-commutative 81.9%

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

      10. distribute-neg-in 81.9%

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

      11. unsub-neg 81.9%

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

      12. remove-double-neg 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in z around inf 84.6%

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

      1. mul-1-neg 84.6%

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

      2. *-commutative 84.6%

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

      3. associate-*r/ 86.6%

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

      4. distribute-lft-neg-in 86.6%

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

   6. Simplified 86.6%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+41} \lor \neg \left(a \leq 10^{+23}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 8: 81.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-115} \lor \neg \left(a \leq 10^{+23}\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.6e-115) (not (<= a 1e+23)))
   (+ y (- x (/ y (/ a z))))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.6e-115) || !(a <= 1e+23)) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.6d-115)) .or. (.not. (a <= 1d+23))) then
        tmp = y + (x - (y / (a / z)))
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.6e-115) || !(a <= 1e+23)) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.6e-115) or not (a <= 1e+23):
		tmp = y + (x - (y / (a / z)))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.6e-115) || !(a <= 1e+23))
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.6e-115) || ~((a <= 1e+23)))
		tmp = y + (x - (y / (a / z)));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.6e-115], N[Not[LessEqual[a, 1e+23]], $MachinePrecision]], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.59999999999999969e-115 or 9.9999999999999992e22 < 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/ 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in t around 0 80.1%

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

      1. associate--l+ 80.1%

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

      2. associate-/l* 82.8%

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

   6. Simplified 82.8%

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

   if -4.59999999999999969e-115 < a < 9.9999999999999992e22

   1. Initial program 69.3%

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

      1. associate--l+ 75.0%

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

      2. sub-neg 75.0%

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

      3. +-commutative 75.0%

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

      4. associate-/l* 78.3%

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

      5. distribute-neg-frac 78.3%

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

      6. associate-/r/ 82.7%

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

      7. fma-def 82.7%

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

      8. sub-neg 82.7%

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

      9. +-commutative 82.7%

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

      10. distribute-neg-in 82.7%

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

      11. unsub-neg 82.7%

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

      12. remove-double-neg 82.7%

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

   3. Simplified 82.7%

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

   4. Taylor expanded in z around inf 87.8%

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

      1. associate-*r/ 87.8%

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

      2. associate-*r* 87.8%

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

      3. neg-mul-1 87.8%

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

   6. Simplified 87.8%

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

   7. Taylor expanded in a around 0 81.9%

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

      1. associate-/l* 84.5%

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

   9. Simplified 84.5%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-115} \lor \neg \left(a \leq 10^{+23}\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 9: 81.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-105} \lor \neg \left(a \leq 3.4 \cdot 10^{+50}\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.2e-105) (not (<= a 3.4e+50)))
   (+ y (- x (/ y (/ a z))))
   (+ x (/ (* y (- z a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.2e-105) || !(a <= 3.4e+50)) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.2d-105)) .or. (.not. (a <= 3.4d+50))) then
        tmp = y + (x - (y / (a / z)))
    else
        tmp = x + ((y * (z - a)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.2e-105) || !(a <= 3.4e+50)) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.2e-105) or not (a <= 3.4e+50):
		tmp = y + (x - (y / (a / z)))
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.2e-105) || !(a <= 3.4e+50))
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.2e-105) || ~((a <= 3.4e+50)))
		tmp = y + (x - (y / (a / z)));
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.2e-105], N[Not[LessEqual[a, 3.4e+50]], $MachinePrecision]], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.19999999999999981e-105 or 3.3999999999999998e50 < a

   1. Initial program 83.1%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in t around 0 82.2%

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

      1. associate--l+ 82.2%

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

      2. associate-/l* 85.2%

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

   6. Simplified 85.2%

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

   if -3.19999999999999981e-105 < a < 3.3999999999999998e50

   1. Initial program 68.7%

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

      1. associate-*l/ 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in t around -inf 84.9%

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

      1. +-commutative 84.9%

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

      2. mul-1-neg 84.9%

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

      3. unsub-neg 84.9%

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

      4. distribute-lft-out-- 84.9%

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

   6. Simplified 84.9%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-105} \lor \neg \left(a \leq 3.4 \cdot 10^{+50}\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]

Alternative 10: 87.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+128} \lor \neg \left(a \leq 3.9 \cdot 10^{+23}\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.2e+128) (not (<= a 3.9e+23)))
   (+ 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 <= -3.2e+128) || !(a <= 3.9e+23)) {
		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 <= (-3.2d+128)) .or. (.not. (a <= 3.9d+23))) 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 <= -3.2e+128) || !(a <= 3.9e+23)) {
		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 <= -3.2e+128) or not (a <= 3.9e+23):
		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 <= -3.2e+128) || !(a <= 3.9e+23))
		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 <= -3.2e+128) || ~((a <= 3.9e+23)))
		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, -3.2e+128], N[Not[LessEqual[a, 3.9e+23]], $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 < -3.19999999999999986e128 or 3.9e23 < a

   1. Initial program 82.9%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in t around 0 86.4%

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

      1. associate--l+ 86.4%

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

      2. associate-/l* 92.1%

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

   6. Simplified 92.1%

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

   if -3.19999999999999986e128 < a < 3.9e23

   1. Initial program 72.9%

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

      1. associate--l+ 77.8%

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

      2. sub-neg 77.8%

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

      3. +-commutative 77.8%

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

      4. associate-/l* 80.4%

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

      5. distribute-neg-frac 80.4%

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

      6. associate-/r/ 84.5%

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

      7. fma-def 84.6%

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

      8. sub-neg 84.6%

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

      9. +-commutative 84.6%

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

      10. distribute-neg-in 84.6%

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

      11. unsub-neg 84.6%

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

      12. remove-double-neg 84.6%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in z around inf 83.6%

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

      1. mul-1-neg 83.6%

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

      2. *-commutative 83.6%

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

      3. associate-*r/ 85.8%

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

      4. distribute-lft-neg-in 85.8%

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

   6. Simplified 85.8%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+128} \lor \neg \left(a \leq 3.9 \cdot 10^{+23}\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 11: 75.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+128} \lor \neg \left(a \leq 5.7 \cdot 10^{+23}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.2e+128) (not (<= a 5.7e+23))) (+ x y) (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.2e+128) || !(a <= 5.7e+23)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.2d+128)) .or. (.not. (a <= 5.7d+23))) then
        tmp = x + y
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.2e+128) || !(a <= 5.7e+23)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.2e+128) or not (a <= 5.7e+23):
		tmp = x + y
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.2e+128) || !(a <= 5.7e+23))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.2e+128) || ~((a <= 5.7e+23)))
		tmp = x + y;
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.2e+128], N[Not[LessEqual[a, 5.7e+23]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.19999999999999986e128 or 5.7e23 < a

   1. Initial program 82.9%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in a around inf 88.8%

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

   if -3.19999999999999986e128 < a < 5.7e23

   1. Initial program 72.9%

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

      1. associate--l+ 77.8%

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

      2. sub-neg 77.8%

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

      3. +-commutative 77.8%

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

      4. associate-/l* 80.4%

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

      5. distribute-neg-frac 80.4%

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

      6. associate-/r/ 84.5%

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

      7. fma-def 84.6%

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

      8. sub-neg 84.6%

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

      9. +-commutative 84.6%

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

      10. distribute-neg-in 84.6%

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

      11. unsub-neg 84.6%

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

      12. remove-double-neg 84.6%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in z around inf 83.6%

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

      1. associate-*r/ 83.6%

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

      2. associate-*r* 83.6%

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

      3. neg-mul-1 83.6%

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

   6. Simplified 83.6%

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

   7. Taylor expanded in a around 0 72.2%

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

      1. associate-/l* 75.0%

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

   9. Simplified 75.0%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+128} \lor \neg \left(a \leq 5.7 \cdot 10^{+23}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 12: 75.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-115}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+23}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.8e-115) (+ x y) (if (<= a 3.9e+23) (+ x (* z (/ y t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e-115) {
		tmp = x + y;
	} else if (a <= 3.9e+23) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.8d-115)) then
        tmp = x + y
    else if (a <= 3.9d+23) then
        tmp = x + (z * (y / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e-115) {
		tmp = x + y;
	} else if (a <= 3.9e+23) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.8e-115:
		tmp = x + y
	elif a <= 3.9e+23:
		tmp = x + (z * (y / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.8e-115)
		tmp = Float64(x + y);
	elseif (a <= 3.9e+23)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.8e-115)
		tmp = x + y;
	elseif (a <= 3.9e+23)
		tmp = x + (z * (y / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.8e-115], N[(x + y), $MachinePrecision], If[LessEqual[a, 3.9e+23], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.80000000000000042e-115 or 3.9e23 < a

   1. Initial program 81.4%

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

      1. associate-*l/ 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in a around inf 75.5%

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

   if -4.80000000000000042e-115 < a < 3.9e23

   1. Initial program 69.9%

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

      1. associate--l+ 75.5%

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

      2. sub-neg 75.5%

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

      3. +-commutative 75.5%

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

      4. associate-/l* 78.6%

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

      5. distribute-neg-frac 78.6%

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

      6. associate-/r/ 83.0%

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

      7. fma-def 83.0%

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

      8. sub-neg 83.0%

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

      9. +-commutative 83.0%

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

      10. distribute-neg-in 83.0%

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

      11. unsub-neg 83.0%

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

      12. remove-double-neg 83.0%

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

   3. Simplified 83.0%

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

   4. Taylor expanded in z around inf 88.0%

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

      1. associate-*r/ 88.0%

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

      2. associate-*r* 88.0%

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

      3. neg-mul-1 88.0%

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

   6. Simplified 88.0%

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

   7. Taylor expanded in a around 0 81.3%

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

      1. associate-/l* 83.9%

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

   9. Simplified 83.9%

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

       1. associate-/r/ 83.0%

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

   11. Applied egg-rr 83.0%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-115}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+23}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13: 62.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+272} \lor \neg \left(z \leq 1.55 \cdot 10^{+216}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.22e+272) (not (<= z 1.55e+216))) (* y (/ z t)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.22e+272) || !(z <= 1.55e+216)) {
		tmp = y * (z / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.22d+272)) .or. (.not. (z <= 1.55d+216))) then
        tmp = y * (z / t)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.22e+272) || !(z <= 1.55e+216)) {
		tmp = y * (z / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.22e+272) or not (z <= 1.55e+216):
		tmp = y * (z / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.22e+272) || !(z <= 1.55e+216))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.22e+272) || ~((z <= 1.55e+216)))
		tmp = y * (z / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.22e+272], N[Not[LessEqual[z, 1.55e+216]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.21999999999999995e272 or 1.55000000000000002e216 < z

   1. Initial program 87.4%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around inf 91.9%

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

   5. Taylor expanded in z around inf 79.1%

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

      1. mul-1-neg 79.1%

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

      2. associate-*r/ 83.1%

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

      3. distribute-rgt-neg-in 83.1%

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

      4. distribute-neg-frac 83.1%

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

   7. Simplified 83.1%

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

   8. Taylor expanded in a around 0 69.8%

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

   if -1.21999999999999995e272 < z < 1.55000000000000002e216

   1. Initial program 75.1%

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

      1. associate-*l/ 79.8%

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

   3. Simplified 79.8%

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

   4. Taylor expanded in a around inf 63.1%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+272} \lor \neg \left(z \leq 1.55 \cdot 10^{+216}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 14: 62.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+263}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+218}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.8e+263)
   (* z (/ (- y) a))
   (if (<= z 5.2e+218) (+ x y) (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.8e+263) {
		tmp = z * (-y / a);
	} else if (z <= 5.2e+218) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.8d+263)) then
        tmp = z * (-y / a)
    else if (z <= 5.2d+218) then
        tmp = x + y
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.8e+263) {
		tmp = z * (-y / a);
	} else if (z <= 5.2e+218) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.8e+263:
		tmp = z * (-y / a)
	elif z <= 5.2e+218:
		tmp = x + y
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.8e+263)
		tmp = Float64(z * Float64(Float64(-y) / a));
	elseif (z <= 5.2e+218)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.8e+263)
		tmp = z * (-y / a);
	elseif (z <= 5.2e+218)
		tmp = x + y;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.8e+263], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+218], N[(x + y), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.7999999999999997e263

   1. Initial program 99.8%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in t around 0 77.9%

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

      1. associate--l+ 77.9%

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

      2. associate-/l* 67.6%

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

   6. Simplified 67.6%

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

   7. Taylor expanded in a around 0 77.9%

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

      1. mul-1-neg 77.9%

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

      2. associate-*l/ 67.3%

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

      3. distribute-rgt-neg-in 67.3%

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

   9. Simplified 67.3%

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

   if -9.7999999999999997e263 < z < 5.20000000000000004e218

   1. Initial program 75.0%

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

      1. associate-*l/ 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in a around inf 63.4%

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

   if 5.20000000000000004e218 < z

   1. Initial program 80.8%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around inf 94.1%

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

   5. Taylor expanded in z around inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. associate-*r/ 80.6%

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

      3. distribute-rgt-neg-in 80.6%

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

      4. distribute-neg-frac 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in a around 0 73.6%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+263}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+218}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 15: 62.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+264}:\\ \;\;\;\;y \cdot \left(-\frac{z}{a}\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+218}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.75e+264)
   (* y (- (/ z a)))
   (if (<= z 6.8e+218) (+ x y) (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.75e+264) {
		tmp = y * -(z / a);
	} else if (z <= 6.8e+218) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.75d+264)) then
        tmp = y * -(z / a)
    else if (z <= 6.8d+218) then
        tmp = x + y
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.75e+264) {
		tmp = y * -(z / a);
	} else if (z <= 6.8e+218) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.75e+264:
		tmp = y * -(z / a)
	elif z <= 6.8e+218:
		tmp = x + y
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.75e+264)
		tmp = Float64(y * Float64(-Float64(z / a)));
	elseif (z <= 6.8e+218)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.75e+264)
		tmp = y * -(z / a);
	elseif (z <= 6.8e+218)
		tmp = x + y;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.75e+264], N[(y * (-N[(z / a), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 6.8e+218], N[(x + y), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.74999999999999994e264

   1. Initial program 99.8%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in t around 0 77.9%

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

      1. associate--l+ 77.9%

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

      2. associate-/l* 67.6%

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

   6. Simplified 67.6%

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

   7. Taylor expanded in a around 0 77.9%

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

      1. mul-1-neg 77.9%

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

      2. associate-*l/ 67.3%

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

      3. distribute-rgt-neg-in 67.3%

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

   9. Simplified 67.3%

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

   10. Taylor expanded in y around 0 77.9%

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

       1. mul-1-neg 77.9%

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

       2. associate-*r/ 67.4%

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

       3. distribute-lft-neg-in 67.4%

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

       4. *-commutative 67.4%

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

   12. Simplified 67.4%

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

   if -1.74999999999999994e264 < z < 6.80000000000000017e218

   1. Initial program 75.0%

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

      1. associate-*l/ 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in a around inf 63.4%

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

   if 6.80000000000000017e218 < z

   1. Initial program 80.8%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around inf 94.1%

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

   5. Taylor expanded in z around inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. associate-*r/ 80.6%

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

      3. distribute-rgt-neg-in 80.6%

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

      4. distribute-neg-frac 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in a around 0 73.6%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+264}:\\ \;\;\;\;y \cdot \left(-\frac{z}{a}\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+218}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 16: 62.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+265}:\\ \;\;\;\;\frac{y \cdot z}{-a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+217}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e+265)
   (/ (* y z) (- a))
   (if (<= z 3.5e+217) (+ x y) (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+265) {
		tmp = (y * z) / -a;
	} else if (z <= 3.5e+217) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.7d+265)) then
        tmp = (y * z) / -a
    else if (z <= 3.5d+217) then
        tmp = x + y
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+265) {
		tmp = (y * z) / -a;
	} else if (z <= 3.5e+217) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e+265:
		tmp = (y * z) / -a
	elif z <= 3.5e+217:
		tmp = x + y
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e+265)
		tmp = Float64(Float64(y * z) / Float64(-a));
	elseif (z <= 3.5e+217)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.7e+265)
		tmp = (y * z) / -a;
	elseif (z <= 3.5e+217)
		tmp = x + y;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e+265], N[(N[(y * z), $MachinePrecision] / (-a)), $MachinePrecision], If[LessEqual[z, 3.5e+217], N[(x + y), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.69999999999999984e265

   1. Initial program 99.8%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in t around 0 77.9%

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

      1. associate--l+ 77.9%

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

      2. associate-/l* 67.6%

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

   6. Simplified 67.6%

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

   7. Taylor expanded in a around 0 77.9%

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

      1. mul-1-neg 77.9%

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

      2. associate-*l/ 67.3%

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

      3. distribute-rgt-neg-in 67.3%

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

   9. Simplified 67.3%

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

       1. associate-*l/ 77.9%

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

       2. add-sqr-sqrt 55.6%

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

       3. times-frac 55.6%

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

       4. add-sqr-sqrt 55.4%

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

       5. sqrt-unprod 44.8%

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

       6. sqr-neg 44.8%

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

       7. sqrt-unprod 0.0%

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

       8. add-sqr-sqrt 0.1%

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

       9. times-frac 0.1%

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

       10. add-sqr-sqrt 11.7%

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

       11. *-commutative 11.7%

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

   11. Applied egg-rr 11.7%

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

       1. *-commutative 11.7%

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

       2. frac-2neg 11.7%

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

       3. div-inv 11.7%

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

       4. distribute-rgt-neg-in 11.7%

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

       5. add-sqr-sqrt 11.7%

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

       6. sqrt-unprod 11.5%

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

       7. sqr-neg 11.5%

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

       8. sqrt-unprod 0.0%

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

       9. add-sqr-sqrt 77.8%

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

   13. Applied egg-rr 77.8%

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

       1. associate-*r/ 77.9%

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

       2. *-rgt-identity 77.9%

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

   15. Simplified 77.9%

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

   if -2.69999999999999984e265 < z < 3.4999999999999998e217

   1. Initial program 75.0%

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

      1. associate-*l/ 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in a around inf 63.4%

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

   if 3.4999999999999998e217 < z

   1. Initial program 80.8%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around inf 94.1%

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

   5. Taylor expanded in z around inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. associate-*r/ 80.6%

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

      3. distribute-rgt-neg-in 80.6%

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

      4. distribute-neg-frac 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in a around 0 73.6%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+265}:\\ \;\;\;\;\frac{y \cdot z}{-a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+217}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 17: 63.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-194}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.5e-194) (+ x y) (if (<= a 1.1e+23) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e-194) {
		tmp = x + y;
	} else if (a <= 1.1e+23) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.5d-194)) then
        tmp = x + y
    else if (a <= 1.1d+23) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e-194) {
		tmp = x + y;
	} else if (a <= 1.1e+23) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.5e-194:
		tmp = x + y
	elif a <= 1.1e+23:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.5e-194)
		tmp = Float64(x + y);
	elseif (a <= 1.1e+23)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.5e-194)
		tmp = x + y;
	elseif (a <= 1.1e+23)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.5e-194], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.1e+23], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.5000000000000005e-194 or 1.10000000000000004e23 < a

   1. Initial program 81.5%

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

      1. associate-*l/ 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in a around inf 73.7%

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

   if -8.5000000000000005e-194 < a < 1.10000000000000004e23

   1. Initial program 67.8%

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

      1. associate-*l/ 71.1%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in x around inf 45.4%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-194}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 18: 50.0% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.32 \cdot 10^{+230}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -1.32e+230) y x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.32e+230) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.32d+230)) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.32e+230) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.32e+230:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.32e+230)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.32e+230)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.32e+230], y, x]

Derivation

1. Split input into 2 regimes

2. if a < -1.32e230

   1. Initial program 76.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 84.4%

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

      1. associate--l+ 84.4%

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

      2. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 76.4%

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

      1. sub-neg 76.4%

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

      2. mul-1-neg 76.4%

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

      3. distribute-rgt-in 76.4%

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

      4. *-lft-identity 76.4%

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

      5. mul-1-neg 76.4%

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

      6. cancel-sign-sub-inv 76.4%

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

      7. *-commutative 76.4%

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

   9. Simplified 76.4%

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

   10. Taylor expanded in z around 0 76.4%

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

   if -1.32e230 < a

   1. Initial program 76.3%

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

      1. associate-*l/ 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in x around inf 51.1%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.32 \cdot 10^{+230}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 50.5% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.2%

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

   1. associate-*l/ 81.1%

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

3. Simplified 81.1%

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

4. Taylor expanded in x around inf 49.8%

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

5. Final simplification 49.8%

   \[\leadsto x \]

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 2023192 
(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))))