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

Percentage Accurate: 84.7% → 90.9%

Time: 13.2s

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: 84.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+179}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+109}:\\ \;\;\;\;\frac{x - y \cdot z}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e+179)
   (/ y (- a (/ t z)))
   (if (<= z 1.55e+109) (/ (- x (* y z)) (- t (* a z))) (/ (- y (/ x z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+179) {
		tmp = y / (a - (t / z));
	} else if (z <= 1.55e+109) {
		tmp = (x - (y * z)) / (t - (a * z));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.3d+179)) then
        tmp = y / (a - (t / z))
    else if (z <= 1.55d+109) then
        tmp = (x - (y * z)) / (t - (a * z))
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+179) {
		tmp = y / (a - (t / z));
	} else if (z <= 1.55e+109) {
		tmp = (x - (y * z)) / (t - (a * z));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e+179:
		tmp = y / (a - (t / z))
	elif z <= 1.55e+109:
		tmp = (x - (y * z)) / (t - (a * z))
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e+179)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= 1.55e+109)
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(a * z)));
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e+179)
		tmp = y / (a - (t / z));
	elseif (z <= 1.55e+109)
		tmp = (x - (y * z)) / (t - (a * z));
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e+179], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+109], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.29999999999999978e179

   1. Initial program 51.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -3.29999999999999978e179 < z < 1.54999999999999996e109

   1. Initial program 95.0%

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

   if 1.54999999999999996e109 < z

   1. Initial program 40.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 52.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+179}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+120}:\\ \;\;\;\;\frac{y}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{z \cdot y}{-t}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+179)
   (/ y a)
   (if (<= z -2.8e+120)
     (/ y (/ (- t) z))
     (if (<= z -4e+25)
       (/ y a)
       (if (<= z -3.3e-55)
         (/ (* z y) (- t))
         (if (<= z 7.4e-93) (/ x t) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+179) {
		tmp = y / a;
	} else if (z <= -2.8e+120) {
		tmp = y / (-t / z);
	} else if (z <= -4e+25) {
		tmp = y / a;
	} else if (z <= -3.3e-55) {
		tmp = (z * y) / -t;
	} else if (z <= 7.4e-93) {
		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 <= (-4.8d+179)) then
        tmp = y / a
    else if (z <= (-2.8d+120)) then
        tmp = y / (-t / z)
    else if (z <= (-4d+25)) then
        tmp = y / a
    else if (z <= (-3.3d-55)) then
        tmp = (z * y) / -t
    else if (z <= 7.4d-93) 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 <= -4.8e+179) {
		tmp = y / a;
	} else if (z <= -2.8e+120) {
		tmp = y / (-t / z);
	} else if (z <= -4e+25) {
		tmp = y / a;
	} else if (z <= -3.3e-55) {
		tmp = (z * y) / -t;
	} else if (z <= 7.4e-93) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e+179:
		tmp = y / a
	elif z <= -2.8e+120:
		tmp = y / (-t / z)
	elif z <= -4e+25:
		tmp = y / a
	elif z <= -3.3e-55:
		tmp = (z * y) / -t
	elif z <= 7.4e-93:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+179)
		tmp = Float64(y / a);
	elseif (z <= -2.8e+120)
		tmp = Float64(y / Float64(Float64(-t) / z));
	elseif (z <= -4e+25)
		tmp = Float64(y / a);
	elseif (z <= -3.3e-55)
		tmp = Float64(Float64(z * y) / Float64(-t));
	elseif (z <= 7.4e-93)
		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 <= -4.8e+179)
		tmp = y / a;
	elseif (z <= -2.8e+120)
		tmp = y / (-t / z);
	elseif (z <= -4e+25)
		tmp = y / a;
	elseif (z <= -3.3e-55)
		tmp = (z * y) / -t;
	elseif (z <= 7.4e-93)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+179], N[(y / a), $MachinePrecision], If[LessEqual[z, -2.8e+120], N[(y / N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e+25], N[(y / a), $MachinePrecision], If[LessEqual[z, -3.3e-55], N[(N[(z * y), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[z, 7.4e-93], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.80000000000000025e179 or -2.8000000000000001e120 < z < -4.00000000000000036e25 or 7.40000000000000005e-93 < z

   1. Initial program 68.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -4.80000000000000025e179 < z < -2.8000000000000001e120

   1. Initial program 66.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if -4.00000000000000036e25 < z < -3.2999999999999999e-55

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if -3.2999999999999999e-55 < z < 7.40000000000000005e-93

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 53.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{-t}{z}}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+179}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.24 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ (- t) z))))
   (if (<= z -7e+179)
     (/ y a)
     (if (<= z -9.2e+123)
       t_1
       (if (<= z -4e+25)
         (/ y a)
         (if (<= z -1.24e-54) t_1 (if (<= z 5.5e-93) (/ x t) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (-t / z);
	double tmp;
	if (z <= -7e+179) {
		tmp = y / a;
	} else if (z <= -9.2e+123) {
		tmp = t_1;
	} else if (z <= -4e+25) {
		tmp = y / a;
	} else if (z <= -1.24e-54) {
		tmp = t_1;
	} else if (z <= 5.5e-93) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y / (-t / z)
    if (z <= (-7d+179)) then
        tmp = y / a
    else if (z <= (-9.2d+123)) then
        tmp = t_1
    else if (z <= (-4d+25)) then
        tmp = y / a
    else if (z <= (-1.24d-54)) then
        tmp = t_1
    else if (z <= 5.5d-93) 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 t_1 = y / (-t / z);
	double tmp;
	if (z <= -7e+179) {
		tmp = y / a;
	} else if (z <= -9.2e+123) {
		tmp = t_1;
	} else if (z <= -4e+25) {
		tmp = y / a;
	} else if (z <= -1.24e-54) {
		tmp = t_1;
	} else if (z <= 5.5e-93) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (-t / z)
	tmp = 0
	if z <= -7e+179:
		tmp = y / a
	elif z <= -9.2e+123:
		tmp = t_1
	elif z <= -4e+25:
		tmp = y / a
	elif z <= -1.24e-54:
		tmp = t_1
	elif z <= 5.5e-93:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(Float64(-t) / z))
	tmp = 0.0
	if (z <= -7e+179)
		tmp = Float64(y / a);
	elseif (z <= -9.2e+123)
		tmp = t_1;
	elseif (z <= -4e+25)
		tmp = Float64(y / a);
	elseif (z <= -1.24e-54)
		tmp = t_1;
	elseif (z <= 5.5e-93)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (-t / z);
	tmp = 0.0;
	if (z <= -7e+179)
		tmp = y / a;
	elseif (z <= -9.2e+123)
		tmp = t_1;
	elseif (z <= -4e+25)
		tmp = y / a;
	elseif (z <= -1.24e-54)
		tmp = t_1;
	elseif (z <= 5.5e-93)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[((-t) / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+179], N[(y / a), $MachinePrecision], If[LessEqual[z, -9.2e+123], t$95$1, If[LessEqual[z, -4e+25], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.24e-54], t$95$1, If[LessEqual[z, 5.5e-93], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.0000000000000003e179 or -9.19999999999999962e123 < z < -4.00000000000000036e25 or 5.49999999999999968e-93 < z

   1. Initial program 68.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -7.0000000000000003e179 < z < -9.19999999999999962e123 or -4.00000000000000036e25 < z < -1.23999999999999999e-54

   1. Initial program 89.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if -1.23999999999999999e-54 < z < 5.49999999999999968e-93

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 67.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - z \cdot y}{t}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;a \leq -6500000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* z y)) t)) (t_2 (/ (- y (/ x z)) a)))
   (if (<= a -6500000.0)
     t_2
     (if (<= a -2.9e-33)
       t_1
       (if (<= a -4.2e-77) t_2 (if (<= a 1.45e-105) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (z * y)) / t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (a <= -6500000.0) {
		tmp = t_2;
	} else if (a <= -2.9e-33) {
		tmp = t_1;
	} else if (a <= -4.2e-77) {
		tmp = t_2;
	} else if (a <= 1.45e-105) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - (z * y)) / t
    t_2 = (y - (x / z)) / a
    if (a <= (-6500000.0d0)) then
        tmp = t_2
    else if (a <= (-2.9d-33)) then
        tmp = t_1
    else if (a <= (-4.2d-77)) then
        tmp = t_2
    else if (a <= 1.45d-105) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (z * y)) / t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (a <= -6500000.0) {
		tmp = t_2;
	} else if (a <= -2.9e-33) {
		tmp = t_1;
	} else if (a <= -4.2e-77) {
		tmp = t_2;
	} else if (a <= 1.45e-105) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (z * y)) / t
	t_2 = (y - (x / z)) / a
	tmp = 0
	if a <= -6500000.0:
		tmp = t_2
	elif a <= -2.9e-33:
		tmp = t_1
	elif a <= -4.2e-77:
		tmp = t_2
	elif a <= 1.45e-105:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(z * y)) / t)
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (a <= -6500000.0)
		tmp = t_2;
	elseif (a <= -2.9e-33)
		tmp = t_1;
	elseif (a <= -4.2e-77)
		tmp = t_2;
	elseif (a <= 1.45e-105)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (z * y)) / t;
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (a <= -6500000.0)
		tmp = t_2;
	elseif (a <= -2.9e-33)
		tmp = t_1;
	elseif (a <= -4.2e-77)
		tmp = t_2;
	elseif (a <= 1.45e-105)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -6500000.0], t$95$2, If[LessEqual[a, -2.9e-33], t$95$1, If[LessEqual[a, -4.2e-77], t$95$2, If[LessEqual[a, 1.45e-105], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.5e6 or -2.90000000000000003e-33 < a < -4.20000000000000031e-77 or 1.45000000000000002e-105 < a

   1. Initial program 73.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -6.5e6 < a < -2.90000000000000003e-33 or -4.20000000000000031e-77 < a < 1.45000000000000002e-105

   1. Initial program 96.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 58.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+103}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{-t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))))
   (if (<= y -2.9e+103)
     (/ y a)
     (if (<= y 4.2e+21)
       t_1
       (if (<= y 2.4e+53)
         (/ y a)
         (if (<= y 2.8e+171) t_1 (/ y (/ (- t) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double tmp;
	if (y <= -2.9e+103) {
		tmp = y / a;
	} else if (y <= 4.2e+21) {
		tmp = t_1;
	} else if (y <= 2.4e+53) {
		tmp = y / a;
	} else if (y <= 2.8e+171) {
		tmp = t_1;
	} else {
		tmp = y / (-t / 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) :: t_1
    real(8) :: tmp
    t_1 = x / (t - (z * a))
    if (y <= (-2.9d+103)) then
        tmp = y / a
    else if (y <= 4.2d+21) then
        tmp = t_1
    else if (y <= 2.4d+53) then
        tmp = y / a
    else if (y <= 2.8d+171) then
        tmp = t_1
    else
        tmp = y / (-t / z)
    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 tmp;
	if (y <= -2.9e+103) {
		tmp = y / a;
	} else if (y <= 4.2e+21) {
		tmp = t_1;
	} else if (y <= 2.4e+53) {
		tmp = y / a;
	} else if (y <= 2.8e+171) {
		tmp = t_1;
	} else {
		tmp = y / (-t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	tmp = 0
	if y <= -2.9e+103:
		tmp = y / a
	elif y <= 4.2e+21:
		tmp = t_1
	elif y <= 2.4e+53:
		tmp = y / a
	elif y <= 2.8e+171:
		tmp = t_1
	else:
		tmp = y / (-t / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (y <= -2.9e+103)
		tmp = Float64(y / a);
	elseif (y <= 4.2e+21)
		tmp = t_1;
	elseif (y <= 2.4e+53)
		tmp = Float64(y / a);
	elseif (y <= 2.8e+171)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(Float64(-t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	tmp = 0.0;
	if (y <= -2.9e+103)
		tmp = y / a;
	elseif (y <= 4.2e+21)
		tmp = t_1;
	elseif (y <= 2.4e+53)
		tmp = y / a;
	elseif (y <= 2.8e+171)
		tmp = t_1;
	else
		tmp = y / (-t / z);
	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]}, If[LessEqual[y, -2.9e+103], N[(y / a), $MachinePrecision], If[LessEqual[y, 4.2e+21], t$95$1, If[LessEqual[y, 2.4e+53], N[(y / a), $MachinePrecision], If[LessEqual[y, 2.8e+171], t$95$1, N[(y / N[((-t) / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8999999999999998e103 or 4.2e21 < y < 2.4e53

   1. Initial program 69.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -2.8999999999999998e103 < y < 4.2e21 or 2.4e53 < y < 2.80000000000000004e171

   1. Initial program 91.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 2.80000000000000004e171 < y

   1. Initial program 61.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 71.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))))
   (if (<= x -1.65e-25) t_1 (if (<= x 2e-19) (/ y (- a (/ t z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double tmp;
	if (x <= -1.65e-25) {
		tmp = t_1;
	} else if (x <= 2e-19) {
		tmp = y / (a - (t / 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 = x / (t - (z * a))
    if (x <= (-1.65d-25)) then
        tmp = t_1
    else if (x <= 2d-19) then
        tmp = y / (a - (t / 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 = x / (t - (z * a));
	double tmp;
	if (x <= -1.65e-25) {
		tmp = t_1;
	} else if (x <= 2e-19) {
		tmp = y / (a - (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	tmp = 0
	if x <= -1.65e-25:
		tmp = t_1
	elif x <= 2e-19:
		tmp = y / (a - (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (x <= -1.65e-25)
		tmp = t_1;
	elseif (x <= 2e-19)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	tmp = 0.0;
	if (x <= -1.65e-25)
		tmp = t_1;
	elseif (x <= 2e-19)
		tmp = y / (a - (t / z));
	else
		tmp = t_1;
	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]}, If[LessEqual[x, -1.65e-25], t$95$1, If[LessEqual[x, 2e-19], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6499999999999999e-25 or 2e-19 < x

   1. Initial program 84.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.6499999999999999e-25 < x < 2e-19

   1. Initial program 82.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 54.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -660000000:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -660000000.0) (/ y a) (if (<= z 7.4e-93) (/ x t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -660000000.0) {
		tmp = y / a;
	} else if (z <= 7.4e-93) {
		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 <= (-660000000.0d0)) then
        tmp = y / a
    else if (z <= 7.4d-93) 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 <= -660000000.0) {
		tmp = y / a;
	} else if (z <= 7.4e-93) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -660000000.0:
		tmp = y / a
	elif z <= 7.4e-93:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -660000000.0)
		tmp = Float64(y / a);
	elseif (z <= 7.4e-93)
		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 <= -660000000.0)
		tmp = y / a;
	elseif (z <= 7.4e-93)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -660000000.0], N[(y / a), $MachinePrecision], If[LessEqual[z, 7.4e-93], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6e8 or 7.40000000000000005e-93 < z

   1. Initial program 70.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -6.6e8 < z < 7.40000000000000005e-93

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 35.0% 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 83.6%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in z around 0 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. 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 2024110 
(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))))