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

Percentage Accurate: 84.7% → 94.8%

Time: 13.5s

Alternatives: 10

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: 84.7% 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: 94.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x}{t_1} - \frac{y}{\frac{t_1}{z}}\\ t_3 := \frac{x - y \cdot z}{t_1}\\ \mathbf{if}\;t_3 \leq -4 \cdot 10^{-320}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{a}}{z}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a)))
        (t_2 (- (/ x t_1) (/ y (/ t_1 z))))
        (t_3 (/ (- x (* y z)) t_1)))
   (if (<= t_3 -4e-320)
     t_2
     (if (<= t_3 0.0)
       (/ (/ (- (* y z) x) a) z)
       (if (<= t_3 INFINITY) t_2 (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (x / t_1) - (y / (t_1 / z));
	double t_3 = (x - (y * z)) / t_1;
	double tmp;
	if (t_3 <= -4e-320) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = (((y * z) - x) / a) / z;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = y / 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 / t_1) - (y / (t_1 / z));
	double t_3 = (x - (y * z)) / t_1;
	double tmp;
	if (t_3 <= -4e-320) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = (((y * z) - x) / a) / z;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	t_2 = (x / t_1) - (y / (t_1 / z))
	t_3 = (x - (y * z)) / t_1
	tmp = 0
	if t_3 <= -4e-320:
		tmp = t_2
	elif t_3 <= 0.0:
		tmp = (((y * z) - x) / a) / z
	elif t_3 <= math.inf:
		tmp = t_2
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(Float64(x / t_1) - Float64(y / Float64(t_1 / z)))
	t_3 = Float64(Float64(x - Float64(y * z)) / t_1)
	tmp = 0.0
	if (t_3 <= -4e-320)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(y * z) - x) / a) / z);
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	t_2 = (x / t_1) - (y / (t_1 / z));
	t_3 = (x - (y * z)) / t_1;
	tmp = 0.0;
	if (t_3 <= -4e-320)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = (((y * z) - x) / a) / z;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = y / 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 / t$95$1), $MachinePrecision] - N[(y / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, -4e-320], t$95$2, If[LessEqual[t$95$3, 0.0], N[(N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / a), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$2, N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -3.99996e-320 or -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

   3. Simplified 92.4%

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

      1. clear-num 91.4%

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

      2. inv-pow 91.4%

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

   5. Applied egg-rr 91.4%

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

   6. Taylor expanded in x around inf 92.0%

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

      1. +-commutative 92.0%

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

      2. mul-1-neg 92.0%

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

      3. unsub-neg 92.0%

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

      4. associate-/l* 97.2%

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

   8. Simplified 97.2%

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

   if -3.99996e-320 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0

   1. Initial program 53.7%

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

      1. *-commutative 53.7%

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

   3. Simplified 53.7%

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

      1. clear-num 53.7%

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

      2. inv-pow 53.7%

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

   5. Applied egg-rr 53.7%

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

   6. Taylor expanded in t around 0 38.3%

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

      1. mul-1-neg 38.3%

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

      2. associate-/r* 84.3%

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

      3. distribute-neg-frac 84.3%

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

      4. *-commutative 84.3%

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

   8. Simplified 84.3%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 100.0%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -4 \cdot 10^{-320}:\\ \;\;\;\;\frac{x}{t - z \cdot a} - \frac{y}{\frac{t - z \cdot a}{z}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{a}}{z}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\frac{x}{t - z \cdot a} - \frac{y}{\frac{t - z \cdot a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 2: 91.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-320}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{a}}{z}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_1 -4e-320)
     t_1
     (if (<= t_1 0.0)
       (/ (/ (- (* y z) x) a) z)
       (if (<= t_1 INFINITY) t_1 (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= -4e-320) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (((y * z) - x) / a) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= -4e-320) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (((y * z) - x) / a) / z;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / (t - (z * a))
	tmp = 0
	if t_1 <= -4e-320:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (((y * z) - x) / a) / z
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_1 <= -4e-320)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(y * z) - x) / a) / z);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / (t - (z * a));
	tmp = 0.0;
	if (t_1 <= -4e-320)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (((y * z) - x) / a) / z;
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-320], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / a), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -3.99996e-320 or -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 92.4%

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

   if -3.99996e-320 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0

   1. Initial program 53.7%

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

      1. *-commutative 53.7%

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

   3. Simplified 53.7%

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

      1. clear-num 53.7%

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

      2. inv-pow 53.7%

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

   5. Applied egg-rr 53.7%

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

   6. Taylor expanded in t around 0 38.3%

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

      1. mul-1-neg 38.3%

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

      2. associate-/r* 84.3%

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

      3. distribute-neg-frac 84.3%

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

      4. *-commutative 84.3%

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

   8. Simplified 84.3%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 100.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -4 \cdot 10^{-320}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{a}}{z}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 3: 54.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+85}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e+85)
   (/ y a)
   (if (<= z -5.7e+35)
     (* z (/ (- y) t))
     (if (<= z 3.8e-74)
       (/ x t)
       (if (<= z 3.7e-44)
         (/ x (* z (- a)))
         (if (<= z 2.35e-30) (/ x t) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+85) {
		tmp = y / a;
	} else if (z <= -5.7e+35) {
		tmp = z * (-y / t);
	} else if (z <= 3.8e-74) {
		tmp = x / t;
	} else if (z <= 3.7e-44) {
		tmp = x / (z * -a);
	} else if (z <= 2.35e-30) {
		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 <= (-2.7d+85)) then
        tmp = y / a
    else if (z <= (-5.7d+35)) then
        tmp = z * (-y / t)
    else if (z <= 3.8d-74) then
        tmp = x / t
    else if (z <= 3.7d-44) then
        tmp = x / (z * -a)
    else if (z <= 2.35d-30) 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 <= -2.7e+85) {
		tmp = y / a;
	} else if (z <= -5.7e+35) {
		tmp = z * (-y / t);
	} else if (z <= 3.8e-74) {
		tmp = x / t;
	} else if (z <= 3.7e-44) {
		tmp = x / (z * -a);
	} else if (z <= 2.35e-30) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e+85:
		tmp = y / a
	elif z <= -5.7e+35:
		tmp = z * (-y / t)
	elif z <= 3.8e-74:
		tmp = x / t
	elif z <= 3.7e-44:
		tmp = x / (z * -a)
	elif z <= 2.35e-30:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e+85)
		tmp = Float64(y / a);
	elseif (z <= -5.7e+35)
		tmp = Float64(z * Float64(Float64(-y) / t));
	elseif (z <= 3.8e-74)
		tmp = Float64(x / t);
	elseif (z <= 3.7e-44)
		tmp = Float64(x / Float64(z * Float64(-a)));
	elseif (z <= 2.35e-30)
		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 <= -2.7e+85)
		tmp = y / a;
	elseif (z <= -5.7e+35)
		tmp = z * (-y / t);
	elseif (z <= 3.8e-74)
		tmp = x / t;
	elseif (z <= 3.7e-44)
		tmp = x / (z * -a);
	elseif (z <= 2.35e-30)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e+85], N[(y / a), $MachinePrecision], If[LessEqual[z, -5.7e+35], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-74], N[(x / t), $MachinePrecision], If[LessEqual[z, 3.7e-44], N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e-30], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.69999999999999983e85 or 2.34999999999999985e-30 < z

   1. Initial program 67.9%

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

      1. *-commutative 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in z around inf 57.3%

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

   if -2.69999999999999983e85 < z < -5.69999999999999993e35

   1. Initial program 78.5%

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

      1. *-commutative 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in x around 0 55.9%

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

      1. associate-*r/ 55.9%

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

      2. *-commutative 55.9%

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

      3. neg-mul-1 55.9%

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

      4. distribute-rgt-neg-in 55.9%

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

   6. Simplified 55.9%

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

   7. Taylor expanded in z around 0 51.0%

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

      1. mul-1-neg 51.0%

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

      2. associate-*l/ 65.4%

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

      3. *-commutative 65.4%

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

      4. distribute-rgt-neg-in 65.4%

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

      5. distribute-neg-frac 65.4%

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

   9. Simplified 65.4%

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

   if -5.69999999999999993e35 < z < 3.7999999999999996e-74 or 3.7e-44 < z < 2.34999999999999985e-30

   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. Taylor expanded in z around 0 61.6%

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

   if 3.7999999999999996e-74 < z < 3.7e-44

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in t around 0 85.7%

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

      1. associate-*r* 85.7%

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

      2. neg-mul-1 85.7%

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

      3. *-commutative 85.7%

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

   9. Simplified 85.7%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+85}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 4: 63.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+85}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.65e+85)
   (/ y a)
   (if (<= z -3.35e+34)
     (* z (/ (- y) t))
     (if (<= z 4.1e-30) (/ x (- t (* z a))) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.65e+85) {
		tmp = y / a;
	} else if (z <= -3.35e+34) {
		tmp = z * (-y / t);
	} else if (z <= 4.1e-30) {
		tmp = x / (t - (z * a));
	} 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 <= (-2.65d+85)) then
        tmp = y / a
    else if (z <= (-3.35d+34)) then
        tmp = z * (-y / t)
    else if (z <= 4.1d-30) then
        tmp = x / (t - (z * a))
    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 <= -2.65e+85) {
		tmp = y / a;
	} else if (z <= -3.35e+34) {
		tmp = z * (-y / t);
	} else if (z <= 4.1e-30) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.65e+85:
		tmp = y / a
	elif z <= -3.35e+34:
		tmp = z * (-y / t)
	elif z <= 4.1e-30:
		tmp = x / (t - (z * a))
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.65e+85)
		tmp = Float64(y / a);
	elseif (z <= -3.35e+34)
		tmp = Float64(z * Float64(Float64(-y) / t));
	elseif (z <= 4.1e-30)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.65e+85)
		tmp = y / a;
	elseif (z <= -3.35e+34)
		tmp = z * (-y / t);
	elseif (z <= 4.1e-30)
		tmp = x / (t - (z * a));
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.65e+85], N[(y / a), $MachinePrecision], If[LessEqual[z, -3.35e+34], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e-30], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.65e85 or 4.1000000000000003e-30 < z

   1. Initial program 67.9%

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

      1. *-commutative 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in z around inf 57.3%

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

   if -2.65e85 < z < -3.3500000000000001e34

   1. Initial program 78.5%

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

      1. *-commutative 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in x around 0 55.9%

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

      1. associate-*r/ 55.9%

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

      2. *-commutative 55.9%

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

      3. neg-mul-1 55.9%

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

      4. distribute-rgt-neg-in 55.9%

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

   6. Simplified 55.9%

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

   7. Taylor expanded in z around 0 51.0%

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

      1. mul-1-neg 51.0%

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

      2. associate-*l/ 65.4%

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

      3. *-commutative 65.4%

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

      4. distribute-rgt-neg-in 65.4%

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

      5. distribute-neg-frac 65.4%

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

   9. Simplified 65.4%

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

   if -3.3500000000000001e34 < z < 4.1000000000000003e-30

   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. Taylor expanded in x around inf 76.8%

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

      1. *-commutative 76.8%

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

   6. Simplified 76.8%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+85}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 5: 67.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+78} \lor \neg \left(a \leq 8 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.12e+78) (not (<= a 8e-7)))
   (- (/ y a) (/ x (* z a)))
   (/ (- x (* y z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.12e+78) || !(a <= 8e-7)) {
		tmp = (y / a) - (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 ((a <= (-1.12d+78)) .or. (.not. (a <= 8d-7))) then
        tmp = (y / a) - (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 ((a <= -1.12e+78) || !(a <= 8e-7)) {
		tmp = (y / a) - (x / (z * a));
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.12e+78) or not (a <= 8e-7):
		tmp = (y / a) - (x / (z * a))
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.12e+78) || !(a <= 8e-7))
		tmp = Float64(Float64(y / a) - Float64(x / Float64(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 ((a <= -1.12e+78) || ~((a <= 8e-7)))
		tmp = (y / a) - (x / (z * a));
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.12e+78], N[Not[LessEqual[a, 8e-7]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] - N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.12e78 or 7.9999999999999996e-7 < a

   1. Initial program 73.3%

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

      1. *-commutative 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in t around 0 57.1%

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

      1. associate-*r* 38.7%

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

      2. neg-mul-1 38.7%

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

      3. *-commutative 38.7%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in x around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. mul-1-neg 75.8%

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

      3. unsub-neg 75.8%

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

      4. *-commutative 75.8%

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

   9. Simplified 75.8%

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

   if -1.12e78 < a < 7.9999999999999996e-7

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around inf 76.6%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+78} \lor \neg \left(a \leq 8 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]

Alternative 6: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.32 \cdot 10^{+76}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+17}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.32e+76)
   (/ y a)
   (if (<= a 7e+17) (/ (- x (* y z)) t) (/ x (- t (* z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.32e+76) {
		tmp = y / a;
	} else if (a <= 7e+17) {
		tmp = (x - (y * z)) / t;
	} 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 (a <= (-1.32d+76)) then
        tmp = y / a
    else if (a <= 7d+17) then
        tmp = (x - (y * z)) / t
    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 (a <= -1.32e+76) {
		tmp = y / a;
	} else if (a <= 7e+17) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.32e+76:
		tmp = y / a
	elif a <= 7e+17:
		tmp = (x - (y * z)) / t
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.32e+76)
		tmp = Float64(y / a);
	elseif (a <= 7e+17)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	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 (a <= -1.32e+76)
		tmp = y / a;
	elseif (a <= 7e+17)
		tmp = (x - (y * z)) / t;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.32e+76], N[(y / a), $MachinePrecision], If[LessEqual[a, 7e+17], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.31999999999999999e76

   1. Initial program 72.7%

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

      1. *-commutative 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in z around inf 57.6%

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

   if -1.31999999999999999e76 < a < 7e17

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in t around inf 75.2%

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

   if 7e17 < a

   1. Initial program 77.0%

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

      1. *-commutative 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in x around inf 52.8%

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

      1. *-commutative 52.8%

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

   6. Simplified 52.8%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.32 \cdot 10^{+76}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+17}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]

Alternative 7: 54.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+106}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+33}:\\ \;\;\;\;\left(-y\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e+106)
   (/ y a)
   (if (<= z -5.8e+33) (* (- y) (/ z t)) (if (<= z 2.6e-30) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+106) {
		tmp = y / a;
	} else if (z <= -5.8e+33) {
		tmp = -y * (z / t);
	} else if (z <= 2.6e-30) {
		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 <= (-2.6d+106)) then
        tmp = y / a
    else if (z <= (-5.8d+33)) then
        tmp = -y * (z / t)
    else if (z <= 2.6d-30) 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 <= -2.6e+106) {
		tmp = y / a;
	} else if (z <= -5.8e+33) {
		tmp = -y * (z / t);
	} else if (z <= 2.6e-30) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e+106:
		tmp = y / a
	elif z <= -5.8e+33:
		tmp = -y * (z / t)
	elif z <= 2.6e-30:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e+106)
		tmp = Float64(y / a);
	elseif (z <= -5.8e+33)
		tmp = Float64(Float64(-y) * Float64(z / t));
	elseif (z <= 2.6e-30)
		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 <= -2.6e+106)
		tmp = y / a;
	elseif (z <= -5.8e+33)
		tmp = -y * (z / t);
	elseif (z <= 2.6e-30)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e+106], N[(y / a), $MachinePrecision], If[LessEqual[z, -5.8e+33], N[((-y) * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e-30], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6000000000000002e106 or 2.59999999999999987e-30 < z

   1. Initial program 67.3%

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

      1. *-commutative 67.3%

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

   3. Simplified 67.3%

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

   4. Taylor expanded in z around inf 57.4%

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

   if -2.6000000000000002e106 < z < -5.80000000000000049e33

   1. Initial program 80.6%

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

      1. *-commutative 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in x around 0 55.3%

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

      1. associate-*r/ 55.3%

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

      2. *-commutative 55.3%

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

      3. neg-mul-1 55.3%

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

      4. distribute-rgt-neg-in 55.3%

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

   6. Simplified 55.3%

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

   7. Taylor expanded in y around 0 55.3%

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

      1. associate-*r/ 55.3%

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

      2. *-rgt-identity 55.3%

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

      3. *-commutative 55.3%

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

      4. associate-*r/ 55.4%

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

      5. mul-1-neg 55.4%

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

      6. distribute-rgt-neg-out 55.4%

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

      7. associate-*l* 69.7%

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

      8. distribute-lft-neg-out 69.7%

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

      9. associate-*r/ 69.8%

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

      10. *-rgt-identity 69.8%

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

      11. *-commutative 69.8%

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

   9. Simplified 69.8%

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

   10. Taylor expanded in z around 0 63.9%

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

   if -5.80000000000000049e33 < z < 2.59999999999999987e-30

   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. Taylor expanded in z around 0 59.2%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+106}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+33}:\\ \;\;\;\;\left(-y\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 8: 54.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+88}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+88)
   (/ y a)
   (if (<= z -3.4e+31) (* z (/ (- y) t)) (if (<= z 4.4e-30) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+88) {
		tmp = y / a;
	} else if (z <= -3.4e+31) {
		tmp = z * (-y / t);
	} else if (z <= 4.4e-30) {
		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 <= (-1.05d+88)) then
        tmp = y / a
    else if (z <= (-3.4d+31)) then
        tmp = z * (-y / t)
    else if (z <= 4.4d-30) 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 <= -1.05e+88) {
		tmp = y / a;
	} else if (z <= -3.4e+31) {
		tmp = z * (-y / t);
	} else if (z <= 4.4e-30) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+88:
		tmp = y / a
	elif z <= -3.4e+31:
		tmp = z * (-y / t)
	elif z <= 4.4e-30:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+88)
		tmp = Float64(y / a);
	elseif (z <= -3.4e+31)
		tmp = Float64(z * Float64(Float64(-y) / t));
	elseif (z <= 4.4e-30)
		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 <= -1.05e+88)
		tmp = y / a;
	elseif (z <= -3.4e+31)
		tmp = z * (-y / t);
	elseif (z <= 4.4e-30)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+88], N[(y / a), $MachinePrecision], If[LessEqual[z, -3.4e+31], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e-30], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e88 or 4.39999999999999967e-30 < z

   1. Initial program 67.9%

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

      1. *-commutative 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in z around inf 57.3%

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

   if -1.05e88 < z < -3.3999999999999998e31

   1. Initial program 78.5%

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

      1. *-commutative 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in x around 0 55.9%

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

      1. associate-*r/ 55.9%

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

      2. *-commutative 55.9%

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

      3. neg-mul-1 55.9%

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

      4. distribute-rgt-neg-in 55.9%

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

   6. Simplified 55.9%

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

   7. Taylor expanded in z around 0 51.0%

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

      1. mul-1-neg 51.0%

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

      2. associate-*l/ 65.4%

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

      3. *-commutative 65.4%

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

      4. distribute-rgt-neg-in 65.4%

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

      5. distribute-neg-frac 65.4%

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

   9. Simplified 65.4%

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

   if -3.3999999999999998e31 < z < 4.39999999999999967e-30

   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. Taylor expanded in z around 0 59.2%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+88}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 9: 54.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+85) (/ y a) (if (<= z 2.9e-30) (/ x t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+85) {
		tmp = y / a;
	} else if (z <= 2.9e-30) {
		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 <= (-1.9d+85)) then
        tmp = y / a
    else if (z <= 2.9d-30) 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 <= -1.9e+85) {
		tmp = y / a;
	} else if (z <= 2.9e-30) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+85:
		tmp = y / a
	elif z <= 2.9e-30:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+85)
		tmp = Float64(y / a);
	elseif (z <= 2.9e-30)
		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 <= -1.9e+85)
		tmp = y / a;
	elseif (z <= 2.9e-30)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+85], N[(y / a), $MachinePrecision], If[LessEqual[z, 2.9e-30], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.89999999999999996e85 or 2.89999999999999989e-30 < z

   1. Initial program 67.9%

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

      1. *-commutative 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in z around inf 57.3%

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

   if -1.89999999999999996e85 < z < 2.89999999999999989e-30

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around 0 54.9%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 10: 35.5% 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. Taylor expanded in z around 0 36.5%

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

5. Final simplification 36.5%

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

Developer target: 97.1% accurate, 0.6× 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 2023279 
(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))))