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

Percentage Accurate: 84.4% → 90.7%

Time: 11.7s

Alternatives: 8

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: 84.4% 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: 90.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+109} \lor \neg \left(z \leq 3.8 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{z \cdot a - t} + \frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.2e+109) (not (<= z 3.8e+83)))
   (/ (- y (/ x z)) a)
   (+ (/ (* z y) (- (* z a) t)) (/ x (- t (* z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+109) || !(z <= 3.8e+83)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = ((z * y) / ((z * a) - t)) + (x / (t - (z * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.2d+109)) .or. (.not. (z <= 3.8d+83))) then
        tmp = (y - (x / z)) / a
    else
        tmp = ((z * y) / ((z * a) - t)) + (x / (t - (z * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+109) || !(z <= 3.8e+83)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = ((z * y) / ((z * a) - t)) + (x / (t - (z * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.2e+109) or not (z <= 3.8e+83):
		tmp = (y - (x / z)) / a
	else:
		tmp = ((z * y) / ((z * a) - t)) + (x / (t - (z * a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.2e+109) || !(z <= 3.8e+83))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(Float64(z * y) / Float64(Float64(z * a) - t)) + Float64(x / Float64(t - Float64(z * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.2e+109) || ~((z <= 3.8e+83)))
		tmp = (y - (x / z)) / a;
	else
		tmp = ((z * y) / ((z * a) - t)) + (x / (t - (z * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.2e+109], N[Not[LessEqual[z, 3.8e+83]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(N[(z * y), $MachinePrecision] / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000003e109 or 3.8000000000000002e83 < z

   1. Initial program 60.2%

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

      1. *-commutative 60.2%

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

   3. Simplified 60.2%

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

   5. Taylor expanded in x around 0 59.0%

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

      1. *-commutative 59.0%

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

      2. *-commutative 59.0%

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

      3. *-un-lft-identity 59.0%

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

      4. times-frac 66.6%

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

   7. Applied egg-rr 66.6%

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

   8. Taylor expanded in a around inf 81.6%

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

      1. mul-1-neg 81.6%

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

      2. unsub-neg 81.6%

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

   10. Simplified 81.6%

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

   if -4.2000000000000003e109 < z < 3.8000000000000002e83

   1. Initial program 98.7%

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

      1. *-commutative 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around 0 98.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t - a \cdot z} + \frac{x}{t - a \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+109} \lor \neg \left(z \leq 3.8 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{z \cdot a - t} + \frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 64.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - z \cdot y}{t}\\ t_2 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;z \leq -620000:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* z y)) t)) (t_2 (/ x (- t (* z a)))))
   (if (<= z -620000.0)
     (/ y a)
     (if (<= z -1.05e-134)
       t_2
       (if (<= z 3e-181)
         t_1
         (if (<= z 6.2e-20) t_2 (if (<= z 4.2e+33) t_1 (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (z * y)) / t;
	double t_2 = x / (t - (z * a));
	double tmp;
	if (z <= -620000.0) {
		tmp = y / a;
	} else if (z <= -1.05e-134) {
		tmp = t_2;
	} else if (z <= 3e-181) {
		tmp = t_1;
	} else if (z <= 6.2e-20) {
		tmp = t_2;
	} else if (z <= 4.2e+33) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - (z * y)) / t
    t_2 = x / (t - (z * a))
    if (z <= (-620000.0d0)) then
        tmp = y / a
    else if (z <= (-1.05d-134)) then
        tmp = t_2
    else if (z <= 3d-181) then
        tmp = t_1
    else if (z <= 6.2d-20) then
        tmp = t_2
    else if (z <= 4.2d+33) then
        tmp = t_1
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (z * y)) / t;
	double t_2 = x / (t - (z * a));
	double tmp;
	if (z <= -620000.0) {
		tmp = y / a;
	} else if (z <= -1.05e-134) {
		tmp = t_2;
	} else if (z <= 3e-181) {
		tmp = t_1;
	} else if (z <= 6.2e-20) {
		tmp = t_2;
	} else if (z <= 4.2e+33) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (z * y)) / t
	t_2 = x / (t - (z * a))
	tmp = 0
	if z <= -620000.0:
		tmp = y / a
	elif z <= -1.05e-134:
		tmp = t_2
	elif z <= 3e-181:
		tmp = t_1
	elif z <= 6.2e-20:
		tmp = t_2
	elif z <= 4.2e+33:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(z * y)) / t)
	t_2 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (z <= -620000.0)
		tmp = Float64(y / a);
	elseif (z <= -1.05e-134)
		tmp = t_2;
	elseif (z <= 3e-181)
		tmp = t_1;
	elseif (z <= 6.2e-20)
		tmp = t_2;
	elseif (z <= 4.2e+33)
		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 - (z * y)) / t;
	t_2 = x / (t - (z * a));
	tmp = 0.0;
	if (z <= -620000.0)
		tmp = y / a;
	elseif (z <= -1.05e-134)
		tmp = t_2;
	elseif (z <= 3e-181)
		tmp = t_1;
	elseif (z <= 6.2e-20)
		tmp = t_2;
	elseif (z <= 4.2e+33)
		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[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -620000.0], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.05e-134], t$95$2, If[LessEqual[z, 3e-181], t$95$1, If[LessEqual[z, 6.2e-20], t$95$2, If[LessEqual[z, 4.2e+33], t$95$1, N[(y / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2e5 or 4.2000000000000001e33 < z

   1. Initial program 69.6%

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

      1. *-commutative 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in z around inf 59.6%

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

   if -6.2e5 < z < -1.05e-134 or 2.99999999999999974e-181 < z < 6.19999999999999999e-20

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 79.7%

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

      1. *-commutative 79.7%

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

   7. Simplified 79.7%

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

   if -1.05e-134 < z < 2.99999999999999974e-181 or 6.19999999999999999e-20 < z < 4.2000000000000001e33

   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 94.0%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -620000:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-134}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-181}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ t_3 := \frac{x - z \cdot y}{t}\\ \mathbf{if}\;z \leq -0.16:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-185}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+29}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a))))
        (t_2 (/ (- y (/ x z)) a))
        (t_3 (/ (- x (* z y)) t)))
   (if (<= z -0.16)
     t_2
     (if (<= z -8.2e-134)
       t_1
       (if (<= z 1.02e-185)
         t_3
         (if (<= z 7.6e-20) t_1 (if (<= z 3.5e+29) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = (y - (x / z)) / a;
	double t_3 = (x - (z * y)) / t;
	double tmp;
	if (z <= -0.16) {
		tmp = t_2;
	} else if (z <= -8.2e-134) {
		tmp = t_1;
	} else if (z <= 1.02e-185) {
		tmp = t_3;
	} else if (z <= 7.6e-20) {
		tmp = t_1;
	} else if (z <= 3.5e+29) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x / (t - (z * a))
    t_2 = (y - (x / z)) / a
    t_3 = (x - (z * y)) / t
    if (z <= (-0.16d0)) then
        tmp = t_2
    else if (z <= (-8.2d-134)) then
        tmp = t_1
    else if (z <= 1.02d-185) then
        tmp = t_3
    else if (z <= 7.6d-20) then
        tmp = t_1
    else if (z <= 3.5d+29) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = (y - (x / z)) / a;
	double t_3 = (x - (z * y)) / t;
	double tmp;
	if (z <= -0.16) {
		tmp = t_2;
	} else if (z <= -8.2e-134) {
		tmp = t_1;
	} else if (z <= 1.02e-185) {
		tmp = t_3;
	} else if (z <= 7.6e-20) {
		tmp = t_1;
	} else if (z <= 3.5e+29) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	t_2 = (y - (x / z)) / a
	t_3 = (x - (z * y)) / t
	tmp = 0
	if z <= -0.16:
		tmp = t_2
	elif z <= -8.2e-134:
		tmp = t_1
	elif z <= 1.02e-185:
		tmp = t_3
	elif z <= 7.6e-20:
		tmp = t_1
	elif z <= 3.5e+29:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	t_3 = Float64(Float64(x - Float64(z * y)) / t)
	tmp = 0.0
	if (z <= -0.16)
		tmp = t_2;
	elseif (z <= -8.2e-134)
		tmp = t_1;
	elseif (z <= 1.02e-185)
		tmp = t_3;
	elseif (z <= 7.6e-20)
		tmp = t_1;
	elseif (z <= 3.5e+29)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	t_2 = (y - (x / z)) / a;
	t_3 = (x - (z * y)) / t;
	tmp = 0.0;
	if (z <= -0.16)
		tmp = t_2;
	elseif (z <= -8.2e-134)
		tmp = t_1;
	elseif (z <= 1.02e-185)
		tmp = t_3;
	elseif (z <= 7.6e-20)
		tmp = t_1;
	elseif (z <= 3.5e+29)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -0.16], t$95$2, If[LessEqual[z, -8.2e-134], t$95$1, If[LessEqual[z, 1.02e-185], t$95$3, If[LessEqual[z, 7.6e-20], t$95$1, If[LessEqual[z, 3.5e+29], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.160000000000000003 or 3.49999999999999979e29 < z

   1. Initial program 69.6%

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

      1. *-commutative 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in x around 0 68.7%

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

      1. *-commutative 68.7%

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

      2. *-commutative 68.7%

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

      3. *-un-lft-identity 68.7%

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

      4. times-frac 72.4%

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

   7. Applied egg-rr 72.4%

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

   8. Taylor expanded in a around inf 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

   10. Simplified 77.7%

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

   if -0.160000000000000003 < z < -8.2000000000000004e-134 or 1.0200000000000001e-185 < z < 7.5999999999999995e-20

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 79.7%

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

      1. *-commutative 79.7%

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

   7. Simplified 79.7%

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

   if -8.2000000000000004e-134 < z < 1.0200000000000001e-185 or 7.5999999999999995e-20 < z < 3.49999999999999979e29

   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 94.0%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.16:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-134}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-185}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+109} \lor \neg \left(z \leq 3.2 \cdot 10^{+94}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y - x}{z \cdot a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e+109) (not (<= z 3.2e+94)))
   (/ (- y (/ x z)) a)
   (/ (- (* z y) x) (- (* z a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+109) || !(z <= 3.2e+94)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = ((z * y) - x) / ((z * a) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9d+109)) .or. (.not. (z <= 3.2d+94))) then
        tmp = (y - (x / z)) / a
    else
        tmp = ((z * y) - x) / ((z * a) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+109) || !(z <= 3.2e+94)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = ((z * y) - x) / ((z * a) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e+109) or not (z <= 3.2e+94):
		tmp = (y - (x / z)) / a
	else:
		tmp = ((z * y) - x) / ((z * a) - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e+109) || !(z <= 3.2e+94))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(Float64(z * y) - x) / Float64(Float64(z * a) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9e+109) || ~((z <= 3.2e+94)))
		tmp = (y - (x / z)) / a;
	else
		tmp = ((z * y) - x) / ((z * a) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9e+109], N[Not[LessEqual[z, 3.2e+94]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.9999999999999992e109 or 3.20000000000000014e94 < z

   1. Initial program 60.2%

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

      1. *-commutative 60.2%

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

   3. Simplified 60.2%

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

   5. Taylor expanded in x around 0 59.0%

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

      1. *-commutative 59.0%

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

      2. *-commutative 59.0%

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

      3. *-un-lft-identity 59.0%

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

      4. times-frac 66.6%

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

   7. Applied egg-rr 66.6%

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

   8. Taylor expanded in a around inf 81.6%

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

      1. mul-1-neg 81.6%

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

      2. unsub-neg 81.6%

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

   10. Simplified 81.6%

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

   if -8.9999999999999992e109 < z < 3.20000000000000014e94

   1. Initial program 98.7%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+109} \lor \neg \left(z \leq 3.2 \cdot 10^{+94}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y - x}{z \cdot a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -440:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-133}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -440.0)
   (/ y a)
   (if (<= z -1.2e-133)
     (/ x (* z (- a)))
     (if (<= z 1.2e+32) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -440.0) {
		tmp = y / a;
	} else if (z <= -1.2e-133) {
		tmp = x / (z * -a);
	} else if (z <= 1.2e+32) {
		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 <= (-440.0d0)) then
        tmp = y / a
    else if (z <= (-1.2d-133)) then
        tmp = x / (z * -a)
    else if (z <= 1.2d+32) 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 <= -440.0) {
		tmp = y / a;
	} else if (z <= -1.2e-133) {
		tmp = x / (z * -a);
	} else if (z <= 1.2e+32) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -440.0:
		tmp = y / a
	elif z <= -1.2e-133:
		tmp = x / (z * -a)
	elif z <= 1.2e+32:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -440.0)
		tmp = Float64(y / a);
	elseif (z <= -1.2e-133)
		tmp = Float64(x / Float64(z * Float64(-a)));
	elseif (z <= 1.2e+32)
		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 <= -440.0)
		tmp = y / a;
	elseif (z <= -1.2e-133)
		tmp = x / (z * -a);
	elseif (z <= 1.2e+32)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -440.0], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.2e-133], N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+32], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -440 or 1.19999999999999996e32 < z

   1. Initial program 69.6%

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

      1. *-commutative 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in z around inf 59.6%

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

   if -440 < z < -1.2e-133

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 78.2%

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

      1. *-commutative 78.2%

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

   7. Simplified 78.2%

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

   8. Taylor expanded in t around 0 51.7%

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

      1. associate-*r* 51.7%

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

      2. neg-mul-1 51.7%

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

      3. *-commutative 51.7%

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

   10. Simplified 51.7%

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

   if -1.2e-133 < z < 1.19999999999999996e32

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 68.2%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -440:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-133}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -460000 \lor \neg \left(z \leq 1.1 \cdot 10^{+116}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -460000.0) (not (<= z 1.1e+116))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -460000.0) || !(z <= 1.1e+116)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-460000.0d0)) .or. (.not. (z <= 1.1d+116))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -460000.0) || !(z <= 1.1e+116)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -460000.0) or not (z <= 1.1e+116):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -460000.0) || !(z <= 1.1e+116))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -460000.0) || ~((z <= 1.1e+116)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -460000.0], N[Not[LessEqual[z, 1.1e+116]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6e5 or 1.1e116 < z

   1. Initial program 67.1%

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

      1. *-commutative 67.1%

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

   3. Simplified 67.1%

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

   5. Taylor expanded in z around inf 62.3%

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

   if -4.6e5 < z < 1.1e116

   1. Initial program 97.9%

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

      1. *-commutative 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in x around inf 73.6%

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

      1. *-commutative 73.6%

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

   7. Simplified 73.6%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -460000 \lor \neg \left(z \leq 1.1 \cdot 10^{+116}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -290000 \lor \neg \left(z \leq 2.2 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -290000.0) (not (<= z 2.2e+34))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -290000.0) || !(z <= 2.2e+34)) {
		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 <= (-290000.0d0)) .or. (.not. (z <= 2.2d+34))) 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 <= -290000.0) || !(z <= 2.2e+34)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -290000.0) or not (z <= 2.2e+34):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -290000.0) || !(z <= 2.2e+34))
		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 <= -290000.0) || ~((z <= 2.2e+34)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -290000.0], N[Not[LessEqual[z, 2.2e+34]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9e5 or 2.2000000000000002e34 < z

   1. Initial program 69.6%

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

      1. *-commutative 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in z around inf 59.6%

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

   if -2.9e5 < z < 2.2000000000000002e34

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 58.8%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -290000 \lor \neg \left(z \leq 2.2 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.2% 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 85.9%

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

   1. *-commutative 85.9%

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

3. Simplified 85.9%

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

5. Taylor expanded in z around 0 36.4%

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

6. Final simplification 36.4%

   \[\leadsto \frac{x}{t} \]
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 2024076 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

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

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