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

Percentage Accurate: 85.5% → 92.2%

Time: 15.5s

Alternatives: 9

Speedup: 0.2×

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: 85.5% 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: 92.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x - y \cdot z}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t\_1}{-z}}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-313}:\\ \;\;\;\;\frac{x}{t\_1} - \frac{y \cdot z}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 0 \lor \neg \left(t\_2 \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (/ t_1 (- z)))
     (if (<= t_2 -5e-313)
       (- (/ x t_1) (/ (* y z) t_1))
       (if (or (<= t_2 0.0) (not (<= t_2 5e+302))) (/ (- y (/ x z)) a) t_2)))))

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 / (t_1 / -z);
	} else if (t_2 <= -5e-313) {
		tmp = (x / t_1) - ((y * z) / t_1);
	} else if ((t_2 <= 0.0) || !(t_2 <= 5e+302)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = t_2;
	}
	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 / (t_1 / -z);
	} else if (t_2 <= -5e-313) {
		tmp = (x / t_1) - ((y * z) / t_1);
	} else if ((t_2 <= 0.0) || !(t_2 <= 5e+302)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = t_2;
	}
	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 / (t_1 / -z)
	elif t_2 <= -5e-313:
		tmp = (x / t_1) - ((y * z) / t_1)
	elif (t_2 <= 0.0) or not (t_2 <= 5e+302):
		tmp = (y - (x / z)) / a
	else:
		tmp = t_2
	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(t_1 / Float64(-z)));
	elseif (t_2 <= -5e-313)
		tmp = Float64(Float64(x / t_1) - Float64(Float64(y * z) / t_1));
	elseif ((t_2 <= 0.0) || !(t_2 <= 5e+302))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = t_2;
	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 / (t_1 / -z);
	elseif (t_2 <= -5e-313)
		tmp = (x / t_1) - ((y * z) / t_1);
	elseif ((t_2 <= 0.0) || ~((t_2 <= 5e+302)))
		tmp = (y - (x / z)) / a;
	else
		tmp = t_2;
	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[(t$95$1 / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-313], N[(N[(x / t$95$1), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$2, 0.0], N[Not[LessEqual[t$95$2, 5e+302]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$2]]]]]

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 52.6%

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

      1. *-commutative 52.6%

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

   3. Simplified 52.6%

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

   5. Taylor expanded in x around 0 36.4%

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

      1. associate-*r/ 36.4%

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

      2. mul-1-neg 36.4%

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

      3. distribute-rgt-neg-out 36.4%

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

      4. associate-/l* 83.7%

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

      5. *-commutative 83.7%

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

   7. Simplified 83.7%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -5.00000000002e-313

   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 -5.00000000002e-313 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0 or 5e302 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 42.4%

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

      1. *-commutative 42.4%

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

   3. Simplified 42.4%

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

   5. Taylor expanded in x around 0 42.4%

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

   6. Taylor expanded in a around inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

   8. Simplified 75.0%

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

   if 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 5e302

   1. Initial program 99.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing
3. Recombined 4 regimes into one program.

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t - z \cdot a}{-z}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -5 \cdot 10^{-313}:\\ \;\;\;\;\frac{x}{t - z \cdot a} - \frac{y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0 \lor \neg \left(\frac{x - y \cdot z}{t - z \cdot a} \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x - y \cdot z}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t\_1}{-z}}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-313} \lor \neg \left(t\_2 \leq 0\right) \land t\_2 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

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 (/ t_1 (- z)))
     (if (or (<= t_2 -5e-313) (and (not (<= t_2 0.0)) (<= t_2 5e+302)))
       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 / (t_1 / -z);
	} else if ((t_2 <= -5e-313) || (!(t_2 <= 0.0) && (t_2 <= 5e+302))) {
		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 / (t_1 / -z);
	} else if ((t_2 <= -5e-313) || (!(t_2 <= 0.0) && (t_2 <= 5e+302))) {
		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 / (t_1 / -z)
	elif (t_2 <= -5e-313) or (not (t_2 <= 0.0) and (t_2 <= 5e+302)):
		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(t_1 / Float64(-z)));
	elseif ((t_2 <= -5e-313) || (!(t_2 <= 0.0) && (t_2 <= 5e+302)))
		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 / (t_1 / -z);
	elseif ((t_2 <= -5e-313) || (~((t_2 <= 0.0)) && (t_2 <= 5e+302)))
		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[(t$95$1 / (-z)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$2, -5e-313], And[N[Not[LessEqual[t$95$2, 0.0]], $MachinePrecision], LessEqual[t$95$2, 5e+302]]], t$95$2, N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 52.6%

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

      1. *-commutative 52.6%

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

   3. Simplified 52.6%

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

   5. Taylor expanded in x around 0 36.4%

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

      1. associate-*r/ 36.4%

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

      2. mul-1-neg 36.4%

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

      3. distribute-rgt-neg-out 36.4%

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

      4. associate-/l* 83.7%

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

      5. *-commutative 83.7%

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

   7. Simplified 83.7%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -5.00000000002e-313 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 5e302

   1. Initial program 99.7%

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

   if -5.00000000002e-313 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0 or 5e302 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 42.4%

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

      1. *-commutative 42.4%

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

   3. Simplified 42.4%

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

   5. Taylor expanded in x around 0 42.4%

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

   6. Taylor expanded in a around inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

   8. Simplified 75.0%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t - z \cdot a}{-z}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -5 \cdot 10^{-313} \lor \neg \left(\frac{x - y \cdot z}{t - z \cdot a} \leq 0\right) \land \frac{x - y \cdot z}{t - z \cdot a} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{-y}{t}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y) t))))
   (if (<= z -3.8e+117)
     (/ y a)
     (if (<= z -1.5e+16)
       t_1
       (if (<= z -6.5e-7)
         (/ y a)
         (if (<= z 1.15e-10) (/ x t) (if (<= z 7.6e+81) t_1 (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (-y / t);
	double tmp;
	if (z <= -3.8e+117) {
		tmp = y / a;
	} else if (z <= -1.5e+16) {
		tmp = t_1;
	} else if (z <= -6.5e-7) {
		tmp = y / a;
	} else if (z <= 1.15e-10) {
		tmp = x / t;
	} else if (z <= 7.6e+81) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * (-y / t)
    if (z <= (-3.8d+117)) then
        tmp = y / a
    else if (z <= (-1.5d+16)) then
        tmp = t_1
    else if (z <= (-6.5d-7)) then
        tmp = y / a
    else if (z <= 1.15d-10) then
        tmp = x / t
    else if (z <= 7.6d+81) then
        tmp = t_1
    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 t_1 = z * (-y / t);
	double tmp;
	if (z <= -3.8e+117) {
		tmp = y / a;
	} else if (z <= -1.5e+16) {
		tmp = t_1;
	} else if (z <= -6.5e-7) {
		tmp = y / a;
	} else if (z <= 1.15e-10) {
		tmp = x / t;
	} else if (z <= 7.6e+81) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (-y / t)
	tmp = 0
	if z <= -3.8e+117:
		tmp = y / a
	elif z <= -1.5e+16:
		tmp = t_1
	elif z <= -6.5e-7:
		tmp = y / a
	elif z <= 1.15e-10:
		tmp = x / t
	elif z <= 7.6e+81:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(-y) / t))
	tmp = 0.0
	if (z <= -3.8e+117)
		tmp = Float64(y / a);
	elseif (z <= -1.5e+16)
		tmp = t_1;
	elseif (z <= -6.5e-7)
		tmp = Float64(y / a);
	elseif (z <= 1.15e-10)
		tmp = Float64(x / t);
	elseif (z <= 7.6e+81)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (-y / t);
	tmp = 0.0;
	if (z <= -3.8e+117)
		tmp = y / a;
	elseif (z <= -1.5e+16)
		tmp = t_1;
	elseif (z <= -6.5e-7)
		tmp = y / a;
	elseif (z <= 1.15e-10)
		tmp = x / t;
	elseif (z <= 7.6e+81)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+117], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.5e+16], t$95$1, If[LessEqual[z, -6.5e-7], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.15e-10], N[(x / t), $MachinePrecision], If[LessEqual[z, 7.6e+81], t$95$1, N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000002e117 or -1.5e16 < z < -6.50000000000000024e-7 or 7.599999999999999e81 < z

   1. Initial program 61.4%

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

      1. *-commutative 61.4%

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

   3. Simplified 61.4%

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

   5. Taylor expanded in z around inf 61.5%

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

   if -3.8000000000000002e117 < z < -1.5e16 or 1.15000000000000004e-10 < z < 7.599999999999999e81

   1. Initial program 88.4%

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

      1. *-commutative 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in t around inf 50.6%

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

      1. clear-num 50.5%

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

      2. inv-pow 50.5%

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

   7. Applied egg-rr 50.5%

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

      1. unpow-1 50.5%

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

   9. Simplified 50.5%

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

   10. Taylor expanded in x around 0 37.2%

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

       1. mul-1-neg 37.2%

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

       2. *-commutative 37.2%

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

       3. associate-/l* 42.8%

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

       4. associate-/r/ 42.9%

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

       5. distribute-rgt-neg-in 42.9%

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

   12. Simplified 42.9%

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

   13. Taylor expanded in z around 0 37.2%

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

       1. mul-1-neg 37.2%

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

       2. associate-*l/ 42.9%

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

   15. Simplified 42.9%

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

   if -6.50000000000000024e-7 < z < 1.15000000000000004e-10

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 58.4%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+81}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+117}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+16}:\\ \;\;\;\;\left(-y\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-9}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+88}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.6e+117)
   (/ y a)
   (if (<= z -1.7e+16)
     (* (- y) (/ z t))
     (if (<= z -2.9e-9)
       (/ y a)
       (if (<= z 5.5e-12)
         (/ x t)
         (if (<= z 2.05e+88) (* z (/ (- y) t)) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.6e+117) {
		tmp = y / a;
	} else if (z <= -1.7e+16) {
		tmp = -y * (z / t);
	} else if (z <= -2.9e-9) {
		tmp = y / a;
	} else if (z <= 5.5e-12) {
		tmp = x / t;
	} else if (z <= 2.05e+88) {
		tmp = z * (-y / 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 <= (-8.6d+117)) then
        tmp = y / a
    else if (z <= (-1.7d+16)) then
        tmp = -y * (z / t)
    else if (z <= (-2.9d-9)) then
        tmp = y / a
    else if (z <= 5.5d-12) then
        tmp = x / t
    else if (z <= 2.05d+88) then
        tmp = z * (-y / 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 <= -8.6e+117) {
		tmp = y / a;
	} else if (z <= -1.7e+16) {
		tmp = -y * (z / t);
	} else if (z <= -2.9e-9) {
		tmp = y / a;
	} else if (z <= 5.5e-12) {
		tmp = x / t;
	} else if (z <= 2.05e+88) {
		tmp = z * (-y / t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.6e+117:
		tmp = y / a
	elif z <= -1.7e+16:
		tmp = -y * (z / t)
	elif z <= -2.9e-9:
		tmp = y / a
	elif z <= 5.5e-12:
		tmp = x / t
	elif z <= 2.05e+88:
		tmp = z * (-y / t)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.6e+117)
		tmp = Float64(y / a);
	elseif (z <= -1.7e+16)
		tmp = Float64(Float64(-y) * Float64(z / t));
	elseif (z <= -2.9e-9)
		tmp = Float64(y / a);
	elseif (z <= 5.5e-12)
		tmp = Float64(x / t);
	elseif (z <= 2.05e+88)
		tmp = Float64(z * Float64(Float64(-y) / 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 <= -8.6e+117)
		tmp = y / a;
	elseif (z <= -1.7e+16)
		tmp = -y * (z / t);
	elseif (z <= -2.9e-9)
		tmp = y / a;
	elseif (z <= 5.5e-12)
		tmp = x / t;
	elseif (z <= 2.05e+88)
		tmp = z * (-y / t);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.6e+117], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.7e+16], N[((-y) * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e-9], N[(y / a), $MachinePrecision], If[LessEqual[z, 5.5e-12], N[(x / t), $MachinePrecision], If[LessEqual[z, 2.05e+88], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.59999999999999996e117 or -1.7e16 < z < -2.89999999999999991e-9 or 2.05000000000000014e88 < z

   1. Initial program 61.4%

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

      1. *-commutative 61.4%

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

   3. Simplified 61.4%

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

   5. Taylor expanded in z around inf 61.5%

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

   if -8.59999999999999996e117 < z < -1.7e16

   1. Initial program 83.1%

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

      1. *-commutative 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in t around inf 53.6%

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

      1. clear-num 53.5%

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

      2. inv-pow 53.5%

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

   7. Applied egg-rr 53.5%

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

      1. unpow-1 53.5%

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

   9. Simplified 53.5%

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

   10. Taylor expanded in x around 0 42.3%

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

       1. mul-1-neg 42.3%

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

       2. *-commutative 42.3%

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

       3. associate-/l* 46.5%

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

       4. associate-/r/ 46.6%

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

       5. distribute-rgt-neg-in 46.6%

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

   12. Simplified 46.6%

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

   if -2.89999999999999991e-9 < z < 5.5000000000000004e-12

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 58.4%

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

   if 5.5000000000000004e-12 < z < 2.05000000000000014e88

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in t around inf 48.1%

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

      1. clear-num 48.0%

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

      2. inv-pow 48.0%

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

   7. Applied egg-rr 48.0%

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

      1. unpow-1 48.0%

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

   9. Simplified 48.0%

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

   10. Taylor expanded in x around 0 32.9%

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

       1. mul-1-neg 32.9%

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

       2. *-commutative 32.9%

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

       3. associate-/l* 39.7%

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

       4. associate-/r/ 39.7%

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

       5. distribute-rgt-neg-in 39.7%

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

   12. Simplified 39.7%

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

   13. Taylor expanded in z around 0 32.9%

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

       1. mul-1-neg 32.9%

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

       2. associate-*l/ 39.8%

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

   15. Simplified 39.8%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+117}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+16}:\\ \;\;\;\;\left(-y\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-9}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+88}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ t_2 := \frac{x}{t} - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -9 \cdot 10^{-31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.35 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)) (t_2 (- (/ x t) (* z (/ y t)))))
   (if (<= t -9e-31)
     t_2
     (if (<= t 1.3e-82)
       t_1
       (if (<= t 3.35e+24) (/ x (- t (* z a))) (if (<= t 4.2e+84) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double t_2 = (x / t) - (z * (y / t));
	double tmp;
	if (t <= -9e-31) {
		tmp = t_2;
	} else if (t <= 1.3e-82) {
		tmp = t_1;
	} else if (t <= 3.35e+24) {
		tmp = x / (t - (z * a));
	} else if (t <= 4.2e+84) {
		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 = (y - (x / z)) / a
    t_2 = (x / t) - (z * (y / t))
    if (t <= (-9d-31)) then
        tmp = t_2
    else if (t <= 1.3d-82) then
        tmp = t_1
    else if (t <= 3.35d+24) then
        tmp = x / (t - (z * a))
    else if (t <= 4.2d+84) 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 = (y - (x / z)) / a;
	double t_2 = (x / t) - (z * (y / t));
	double tmp;
	if (t <= -9e-31) {
		tmp = t_2;
	} else if (t <= 1.3e-82) {
		tmp = t_1;
	} else if (t <= 3.35e+24) {
		tmp = x / (t - (z * a));
	} else if (t <= 4.2e+84) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	t_2 = (x / t) - (z * (y / t))
	tmp = 0
	if t <= -9e-31:
		tmp = t_2
	elif t <= 1.3e-82:
		tmp = t_1
	elif t <= 3.35e+24:
		tmp = x / (t - (z * a))
	elif t <= 4.2e+84:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	t_2 = Float64(Float64(x / t) - Float64(z * Float64(y / t)))
	tmp = 0.0
	if (t <= -9e-31)
		tmp = t_2;
	elseif (t <= 1.3e-82)
		tmp = t_1;
	elseif (t <= 3.35e+24)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (t <= 4.2e+84)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	t_2 = (x / t) - (z * (y / t));
	tmp = 0.0;
	if (t <= -9e-31)
		tmp = t_2;
	elseif (t <= 1.3e-82)
		tmp = t_1;
	elseif (t <= 3.35e+24)
		tmp = x / (t - (z * a));
	elseif (t <= 4.2e+84)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t), $MachinePrecision] - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e-31], t$95$2, If[LessEqual[t, 1.3e-82], t$95$1, If[LessEqual[t, 3.35e+24], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+84], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.0000000000000008e-31 or 4.20000000000000037e84 < t

   1. Initial program 85.8%

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

      1. *-commutative 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in z around 0 69.1%

      \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \frac{y}{t} - -1 \cdot \frac{a \cdot x}{{t}^{2}}\right) + \frac{x}{t}} \]

   6. Taylor expanded in y around inf 77.3%

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

      1. associate-*r/ 77.3%

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

      2. neg-mul-1 77.3%

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

   8. Simplified 77.3%

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

   if -9.0000000000000008e-31 < t < 1.3e-82 or 3.35e24 < t < 4.20000000000000037e84

   1. Initial program 82.2%

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

      1. *-commutative 82.2%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in x around 0 81.3%

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

   6. Taylor expanded in a around inf 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

   8. Simplified 75.5%

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

   if 1.3e-82 < t < 3.35e24

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in x around inf 72.6%

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

      1. *-commutative 72.6%

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

   7. Simplified 72.6%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{t} - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-82}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t \leq 3.35 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+84}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ t_2 := \frac{x - y \cdot z}{t}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{-30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.76 \cdot 10^{-84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)) (t_2 (/ (- x (* y z)) t)))
   (if (<= t -5.6e-30)
     t_2
     (if (<= t 1.76e-84)
       t_1
       (if (<= t 6e+23) (/ x (- t (* z a))) (if (<= t 8.5e+80) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double t_2 = (x - (y * z)) / t;
	double tmp;
	if (t <= -5.6e-30) {
		tmp = t_2;
	} else if (t <= 1.76e-84) {
		tmp = t_1;
	} else if (t <= 6e+23) {
		tmp = x / (t - (z * a));
	} else if (t <= 8.5e+80) {
		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 = (y - (x / z)) / a
    t_2 = (x - (y * z)) / t
    if (t <= (-5.6d-30)) then
        tmp = t_2
    else if (t <= 1.76d-84) then
        tmp = t_1
    else if (t <= 6d+23) then
        tmp = x / (t - (z * a))
    else if (t <= 8.5d+80) 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 = (y - (x / z)) / a;
	double t_2 = (x - (y * z)) / t;
	double tmp;
	if (t <= -5.6e-30) {
		tmp = t_2;
	} else if (t <= 1.76e-84) {
		tmp = t_1;
	} else if (t <= 6e+23) {
		tmp = x / (t - (z * a));
	} else if (t <= 8.5e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	t_2 = (x - (y * z)) / t
	tmp = 0
	if t <= -5.6e-30:
		tmp = t_2
	elif t <= 1.76e-84:
		tmp = t_1
	elif t <= 6e+23:
		tmp = x / (t - (z * a))
	elif t <= 8.5e+80:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	t_2 = Float64(Float64(x - Float64(y * z)) / t)
	tmp = 0.0
	if (t <= -5.6e-30)
		tmp = t_2;
	elseif (t <= 1.76e-84)
		tmp = t_1;
	elseif (t <= 6e+23)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (t <= 8.5e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	t_2 = (x - (y * z)) / t;
	tmp = 0.0;
	if (t <= -5.6e-30)
		tmp = t_2;
	elseif (t <= 1.76e-84)
		tmp = t_1;
	elseif (t <= 6e+23)
		tmp = x / (t - (z * a));
	elseif (t <= 8.5e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -5.6e-30], t$95$2, If[LessEqual[t, 1.76e-84], t$95$1, If[LessEqual[t, 6e+23], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+80], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.59999999999999977e-30 or 8.50000000000000007e80 < t

   1. Initial program 85.7%

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

      1. *-commutative 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in t around inf 72.4%

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

   if -5.59999999999999977e-30 < t < 1.76e-84 or 6.0000000000000002e23 < t < 8.50000000000000007e80

   1. Initial program 82.4%

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

      1. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in x around 0 81.5%

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

   6. Taylor expanded in a around inf 74.8%

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

      1. mul-1-neg 74.8%

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

      2. unsub-neg 74.8%

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

   8. Simplified 74.8%

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

   if 1.76e-84 < t < 6.0000000000000002e23

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in x around inf 72.6%

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

      1. *-commutative 72.6%

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

   7. Simplified 72.6%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-30}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.76 \cdot 10^{-84}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+142} \lor \neg \left(z \leq 5 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.4e+142) (not (<= z 5e+79))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e+142) || !(z <= 5e+79)) {
		tmp = y / a;
	} else {
		tmp = x / (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 <= (-4.4d+142)) .or. (.not. (z <= 5d+79))) then
        tmp = y / a
    else
        tmp = x / (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 <= -4.4e+142) || !(z <= 5e+79)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.4e+142) or not (z <= 5e+79):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.4e+142) || !(z <= 5e+79))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.4e+142) || ~((z <= 5e+79)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.4e+142], N[Not[LessEqual[z, 5e+79]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.39999999999999974e142 or 5e79 < z

   1. Initial program 56.4%

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

      1. *-commutative 56.4%

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

   3. Simplified 56.4%

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

   5. Taylor expanded in z around inf 62.7%

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

   if -4.39999999999999974e142 < z < 5e79

   1. Initial program 96.6%

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

      1. *-commutative 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in x around inf 67.6%

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

      1. *-commutative 67.6%

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

   7. Simplified 67.6%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+142} \lor \neg \left(z \leq 5 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-7} \lor \neg \left(z \leq 4.2 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1e-7) (not (<= z 4.2e+80))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1e-7) || !(z <= 4.2e+80)) {
		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 <= (-1d-7)) .or. (.not. (z <= 4.2d+80))) 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 <= -1e-7) || !(z <= 4.2e+80)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1e-7) or not (z <= 4.2e+80):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1e-7) || !(z <= 4.2e+80))
		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 <= -1e-7) || ~((z <= 4.2e+80)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1e-7], N[Not[LessEqual[z, 4.2e+80]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999995e-8 or 4.20000000000000003e80 < z

   1. Initial program 65.3%

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

      1. *-commutative 65.3%

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

   3. Simplified 65.3%

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

   5. Taylor expanded in z around inf 52.6%

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

   if -9.9999999999999995e-8 < z < 4.20000000000000003e80

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 52.2%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-7} \lor \neg \left(z \leq 4.2 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.7% 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 84.5%

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

   1. *-commutative 84.5%

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

3. Simplified 84.5%

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

5. Taylor expanded in z around 0 36.0%

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

6. Final simplification 36.0%

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

Developer target: 97.4% 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 2024041 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (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))))