Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A

Percentage Accurate: 84.8% → 95.5%

Time: 15.5s

Alternatives: 14

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

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

C

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

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 - (a * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

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

C

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

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 - (a * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := t - z \cdot a\\ t_3 := \frac{x - y \cdot z}{t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{z}{t\_1} + \frac{x}{y \cdot t\_2}\right)\\ \mathbf{elif}\;t\_3 \leq -1 \cdot 10^{-320}:\\ \;\;\;\;\frac{y \cdot z}{t\_1} + \frac{x}{t\_2}\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+294}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t)) (t_2 (- t (* z a))) (t_3 (/ (- x (* y z)) t_2)))
   (if (<= t_3 (- INFINITY))
     (* y (+ (/ z t_1) (/ x (* y t_2))))
     (if (<= t_3 -1e-320)
       (+ (/ (* y z) t_1) (/ x t_2))
       (if (<= t_3 0.0)
         (/ y (- a (/ t z)))
         (if (<= t_3 5e+294) t_3 (/ (- y (/ x z)) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = t - (z * a);
	double t_3 = (x - (y * z)) / t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = y * ((z / t_1) + (x / (y * t_2)));
	} else if (t_3 <= -1e-320) {
		tmp = ((y * z) / t_1) + (x / t_2);
	} else if (t_3 <= 0.0) {
		tmp = y / (a - (t / z));
	} else if (t_3 <= 5e+294) {
		tmp = t_3;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = t - (z * a);
	double t_3 = (x - (y * z)) / t_2;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((z / t_1) + (x / (y * t_2)));
	} else if (t_3 <= -1e-320) {
		tmp = ((y * z) / t_1) + (x / t_2);
	} else if (t_3 <= 0.0) {
		tmp = y / (a - (t / z));
	} else if (t_3 <= 5e+294) {
		tmp = t_3;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	t_2 = t - (z * a)
	t_3 = (x - (y * z)) / t_2
	tmp = 0
	if t_3 <= -math.inf:
		tmp = y * ((z / t_1) + (x / (y * t_2)))
	elif t_3 <= -1e-320:
		tmp = ((y * z) / t_1) + (x / t_2)
	elif t_3 <= 0.0:
		tmp = y / (a - (t / z))
	elif t_3 <= 5e+294:
		tmp = t_3
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(t - Float64(z * a))
	t_3 = Float64(Float64(x - Float64(y * z)) / t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(z / t_1) + Float64(x / Float64(y * t_2))));
	elseif (t_3 <= -1e-320)
		tmp = Float64(Float64(Float64(y * z) / t_1) + Float64(x / t_2));
	elseif (t_3 <= 0.0)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (t_3 <= 5e+294)
		tmp = t_3;
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * a) - t;
	t_2 = t - (z * a);
	t_3 = (x - (y * z)) / t_2;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = y * ((z / t_1) + (x / (y * t_2)));
	elseif (t_3 <= -1e-320)
		tmp = ((y * z) / t_1) + (x / t_2);
	elseif (t_3 <= 0.0)
		tmp = y / (a - (t / z));
	elseif (t_3 <= 5e+294)
		tmp = t_3;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(y * N[(N[(z / t$95$1), $MachinePrecision] + N[(x / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -1e-320], N[(N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(x / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+294], t$95$3, N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 67.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 67.2%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in y around inf 99.8%

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

   7. Simplified 99.8%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -9.99989e-321

   1. Initial program 99.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 99.7%

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

   if -9.99989e-321 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 54.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 54.8%

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

   3. Simplified 54.8%

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

   5. Taylor expanded in z around inf 54.8%

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

   6. Taylor expanded in x around 0 85.4%

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

      1. associate-*r/ 85.4%

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

      2. mul-1-neg 85.4%

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

   8. Simplified 85.4%

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

   if 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 4.9999999999999999e294

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   if 4.9999999999999999e294 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 38.3%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 38.3%

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

   3. Simplified 38.3%

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

   5. Taylor expanded in y around -inf 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in a around inf 90.0%

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

      1. associate-*r/ 90.0%

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

      2. associate-*r* 90.0%

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

      3. mul-1-neg 90.0%

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

      4. sub-neg 90.0%

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

      5. metadata-eval 90.0%

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

   10. Simplified 90.0%

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

   11. Taylor expanded in y around 0 90.0%

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

       1. mul-1-neg 90.0%

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

       2. unsub-neg 90.0%

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

   13. Simplified 90.0%

       \[\leadsto \frac{\color{blue}{y - \frac{x}{z}}}{a} \]
3. Recombined 5 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot \left(t - z \cdot a\right)}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -1 \cdot 10^{-320}:\\ \;\;\;\;\frac{y \cdot z}{z \cdot a - t} + \frac{x}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 5 \cdot 10^{+294}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x - y \cdot z}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot t\_1}\right)\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-320}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+294}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))) (t_2 (/ (- x (* y z)) t_1)))
   (if (<= t_2 (- INFINITY))
     (* y (+ (/ z (- (* z a) t)) (/ x (* y t_1))))
     (if (<= t_2 -1e-320)
       t_2
       (if (<= t_2 0.0)
         (/ y (- a (/ t z)))
         (if (<= t_2 5e+294) t_2 (/ (- y (/ x z)) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (x - (y * z)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = y * ((z / ((z * a) - t)) + (x / (y * t_1)));
	} else if (t_2 <= -1e-320) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y / (a - (t / z));
	} else if (t_2 <= 5e+294) {
		tmp = t_2;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (x - (y * z)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((z / ((z * a) - t)) + (x / (y * t_1)));
	} else if (t_2 <= -1e-320) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y / (a - (t / z));
	} else if (t_2 <= 5e+294) {
		tmp = t_2;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	t_2 = (x - (y * z)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = y * ((z / ((z * a) - t)) + (x / (y * t_1)))
	elif t_2 <= -1e-320:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y / (a - (t / z))
	elif t_2 <= 5e+294:
		tmp = t_2
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(Float64(x - Float64(y * z)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(z / Float64(Float64(z * a) - t)) + Float64(x / Float64(y * t_1))));
	elseif (t_2 <= -1e-320)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (t_2 <= 5e+294)
		tmp = t_2;
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	t_2 = (x - (y * z)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = y * ((z / ((z * a) - t)) + (x / (y * t_1)));
	elseif (t_2 <= -1e-320)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y / (a - (t / z));
	elseif (t_2 <= 5e+294)
		tmp = t_2;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(y * N[(N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(x / N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-320], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+294], t$95$2, N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 67.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 67.2%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in y around inf 99.8%

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

   7. Simplified 99.8%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -9.99989e-321 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 4.9999999999999999e294

   1. Initial program 99.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   if -9.99989e-321 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 54.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 54.8%

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

   3. Simplified 54.8%

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

   5. Taylor expanded in z around inf 54.8%

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

   6. Taylor expanded in x around 0 85.4%

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

      1. associate-*r/ 85.4%

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

      2. mul-1-neg 85.4%

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

   8. Simplified 85.4%

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

   if 4.9999999999999999e294 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 38.3%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 38.3%

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

   3. Simplified 38.3%

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

   5. Taylor expanded in y around -inf 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in a around inf 90.0%

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

      1. associate-*r/ 90.0%

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

      2. associate-*r* 90.0%

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

      3. mul-1-neg 90.0%

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

      4. sub-neg 90.0%

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

      5. metadata-eval 90.0%

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

   10. Simplified 90.0%

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

   11. Taylor expanded in y around 0 90.0%

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

       1. mul-1-neg 90.0%

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

       2. unsub-neg 90.0%

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

   13. Simplified 90.0%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot \left(t - z \cdot a\right)}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -1 \cdot 10^{-320}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 5 \cdot 10^{+294}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a - \frac{t}{z}}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ t_3 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-201}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-275}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- a (/ t z))))
        (t_2 (/ (- y (/ x z)) a))
        (t_3 (/ x (- t (* z a)))))
   (if (<= z -2.8e+130)
     t_2
     (if (<= z -9.2e+63)
       t_1
       (if (<= z -4.1e-16)
         t_2
         (if (<= z -2.1e-69)
           t_1
           (if (<= z -4.5e-201)
             t_3
             (if (<= z 1.32e-275)
               (/ (- x (* y z)) t)
               (if (<= z 6.5e+18) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a - (t / z));
	double t_2 = (y - (x / z)) / a;
	double t_3 = x / (t - (z * a));
	double tmp;
	if (z <= -2.8e+130) {
		tmp = t_2;
	} else if (z <= -9.2e+63) {
		tmp = t_1;
	} else if (z <= -4.1e-16) {
		tmp = t_2;
	} else if (z <= -2.1e-69) {
		tmp = t_1;
	} else if (z <= -4.5e-201) {
		tmp = t_3;
	} else if (z <= 1.32e-275) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 6.5e+18) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = y / (a - (t / z))
    t_2 = (y - (x / z)) / a
    t_3 = x / (t - (z * a))
    if (z <= (-2.8d+130)) then
        tmp = t_2
    else if (z <= (-9.2d+63)) then
        tmp = t_1
    else if (z <= (-4.1d-16)) then
        tmp = t_2
    else if (z <= (-2.1d-69)) then
        tmp = t_1
    else if (z <= (-4.5d-201)) then
        tmp = t_3
    else if (z <= 1.32d-275) then
        tmp = (x - (y * z)) / t
    else if (z <= 6.5d+18) then
        tmp = t_3
    else
        tmp = t_2
    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 / (a - (t / z));
	double t_2 = (y - (x / z)) / a;
	double t_3 = x / (t - (z * a));
	double tmp;
	if (z <= -2.8e+130) {
		tmp = t_2;
	} else if (z <= -9.2e+63) {
		tmp = t_1;
	} else if (z <= -4.1e-16) {
		tmp = t_2;
	} else if (z <= -2.1e-69) {
		tmp = t_1;
	} else if (z <= -4.5e-201) {
		tmp = t_3;
	} else if (z <= 1.32e-275) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 6.5e+18) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a - (t / z))
	t_2 = (y - (x / z)) / a
	t_3 = x / (t - (z * a))
	tmp = 0
	if z <= -2.8e+130:
		tmp = t_2
	elif z <= -9.2e+63:
		tmp = t_1
	elif z <= -4.1e-16:
		tmp = t_2
	elif z <= -2.1e-69:
		tmp = t_1
	elif z <= -4.5e-201:
		tmp = t_3
	elif z <= 1.32e-275:
		tmp = (x - (y * z)) / t
	elif z <= 6.5e+18:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a - Float64(t / z)))
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	t_3 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (z <= -2.8e+130)
		tmp = t_2;
	elseif (z <= -9.2e+63)
		tmp = t_1;
	elseif (z <= -4.1e-16)
		tmp = t_2;
	elseif (z <= -2.1e-69)
		tmp = t_1;
	elseif (z <= -4.5e-201)
		tmp = t_3;
	elseif (z <= 1.32e-275)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 6.5e+18)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a - (t / z));
	t_2 = (y - (x / z)) / a;
	t_3 = x / (t - (z * a));
	tmp = 0.0;
	if (z <= -2.8e+130)
		tmp = t_2;
	elseif (z <= -9.2e+63)
		tmp = t_1;
	elseif (z <= -4.1e-16)
		tmp = t_2;
	elseif (z <= -2.1e-69)
		tmp = t_1;
	elseif (z <= -4.5e-201)
		tmp = t_3;
	elseif (z <= 1.32e-275)
		tmp = (x - (y * z)) / t;
	elseif (z <= 6.5e+18)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+130], t$95$2, If[LessEqual[z, -9.2e+63], t$95$1, If[LessEqual[z, -4.1e-16], t$95$2, If[LessEqual[z, -2.1e-69], t$95$1, If[LessEqual[z, -4.5e-201], t$95$3, If[LessEqual[z, 1.32e-275], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 6.5e+18], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.7999999999999999e130 or -9.19999999999999973e63 < z < -4.10000000000000006e-16 or 6.5e18 < z

   1. Initial program 70.3%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in y around -inf 76.3%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in a around inf 80.1%

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

      1. associate-*r/ 80.1%

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

      2. associate-*r* 80.1%

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

      3. mul-1-neg 80.1%

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

      4. sub-neg 80.1%

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

      5. metadata-eval 80.1%

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

   10. Simplified 80.1%

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

   11. Taylor expanded in y around 0 82.6%

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

       1. mul-1-neg 82.6%

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

       2. unsub-neg 82.6%

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

   13. Simplified 82.6%

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

   if -2.7999999999999999e130 < z < -9.19999999999999973e63 or -4.10000000000000006e-16 < z < -2.1e-69

   1. Initial program 80.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in z around inf 77.5%

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

   6. Taylor expanded in x around 0 80.8%

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

      1. associate-*r/ 80.8%

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

      2. mul-1-neg 80.8%

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

   8. Simplified 80.8%

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

   if -2.1e-69 < z < -4.5000000000000002e-201 or 1.31999999999999996e-275 < z < 6.5e18

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 81.3%

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

      1. *-commutative 81.3%

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

   7. Simplified 81.3%

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

   if -4.5000000000000002e-201 < z < 1.31999999999999996e-275

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 90.1%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+130}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-275}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+60}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-273}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -5.2e+130)
     t_2
     (if (<= z -1.15e+60)
       (/ y (- a (/ t z)))
       (if (<= z -1.9e-16)
         t_2
         (if (<= z -1.95e-69)
           (* y (/ z (- (* z a) t)))
           (if (<= z -2.7e-201)
             t_1
             (if (<= z 9.2e-273)
               (/ (- x (* y z)) t)
               (if (<= z 1.5e+21) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -5.2e+130) {
		tmp = t_2;
	} else if (z <= -1.15e+60) {
		tmp = y / (a - (t / z));
	} else if (z <= -1.9e-16) {
		tmp = t_2;
	} else if (z <= -1.95e-69) {
		tmp = y * (z / ((z * a) - t));
	} else if (z <= -2.7e-201) {
		tmp = t_1;
	} else if (z <= 9.2e-273) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 1.5e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = x / (t - (z * a))
    t_2 = (y - (x / z)) / a
    if (z <= (-5.2d+130)) then
        tmp = t_2
    else if (z <= (-1.15d+60)) then
        tmp = y / (a - (t / z))
    else if (z <= (-1.9d-16)) then
        tmp = t_2
    else if (z <= (-1.95d-69)) then
        tmp = y * (z / ((z * a) - t))
    else if (z <= (-2.7d-201)) then
        tmp = t_1
    else if (z <= 9.2d-273) then
        tmp = (x - (y * z)) / t
    else if (z <= 1.5d+21) then
        tmp = t_1
    else
        tmp = t_2
    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 / (t - (z * a));
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -5.2e+130) {
		tmp = t_2;
	} else if (z <= -1.15e+60) {
		tmp = y / (a - (t / z));
	} else if (z <= -1.9e-16) {
		tmp = t_2;
	} else if (z <= -1.95e-69) {
		tmp = y * (z / ((z * a) - t));
	} else if (z <= -2.7e-201) {
		tmp = t_1;
	} else if (z <= 9.2e-273) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 1.5e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -5.2e+130:
		tmp = t_2
	elif z <= -1.15e+60:
		tmp = y / (a - (t / z))
	elif z <= -1.9e-16:
		tmp = t_2
	elif z <= -1.95e-69:
		tmp = y * (z / ((z * a) - t))
	elif z <= -2.7e-201:
		tmp = t_1
	elif z <= 9.2e-273:
		tmp = (x - (y * z)) / t
	elif z <= 1.5e+21:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -5.2e+130)
		tmp = t_2;
	elseif (z <= -1.15e+60)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= -1.9e-16)
		tmp = t_2;
	elseif (z <= -1.95e-69)
		tmp = Float64(y * Float64(z / Float64(Float64(z * a) - t)));
	elseif (z <= -2.7e-201)
		tmp = t_1;
	elseif (z <= 9.2e-273)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 1.5e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -5.2e+130)
		tmp = t_2;
	elseif (z <= -1.15e+60)
		tmp = y / (a - (t / z));
	elseif (z <= -1.9e-16)
		tmp = t_2;
	elseif (z <= -1.95e-69)
		tmp = y * (z / ((z * a) - t));
	elseif (z <= -2.7e-201)
		tmp = t_1;
	elseif (z <= 9.2e-273)
		tmp = (x - (y * z)) / t;
	elseif (z <= 1.5e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -5.2e+130], t$95$2, If[LessEqual[z, -1.15e+60], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.9e-16], t$95$2, If[LessEqual[z, -1.95e-69], N[(y * N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-201], t$95$1, If[LessEqual[z, 9.2e-273], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.5e+21], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.1999999999999996e130 or -1.15000000000000008e60 < z < -1.90000000000000006e-16 or 1.5e21 < z

   1. Initial program 70.3%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in y around -inf 76.3%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in a around inf 80.1%

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

      1. associate-*r/ 80.1%

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

      2. associate-*r* 80.1%

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

      3. mul-1-neg 80.1%

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

      4. sub-neg 80.1%

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

      5. metadata-eval 80.1%

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

   10. Simplified 80.1%

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

   11. Taylor expanded in y around 0 82.6%

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

       1. mul-1-neg 82.6%

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

       2. unsub-neg 82.6%

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

   13. Simplified 82.6%

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

   if -5.1999999999999996e130 < z < -1.15000000000000008e60

   1. Initial program 68.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in z around inf 68.2%

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

   6. Taylor expanded in x around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. mul-1-neg 83.9%

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

   8. Simplified 83.9%

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

   if -1.90000000000000006e-16 < z < -1.9499999999999999e-69

   1. Initial program 99.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 84.0%

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

      1. mul-1-neg 84.0%

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

      2. associate-/l* 82.8%

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

      3. distribute-rgt-neg-in 82.8%

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

      4. distribute-neg-frac2 82.8%

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

      5. cancel-sign-sub-inv 82.8%

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

      6. *-commutative 82.8%

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

      7. +-commutative 82.8%

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

      8. distribute-rgt-neg-out 82.8%

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

      9. distribute-lft-neg-in 82.8%

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

      10. *-commutative 82.8%

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

      11. fma-undefine 82.8%

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

      12. neg-sub0 82.8%

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

      13. fma-undefine 82.8%

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

      14. distribute-rgt-neg-in 82.8%

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

      15. mul-1-neg 82.8%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{-1 \cdot \left(a \cdot z\right)} + t\right)} \]

      16. associate-*r* 82.8%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-1 \cdot a\right) \cdot z} + t\right)} \]

      17. neg-mul-1 82.8%

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

      18. *-commutative 82.8%

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

      19. associate--r+ 82.8%

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

      20. neg-sub0 82.8%

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

      21. distribute-rgt-neg-out 82.8%

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

      22. remove-double-neg 82.8%

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

   7. Simplified 82.8%

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

   if -1.9499999999999999e-69 < z < -2.70000000000000005e-201 or 9.19999999999999923e-273 < z < 1.5e21

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 81.3%

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

      1. *-commutative 81.3%

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

   7. Simplified 81.3%

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

   if -2.70000000000000005e-201 < z < 9.19999999999999923e-273

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 90.1%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+130}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+60}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-16}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-273}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ t_3 := x - y \cdot z\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{+129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+56}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-16}:\\ \;\;\;\;t\_3 \cdot \frac{-1}{z \cdot a}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-276}:\\ \;\;\;\;\frac{t\_3}{t}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a))))
        (t_2 (/ (- y (/ x z)) a))
        (t_3 (- x (* y z))))
   (if (<= z -4.7e+129)
     t_2
     (if (<= z -3.2e+56)
       (/ y (- a (/ t z)))
       (if (<= z -3.1e-16)
         (* t_3 (/ -1.0 (* z a)))
         (if (<= z -1.65e-69)
           (* y (/ z (- (* z a) t)))
           (if (<= z -5.2e-201)
             t_1
             (if (<= z 3.1e-276) (/ t_3 t) (if (<= z 4.4e+18) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = (y - (x / z)) / a;
	double t_3 = x - (y * z);
	double tmp;
	if (z <= -4.7e+129) {
		tmp = t_2;
	} else if (z <= -3.2e+56) {
		tmp = y / (a - (t / z));
	} else if (z <= -3.1e-16) {
		tmp = t_3 * (-1.0 / (z * a));
	} else if (z <= -1.65e-69) {
		tmp = y * (z / ((z * a) - t));
	} else if (z <= -5.2e-201) {
		tmp = t_1;
	} else if (z <= 3.1e-276) {
		tmp = t_3 / t;
	} else if (z <= 4.4e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = x / (t - (z * a))
    t_2 = (y - (x / z)) / a
    t_3 = x - (y * z)
    if (z <= (-4.7d+129)) then
        tmp = t_2
    else if (z <= (-3.2d+56)) then
        tmp = y / (a - (t / z))
    else if (z <= (-3.1d-16)) then
        tmp = t_3 * ((-1.0d0) / (z * a))
    else if (z <= (-1.65d-69)) then
        tmp = y * (z / ((z * a) - t))
    else if (z <= (-5.2d-201)) then
        tmp = t_1
    else if (z <= 3.1d-276) then
        tmp = t_3 / t
    else if (z <= 4.4d+18) then
        tmp = t_1
    else
        tmp = t_2
    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 / (t - (z * a));
	double t_2 = (y - (x / z)) / a;
	double t_3 = x - (y * z);
	double tmp;
	if (z <= -4.7e+129) {
		tmp = t_2;
	} else if (z <= -3.2e+56) {
		tmp = y / (a - (t / z));
	} else if (z <= -3.1e-16) {
		tmp = t_3 * (-1.0 / (z * a));
	} else if (z <= -1.65e-69) {
		tmp = y * (z / ((z * a) - t));
	} else if (z <= -5.2e-201) {
		tmp = t_1;
	} else if (z <= 3.1e-276) {
		tmp = t_3 / t;
	} else if (z <= 4.4e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	t_2 = (y - (x / z)) / a
	t_3 = x - (y * z)
	tmp = 0
	if z <= -4.7e+129:
		tmp = t_2
	elif z <= -3.2e+56:
		tmp = y / (a - (t / z))
	elif z <= -3.1e-16:
		tmp = t_3 * (-1.0 / (z * a))
	elif z <= -1.65e-69:
		tmp = y * (z / ((z * a) - t))
	elif z <= -5.2e-201:
		tmp = t_1
	elif z <= 3.1e-276:
		tmp = t_3 / t
	elif z <= 4.4e+18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	t_3 = Float64(x - Float64(y * z))
	tmp = 0.0
	if (z <= -4.7e+129)
		tmp = t_2;
	elseif (z <= -3.2e+56)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= -3.1e-16)
		tmp = Float64(t_3 * Float64(-1.0 / Float64(z * a)));
	elseif (z <= -1.65e-69)
		tmp = Float64(y * Float64(z / Float64(Float64(z * a) - t)));
	elseif (z <= -5.2e-201)
		tmp = t_1;
	elseif (z <= 3.1e-276)
		tmp = Float64(t_3 / t);
	elseif (z <= 4.4e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	t_2 = (y - (x / z)) / a;
	t_3 = x - (y * z);
	tmp = 0.0;
	if (z <= -4.7e+129)
		tmp = t_2;
	elseif (z <= -3.2e+56)
		tmp = y / (a - (t / z));
	elseif (z <= -3.1e-16)
		tmp = t_3 * (-1.0 / (z * a));
	elseif (z <= -1.65e-69)
		tmp = y * (z / ((z * a) - t));
	elseif (z <= -5.2e-201)
		tmp = t_1;
	elseif (z <= 3.1e-276)
		tmp = t_3 / t;
	elseif (z <= 4.4e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.7e+129], t$95$2, If[LessEqual[z, -3.2e+56], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e-16], N[(t$95$3 * N[(-1.0 / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.65e-69], N[(y * N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.2e-201], t$95$1, If[LessEqual[z, 3.1e-276], N[(t$95$3 / t), $MachinePrecision], If[LessEqual[z, 4.4e+18], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -4.70000000000000008e129 or 4.4e18 < z

   1. Initial program 66.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 66.2%

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

   3. Simplified 66.2%

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

   5. Taylor expanded in y around -inf 74.0%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in a around inf 81.1%

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

      1. associate-*r/ 81.1%

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

      2. associate-*r* 81.1%

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

      3. mul-1-neg 81.1%

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

      4. sub-neg 81.1%

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

      5. metadata-eval 81.1%

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

   10. Simplified 81.1%

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

   11. Taylor expanded in y around 0 84.0%

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

       1. mul-1-neg 84.0%

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

       2. unsub-neg 84.0%

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

   13. Simplified 84.0%

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

   if -4.70000000000000008e129 < z < -3.20000000000000003e56

   1. Initial program 68.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in z around inf 68.2%

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

   6. Taylor expanded in x around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. mul-1-neg 83.9%

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

   8. Simplified 83.9%

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

   if -3.20000000000000003e56 < z < -3.1000000000000001e-16

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around inf 72.8%

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

      1. *-commutative 72.8%

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

   9. Simplified 72.8%

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

   if -3.1000000000000001e-16 < z < -1.65e-69

   1. Initial program 99.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 84.0%

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

      1. mul-1-neg 84.0%

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

      2. associate-/l* 82.8%

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

      3. distribute-rgt-neg-in 82.8%

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

      4. distribute-neg-frac2 82.8%

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

      5. cancel-sign-sub-inv 82.8%

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

      6. *-commutative 82.8%

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

      7. +-commutative 82.8%

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

      8. distribute-rgt-neg-out 82.8%

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

      9. distribute-lft-neg-in 82.8%

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

      10. *-commutative 82.8%

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

      11. fma-undefine 82.8%

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

      12. neg-sub0 82.8%

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

      13. fma-undefine 82.8%

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

      14. distribute-rgt-neg-in 82.8%

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

      15. mul-1-neg 82.8%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{-1 \cdot \left(a \cdot z\right)} + t\right)} \]

      16. associate-*r* 82.8%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-1 \cdot a\right) \cdot z} + t\right)} \]

      17. neg-mul-1 82.8%

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

      18. *-commutative 82.8%

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

      19. associate--r+ 82.8%

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

      20. neg-sub0 82.8%

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

      21. distribute-rgt-neg-out 82.8%

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

      22. remove-double-neg 82.8%

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

   7. Simplified 82.8%

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

   if -1.65e-69 < z < -5.19999999999999965e-201 or 3.09999999999999989e-276 < z < 4.4e18

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 81.3%

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

      1. *-commutative 81.3%

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

   7. Simplified 81.3%

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

   if -5.19999999999999965e-201 < z < 3.09999999999999989e-276

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 90.1%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+129}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+56}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-16}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{-1}{z \cdot a}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-276}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+197} \lor \neg \left(z \leq 5.5 \cdot 10^{+237}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e-16)
   (/ y a)
   (if (<= z -6.1e-80)
     (* z (/ (- y) t))
     (if (<= z 9e+19)
       (/ x t)
       (if (or (<= z 1.02e+197) (not (<= z 5.5e+237)))
         (/ y a)
         (/ (/ (- x) z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e-16) {
		tmp = y / a;
	} else if (z <= -6.1e-80) {
		tmp = z * (-y / t);
	} else if (z <= 9e+19) {
		tmp = x / t;
	} else if ((z <= 1.02e+197) || !(z <= 5.5e+237)) {
		tmp = y / a;
	} else {
		tmp = (-x / z) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.8d-16)) then
        tmp = y / a
    else if (z <= (-6.1d-80)) then
        tmp = z * (-y / t)
    else if (z <= 9d+19) then
        tmp = x / t
    else if ((z <= 1.02d+197) .or. (.not. (z <= 5.5d+237))) then
        tmp = y / a
    else
        tmp = (-x / z) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e-16) {
		tmp = y / a;
	} else if (z <= -6.1e-80) {
		tmp = z * (-y / t);
	} else if (z <= 9e+19) {
		tmp = x / t;
	} else if ((z <= 1.02e+197) || !(z <= 5.5e+237)) {
		tmp = y / a;
	} else {
		tmp = (-x / z) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e-16:
		tmp = y / a
	elif z <= -6.1e-80:
		tmp = z * (-y / t)
	elif z <= 9e+19:
		tmp = x / t
	elif (z <= 1.02e+197) or not (z <= 5.5e+237):
		tmp = y / a
	else:
		tmp = (-x / z) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e-16)
		tmp = Float64(y / a);
	elseif (z <= -6.1e-80)
		tmp = Float64(z * Float64(Float64(-y) / t));
	elseif (z <= 9e+19)
		tmp = Float64(x / t);
	elseif ((z <= 1.02e+197) || !(z <= 5.5e+237))
		tmp = Float64(y / a);
	else
		tmp = Float64(Float64(Float64(-x) / z) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.8e-16)
		tmp = y / a;
	elseif (z <= -6.1e-80)
		tmp = z * (-y / t);
	elseif (z <= 9e+19)
		tmp = x / t;
	elseif ((z <= 1.02e+197) || ~((z <= 5.5e+237)))
		tmp = y / a;
	else
		tmp = (-x / z) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e-16], N[(y / a), $MachinePrecision], If[LessEqual[z, -6.1e-80], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+19], N[(x / t), $MachinePrecision], If[Or[LessEqual[z, 1.02e+197], N[Not[LessEqual[z, 5.5e+237]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(N[((-x) / z), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.8e-16 or 9e19 < z < 1.02000000000000008e197 or 5.5000000000000001e237 < z

   1. Initial program 68.3%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in z around inf 57.4%

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

   if -6.8e-16 < z < -6.1000000000000002e-80

   1. Initial program 99.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.5%

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

      2. associate-/r/ 99.5%

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

      3. sub-neg 99.5%

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

      4. +-commutative 99.5%

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

      5. *-commutative 99.5%

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

      6. distribute-rgt-neg-in 99.5%

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

      7. fma-define 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in a around 0 60.7%

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

   8. Taylor expanded in x around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. *-commutative 61.7%

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

      3. associate-/l* 61.7%

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

      4. distribute-rgt-neg-in 61.7%

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

      5. distribute-neg-frac2 61.7%

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

   10. Simplified 61.7%

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

   if -6.1000000000000002e-80 < z < 9e19

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 61.1%

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

   if 1.02000000000000008e197 < z < 5.5000000000000001e237

   1. Initial program 86.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in y around -inf 86.6%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in a around inf 80.5%

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

      1. associate-*r/ 80.5%

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

      2. associate-*r* 80.5%

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

      3. mul-1-neg 80.5%

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

      4. sub-neg 80.5%

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

      5. metadata-eval 80.5%

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

   10. Simplified 80.5%

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

   11. Taylor expanded in y around 0 79.8%

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

       1. associate-*r/ 79.8%

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

       2. neg-mul-1 79.8%

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

   13. Simplified 79.8%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+197} \lor \neg \left(z \leq 5.5 \cdot 10^{+237}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+55}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+197} \lor \neg \left(z \leq 9 \cdot 10^{+237}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.12e+55)
   (/ y a)
   (if (<= z 8.2e+62)
     (/ x (- t (* z a)))
     (if (or (<= z 1.02e+197) (not (<= z 9e+237)))
       (/ y a)
       (/ (/ (- x) z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.12e+55) {
		tmp = y / a;
	} else if (z <= 8.2e+62) {
		tmp = x / (t - (z * a));
	} else if ((z <= 1.02e+197) || !(z <= 9e+237)) {
		tmp = y / a;
	} else {
		tmp = (-x / z) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.12d+55)) then
        tmp = y / a
    else if (z <= 8.2d+62) then
        tmp = x / (t - (z * a))
    else if ((z <= 1.02d+197) .or. (.not. (z <= 9d+237))) then
        tmp = y / a
    else
        tmp = (-x / z) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.12e+55) {
		tmp = y / a;
	} else if (z <= 8.2e+62) {
		tmp = x / (t - (z * a));
	} else if ((z <= 1.02e+197) || !(z <= 9e+237)) {
		tmp = y / a;
	} else {
		tmp = (-x / z) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.12e+55:
		tmp = y / a
	elif z <= 8.2e+62:
		tmp = x / (t - (z * a))
	elif (z <= 1.02e+197) or not (z <= 9e+237):
		tmp = y / a
	else:
		tmp = (-x / z) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.12e+55)
		tmp = Float64(y / a);
	elseif (z <= 8.2e+62)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif ((z <= 1.02e+197) || !(z <= 9e+237))
		tmp = Float64(y / a);
	else
		tmp = Float64(Float64(Float64(-x) / z) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.12e+55)
		tmp = y / a;
	elseif (z <= 8.2e+62)
		tmp = x / (t - (z * a));
	elseif ((z <= 1.02e+197) || ~((z <= 9e+237)))
		tmp = y / a;
	else
		tmp = (-x / z) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.12e+55], N[(y / a), $MachinePrecision], If[LessEqual[z, 8.2e+62], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.02e+197], N[Not[LessEqual[z, 9e+237]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(N[((-x) / z), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.12000000000000006e55 or 8.19999999999999967e62 < z < 1.02000000000000008e197 or 8.99999999999999928e237 < z

   1. Initial program 61.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in z around inf 62.0%

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

   if -1.12000000000000006e55 < z < 8.19999999999999967e62

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 73.9%

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

      1. *-commutative 73.9%

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

   7. Simplified 73.9%

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

   if 1.02000000000000008e197 < z < 8.99999999999999928e237

   1. Initial program 86.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in y around -inf 86.6%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in a around inf 80.5%

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

      1. associate-*r/ 80.5%

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

      2. associate-*r* 80.5%

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

      3. mul-1-neg 80.5%

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

      4. sub-neg 80.5%

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

      5. metadata-eval 80.5%

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

   10. Simplified 80.5%

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

   11. Taylor expanded in y around 0 79.8%

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

       1. associate-*r/ 79.8%

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

       2. neg-mul-1 79.8%

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

   13. Simplified 79.8%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+55}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+197} \lor \neg \left(z \leq 9 \cdot 10^{+237}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+132} \lor \neg \left(z \leq 5.6 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.6e+132) (not (<= z 5.6e+79)))
   (/ (- y (/ x z)) a)
   (/ (- x (* y z)) (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.6e+132) || !(z <= 5.6e+79)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.6d+132)) .or. (.not. (z <= 5.6d+79))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (y * z)) / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.6e+132) || !(z <= 5.6e+79)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.6e+132) or not (z <= 5.6e+79):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (y * z)) / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.6e+132) || !(z <= 5.6e+79))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.6e+132) || ~((z <= 5.6e+79)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (y * z)) / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.6e+132], N[Not[LessEqual[z, 5.6e+79]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.59999999999999964e132 or 5.6000000000000002e79 < z

   1. Initial program 61.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 61.2%

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

   3. Simplified 61.2%

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

   5. Taylor expanded in y around -inf 72.4%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in a around inf 83.8%

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

      1. associate-*r/ 83.8%

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

      2. associate-*r* 83.8%

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

      3. mul-1-neg 83.8%

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

      4. sub-neg 83.8%

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

      5. metadata-eval 83.8%

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

   10. Simplified 83.8%

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

   11. Taylor expanded in y around 0 84.9%

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

       1. mul-1-neg 84.9%

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

       2. unsub-neg 84.9%

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

   13. Simplified 84.9%

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

   if -8.59999999999999964e132 < z < 5.6000000000000002e79

   1. Initial program 96.4%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+132} \lor \neg \left(z \leq 5.6 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+131}:\\ \;\;\;\;\frac{y \cdot \left(\left(--1\right) - \frac{x}{y \cdot z}\right)}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+80}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+131)
   (/ (* y (- (- -1.0) (/ x (* y z)))) a)
   (if (<= z 5.2e+80) (/ (- x (* y z)) (- t (* z a))) (/ (- y (/ x z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+131) {
		tmp = (y * (-(-1.0) - (x / (y * z)))) / a;
	} else if (z <= 5.2e+80) {
		tmp = (x - (y * z)) / (t - (z * a));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.8d+131)) then
        tmp = (y * (-(-1.0d0) - (x / (y * z)))) / a
    else if (z <= 5.2d+80) then
        tmp = (x - (y * z)) / (t - (z * a))
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+131) {
		tmp = (y * (-(-1.0) - (x / (y * z)))) / a;
	} else if (z <= 5.2e+80) {
		tmp = (x - (y * z)) / (t - (z * a));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e+131:
		tmp = (y * (-(-1.0) - (x / (y * z)))) / a
	elif z <= 5.2e+80:
		tmp = (x - (y * z)) / (t - (z * a))
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+131)
		tmp = Float64(Float64(y * Float64(Float64(-(-1.0)) - Float64(x / Float64(y * z)))) / a);
	elseif (z <= 5.2e+80)
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)));
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.8e+131)
		tmp = (y * (-(-1.0) - (x / (y * z)))) / a;
	elseif (z <= 5.2e+80)
		tmp = (x - (y * z)) / (t - (z * a));
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+131], N[(N[(y * N[((--1.0) - N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 5.2e+80], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7999999999999999e131

   1. Initial program 59.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 59.8%

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

   3. Simplified 59.8%

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

   5. Taylor expanded in y around -inf 69.6%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in a around inf 84.3%

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

      1. associate-*r/ 84.3%

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

      2. associate-*r* 84.3%

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

      3. mul-1-neg 84.3%

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

      4. sub-neg 84.3%

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

      5. metadata-eval 84.3%

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

   10. Simplified 84.3%

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

   if -4.7999999999999999e131 < z < 5.19999999999999963e80

   1. Initial program 96.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   if 5.19999999999999963e80 < z

   1. Initial program 63.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 63.1%

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

   3. Simplified 63.1%

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

   5. Taylor expanded in y around -inf 76.1%

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

   7. Simplified 64.1%

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

   8. Taylor expanded in a around inf 83.2%

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

      1. associate-*r/ 83.2%

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

      2. associate-*r* 83.2%

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

      3. mul-1-neg 83.2%

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

      4. sub-neg 83.2%

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

      5. metadata-eval 83.2%

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

   10. Simplified 83.2%

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

   11. Taylor expanded in y around 0 85.7%

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

       1. mul-1-neg 85.7%

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

       2. unsub-neg 85.7%

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

   13. Simplified 85.7%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+131}:\\ \;\;\;\;\frac{y \cdot \left(\left(--1\right) - \frac{x}{y \cdot z}\right)}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+80}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e+123)
   (/ y a)
   (if (<= z -1.6e-75) (* y (/ (- z) t)) (if (<= z 7.5e+19) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+123) {
		tmp = y / a;
	} else if (z <= -1.6e-75) {
		tmp = y * (-z / t);
	} else if (z <= 7.5e+19) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.5d+123)) then
        tmp = y / a
    else if (z <= (-1.6d-75)) then
        tmp = y * (-z / t)
    else if (z <= 7.5d+19) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+123) {
		tmp = y / a;
	} else if (z <= -1.6e-75) {
		tmp = y * (-z / t);
	} else if (z <= 7.5e+19) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e+123:
		tmp = y / a
	elif z <= -1.6e-75:
		tmp = y * (-z / t)
	elif z <= 7.5e+19:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e+123)
		tmp = Float64(y / a);
	elseif (z <= -1.6e-75)
		tmp = Float64(y * Float64(Float64(-z) / t));
	elseif (z <= 7.5e+19)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.5e+123)
		tmp = y / a;
	elseif (z <= -1.6e-75)
		tmp = y * (-z / t);
	elseif (z <= 7.5e+19)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e+123], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.6e-75], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+19], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5e123 or 7.5e19 < z

   1. Initial program 66.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 66.8%

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

   3. Simplified 66.8%

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

   5. Taylor expanded in z around inf 61.9%

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

   if -3.5e123 < z < -1.59999999999999988e-75

   1. Initial program 86.5%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in x around 0 53.9%

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

      1. mul-1-neg 53.9%

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

      2. associate-/l* 64.6%

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

      3. distribute-rgt-neg-in 64.6%

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

      4. distribute-neg-frac2 64.6%

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

      5. cancel-sign-sub-inv 64.6%

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

      6. *-commutative 64.6%

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

      7. +-commutative 64.6%

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

      8. distribute-rgt-neg-out 64.6%

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

      9. distribute-lft-neg-in 64.6%

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

      10. *-commutative 64.6%

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

      11. fma-undefine 64.6%

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

      12. neg-sub0 64.6%

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

      13. fma-undefine 64.6%

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

      14. distribute-rgt-neg-in 64.6%

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

      15. mul-1-neg 64.6%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{-1 \cdot \left(a \cdot z\right)} + t\right)} \]

      16. associate-*r* 64.6%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-1 \cdot a\right) \cdot z} + t\right)} \]

      17. neg-mul-1 64.6%

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

      18. *-commutative 64.6%

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

      19. associate--r+ 64.6%

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

      20. neg-sub0 64.6%

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

      21. distribute-rgt-neg-out 64.6%

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

      22. remove-double-neg 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in z around 0 42.2%

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

      1. associate-*r/ 42.2%

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

      2. mul-1-neg 42.2%

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

   10. Simplified 42.2%

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

   if -1.59999999999999988e-75 < z < 7.5e19

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 60.5%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e-15)
   (/ y a)
   (if (<= z -3.15e-80)
     (* z (/ (- y) t))
     (if (<= z 1.35e+21) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e-15) {
		tmp = y / a;
	} else if (z <= -3.15e-80) {
		tmp = z * (-y / t);
	} else if (z <= 1.35e+21) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.5d-15)) then
        tmp = y / a
    else if (z <= (-3.15d-80)) then
        tmp = z * (-y / t)
    else if (z <= 1.35d+21) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e-15) {
		tmp = y / a;
	} else if (z <= -3.15e-80) {
		tmp = z * (-y / t);
	} else if (z <= 1.35e+21) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.5e-15:
		tmp = y / a
	elif z <= -3.15e-80:
		tmp = z * (-y / t)
	elif z <= 1.35e+21:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e-15)
		tmp = Float64(y / a);
	elseif (z <= -3.15e-80)
		tmp = Float64(z * Float64(Float64(-y) / t));
	elseif (z <= 1.35e+21)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.5e-15)
		tmp = y / a;
	elseif (z <= -3.15e-80)
		tmp = z * (-y / t);
	elseif (z <= 1.35e+21)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e-15], N[(y / a), $MachinePrecision], If[LessEqual[z, -3.15e-80], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+21], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5e-15 or 1.35e21 < z

   1. Initial program 69.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 69.8%

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

   3. Simplified 69.8%

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

   5. Taylor expanded in z around inf 55.6%

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

   if -1.5e-15 < z < -3.14999999999999983e-80

   1. Initial program 99.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.5%

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

      2. associate-/r/ 99.5%

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

      3. sub-neg 99.5%

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

      4. +-commutative 99.5%

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

      5. *-commutative 99.5%

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

      6. distribute-rgt-neg-in 99.5%

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

      7. fma-define 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in a around 0 60.7%

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

   8. Taylor expanded in x around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. *-commutative 61.7%

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

      3. associate-/l* 61.7%

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

      4. distribute-rgt-neg-in 61.7%

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

      5. distribute-neg-frac2 61.7%

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

   10. Simplified 61.7%

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

   if -3.14999999999999983e-80 < z < 1.35e21

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 61.1%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 71.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-16} \lor \neg \left(z \leq 2 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.4e-16) (not (<= z 2e-72)))
   (/ (- y (/ x z)) a)
   (/ (- x (* y z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e-16) || !(z <= 2e-72)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.4d-16)) .or. (.not. (z <= 2d-72))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (y * z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e-16) || !(z <= 2e-72)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.4e-16) or not (z <= 2e-72):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.4e-16) || !(z <= 2e-72))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.4e-16) || ~((z <= 2e-72)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.4e-16], N[Not[LessEqual[z, 2e-72]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000001e-16 or 1.9999999999999999e-72 < z

   1. Initial program 72.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in y around -inf 78.2%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in a around inf 73.1%

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

      1. associate-*r/ 73.1%

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

      2. associate-*r* 73.1%

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

      3. mul-1-neg 73.1%

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

      4. sub-neg 73.1%

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

      5. metadata-eval 73.1%

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

   10. Simplified 73.1%

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

   11. Taylor expanded in y around 0 77.7%

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

       1. mul-1-neg 77.7%

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

       2. unsub-neg 77.7%

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

   13. Simplified 77.7%

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

   if -4.40000000000000001e-16 < z < 1.9999999999999999e-72

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 77.7%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-16} \lor \neg \left(z \leq 2 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-36} \lor \neg \left(z \leq 4.6 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.5e-36) (not (<= z 4.6e+18))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e-36) || !(z <= 4.6e+18)) {
		tmp = y / a;
	} else {
		tmp = x / 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 <= (-2.5d-36)) .or. (.not. (z <= 4.6d+18))) then
        tmp = y / a
    else
        tmp = x / 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 <= -2.5e-36) || !(z <= 4.6e+18)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.5e-36) or not (z <= 4.6e+18):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.5e-36) || !(z <= 4.6e+18))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.5e-36) || ~((z <= 4.6e+18)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.5e-36], N[Not[LessEqual[z, 4.6e+18]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000002e-36 or 4.6e18 < z

   1. Initial program 71.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 71.7%

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

   3. Simplified 71.7%

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

   5. Taylor expanded in z around inf 53.6%

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

   if -2.50000000000000002e-36 < z < 4.6e18

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 58.0%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-36} \lor \neg \left(z \leq 4.6 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 34.9% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x / t), $MachinePrecision]

Derivation

1. Initial program 84.3%

   \[\frac{x - y \cdot z}{t - a \cdot z} \]
2. Step-by-step derivation

   1. *-commutative 84.3%

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

3. Simplified 84.3%

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

5. Taylor expanded in z around 0 32.8%

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

6. Final simplification 32.8%

   \[\leadsto \frac{x}{t} \]
7. Add Preprocessing

Developer target: 97.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{x}{t\_1} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{if}\;z < -32113435955957344:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z < 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))) (t_2 (- (/ x t_1) (/ y (- (/ t z) a)))))
   (if (< z -32113435955957344.0)
     t_2
     (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 t_1)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	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 = t - (a * z)
    t_2 = (x / t_1) - (y / ((t / z) - a))
    if (z < (-32113435955957344.0d0)) then
        tmp = t_2
    else if (z < 3.5139522372978296d-86) then
        tmp = (x - (y * z)) * (1.0d0 / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * z)
	t_2 = (x / t_1) - (y / ((t / z) - a))
	tmp = 0
	if z < -32113435955957344.0:
		tmp = t_2
	elif z < 3.5139522372978296e-86:
		tmp = (x - (y * z)) * (1.0 / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	t_2 = Float64(Float64(x / t_1) - Float64(y / Float64(Float64(t / z) - a)))
	tmp = 0.0
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = Float64(Float64(x - Float64(y * z)) * Float64(1.0 / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * z);
	t_2 = (x / t_1) - (y / ((t / z) - a));
	tmp = 0.0;
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = (x - (y * z)) * (1.0 / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t$95$1), $MachinePrecision] - N[(y / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -32113435955957344.0], t$95$2, If[Less[z, 3.5139522372978296e-86], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (if (< z -32113435955957344.0) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))