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

Percentage Accurate: 84.1% → 90.1%

Time: 13.3s

Alternatives: 14

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.1% 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: 90.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+213} \lor \neg \left(a \leq 1.15 \cdot 10^{+214}\right):\\ \;\;\;\;\frac{y}{a} + \frac{\frac{y}{\frac{{a}^{2}}{t}} - \frac{x}{a}}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{y}{\frac{t\_1}{z}}, \frac{x}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))))
   (if (or (<= a -4.2e+213) (not (<= a 1.15e+214)))
     (+ (/ y a) (/ (- (/ y (/ (pow a 2.0) t)) (/ x a)) z))
     (fma -1.0 (/ y (/ t_1 z)) (/ x t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double tmp;
	if ((a <= -4.2e+213) || !(a <= 1.15e+214)) {
		tmp = (y / a) + (((y / (pow(a, 2.0) / t)) - (x / a)) / z);
	} else {
		tmp = fma(-1.0, (y / (t_1 / z)), (x / t_1));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	tmp = 0.0
	if ((a <= -4.2e+213) || !(a <= 1.15e+214))
		tmp = Float64(Float64(y / a) + Float64(Float64(Float64(y / Float64((a ^ 2.0) / t)) - Float64(x / a)) / z));
	else
		tmp = fma(-1.0, Float64(y / Float64(t_1 / z)), Float64(x / t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -4.2e+213], N[Not[LessEqual[a, 1.15e+214]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] + N[(N[(N[(y / N[(N[Power[a, 2.0], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(y / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.2000000000000001e213 or 1.15e214 < a

   1. Initial program 45.8%

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

      1. *-commutative 45.8%

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

   3. Simplified 45.8%

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

   5. Taylor expanded in z around inf 67.2%

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

      1. +-commutative 67.2%

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

      2. associate--l+ 67.2%

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

      3. associate-/r* 76.8%

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

      4. associate-*r/ 76.8%

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

      5. associate-/r* 76.8%

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

      6. associate-*r/ 76.8%

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

      7. div-sub 76.8%

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

      8. distribute-lft-out-- 76.8%

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

      9. associate-*r/ 76.8%

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

      10. mul-1-neg 76.8%

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

      11. unsub-neg 76.8%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   7. Simplified 94.5%

      \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{y}{\frac{{a}^{2}}{t}}}{z}} \]

   if -4.2000000000000001e213 < a < 1.15e214

   1. Initial program 90.4%

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

      1. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in x around 0 90.4%

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

      1. fma-def 90.4%

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

      2. associate-/l* 94.7%

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

      3. *-commutative 94.7%

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

      4. *-commutative 94.7%

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

   7. Simplified 94.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-1, \frac{y}{\frac{t - z \cdot a}{z}}, \frac{x}{t - z \cdot a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+213} \lor \neg \left(a \leq 1.15 \cdot 10^{+214}\right):\\ \;\;\;\;\frac{y}{a} + \frac{\frac{y}{\frac{{a}^{2}}{t}} - \frac{x}{a}}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{y}{\frac{t - a \cdot z}{z}}, \frac{x}{t - a \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+213} \lor \neg \left(a \leq 9.5 \cdot 10^{+211}\right):\\ \;\;\;\;\frac{y}{a} + \frac{\frac{y}{\frac{{a}^{2}}{t}} - \frac{x}{a}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - a \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.8e+213) (not (<= a 9.5e+211)))
   (+ (/ y a) (/ (- (/ y (/ (pow a 2.0) t)) (/ x a)) z))
   (/ (- x (* y z)) (- t (* a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.8e+213) || !(a <= 9.5e+211)) {
		tmp = (y / a) + (((y / (pow(a, 2.0) / t)) - (x / a)) / z);
	} else {
		tmp = (x - (y * z)) / (t - (a * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-6.8d+213)) .or. (.not. (a <= 9.5d+211))) then
        tmp = (y / a) + (((y / ((a ** 2.0d0) / t)) - (x / a)) / z)
    else
        tmp = (x - (y * z)) / (t - (a * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.8e+213) || !(a <= 9.5e+211)) {
		tmp = (y / a) + (((y / (Math.pow(a, 2.0) / t)) - (x / a)) / z);
	} else {
		tmp = (x - (y * z)) / (t - (a * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6.8e+213) or not (a <= 9.5e+211):
		tmp = (y / a) + (((y / (math.pow(a, 2.0) / t)) - (x / a)) / z)
	else:
		tmp = (x - (y * z)) / (t - (a * z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.8e+213) || !(a <= 9.5e+211))
		tmp = Float64(Float64(y / a) + Float64(Float64(Float64(y / Float64((a ^ 2.0) / t)) - Float64(x / a)) / z));
	else
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(a * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6.8e+213) || ~((a <= 9.5e+211)))
		tmp = (y / a) + (((y / ((a ^ 2.0) / t)) - (x / a)) / z);
	else
		tmp = (x - (y * z)) / (t - (a * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6.8e+213], N[Not[LessEqual[a, 9.5e+211]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] + N[(N[(N[(y / N[(N[Power[a, 2.0], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.79999999999999983e213 or 9.4999999999999997e211 < a

   1. Initial program 45.8%

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

      1. *-commutative 45.8%

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

   3. Simplified 45.8%

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

   5. Taylor expanded in z around inf 67.2%

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

      1. +-commutative 67.2%

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

      2. associate--l+ 67.2%

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

      3. associate-/r* 76.8%

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

      4. associate-*r/ 76.8%

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

      5. associate-/r* 76.8%

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

      6. associate-*r/ 76.8%

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

      7. div-sub 76.8%

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

      8. distribute-lft-out-- 76.8%

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

      9. associate-*r/ 76.8%

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

      10. mul-1-neg 76.8%

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

      11. unsub-neg 76.8%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   7. Simplified 94.5%

      \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{y}{\frac{{a}^{2}}{t}}}{z}} \]

   if -6.79999999999999983e213 < a < 9.4999999999999997e211

   1. Initial program 90.4%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+213} \lor \neg \left(a \leq 9.5 \cdot 10^{+211}\right):\\ \;\;\;\;\frac{y}{a} + \frac{\frac{y}{\frac{{a}^{2}}{t}} - \frac{x}{a}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - a \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t} - z \cdot \frac{y}{t}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{t - a \cdot z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.00064 \lor \neg \left(z \leq 1.8 \cdot 10^{+44}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (/ x t) (* z (/ y t)))) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -1.2e+74)
     t_2
     (if (<= z -7e-166)
       t_1
       (if (<= z 7e-108)
         (/ x (- t (* a z)))
         (if (<= z 7.5e-16)
           t_1
           (if (or (<= z 0.00064) (not (<= z 1.8e+44)))
             t_2
             (/ (- x (* y z)) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / t) - (z * (y / t));
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.2e+74) {
		tmp = t_2;
	} else if (z <= -7e-166) {
		tmp = t_1;
	} else if (z <= 7e-108) {
		tmp = x / (t - (a * z));
	} else if (z <= 7.5e-16) {
		tmp = t_1;
	} else if ((z <= 0.00064) || !(z <= 1.8e+44)) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / t) - (z * (y / t))
    t_2 = (y - (x / z)) / a
    if (z <= (-1.2d+74)) then
        tmp = t_2
    else if (z <= (-7d-166)) then
        tmp = t_1
    else if (z <= 7d-108) then
        tmp = x / (t - (a * z))
    else if (z <= 7.5d-16) then
        tmp = t_1
    else if ((z <= 0.00064d0) .or. (.not. (z <= 1.8d+44))) then
        tmp = t_2
    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 t_1 = (x / t) - (z * (y / t));
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.2e+74) {
		tmp = t_2;
	} else if (z <= -7e-166) {
		tmp = t_1;
	} else if (z <= 7e-108) {
		tmp = x / (t - (a * z));
	} else if (z <= 7.5e-16) {
		tmp = t_1;
	} else if ((z <= 0.00064) || !(z <= 1.8e+44)) {
		tmp = t_2;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x / t) - (z * (y / t))
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.2e+74:
		tmp = t_2
	elif z <= -7e-166:
		tmp = t_1
	elif z <= 7e-108:
		tmp = x / (t - (a * z))
	elif z <= 7.5e-16:
		tmp = t_1
	elif (z <= 0.00064) or not (z <= 1.8e+44):
		tmp = t_2
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / t) - Float64(z * Float64(y / t)))
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.2e+74)
		tmp = t_2;
	elseif (z <= -7e-166)
		tmp = t_1;
	elseif (z <= 7e-108)
		tmp = Float64(x / Float64(t - Float64(a * z)));
	elseif (z <= 7.5e-16)
		tmp = t_1;
	elseif ((z <= 0.00064) || !(z <= 1.8e+44))
		tmp = t_2;
	else
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x / t) - (z * (y / t));
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.2e+74)
		tmp = t_2;
	elseif (z <= -7e-166)
		tmp = t_1;
	elseif (z <= 7e-108)
		tmp = x / (t - (a * z));
	elseif (z <= 7.5e-16)
		tmp = t_1;
	elseif ((z <= 0.00064) || ~((z <= 1.8e+44)))
		tmp = t_2;
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -1.2e+74], t$95$2, If[LessEqual[z, -7e-166], t$95$1, If[LessEqual[z, 7e-108], N[(x / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-16], t$95$1, If[Or[LessEqual[z, 0.00064], N[Not[LessEqual[z, 1.8e+44]], $MachinePrecision]], t$95$2, N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.20000000000000004e74 or 7.5e-16 < z < 6.40000000000000052e-4 or 1.8e44 < z

   1. Initial program 70.5%

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

      1. *-commutative 70.5%

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

   3. Simplified 70.5%

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

   5. Taylor expanded in x around 0 70.4%

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

      1. fma-def 70.4%

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

      2. associate-/l* 79.6%

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

      3. *-commutative 79.6%

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

      4. *-commutative 79.6%

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

   7. Simplified 79.6%

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

   8. Taylor expanded in a around inf 78.1%

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

      1. mul-1-neg 78.1%

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

      2. unsub-neg 78.1%

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

   10. Simplified 78.1%

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

   if -1.20000000000000004e74 < z < -6.9999999999999998e-166 or 6.9999999999999997e-108 < z < 7.5e-16

   1. Initial program 91.7%

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

      1. *-commutative 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in t around inf 70.5%

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

      1. div-sub 70.4%

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

      2. *-commutative 70.4%

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

      3. associate-/l* 75.1%

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

   7. Applied egg-rr 75.1%

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

      1. clear-num 75.0%

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

      2. associate-/r/ 75.0%

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

      3. clear-num 75.1%

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

   9. Applied egg-rr 75.1%

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

   if -6.9999999999999998e-166 < z < 6.9999999999999997e-108

   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 x around inf 87.0%

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

      1. *-commutative 87.0%

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

   7. Simplified 87.0%

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

   if 6.40000000000000052e-4 < z < 1.8e44

   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 t around inf 69.6%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+74}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-166}:\\ \;\;\;\;\frac{x}{t} - z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{t - a \cdot z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{t} - z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 0.00064 \lor \neg \left(z \leq 1.8 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+74} \lor \neg \left(z \leq 1.45 \cdot 10^{-13}\right) \land \left(z \leq 5.9 \cdot 10^{-5} \lor \neg \left(z \leq 1.3 \cdot 10^{+44}\right)\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.25e+74)
         (and (not (<= z 1.45e-13)) (or (<= z 5.9e-5) (not (<= z 1.3e+44)))))
   (/ (- y (/ x z)) a)
   (/ (- x (* y z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e+74) || (!(z <= 1.45e-13) && ((z <= 5.9e-5) || !(z <= 1.3e+44)))) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.25d+74)) .or. (.not. (z <= 1.45d-13)) .and. (z <= 5.9d-5) .or. (.not. (z <= 1.3d+44))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (y * z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e+74) || (!(z <= 1.45e-13) && ((z <= 5.9e-5) || !(z <= 1.3e+44)))) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.25e+74) or (not (z <= 1.45e-13) and ((z <= 5.9e-5) or not (z <= 1.3e+44))):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.25e+74) || (!(z <= 1.45e-13) && ((z <= 5.9e-5) || !(z <= 1.3e+44))))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.25e+74) || (~((z <= 1.45e-13)) && ((z <= 5.9e-5) || ~((z <= 1.3e+44)))))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.25e+74], And[N[Not[LessEqual[z, 1.45e-13]], $MachinePrecision], Or[LessEqual[z, 5.9e-5], N[Not[LessEqual[z, 1.3e+44]], $MachinePrecision]]]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.24999999999999991e74 or 1.4499999999999999e-13 < z < 5.8999999999999998e-5 or 1.3e44 < z

   1. Initial program 70.5%

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

      1. *-commutative 70.5%

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

   3. Simplified 70.5%

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

   5. Taylor expanded in x around 0 70.4%

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

      1. fma-def 70.4%

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

      2. associate-/l* 79.6%

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

      3. *-commutative 79.6%

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

      4. *-commutative 79.6%

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

   7. Simplified 79.6%

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

   8. Taylor expanded in a around inf 78.1%

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

      1. mul-1-neg 78.1%

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

      2. unsub-neg 78.1%

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

   10. Simplified 78.1%

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

   if -1.24999999999999991e74 < z < 1.4499999999999999e-13 or 5.8999999999999998e-5 < z < 1.3e44

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in t around inf 77.2%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+74} \lor \neg \left(z \leq 1.45 \cdot 10^{-13}\right) \land \left(z \leq 5.9 \cdot 10^{-5} \lor \neg \left(z \leq 1.3 \cdot 10^{+44}\right)\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.06 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 0.000112 \lor \neg \left(z \leq 7.8 \cdot 10^{+43}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -1.06e+74)
     t_1
     (if (<= z 8.5e-14)
       (- (/ x t) (/ z (/ t y)))
       (if (or (<= z 0.000112) (not (<= z 7.8e+43)))
         t_1
         (/ (- x (* y z)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.06e+74) {
		tmp = t_1;
	} else if (z <= 8.5e-14) {
		tmp = (x / t) - (z / (t / y));
	} else if ((z <= 0.000112) || !(z <= 7.8e+43)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    if (z <= (-1.06d+74)) then
        tmp = t_1
    else if (z <= 8.5d-14) then
        tmp = (x / t) - (z / (t / y))
    else if ((z <= 0.000112d0) .or. (.not. (z <= 7.8d+43))) then
        tmp = t_1
    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 t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.06e+74) {
		tmp = t_1;
	} else if (z <= 8.5e-14) {
		tmp = (x / t) - (z / (t / y));
	} else if ((z <= 0.000112) || !(z <= 7.8e+43)) {
		tmp = t_1;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.06e+74:
		tmp = t_1
	elif z <= 8.5e-14:
		tmp = (x / t) - (z / (t / y))
	elif (z <= 0.000112) or not (z <= 7.8e+43):
		tmp = t_1
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.06e+74)
		tmp = t_1;
	elseif (z <= 8.5e-14)
		tmp = Float64(Float64(x / t) - Float64(z / Float64(t / y)));
	elseif ((z <= 0.000112) || !(z <= 7.8e+43))
		tmp = t_1;
	else
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.06e+74)
		tmp = t_1;
	elseif (z <= 8.5e-14)
		tmp = (x / t) - (z / (t / y));
	elseif ((z <= 0.000112) || ~((z <= 7.8e+43)))
		tmp = t_1;
	else
		tmp = (x - (y * z)) / t;
	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]}, If[LessEqual[z, -1.06e+74], t$95$1, If[LessEqual[z, 8.5e-14], N[(N[(x / t), $MachinePrecision] - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 0.000112], N[Not[LessEqual[z, 7.8e+43]], $MachinePrecision]], t$95$1, N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05999999999999999e74 or 8.50000000000000038e-14 < z < 1.11999999999999998e-4 or 7.8000000000000001e43 < z

   1. Initial program 70.5%

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

      1. *-commutative 70.5%

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

   3. Simplified 70.5%

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

   5. Taylor expanded in x around 0 70.4%

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

      1. fma-def 70.4%

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

      2. associate-/l* 79.6%

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

      3. *-commutative 79.6%

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

      4. *-commutative 79.6%

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

   7. Simplified 79.6%

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

   8. Taylor expanded in a around inf 78.1%

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

      1. mul-1-neg 78.1%

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

      2. unsub-neg 78.1%

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

   10. Simplified 78.1%

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

   if -1.05999999999999999e74 < z < 8.50000000000000038e-14

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t around inf 78.0%

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

      1. div-sub 78.0%

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

      2. *-commutative 78.0%

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

      3. associate-/l* 78.7%

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

   7. Applied egg-rr 78.7%

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

   if 1.11999999999999998e-4 < z < 7.8000000000000001e43

   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 t around inf 69.6%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+74}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 0.000112 \lor \neg \left(z \leq 7.8 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+44}:\\ \;\;\;\;z \cdot \frac{-y}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -1.3e+74)
     t_1
     (if (<= z 8.5e-24)
       (- (/ x t) (/ z (/ t y)))
       (if (<= z 1.4e+44) (* z (/ (- y) (- t (* a z)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.3e+74) {
		tmp = t_1;
	} else if (z <= 8.5e-24) {
		tmp = (x / t) - (z / (t / y));
	} else if (z <= 1.4e+44) {
		tmp = z * (-y / (t - (a * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    if (z <= (-1.3d+74)) then
        tmp = t_1
    else if (z <= 8.5d-24) then
        tmp = (x / t) - (z / (t / y))
    else if (z <= 1.4d+44) then
        tmp = z * (-y / (t - (a * z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.3e+74) {
		tmp = t_1;
	} else if (z <= 8.5e-24) {
		tmp = (x / t) - (z / (t / y));
	} else if (z <= 1.4e+44) {
		tmp = z * (-y / (t - (a * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.3e+74:
		tmp = t_1
	elif z <= 8.5e-24:
		tmp = (x / t) - (z / (t / y))
	elif z <= 1.4e+44:
		tmp = z * (-y / (t - (a * z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.3e+74)
		tmp = t_1;
	elseif (z <= 8.5e-24)
		tmp = Float64(Float64(x / t) - Float64(z / Float64(t / y)));
	elseif (z <= 1.4e+44)
		tmp = Float64(z * Float64(Float64(-y) / Float64(t - Float64(a * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.3e+74)
		tmp = t_1;
	elseif (z <= 8.5e-24)
		tmp = (x / t) - (z / (t / y));
	elseif (z <= 1.4e+44)
		tmp = z * (-y / (t - (a * z)));
	else
		tmp = t_1;
	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]}, If[LessEqual[z, -1.3e+74], t$95$1, If[LessEqual[z, 8.5e-24], N[(N[(x / t), $MachinePrecision] - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+44], N[(z * N[((-y) / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e74 or 1.4e44 < z

   1. Initial program 68.9%

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

      1. *-commutative 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in x around 0 68.9%

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

      1. fma-def 68.9%

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

      2. associate-/l* 78.5%

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

      3. *-commutative 78.5%

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

      4. *-commutative 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in a around inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. unsub-neg 76.9%

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

   10. Simplified 76.9%

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

   if -1.3e74 < z < 8.5000000000000002e-24

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t around inf 77.9%

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

      1. div-sub 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-/l* 78.5%

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

   7. Applied egg-rr 78.5%

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

   if 8.5000000000000002e-24 < z < 1.4e44

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 85.8%

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

      1. mul-1-neg 85.8%

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

      2. associate-/l* 86.0%

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

      3. associate-/r/ 85.7%

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

      4. sub-neg 85.7%

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

      5. +-commutative 85.7%

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

      6. distribute-rgt-neg-in 85.7%

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

      7. fma-udef 85.7%

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

      8. distribute-rgt-neg-in 85.7%

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

      9. fma-udef 85.7%

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

      10. distribute-rgt-neg-in 85.7%

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

      11. +-commutative 85.7%

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

      12. sub-neg 85.7%

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

      13. *-commutative 85.7%

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

   7. Simplified 85.7%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+74}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+44}:\\ \;\;\;\;z \cdot \frac{-y}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+44}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -1.1e+74)
     t_1
     (if (<= z 7.5e-15)
       (- (/ x t) (/ z (/ t y)))
       (if (<= z 1.45e+44) (/ (* y (- z)) (- t (* a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.1e+74) {
		tmp = t_1;
	} else if (z <= 7.5e-15) {
		tmp = (x / t) - (z / (t / y));
	} else if (z <= 1.45e+44) {
		tmp = (y * -z) / (t - (a * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    if (z <= (-1.1d+74)) then
        tmp = t_1
    else if (z <= 7.5d-15) then
        tmp = (x / t) - (z / (t / y))
    else if (z <= 1.45d+44) then
        tmp = (y * -z) / (t - (a * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.1e+74) {
		tmp = t_1;
	} else if (z <= 7.5e-15) {
		tmp = (x / t) - (z / (t / y));
	} else if (z <= 1.45e+44) {
		tmp = (y * -z) / (t - (a * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.1e+74:
		tmp = t_1
	elif z <= 7.5e-15:
		tmp = (x / t) - (z / (t / y))
	elif z <= 1.45e+44:
		tmp = (y * -z) / (t - (a * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.1e+74)
		tmp = t_1;
	elseif (z <= 7.5e-15)
		tmp = Float64(Float64(x / t) - Float64(z / Float64(t / y)));
	elseif (z <= 1.45e+44)
		tmp = Float64(Float64(y * Float64(-z)) / Float64(t - Float64(a * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.1e+74)
		tmp = t_1;
	elseif (z <= 7.5e-15)
		tmp = (x / t) - (z / (t / y));
	elseif (z <= 1.45e+44)
		tmp = (y * -z) / (t - (a * z));
	else
		tmp = t_1;
	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]}, If[LessEqual[z, -1.1e+74], t$95$1, If[LessEqual[z, 7.5e-15], N[(N[(x / t), $MachinePrecision] - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+44], N[(N[(y * (-z)), $MachinePrecision] / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1000000000000001e74 or 1.4500000000000001e44 < z

   1. Initial program 68.9%

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

      1. *-commutative 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in x around 0 68.9%

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

      1. fma-def 68.9%

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

      2. associate-/l* 78.5%

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

      3. *-commutative 78.5%

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

      4. *-commutative 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in a around inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. unsub-neg 76.9%

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

   10. Simplified 76.9%

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

   if -1.1000000000000001e74 < z < 7.4999999999999996e-15

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t around inf 78.0%

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

      1. div-sub 78.0%

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

      2. *-commutative 78.0%

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

      3. associate-/l* 78.7%

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

   7. Applied egg-rr 78.7%

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

   if 7.4999999999999996e-15 < z < 1.4500000000000001e44

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. *-commutative 85.2%

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

      3. distribute-rgt-neg-in 85.2%

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

   7. Simplified 85.2%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+74}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+44}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.52e+102)
   (/ y a)
   (if (<= z -5.8e+37)
     (* y (/ (- z) t))
     (if (<= z 1.4e-12) (/ x (- t (* a z))) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.52e+102) {
		tmp = y / a;
	} else if (z <= -5.8e+37) {
		tmp = y * (-z / t);
	} else if (z <= 1.4e-12) {
		tmp = x / (t - (a * z));
	} 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 <= (-1.52d+102)) then
        tmp = y / a
    else if (z <= (-5.8d+37)) then
        tmp = y * (-z / t)
    else if (z <= 1.4d-12) then
        tmp = x / (t - (a * z))
    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 <= -1.52e+102) {
		tmp = y / a;
	} else if (z <= -5.8e+37) {
		tmp = y * (-z / t);
	} else if (z <= 1.4e-12) {
		tmp = x / (t - (a * z));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.52e+102:
		tmp = y / a
	elif z <= -5.8e+37:
		tmp = y * (-z / t)
	elif z <= 1.4e-12:
		tmp = x / (t - (a * z))
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.52e+102)
		tmp = Float64(y / a);
	elseif (z <= -5.8e+37)
		tmp = Float64(y * Float64(Float64(-z) / t));
	elseif (z <= 1.4e-12)
		tmp = Float64(x / Float64(t - Float64(a * z)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.52e+102)
		tmp = y / a;
	elseif (z <= -5.8e+37)
		tmp = y * (-z / t);
	elseif (z <= 1.4e-12)
		tmp = x / (t - (a * z));
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.52e+102], N[(y / a), $MachinePrecision], If[LessEqual[z, -5.8e+37], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-12], N[(x / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5199999999999999e102 or 1.4000000000000001e-12 < z

   1. Initial program 73.6%

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

      1. *-commutative 73.6%

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

   3. Simplified 73.6%

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

   5. Taylor expanded in z around inf 60.7%

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

   if -1.5199999999999999e102 < z < -5.79999999999999957e37

   1. Initial program 69.9%

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

      1. *-commutative 69.9%

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

   3. Simplified 69.9%

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

      1. clear-num 69.8%

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

      2. associate-/r/ 69.9%

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

      3. sub-neg 69.9%

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

      4. +-commutative 69.9%

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

      5. *-commutative 69.9%

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

      6. distribute-rgt-neg-in 69.9%

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

      7. fma-def 69.9%

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

   6. Applied egg-rr 69.9%

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

   7. Taylor expanded in a around 0 52.3%

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

   8. Taylor expanded in x around 0 39.8%

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

      1. mul-1-neg 39.8%

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

      2. associate-*r/ 55.1%

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

      3. distribute-rgt-neg-in 55.1%

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

      4. distribute-neg-frac 55.1%

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

   10. Simplified 55.1%

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

   if -5.79999999999999957e37 < z < 1.4000000000000001e-12

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in x around inf 76.3%

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

      1. *-commutative 76.3%

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

   7. Simplified 76.3%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+118} \lor \neg \left(z \leq 3.5 \cdot 10^{+188}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - a \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.1e+118) (not (<= z 3.5e+188)))
   (/ (- y (/ x z)) a)
   (/ (- x (* y z)) (- t (* a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+118) || !(z <= 3.5e+188)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / (t - (a * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.1d+118)) .or. (.not. (z <= 3.5d+188))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (y * z)) / (t - (a * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+118) || !(z <= 3.5e+188)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / (t - (a * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.1e+118) or not (z <= 3.5e+188):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (y * z)) / (t - (a * z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.1e+118) || !(z <= 3.5e+188))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(a * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.1e+118) || ~((z <= 3.5e+188)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (y * z)) / (t - (a * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.1e+118], N[Not[LessEqual[z, 3.5e+188]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.09999999999999993e118 or 3.50000000000000008e188 < z

   1. Initial program 60.0%

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

      1. *-commutative 60.0%

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

   3. Simplified 60.0%

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

   5. Taylor expanded in x around 0 60.0%

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

      1. fma-def 60.0%

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

      2. associate-/l* 71.1%

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

      3. *-commutative 71.1%

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

      4. *-commutative 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in a around inf 86.3%

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

      1. mul-1-neg 86.3%

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

      2. unsub-neg 86.3%

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

   10. Simplified 86.3%

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

   if -1.09999999999999993e118 < z < 3.50000000000000008e188

   1. Initial program 92.4%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+118} \lor \neg \left(z \leq 3.5 \cdot 10^{+188}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - a \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-46} \lor \neg \left(a \leq 8.5 \cdot 10^{+132}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.2e-46) (not (<= a 8.5e+132)))
   (/ (- y (/ x z)) a)
   (- (/ x t) (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.2e-46) || !(a <= 8.5e+132)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x / t) - (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 <= (-2.2d-46)) .or. (.not. (a <= 8.5d+132))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x / t) - (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 <= -2.2e-46) || !(a <= 8.5e+132)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x / t) - (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.2e-46) or not (a <= 8.5e+132):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x / t) - (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.2e-46) || !(a <= 8.5e+132))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x / t) - Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.2e-46) || ~((a <= 8.5e+132)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x / t) - (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.2e-46], N[Not[LessEqual[a, 8.5e+132]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / t), $MachinePrecision] - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.2000000000000001e-46 or 8.49999999999999969e132 < a

   1. Initial program 71.3%

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

      1. *-commutative 71.3%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in x around 0 71.4%

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

      1. fma-def 71.4%

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

      2. associate-/l* 73.8%

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

      3. *-commutative 73.8%

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

      4. *-commutative 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in a around inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. unsub-neg 78.3%

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

   10. Simplified 78.3%

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

   if -2.2000000000000001e-46 < a < 8.49999999999999969e132

   1. Initial program 92.2%

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

      1. *-commutative 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in t around inf 69.0%

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

      1. div-sub 69.0%

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

      2. sub-neg 69.0%

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

      3. *-commutative 69.0%

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

      4. associate-/l* 70.1%

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

   7. Applied egg-rr 70.1%

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

      1. sub-neg 70.1%

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

      2. associate-/r/ 71.9%

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

   9. Simplified 71.9%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-46} \lor \neg \left(a \leq 8.5 \cdot 10^{+132}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5e+102)
   (/ y a)
   (if (<= z -1.2e+19) (* y (/ (- z) t)) (if (<= z 4.8e-14) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e+102) {
		tmp = y / a;
	} else if (z <= -1.2e+19) {
		tmp = y * (-z / t);
	} else if (z <= 4.8e-14) {
		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 <= (-5d+102)) then
        tmp = y / a
    else if (z <= (-1.2d+19)) then
        tmp = y * (-z / t)
    else if (z <= 4.8d-14) 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 <= -5e+102) {
		tmp = y / a;
	} else if (z <= -1.2e+19) {
		tmp = y * (-z / t);
	} else if (z <= 4.8e-14) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5e+102:
		tmp = y / a
	elif z <= -1.2e+19:
		tmp = y * (-z / t)
	elif z <= 4.8e-14:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5e+102)
		tmp = Float64(y / a);
	elseif (z <= -1.2e+19)
		tmp = Float64(y * Float64(Float64(-z) / t));
	elseif (z <= 4.8e-14)
		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 <= -5e+102)
		tmp = y / a;
	elseif (z <= -1.2e+19)
		tmp = y * (-z / t);
	elseif (z <= 4.8e-14)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5e+102], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.2e+19], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-14], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5e102 or 4.8e-14 < z

   1. Initial program 73.6%

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

      1. *-commutative 73.6%

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

   3. Simplified 73.6%

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

   5. Taylor expanded in z around inf 60.7%

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

   if -5e102 < z < -1.2e19

   1. Initial program 70.9%

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

      1. *-commutative 70.9%

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

   3. Simplified 70.9%

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

      1. clear-num 70.8%

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

      2. associate-/r/ 70.8%

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

      3. sub-neg 70.8%

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

      4. +-commutative 70.8%

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

      5. *-commutative 70.8%

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

      6. distribute-rgt-neg-in 70.8%

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

      7. fma-def 70.8%

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

   6. Applied egg-rr 70.8%

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

   7. Taylor expanded in a around 0 52.2%

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

   8. Taylor expanded in x around 0 41.6%

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

      1. mul-1-neg 41.6%

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

      2. associate-*r/ 54.4%

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

      3. distribute-rgt-neg-in 54.4%

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

      4. distribute-neg-frac 54.4%

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

   10. Simplified 54.4%

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

   if -1.2e19 < z < 4.8e-14

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 65.8%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+102} \lor \neg \left(z \leq 8.2 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.2e+102) (not (<= z 8.2e+43))) (/ y a) (/ (- x (* y z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+102) || !(z <= 8.2e+43)) {
		tmp = y / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.2d+102)) .or. (.not. (z <= 8.2d+43))) then
        tmp = y / a
    else
        tmp = (x - (y * z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+102) || !(z <= 8.2e+43)) {
		tmp = y / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.2e+102) or not (z <= 8.2e+43):
		tmp = y / a
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.2e+102) || !(z <= 8.2e+43))
		tmp = Float64(y / a);
	else
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.2e+102) || ~((z <= 8.2e+43)))
		tmp = y / a;
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.2e+102], N[Not[LessEqual[z, 8.2e+43]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.20000000000000003e102 or 8.2000000000000001e43 < z

   1. Initial program 68.4%

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

      1. *-commutative 68.4%

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

   3. Simplified 68.4%

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

   5. Taylor expanded in z around inf 63.5%

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

   if -4.20000000000000003e102 < z < 8.2000000000000001e43

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in t around inf 71.7%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+102} \lor \neg \left(z \leq 8.2 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9500000 \lor \neg \left(z \leq 2.6 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9500000.0) (not (<= z 2.6e-15))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9500000.0) || !(z <= 2.6e-15)) {
		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 <= (-9500000.0d0)) .or. (.not. (z <= 2.6d-15))) 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 <= -9500000.0) || !(z <= 2.6e-15)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9500000.0) or not (z <= 2.6e-15):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9500000.0) || !(z <= 2.6e-15))
		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 <= -9500000.0) || ~((z <= 2.6e-15)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9500000.0], N[Not[LessEqual[z, 2.6e-15]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5e6 or 2.60000000000000004e-15 < z

   1. Initial program 73.4%

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

      1. *-commutative 73.4%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in z around inf 54.8%

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

   if -9.5e6 < z < 2.60000000000000004e-15

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 66.9%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9500000 \lor \neg \left(z \leq 2.6 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 34.6% 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 84.4%

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

   1. *-commutative 84.4%

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

3. Simplified 84.4%

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

5. Taylor expanded in z around 0 37.0%

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

6. Final simplification 37.0%

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

Developer target: 97.3% 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 2024027 
(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))))