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

Percentage Accurate: 95.8% → 97.7%

Time: 8.5s

Alternatives: 9

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq 10^{+272}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(z, -t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) 1e+272) (/ x (fma z (- t) y)) (/ (/ x z) (- t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= 1e+272) {
		tmp = x / fma(z, -t, y);
	} else {
		tmp = (x / z) / -t;
	}
	return tmp;
}

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= 1e+272)
		tmp = Float64(x / fma(z, Float64(-t), y));
	else
		tmp = Float64(Float64(x / z) / Float64(-t));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], 1e+272], N[(x / N[(z * (-t) + y), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < 1.0000000000000001e272

   1. Initial program 99.0%

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

      1. cancel-sign-sub-inv 99.0%

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

      2. +-commutative 99.0%

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

      3. distribute-lft-neg-out 99.0%

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

      4. distribute-rgt-neg-out 99.0%

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

      5. fma-define 99.0%

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

   3. Simplified 99.0%

      \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(z, -t, y\right)}} \]
   4. Add Preprocessing

   if 1.0000000000000001e272 < (*.f64 z t)

   1. Initial program 64.3%

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

   3. Taylor expanded in t around -inf 90.4%

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

   4. Taylor expanded in z around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-neg-frac2 99.9%

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

   6. Applied egg-rr 99.9%

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

Alternative 2: 78.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-118}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 10^{+272}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -5e-118)
   (/ -1.0 (* z (/ t x)))
   (if (<= (* z t) 4e-57)
     (/ x y)
     (if (<= (* z t) 1e+272) (/ (- x) (* z t)) (/ (/ x z) (- t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -5e-118) {
		tmp = -1.0 / (z * (t / x));
	} else if ((z * t) <= 4e-57) {
		tmp = x / y;
	} else if ((z * t) <= 1e+272) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / z) / -t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * t) <= (-5d-118)) then
        tmp = (-1.0d0) / (z * (t / x))
    else if ((z * t) <= 4d-57) then
        tmp = x / y
    else if ((z * t) <= 1d+272) then
        tmp = -x / (z * t)
    else
        tmp = (x / z) / -t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -5e-118) {
		tmp = -1.0 / (z * (t / x));
	} else if ((z * t) <= 4e-57) {
		tmp = x / y;
	} else if ((z * t) <= 1e+272) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / z) / -t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -5e-118:
		tmp = -1.0 / (z * (t / x))
	elif (z * t) <= 4e-57:
		tmp = x / y
	elif (z * t) <= 1e+272:
		tmp = -x / (z * t)
	else:
		tmp = (x / z) / -t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -5e-118)
		tmp = Float64(-1.0 / Float64(z * Float64(t / x)));
	elseif (Float64(z * t) <= 4e-57)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= 1e+272)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(Float64(x / z) / Float64(-t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -5e-118)
		tmp = -1.0 / (z * (t / x));
	elseif ((z * t) <= 4e-57)
		tmp = x / y;
	elseif ((z * t) <= 1e+272)
		tmp = -x / (z * t);
	else
		tmp = (x / z) / -t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e-118], N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 4e-57], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e+272], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z t) < -5.00000000000000015e-118

   1. Initial program 97.3%

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

   3. Taylor expanded in t around -inf 65.8%

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

   4. Taylor expanded in z around inf 73.9%

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

      1. clear-num 73.9%

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

      2. un-div-inv 73.9%

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

      3. div-inv 73.1%

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

      4. clear-num 74.3%

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

      5. add-sqr-sqrt 34.4%

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

      6. sqrt-unprod 44.6%

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

      7. sqr-neg 44.6%

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

      8. sqrt-unprod 13.9%

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

      9. add-sqr-sqrt 31.6%

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

      10. associate-/l* 29.2%

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

      11. *-commutative 29.2%

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

      12. associate-/l* 30.6%

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

      13. add-sqr-sqrt 12.7%

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

      14. sqrt-unprod 46.9%

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

      15. sqr-neg 46.9%

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

      16. sqrt-unprod 39.4%

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

      17. add-sqr-sqrt 75.6%

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

   6. Applied egg-rr 75.6%

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

   if -5.00000000000000015e-118 < (*.f64 z t) < 3.99999999999999982e-57

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 89.8%

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

   if 3.99999999999999982e-57 < (*.f64 z t) < 1.0000000000000001e272

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 80.6%

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

      1. associate-*r/ 80.6%

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

      2. neg-mul-1 80.6%

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

   5. Simplified 80.6%

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

   if 1.0000000000000001e272 < (*.f64 z t)

   1. Initial program 64.3%

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

   3. Taylor expanded in t around -inf 90.4%

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

   4. Taylor expanded in z around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-neg-frac2 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-118}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 10^{+272}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 10^{+272}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -5e-118)
   (/ (/ x (- t)) z)
   (if (<= (* z t) 4e-57)
     (/ x y)
     (if (<= (* z t) 1e+272) (/ (- x) (* z t)) (/ (/ x z) (- t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -5e-118) {
		tmp = (x / -t) / z;
	} else if ((z * t) <= 4e-57) {
		tmp = x / y;
	} else if ((z * t) <= 1e+272) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / z) / -t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * t) <= (-5d-118)) then
        tmp = (x / -t) / z
    else if ((z * t) <= 4d-57) then
        tmp = x / y
    else if ((z * t) <= 1d+272) then
        tmp = -x / (z * t)
    else
        tmp = (x / z) / -t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -5e-118) {
		tmp = (x / -t) / z;
	} else if ((z * t) <= 4e-57) {
		tmp = x / y;
	} else if ((z * t) <= 1e+272) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / z) / -t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -5e-118:
		tmp = (x / -t) / z
	elif (z * t) <= 4e-57:
		tmp = x / y
	elif (z * t) <= 1e+272:
		tmp = -x / (z * t)
	else:
		tmp = (x / z) / -t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -5e-118)
		tmp = Float64(Float64(x / Float64(-t)) / z);
	elseif (Float64(z * t) <= 4e-57)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= 1e+272)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(Float64(x / z) / Float64(-t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -5e-118)
		tmp = (x / -t) / z;
	elseif ((z * t) <= 4e-57)
		tmp = x / y;
	elseif ((z * t) <= 1e+272)
		tmp = -x / (z * t);
	else
		tmp = (x / z) / -t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e-118], N[(N[(x / (-t)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 4e-57], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e+272], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z t) < -5.00000000000000015e-118

   1. Initial program 97.3%

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

      1. add-cube-cbrt 96.6%

         \[\leadsto \frac{x}{y - \color{blue}{\left(\sqrt[3]{z \cdot t} \cdot \sqrt[3]{z \cdot t}\right) \cdot \sqrt[3]{z \cdot t}}} \]

      2. pow3 96.6%

         \[\leadsto \frac{x}{y - \color{blue}{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}} \]

   4. Applied egg-rr 96.6%

      \[\leadsto \frac{x}{y - \color{blue}{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}} \]

   5. Taylor expanded in y around 0 75.4%

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

      1. mul-1-neg 75.4%

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

      2. associate-/r* 74.4%

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

      3. distribute-neg-frac 74.4%

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

      4. distribute-frac-neg 74.4%

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

   7. Simplified 74.4%

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

   if -5.00000000000000015e-118 < (*.f64 z t) < 3.99999999999999982e-57

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 89.8%

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

   if 3.99999999999999982e-57 < (*.f64 z t) < 1.0000000000000001e272

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 80.6%

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

      1. associate-*r/ 80.6%

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

      2. neg-mul-1 80.6%

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

   5. Simplified 80.6%

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

   if 1.0000000000000001e272 < (*.f64 z t)

   1. Initial program 64.3%

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

   3. Taylor expanded in t around -inf 90.4%

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

   4. Taylor expanded in z around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-neg-frac2 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 10^{+272}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot t}\\ \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 10^{+272}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z t))))
   (if (<= (* z t) -5e-118)
     t_1
     (if (<= (* z t) 4e-57)
       (/ x y)
       (if (<= (* z t) 1e+272) t_1 (/ (/ x z) (- t)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double tmp;
	if ((z * t) <= -5e-118) {
		tmp = t_1;
	} else if ((z * t) <= 4e-57) {
		tmp = x / y;
	} else if ((z * t) <= 1e+272) {
		tmp = t_1;
	} else {
		tmp = (x / z) / -t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -x / (z * t)
    if ((z * t) <= (-5d-118)) then
        tmp = t_1
    else if ((z * t) <= 4d-57) then
        tmp = x / y
    else if ((z * t) <= 1d+272) then
        tmp = t_1
    else
        tmp = (x / z) / -t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double tmp;
	if ((z * t) <= -5e-118) {
		tmp = t_1;
	} else if ((z * t) <= 4e-57) {
		tmp = x / y;
	} else if ((z * t) <= 1e+272) {
		tmp = t_1;
	} else {
		tmp = (x / z) / -t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = -x / (z * t)
	tmp = 0
	if (z * t) <= -5e-118:
		tmp = t_1
	elif (z * t) <= 4e-57:
		tmp = x / y
	elif (z * t) <= 1e+272:
		tmp = t_1
	else:
		tmp = (x / z) / -t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z * t))
	tmp = 0.0
	if (Float64(z * t) <= -5e-118)
		tmp = t_1;
	elseif (Float64(z * t) <= 4e-57)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= 1e+272)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) / Float64(-t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z * t);
	tmp = 0.0;
	if ((z * t) <= -5e-118)
		tmp = t_1;
	elseif ((z * t) <= 4e-57)
		tmp = x / y;
	elseif ((z * t) <= 1e+272)
		tmp = t_1;
	else
		tmp = (x / z) / -t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -5e-118], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 4e-57], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e+272], t$95$1, N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -5.00000000000000015e-118 or 3.99999999999999982e-57 < (*.f64 z t) < 1.0000000000000001e272

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 77.7%

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

      1. associate-*r/ 77.7%

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

      2. neg-mul-1 77.7%

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

   5. Simplified 77.7%

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

   if -5.00000000000000015e-118 < (*.f64 z t) < 3.99999999999999982e-57

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 89.8%

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

   if 1.0000000000000001e272 < (*.f64 z t)

   1. Initial program 64.3%

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

   3. Taylor expanded in t around -inf 90.4%

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

   4. Taylor expanded in z around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-neg-frac2 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-118}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 10^{+272}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+221} \lor \neg \left(z \cdot t \leq 10^{+249}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -5e+221) (not (<= (* z t) 1e+249)))
   (/ x (* z t))
   (/ x y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -5e+221) || !((z * t) <= 1e+249)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * t) <= (-5d+221)) .or. (.not. ((z * t) <= 1d+249))) then
        tmp = x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -5e+221) || !((z * t) <= 1e+249)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -5e+221) or not ((z * t) <= 1e+249):
		tmp = x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -5e+221) || !(Float64(z * t) <= 1e+249))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -5e+221) || ~(((z * t) <= 1e+249)))
		tmp = x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -5e+221], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e+249]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -5.0000000000000002e221 or 9.9999999999999992e248 < (*.f64 z t)

   1. Initial program 80.2%

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

   3. Taylor expanded in t around -inf 91.5%

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

   4. Taylor expanded in z around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. associate-/l/ 80.2%

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

      3. distribute-frac-neg 80.2%

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

      4. add-sqr-sqrt 44.4%

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

      5. sqrt-unprod 71.3%

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

      6. sqr-neg 71.3%

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

      7. sqrt-unprod 31.8%

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

      8. *-commutative 31.8%

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

      9. add-sqr-sqrt 64.4%

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

   6. Applied egg-rr 64.4%

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

   if -5.0000000000000002e221 < (*.f64 z t) < 9.9999999999999992e248

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 60.0%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+221} \lor \neg \left(z \cdot t \leq 10^{+249}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-23} \lor \neg \left(y \leq 9.6 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{1}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.5e-23) (not (<= y 9.6e+84)))
   (/ 1.0 (/ y x))
   (/ (- x) (* z t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.5e-23) || !(y <= 9.6e+84)) {
		tmp = 1.0 / (y / x);
	} else {
		tmp = -x / (z * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.5d-23)) .or. (.not. (y <= 9.6d+84))) then
        tmp = 1.0d0 / (y / x)
    else
        tmp = -x / (z * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.5e-23) || !(y <= 9.6e+84)) {
		tmp = 1.0 / (y / x);
	} else {
		tmp = -x / (z * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -4.5e-23) or not (y <= 9.6e+84):
		tmp = 1.0 / (y / x)
	else:
		tmp = -x / (z * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.5e-23) || !(y <= 9.6e+84))
		tmp = Float64(1.0 / Float64(y / x));
	else
		tmp = Float64(Float64(-x) / Float64(z * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.5e-23) || ~((y <= 9.6e+84)))
		tmp = 1.0 / (y / x);
	else
		tmp = -x / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.5e-23], N[Not[LessEqual[y, 9.6e+84]], $MachinePrecision]], N[(1.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.49999999999999975e-23 or 9.5999999999999999e84 < y

   1. Initial program 96.2%

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

   3. Taylor expanded in y around inf 82.4%

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

      1. clear-num 83.6%

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

      2. inv-pow 83.6%

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

   5. Applied egg-rr 83.6%

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

      1. unpow-1 83.6%

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

   7. Simplified 83.6%

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

   if -4.49999999999999975e-23 < y < 9.5999999999999999e84

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0 79.1%

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

      1. associate-*r/ 79.1%

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

      2. neg-mul-1 79.1%

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

   5. Simplified 79.1%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-23} \lor \neg \left(y \leq 9.6 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{1}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq 10^{+272}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) 1e+272) (/ x (- y (* z t))) (/ (/ x z) (- t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= 1e+272) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x / z) / -t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * t) <= 1d+272) then
        tmp = x / (y - (z * t))
    else
        tmp = (x / z) / -t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= 1e+272) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x / z) / -t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z * t) <= 1e+272:
		tmp = x / (y - (z * t))
	else:
		tmp = (x / z) / -t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= 1e+272)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(Float64(x / z) / Float64(-t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= 1e+272)
		tmp = x / (y - (z * t));
	else
		tmp = (x / z) / -t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], 1e+272], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < 1.0000000000000001e272

   1. Initial program 99.0%

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

   if 1.0000000000000001e272 < (*.f64 z t)

   1. Initial program 64.3%

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

   3. Taylor expanded in t around -inf 90.4%

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

   4. Taylor expanded in z around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-neg-frac2 99.9%

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

   6. Applied egg-rr 99.9%

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

Alternative 8: 53.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{1}{\frac{y}{x}} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ 1.0 (/ y x)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return 1.0 / (y / x);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 / (y / x)
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return 1.0 / (y / x);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0 / (y / x)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(1.0 / Float64(y / x))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 / (y / x);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(1.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.2%

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

3. Taylor expanded in y around inf 52.4%

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

   1. clear-num 52.9%

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

   2. inv-pow 52.9%

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

5. Applied egg-rr 52.9%

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

   1. unpow-1 52.9%

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

7. Simplified 52.9%

   \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]
8. Add Preprocessing

Alternative 9: 53.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{x}{y} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x y))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return x / y;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / y
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return x / y;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return x / y

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(x / y)
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = x / y;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 96.2%

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

3. Taylor expanded in y around inf 52.4%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
4. Add Preprocessing

Developer Target 1: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{if}\;x < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x < 2.1378306434876444 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (- (/ y x) (* (/ z x) t)))))
   (if (< x -1.618195973607049e+50)
     t_1
     (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / ((y / x) - ((z / x) * t));
	double tmp;
	if (x < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (x < 2.1378306434876444e+131) {
		tmp = x / (y - (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / ((y / x) - ((z / x) * t))
    if (x < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (x < 2.1378306434876444d+131) then
        tmp = x / (y - (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / ((y / x) - ((z / x) * t));
	double tmp;
	if (x < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (x < 2.1378306434876444e+131) {
		tmp = x / (y - (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 / ((y / x) - ((z / x) * t))
	tmp = 0
	if x < -1.618195973607049e+50:
		tmp = t_1
	elif x < 2.1378306434876444e+131:
		tmp = x / (y - (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(Float64(y / x) - Float64(Float64(z / x) * t)))
	tmp = 0.0
	if (x < -1.618195973607049e+50)
		tmp = t_1;
	elseif (x < 2.1378306434876444e+131)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / ((y / x) - ((z / x) * t));
	tmp = 0.0;
	if (x < -1.618195973607049e+50)
		tmp = t_1;
	elseif (x < 2.1378306434876444e+131)
		tmp = x / (y - (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(N[(y / x), $MachinePrecision] - N[(N[(z / x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[x, -1.618195973607049e+50], t$95$1, If[Less[x, 2.1378306434876444e+131], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024131 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -161819597360704900000000000000000000000000000000000) (/ 1 (- (/ y x) (* (/ z x) t))) (if (< x 213783064348764440000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (- y (* z t))) (/ 1 (- (/ y x) (* (/ z x) t))))))

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