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

Percentage Accurate: 95.9% → 99.8%

Time: 7.5s

Alternatives: 6

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: 95.9% 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: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (/ -1.0 (* t (/ z x)))
   (if (<= (* z t) 5e+297) (/ x (- y (* z t))) (/ (/ x t) (- z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -((double) INFINITY)) {
		tmp = -1.0 / (t * (z / x));
	} else if ((z * t) <= 5e+297) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x / t) / -z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = -1.0 / (t * (z / x));
	} else if ((z * t) <= 5e+297) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x / t) / -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -math.inf:
		tmp = -1.0 / (t * (z / x))
	elif (z * t) <= 5e+297:
		tmp = x / (y - (z * t))
	else:
		tmp = (x / t) / -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(-1.0 / Float64(t * Float64(z / x)));
	elseif (Float64(z * t) <= 5e+297)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(Float64(x / t) / Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -Inf)
		tmp = -1.0 / (t * (z / x));
	elseif ((z * t) <= 5e+297)
		tmp = x / (y - (z * t));
	else
		tmp = (x / t) / -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[(-1.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+297], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -inf.0

   1. Initial program 73.0%

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

      1. clear-num 73.0%

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

      2. associate-/r/ 73.0%

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

   3. Applied egg-rr 73.0%

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

   4. Taylor expanded in y around 0 73.0%

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

      1. associate-*l/ 73.0%

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

      2. associate-/l* 73.0%

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

      3. associate-*l/ 99.7%

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

      4. clear-num 99.6%

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

      5. associate-*l/ 99.7%

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

      6. *-un-lft-identity 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. associate-/r/ 99.9%

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

   8. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 z t) < 4.9999999999999998e297

   1. Initial program 99.9%

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

   if 4.9999999999999998e297 < (*.f64 z t)

   1. Initial program 72.3%

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

      1. clear-num 72.3%

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

      2. associate-/r/ 72.3%

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

   3. Applied egg-rr 72.3%

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

   4. Taylor expanded in y around 0 72.3%

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

      1. *-commutative 72.3%

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

      2. clear-num 72.3%

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

      3. un-div-inv 72.3%

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

      4. div-inv 72.3%

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

      5. *-commutative 72.3%

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

      6. metadata-eval 72.3%

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

   6. Applied egg-rr 72.3%

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

      1. associate-/r* 72.3%

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

      2. associate-/l/ 99.9%

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

      3. associate-/l/ 99.9%

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

      4. neg-mul-1 99.9%

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

   8. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \end{array} \]

Alternative 2: 79.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq 1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -5e-7)
   (/ (/ x t) (- z))
   (if (<= (* z t) 1.0) (/ x y) (/ -1.0 (* z (/ t x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -5e-7) {
		tmp = (x / t) / -z;
	} else if ((z * t) <= 1.0) {
		tmp = x / y;
	} else {
		tmp = -1.0 / (z * (t / x));
	}
	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-7)) then
        tmp = (x / t) / -z
    else if ((z * t) <= 1.0d0) then
        tmp = x / y
    else
        tmp = (-1.0d0) / (z * (t / x))
    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-7) {
		tmp = (x / t) / -z;
	} else if ((z * t) <= 1.0) {
		tmp = x / y;
	} else {
		tmp = -1.0 / (z * (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -5e-7:
		tmp = (x / t) / -z
	elif (z * t) <= 1.0:
		tmp = x / y
	else:
		tmp = -1.0 / (z * (t / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -5e-7)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (Float64(z * t) <= 1.0)
		tmp = Float64(x / y);
	else
		tmp = Float64(-1.0 / Float64(z * Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -5e-7)
		tmp = (x / t) / -z;
	elseif ((z * t) <= 1.0)
		tmp = x / y;
	else
		tmp = -1.0 / (z * (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e-7], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1.0], N[(x / y), $MachinePrecision], N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4.99999999999999977e-7

   1. Initial program 91.7%

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

      1. clear-num 91.0%

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

      2. associate-/r/ 91.6%

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

   3. Applied egg-rr 91.6%

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

   4. Taylor expanded in y around 0 79.1%

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

      1. *-commutative 79.1%

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

      2. clear-num 79.1%

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

      3. un-div-inv 79.2%

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

      4. div-inv 79.2%

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

      5. *-commutative 79.2%

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

      6. metadata-eval 79.2%

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

   6. Applied egg-rr 79.2%

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

      1. associate-/r* 79.2%

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

      2. associate-/l/ 75.1%

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

      3. associate-/l/ 75.1%

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

      4. neg-mul-1 75.1%

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

   8. Simplified 75.1%

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

   if -4.99999999999999977e-7 < (*.f64 z t) < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 85.0%

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

   if 1 < (*.f64 z t)

   1. Initial program 92.7%

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

      1. clear-num 91.9%

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

      2. associate-/r/ 92.6%

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

   3. Applied egg-rr 92.6%

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

   4. Taylor expanded in y around 0 80.1%

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

      1. associate-*l/ 80.2%

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

      2. associate-/l* 80.4%

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

      3. associate-*l/ 88.9%

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

      4. clear-num 88.8%

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

      5. associate-*l/ 87.4%

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

      6. *-un-lft-identity 87.4%

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

   6. Applied egg-rr 87.4%

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

      1. clear-num 87.5%

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

      2. associate-/r/ 88.8%

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

      3. clear-num 88.9%

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

   8. Applied egg-rr 88.9%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq 1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \]

Alternative 3: 77.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-7} \lor \neg \left(z \cdot t \leq 1\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -5e-7) (not (<= (* z t) 1.0))) (/ (- x) (* z t)) (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -5e-7) || !((z * t) <= 1.0)) {
		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-7)) .or. (.not. ((z * t) <= 1.0d0))) 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-7) || !((z * t) <= 1.0)) {
		tmp = -x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -5e-7) or not ((z * t) <= 1.0):
		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-7) || !(Float64(z * t) <= 1.0))
		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) <= -5e-7) || ~(((z * t) <= 1.0)))
		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-7], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1.0]], $MachinePrecision]], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.99999999999999977e-7 or 1 < (*.f64 z t)

   1. Initial program 92.2%

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

   2. Taylor expanded in y around 0 79.7%

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

      1. associate-*r/ 79.7%

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

      2. neg-mul-1 79.7%

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

   4. Simplified 79.7%

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

   if -4.99999999999999977e-7 < (*.f64 z t) < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 85.0%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-7} \lor \neg \left(z \cdot t \leq 1\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 4: 79.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-7} \lor \neg \left(z \cdot t \leq 1\right):\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -5e-7) (not (<= (* z t) 1.0))) (/ (/ x t) (- z)) (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -5e-7) || !((z * t) <= 1.0)) {
		tmp = (x / t) / -z;
	} 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-7)) .or. (.not. ((z * t) <= 1.0d0))) then
        tmp = (x / t) / -z
    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-7) || !((z * t) <= 1.0)) {
		tmp = (x / t) / -z;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -5e-7) or not ((z * t) <= 1.0):
		tmp = (x / t) / -z
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -5e-7) || !(Float64(z * t) <= 1.0))
		tmp = Float64(Float64(x / t) / Float64(-z));
	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-7) || ~(((z * t) <= 1.0)))
		tmp = (x / t) / -z;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -5e-7], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1.0]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.99999999999999977e-7 or 1 < (*.f64 z t)

   1. Initial program 92.2%

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

      1. clear-num 91.4%

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

      2. associate-/r/ 92.0%

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

   3. Applied egg-rr 92.0%

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

   4. Taylor expanded in y around 0 79.6%

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

      1. *-commutative 79.6%

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

      2. clear-num 79.6%

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

      3. un-div-inv 79.7%

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

      4. div-inv 79.7%

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

      5. *-commutative 79.7%

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

      6. metadata-eval 79.7%

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

   6. Applied egg-rr 79.7%

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

      1. associate-/r* 79.7%

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

      2. associate-/l/ 81.5%

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

      3. associate-/l/ 81.5%

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

      4. neg-mul-1 81.5%

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

   8. Simplified 81.5%

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

   if -4.99999999999999977e-7 < (*.f64 z t) < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 85.0%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-7} \lor \neg \left(z \cdot t \leq 1\right):\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 5: 63.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+198} \lor \neg \left(z \cdot t \leq 10^{+108}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -2e+198) (not (<= (* z t) 1e+108)))
   (/ x (* z t))
   (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -2e+198) || !((z * t) <= 1e+108)) {
		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) <= (-2d+198)) .or. (.not. ((z * t) <= 1d+108))) 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) <= -2e+198) || !((z * t) <= 1e+108)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -2e+198) or not ((z * t) <= 1e+108):
		tmp = x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -2e+198) || !(Float64(z * t) <= 1e+108))
		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) <= -2e+198) || ~(((z * t) <= 1e+108)))
		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], -2e+198], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e+108]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -2.00000000000000004e198 or 1e108 < (*.f64 z t)

   1. Initial program 85.9%

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

      1. clear-num 84.7%

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

      2. associate-/r/ 85.9%

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

   3. Applied egg-rr 85.9%

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

   4. Taylor expanded in y around 0 85.9%

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

      1. associate-*l/ 85.9%

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

      2. neg-mul-1 85.9%

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

      3. add-sqr-sqrt 46.3%

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

      4. sqrt-unprod 72.3%

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

      5. sqr-neg 72.3%

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

      6. sqrt-unprod 26.6%

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

      7. add-sqr-sqrt 65.1%

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

      8. *-commutative 65.1%

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

   6. Applied egg-rr 65.1%

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

   if -2.00000000000000004e198 < (*.f64 z t) < 1e108

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 68.2%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+198} \lor \neg \left(z \cdot t \leq 10^{+108}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 6: 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 95.8%

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

2. Taylor expanded in y around inf 53.8%

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

3. Final simplification 53.8%

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

Developer target: 96.7% 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 2023258 
(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))))