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

Percentage Accurate: 96.0% → 97.5%

Time: 9.4s

Alternatives: 10

Speedup: 0.6×

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: 96.0% 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: 97.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq 10^{+212}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{-1}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) 1e+212) (/ x (- y (* z t))) (/ (* x (/ -1.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= 1e+212) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x * (-1.0 / z)) / t;
	}
	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) :: tmp
    if ((z * t) <= 1d+212) then
        tmp = x / (y - (z * t))
    else
        tmp = (x * ((-1.0d0) / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= 1e+212) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x * (-1.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= 1e+212:
		tmp = x / (y - (z * t))
	else:
		tmp = (x * (-1.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= 1e+212)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(Float64(x * Float64(-1.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= 1e+212)
		tmp = x / (y - (z * t));
	else
		tmp = (x * (-1.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], 1e+212], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < 9.9999999999999991e211

   1. Initial program 98.3%

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

   if 9.9999999999999991e211 < (*.f64 z t)

   1. Initial program 82.6%

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

      1. clear-num 80.0%

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

      2. associate-/r/ 82.6%

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

   3. Applied egg-rr 82.6%

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

   4. Taylor expanded in y around 0 82.6%

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

      1. associate-/r* 87.2%

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

      2. div-inv 87.2%

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

   6. Applied egg-rr 87.2%

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

      1. associate-*l/ 87.3%

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

      2. associate-*l/ 99.9%

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

      3. un-div-inv 99.9%

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

   8. Applied egg-rr 99.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq 10^{+212}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{-1}{z}}{t}\\ \end{array} \]

Alternative 2: 79.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{-x}{z}}{t}\\ \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+30}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ (- x) z) t)))
   (if (<= (* z t) -1e+43)
     t_1
     (if (<= (* z t) 5e-29)
       (/ x y)
       (if (<= (* z t) 2e+30)
         (/ (- x) (* z t))
         (if (<= (* z t) 2e+49) (/ x y) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-x / z) / t;
	double tmp;
	if ((z * t) <= -1e+43) {
		tmp = t_1;
	} else if ((z * t) <= 5e-29) {
		tmp = x / y;
	} else if ((z * t) <= 2e+30) {
		tmp = -x / (z * t);
	} else if ((z * t) <= 2e+49) {
		tmp = x / y;
	} 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 = (-x / z) / t
    if ((z * t) <= (-1d+43)) then
        tmp = t_1
    else if ((z * t) <= 5d-29) then
        tmp = x / y
    else if ((z * t) <= 2d+30) then
        tmp = -x / (z * t)
    else if ((z * t) <= 2d+49) then
        tmp = x / y
    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 = (-x / z) / t;
	double tmp;
	if ((z * t) <= -1e+43) {
		tmp = t_1;
	} else if ((z * t) <= 5e-29) {
		tmp = x / y;
	} else if ((z * t) <= 2e+30) {
		tmp = -x / (z * t);
	} else if ((z * t) <= 2e+49) {
		tmp = x / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (-x / z) / t
	tmp = 0
	if (z * t) <= -1e+43:
		tmp = t_1
	elif (z * t) <= 5e-29:
		tmp = x / y
	elif (z * t) <= 2e+30:
		tmp = -x / (z * t)
	elif (z * t) <= 2e+49:
		tmp = x / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-x) / z) / t)
	tmp = 0.0
	if (Float64(z * t) <= -1e+43)
		tmp = t_1;
	elseif (Float64(z * t) <= 5e-29)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= 2e+30)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (Float64(z * t) <= 2e+49)
		tmp = Float64(x / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (-x / z) / t;
	tmp = 0.0;
	if ((z * t) <= -1e+43)
		tmp = t_1;
	elseif ((z * t) <= 5e-29)
		tmp = x / y;
	elseif ((z * t) <= 2e+30)
		tmp = -x / (z * t);
	elseif ((z * t) <= 2e+49)
		tmp = x / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[((-x) / z), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1e+43], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 5e-29], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+30], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+49], N[(x / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.00000000000000001e43 or 1.99999999999999989e49 < (*.f64 z t)

   1. Initial program 91.9%

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

      1. clear-num 90.9%

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

      2. associate-/r/ 91.8%

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

   3. Applied egg-rr 91.8%

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

   4. Taylor expanded in y around 0 82.3%

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

      1. associate-*l/ 82.4%

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

      2. neg-mul-1 82.4%

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

      3. *-commutative 82.4%

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

      4. associate-/r* 87.5%

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

   6. Applied egg-rr 87.5%

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

   if -1.00000000000000001e43 < (*.f64 z t) < 4.99999999999999986e-29 or 2e30 < (*.f64 z t) < 1.99999999999999989e49

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 82.8%

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

   if 4.99999999999999986e-29 < (*.f64 z t) < 2e30

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 77.1%

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

      1. associate-*r/ 77.1%

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

      2. neg-mul-1 77.1%

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

   4. Simplified 77.1%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+43}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+30}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \end{array} \]

Alternative 3: 79.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{-x}{z}}{t}\\ \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{-1}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ (- x) z) t)))
   (if (<= (* z t) -1e+43)
     t_1
     (if (<= (* z t) 5e-29)
       (/ x y)
       (if (<= (* z t) 2e+30)
         (* x (/ -1.0 (* z t)))
         (if (<= (* z t) 2e+49) (/ x y) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-x / z) / t;
	double tmp;
	if ((z * t) <= -1e+43) {
		tmp = t_1;
	} else if ((z * t) <= 5e-29) {
		tmp = x / y;
	} else if ((z * t) <= 2e+30) {
		tmp = x * (-1.0 / (z * t));
	} else if ((z * t) <= 2e+49) {
		tmp = x / y;
	} 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 = (-x / z) / t
    if ((z * t) <= (-1d+43)) then
        tmp = t_1
    else if ((z * t) <= 5d-29) then
        tmp = x / y
    else if ((z * t) <= 2d+30) then
        tmp = x * ((-1.0d0) / (z * t))
    else if ((z * t) <= 2d+49) then
        tmp = x / y
    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 = (-x / z) / t;
	double tmp;
	if ((z * t) <= -1e+43) {
		tmp = t_1;
	} else if ((z * t) <= 5e-29) {
		tmp = x / y;
	} else if ((z * t) <= 2e+30) {
		tmp = x * (-1.0 / (z * t));
	} else if ((z * t) <= 2e+49) {
		tmp = x / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (-x / z) / t
	tmp = 0
	if (z * t) <= -1e+43:
		tmp = t_1
	elif (z * t) <= 5e-29:
		tmp = x / y
	elif (z * t) <= 2e+30:
		tmp = x * (-1.0 / (z * t))
	elif (z * t) <= 2e+49:
		tmp = x / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-x) / z) / t)
	tmp = 0.0
	if (Float64(z * t) <= -1e+43)
		tmp = t_1;
	elseif (Float64(z * t) <= 5e-29)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= 2e+30)
		tmp = Float64(x * Float64(-1.0 / Float64(z * t)));
	elseif (Float64(z * t) <= 2e+49)
		tmp = Float64(x / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (-x / z) / t;
	tmp = 0.0;
	if ((z * t) <= -1e+43)
		tmp = t_1;
	elseif ((z * t) <= 5e-29)
		tmp = x / y;
	elseif ((z * t) <= 2e+30)
		tmp = x * (-1.0 / (z * t));
	elseif ((z * t) <= 2e+49)
		tmp = x / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[((-x) / z), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1e+43], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 5e-29], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+30], N[(x * N[(-1.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+49], N[(x / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.00000000000000001e43 or 1.99999999999999989e49 < (*.f64 z t)

   1. Initial program 91.9%

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

      1. clear-num 90.9%

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

      2. associate-/r/ 91.8%

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

   3. Applied egg-rr 91.8%

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

   4. Taylor expanded in y around 0 82.3%

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

      1. associate-*l/ 82.4%

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

      2. neg-mul-1 82.4%

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

      3. *-commutative 82.4%

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

      4. associate-/r* 87.5%

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

   6. Applied egg-rr 87.5%

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

   if -1.00000000000000001e43 < (*.f64 z t) < 4.99999999999999986e-29 or 2e30 < (*.f64 z t) < 1.99999999999999989e49

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 82.8%

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

   if 4.99999999999999986e-29 < (*.f64 z t) < 2e30

   1. Initial program 99.7%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in y around 0 77.2%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+43}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{-1}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \end{array} \]

Alternative 4: 79.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot t}\\ \mathbf{if}\;z \cdot t \leq -40000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 10^{+258}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z t))))
   (if (<= (* z t) -40000000.0)
     t_1
     (if (<= (* z t) 5e-29)
       (/ x y)
       (if (<= (* z t) 1e+258) t_1 (/ (/ (- x) t) z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double tmp;
	if ((z * t) <= -40000000.0) {
		tmp = t_1;
	} else if ((z * t) <= 5e-29) {
		tmp = x / y;
	} else if ((z * t) <= 1e+258) {
		tmp = t_1;
	} else {
		tmp = (-x / t) / z;
	}
	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 = -x / (z * t)
    if ((z * t) <= (-40000000.0d0)) then
        tmp = t_1
    else if ((z * t) <= 5d-29) then
        tmp = x / y
    else if ((z * t) <= 1d+258) then
        tmp = t_1
    else
        tmp = (-x / t) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double tmp;
	if ((z * t) <= -40000000.0) {
		tmp = t_1;
	} else if ((z * t) <= 5e-29) {
		tmp = x / y;
	} else if ((z * t) <= 1e+258) {
		tmp = t_1;
	} else {
		tmp = (-x / t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x / (z * t)
	tmp = 0
	if (z * t) <= -40000000.0:
		tmp = t_1
	elif (z * t) <= 5e-29:
		tmp = x / y
	elif (z * t) <= 1e+258:
		tmp = t_1
	else:
		tmp = (-x / t) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z * t))
	tmp = 0.0
	if (Float64(z * t) <= -40000000.0)
		tmp = t_1;
	elseif (Float64(z * t) <= 5e-29)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= 1e+258)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(-x) / t) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z * t);
	tmp = 0.0;
	if ((z * t) <= -40000000.0)
		tmp = t_1;
	elseif ((z * t) <= 5e-29)
		tmp = x / y;
	elseif ((z * t) <= 1e+258)
		tmp = t_1;
	else
		tmp = (-x / t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -40000000.0], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 5e-29], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e+258], t$95$1, N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4e7 or 4.99999999999999986e-29 < (*.f64 z t) < 1.00000000000000006e258

   1. Initial program 96.6%

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

   2. Taylor expanded in y around 0 78.7%

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

      1. associate-*r/ 78.7%

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

      2. neg-mul-1 78.7%

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

   4. Simplified 78.7%

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

   if -4e7 < (*.f64 z t) < 4.99999999999999986e-29

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 85.6%

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

   if 1.00000000000000006e258 < (*.f64 z t)

   1. Initial program 74.6%

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

      1. clear-num 70.8%

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

      2. associate-/r/ 74.5%

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

   3. Applied egg-rr 74.5%

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

   4. Taylor expanded in y around 0 74.5%

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

      1. associate-*l/ 74.6%

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

      2. neg-mul-1 74.6%

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

      3. associate-/r* 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -40000000:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 10^{+258}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \end{array} \]

Alternative 5: 78.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -40000000 \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -40000000.0) (not (<= (* z t) 5e-29)))
   (/ (- x) (* z t))
   (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -40000000.0) || !((z * t) <= 5e-29)) {
		tmp = -x / (z * t);
	} else {
		tmp = x / y;
	}
	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) :: tmp
    if (((z * t) <= (-40000000.0d0)) .or. (.not. ((z * t) <= 5d-29))) then
        tmp = -x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -40000000.0) || !((z * t) <= 5e-29)) {
		tmp = -x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -40000000.0) or not ((z * t) <= 5e-29):
		tmp = -x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -40000000.0) || !(Float64(z * t) <= 5e-29))
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -40000000.0) || ~(((z * t) <= 5e-29)))
		tmp = -x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -40000000.0], N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e-29]], $MachinePrecision]], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4e7 or 4.99999999999999986e-29 < (*.f64 z t)

   1. Initial program 93.4%

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

   2. Taylor expanded in y around 0 78.1%

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

      1. associate-*r/ 78.1%

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

      2. neg-mul-1 78.1%

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

   4. Simplified 78.1%

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

   if -4e7 < (*.f64 z t) < 4.99999999999999986e-29

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 85.6%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -40000000 \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 6: 63.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+179} \lor \neg \left(z \cdot t \leq 1.8 \cdot 10^{+110}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -5e+179) (not (<= (* z t) 1.8e+110)))
   (/ x (* z t))
   (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -5e+179) || !((z * t) <= 1.8e+110)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	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) :: tmp
    if (((z * t) <= (-5d+179)) .or. (.not. ((z * t) <= 1.8d+110))) then
        tmp = x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -5e+179) || !((z * t) <= 1.8e+110)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -5e+179) or not ((z * t) <= 1.8e+110):
		tmp = x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -5e+179) || !(Float64(z * t) <= 1.8e+110))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -5e+179) || ~(((z * t) <= 1.8e+110)))
		tmp = x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -5e+179], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1.8e+110]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -5e179 or 1.7999999999999998e110 < (*.f64 z t)

   1. Initial program 88.7%

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

      1. clear-num 87.5%

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

      2. associate-/r/ 88.6%

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

   3. Applied egg-rr 88.6%

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

   4. Taylor expanded in y around 0 88.6%

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

      1. associate-/r* 91.3%

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

      2. div-inv 91.3%

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

   6. Applied egg-rr 91.3%

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

      1. un-div-inv 91.3%

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

      2. associate-/l/ 88.6%

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

      3. associate-*l/ 88.7%

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

      4. neg-mul-1 88.7%

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

      5. add-sqr-sqrt 45.4%

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

      6. sqrt-unprod 64.4%

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

      7. sqr-neg 64.4%

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

      8. sqrt-unprod 27.1%

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

      9. add-sqr-sqrt 52.6%

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

   8. Applied egg-rr 52.6%

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

   if -5e179 < (*.f64 z t) < 1.7999999999999998e110

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 70.8%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+179} \lor \neg \left(z \cdot t \leq 1.8 \cdot 10^{+110}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 7: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) 5e+264) (/ x (- y (* z t))) (/ (/ (- x) z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= 5e+264) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (-x / z) / t;
	}
	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) :: tmp
    if ((z * t) <= 5d+264) then
        tmp = x / (y - (z * t))
    else
        tmp = (-x / z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= 5e+264) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (-x / z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= 5e+264:
		tmp = x / (y - (z * t))
	else:
		tmp = (-x / z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= 5e+264)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(Float64(Float64(-x) / z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= 5e+264)
		tmp = x / (y - (z * t));
	else
		tmp = (-x / z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], 5e+264], 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) < 5.00000000000000033e264

   1. Initial program 98.3%

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

   if 5.00000000000000033e264 < (*.f64 z t)

   1. Initial program 71.6%

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

      1. clear-num 67.5%

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

      2. associate-/r/ 71.6%

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

   3. Applied egg-rr 71.6%

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

   4. Taylor expanded in y around 0 71.6%

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

      1. associate-*l/ 71.6%

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

      2. neg-mul-1 71.6%

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

      3. *-commutative 71.6%

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

      4. associate-/r* 99.8%

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

   6. Applied egg-rr 99.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \end{array} \]

Alternative 8: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq 10^{+258}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{-1}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) 1e+258) (/ x (- y (* z t))) (/ (* x (/ -1.0 t)) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= 1e+258) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x * (-1.0 / t)) / z;
	}
	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) :: tmp
    if ((z * t) <= 1d+258) then
        tmp = x / (y - (z * t))
    else
        tmp = (x * ((-1.0d0) / t)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= 1e+258) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x * (-1.0 / t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= 1e+258:
		tmp = x / (y - (z * t))
	else:
		tmp = (x * (-1.0 / t)) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= 1e+258)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(Float64(x * Float64(-1.0 / t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= 1e+258)
		tmp = x / (y - (z * t));
	else
		tmp = (x * (-1.0 / t)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], 1e+258], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < 1.00000000000000006e258

   1. Initial program 98.3%

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

   if 1.00000000000000006e258 < (*.f64 z t)

   1. Initial program 74.6%

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

      1. clear-num 70.8%

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

      2. associate-/r/ 74.5%

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

   3. Applied egg-rr 74.5%

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

   4. Taylor expanded in y around 0 74.5%

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

      1. associate-/r* 81.5%

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

      2. associate-*l/ 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq 10^{+258}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{-1}{t}}{z}\\ \end{array} \]

Alternative 9: 54.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{y}{x}} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ 1.0 (/ y x)))

C

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

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 = 1.0d0 / (y / x)
end function

Java

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

Python

def code(x, y, z, t):
	return 1.0 / (y / x)

Julia

function code(x, y, z, t)
	return Float64(1.0 / Float64(y / x))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 / (y / x);
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.5%

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

   1. clear-num 96.0%

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

   2. associate-/r/ 96.4%

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

3. Applied egg-rr 96.4%

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

4. Taylor expanded in y around inf 54.1%

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

   1. associate-*l/ 54.2%

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

   2. associate-/l* 54.3%

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

6. Applied egg-rr 54.3%

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

7. Final simplification 54.3%

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

Alternative 10: 55.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

2. Taylor expanded in y around inf 54.2%

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

3. Final simplification 54.2%

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

Developer target: 96.8% accurate, 0.5× 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 2023182 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< x -1.618195973607049e+50) (/ 1.0 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1.0 (- (/ y x) (* (/ z x) t)))))

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