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

Percentage Accurate: 96.0% → 99.8%

Time: 8.0s

Alternatives: 7

Speedup: 0.3×

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: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+260}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (/ (/ x (- t)) z)
   (if (<= (* z t) 5e+260) (/ x (- y (* z t))) (* (/ -1.0 z) (/ x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -((double) INFINITY)) {
		tmp = (x / -t) / z;
	} else if ((z * t) <= 5e+260) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (-1.0 / z) * (x / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = (x / -t) / z;
	} else if ((z * t) <= 5e+260) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (-1.0 / z) * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -math.inf:
		tmp = (x / -t) / z
	elif (z * t) <= 5e+260:
		tmp = x / (y - (z * t))
	else:
		tmp = (-1.0 / z) * (x / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(Float64(x / Float64(-t)) / z);
	elseif (Float64(z * t) <= 5e+260)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(Float64(-1.0 / z) * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -Inf)
		tmp = (x / -t) / z;
	elseif ((z * t) <= 5e+260)
		tmp = x / (y - (z * t));
	else
		tmp = (-1.0 / z) * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[(N[(x / (-t)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+260], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 58.8%

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

   3. Taylor expanded in y around 0 58.8%

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

      1. associate-*r/ 58.8%

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

      2. neg-mul-1 58.8%

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

   5. Simplified 58.8%

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

      1. neg-mul-1 58.8%

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

      2. *-commutative 58.8%

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

      3. times-frac 100.0%

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

   7. Applied egg-rr 100.0%

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

      1. associate-*l/ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. associate-*l/ 99.7%

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

      4. frac-2neg 99.7%

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

      5. metadata-eval 99.7%

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

      6. associate-*l/ 100.0%

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

      7. *-un-lft-identity 100.0%

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

   9. Applied egg-rr 100.0%

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

   if -inf.0 < (*.f64 z t) < 4.9999999999999996e260

   1. Initial program 99.9%

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

   if 4.9999999999999996e260 < (*.f64 z t)

   1. Initial program 77.9%

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

   3. Taylor expanded in y around 0 77.9%

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

      1. associate-*r/ 77.9%

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

      2. neg-mul-1 77.9%

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

   5. Simplified 77.9%

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

      1. neg-mul-1 77.9%

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

      2. *-commutative 77.9%

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

      3. times-frac 100.0%

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

   7. Applied egg-rr 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+260}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-274}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-128}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-67}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.4e+37)
   (/ x y)
   (if (<= y 1.4e-274)
     (/ (/ x (- t)) z)
     (if (<= y 1.35e-128)
       (/ (/ (- x) z) t)
       (if (<= y 1.35e-67) (/ (- x) (* z t)) (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e+37) {
		tmp = x / y;
	} else if (y <= 1.4e-274) {
		tmp = (x / -t) / z;
	} else if (y <= 1.35e-128) {
		tmp = (-x / z) / t;
	} else if (y <= 1.35e-67) {
		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 (y <= (-3.4d+37)) then
        tmp = x / y
    else if (y <= 1.4d-274) then
        tmp = (x / -t) / z
    else if (y <= 1.35d-128) then
        tmp = (-x / z) / t
    else if (y <= 1.35d-67) 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 (y <= -3.4e+37) {
		tmp = x / y;
	} else if (y <= 1.4e-274) {
		tmp = (x / -t) / z;
	} else if (y <= 1.35e-128) {
		tmp = (-x / z) / t;
	} else if (y <= 1.35e-67) {
		tmp = -x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.4e+37:
		tmp = x / y
	elif y <= 1.4e-274:
		tmp = (x / -t) / z
	elif y <= 1.35e-128:
		tmp = (-x / z) / t
	elif y <= 1.35e-67:
		tmp = -x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.4e+37)
		tmp = Float64(x / y);
	elseif (y <= 1.4e-274)
		tmp = Float64(Float64(x / Float64(-t)) / z);
	elseif (y <= 1.35e-128)
		tmp = Float64(Float64(Float64(-x) / z) / t);
	elseif (y <= 1.35e-67)
		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 (y <= -3.4e+37)
		tmp = x / y;
	elseif (y <= 1.4e-274)
		tmp = (x / -t) / z;
	elseif (y <= 1.35e-128)
		tmp = (-x / z) / t;
	elseif (y <= 1.35e-67)
		tmp = -x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.4e+37], N[(x / y), $MachinePrecision], If[LessEqual[y, 1.4e-274], N[(N[(x / (-t)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.35e-128], N[(N[((-x) / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 1.35e-67], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.40000000000000006e37 or 1.35000000000000008e-67 < y

   1. Initial program 99.3%

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

   3. Taylor expanded in y around inf 75.6%

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

   if -3.40000000000000006e37 < y < 1.39999999999999988e-274

   1. Initial program 87.8%

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

   3. Taylor expanded in y around 0 67.3%

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

      1. associate-*r/ 67.3%

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

      2. neg-mul-1 67.3%

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

   5. Simplified 67.3%

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

      1. neg-mul-1 67.3%

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

      2. *-commutative 67.3%

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

      3. times-frac 75.7%

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

   7. Applied egg-rr 75.7%

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

      1. associate-*l/ 75.9%

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

      2. associate-*r/ 75.9%

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

      3. associate-*l/ 75.7%

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

      4. frac-2neg 75.7%

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

      5. metadata-eval 75.7%

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

      6. associate-*l/ 75.9%

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

      7. *-un-lft-identity 75.9%

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

   9. Applied egg-rr 75.9%

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

   if 1.39999999999999988e-274 < y < 1.35000000000000003e-128

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0 86.5%

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

      1. associate-*r/ 86.5%

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

      2. neg-mul-1 86.5%

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

      3. *-commutative 86.5%

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

      4. associate-/r* 83.0%

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

   5. Simplified 83.0%

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

   if 1.35000000000000003e-128 < y < 1.35000000000000008e-67

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-274}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-128}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-67}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-20} \lor \neg \left(y \leq 4.1 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.4e-20) (not (<= y 4.1e+26))) (/ x y) (/ (- x) (* z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.4e-20) || !(y <= 4.1e+26)) {
		tmp = x / y;
	} 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 ((y <= (-2.4d-20)) .or. (.not. (y <= 4.1d+26))) then
        tmp = x / y
    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 ((y <= -2.4e-20) || !(y <= 4.1e+26)) {
		tmp = x / y;
	} else {
		tmp = -x / (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.4e-20) or not (y <= 4.1e+26):
		tmp = x / y
	else:
		tmp = -x / (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.4e-20) || !(y <= 4.1e+26))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(-x) / Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.4e-20) || ~((y <= 4.1e+26)))
		tmp = x / y;
	else
		tmp = -x / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.4e-20], N[Not[LessEqual[y, 4.1e+26]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999993e-20 or 4.09999999999999983e26 < y

   1. Initial program 96.5%

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

   3. Taylor expanded in y around inf 77.6%

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

   if -2.39999999999999993e-20 < y < 4.09999999999999983e26

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0 74.5%

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

      1. associate-*r/ 74.5%

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

      2. neg-mul-1 74.5%

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

   5. Simplified 74.5%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-20} \lor \neg \left(y \leq 4.1 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+37} \lor \neg \left(y \leq 10^{-67}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.1e+37) (not (<= y 1e-67))) (/ x y) (/ (/ x (- t)) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.1e+37) || !(y <= 1e-67)) {
		tmp = x / y;
	} 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) :: tmp
    if ((y <= (-3.1d+37)) .or. (.not. (y <= 1d-67))) then
        tmp = x / y
    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 tmp;
	if ((y <= -3.1e+37) || !(y <= 1e-67)) {
		tmp = x / y;
	} else {
		tmp = (x / -t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.1e+37) or not (y <= 1e-67):
		tmp = x / y
	else:
		tmp = (x / -t) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.1e+37) || !(y <= 1e-67))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / Float64(-t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.1e+37) || ~((y <= 1e-67)))
		tmp = x / y;
	else
		tmp = (x / -t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.1e+37], N[Not[LessEqual[y, 1e-67]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(x / (-t)), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1000000000000002e37 or 9.99999999999999943e-68 < y

   1. Initial program 99.3%

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

   3. Taylor expanded in y around inf 75.6%

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

   if -3.1000000000000002e37 < y < 9.99999999999999943e-68

   1. Initial program 90.9%

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

   3. Taylor expanded in y around 0 75.1%

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

      1. associate-*r/ 75.1%

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

      2. neg-mul-1 75.1%

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

   5. Simplified 75.1%

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

      1. neg-mul-1 75.1%

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

      2. *-commutative 75.1%

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

      3. times-frac 78.1%

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

   7. Applied egg-rr 78.1%

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

      1. associate-*l/ 78.2%

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

      2. associate-*r/ 78.2%

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

      3. associate-*l/ 78.1%

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

      4. frac-2neg 78.1%

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

      5. metadata-eval 78.1%

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

      6. associate-*l/ 78.2%

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

      7. *-un-lft-identity 78.2%

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

   9. Applied egg-rr 78.2%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+37} \lor \neg \left(y \leq 10^{-67}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-48} \lor \neg \left(t \leq 1.35 \cdot 10^{+217}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.9e-48) (not (<= t 1.35e+217))) (/ x (* z t)) (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.9e-48) || !(t <= 1.35e+217)) {
		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 ((t <= (-2.9d-48)) .or. (.not. (t <= 1.35d+217))) 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 ((t <= -2.9e-48) || !(t <= 1.35e+217)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.9e-48) or not (t <= 1.35e+217):
		tmp = x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.9e-48) || !(t <= 1.35e+217))
		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 ((t <= -2.9e-48) || ~((t <= 1.35e+217)))
		tmp = x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.9e-48], N[Not[LessEqual[t, 1.35e+217]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9000000000000003e-48 or 1.35000000000000001e217 < t

   1. Initial program 92.8%

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

   3. Taylor expanded in y around 0 66.4%

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

      1. associate-*r/ 66.4%

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

      2. neg-mul-1 66.4%

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

   5. Simplified 66.4%

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

      1. associate-/l/ 69.2%

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

      2. expm1-log1p-u 66.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{-x}{z}}{t}\right)\right)} \]

      3. expm1-udef 42.9%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{-x}{z}}{t}\right)} - 1} \]

      4. associate-/r* 44.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-x}{z \cdot t}}\right)} - 1 \]

      5. add-sqr-sqrt 18.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z \cdot t}\right)} - 1 \]

      6. sqrt-unprod 39.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z \cdot t}\right)} - 1 \]

      7. sqr-neg 39.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{z \cdot t}\right)} - 1 \]

      8. sqrt-unprod 21.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z \cdot t}\right)} - 1 \]

      9. add-sqr-sqrt 39.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{z \cdot t}\right)} - 1 \]

   7. Applied egg-rr 39.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 35.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)\right)} \]

      2. expm1-log1p 36.2%

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

      3. associate-/r* 36.0%

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

   9. Simplified 36.0%

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

   10. Taylor expanded in x around 0 36.2%

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

   if -2.9000000000000003e-48 < t < 1.35000000000000001e217

   1. Initial program 97.6%

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

   3. Taylor expanded in y around inf 61.2%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-48} \lor \neg \left(t \leq 1.35 \cdot 10^{+217}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+216}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.9e-48) (/ x (* z t)) (if (<= t 2.7e+216) (/ x y) (/ (/ x t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.9e-48) {
		tmp = x / (z * t);
	} else if (t <= 2.7e+216) {
		tmp = x / y;
	} 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) :: tmp
    if (t <= (-2.9d-48)) then
        tmp = x / (z * t)
    else if (t <= 2.7d+216) then
        tmp = x / y
    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 tmp;
	if (t <= -2.9e-48) {
		tmp = x / (z * t);
	} else if (t <= 2.7e+216) {
		tmp = x / y;
	} else {
		tmp = (x / t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.9e-48:
		tmp = x / (z * t)
	elif t <= 2.7e+216:
		tmp = x / y
	else:
		tmp = (x / t) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.9e-48)
		tmp = Float64(x / Float64(z * t));
	elseif (t <= 2.7e+216)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / t) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.9e-48)
		tmp = x / (z * t);
	elseif (t <= 2.7e+216)
		tmp = x / y;
	else
		tmp = (x / t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.9e-48], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+216], N[(x / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.9000000000000003e-48

   1. Initial program 94.2%

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

   3. Taylor expanded in y around 0 64.5%

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

      1. associate-*r/ 64.5%

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

      2. neg-mul-1 64.5%

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

   5. Simplified 64.5%

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

      1. associate-/l/ 67.1%

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

      2. expm1-log1p-u 63.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{-x}{z}}{t}\right)\right)} \]

      3. expm1-udef 40.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{-x}{z}}{t}\right)} - 1} \]

      4. associate-/r* 42.0%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-x}{z \cdot t}}\right)} - 1 \]

      5. add-sqr-sqrt 17.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z \cdot t}\right)} - 1 \]

      6. sqrt-unprod 37.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z \cdot t}\right)} - 1 \]

      7. sqr-neg 37.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{z \cdot t}\right)} - 1 \]

      8. sqrt-unprod 19.5%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z \cdot t}\right)} - 1 \]

      9. add-sqr-sqrt 36.5%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{z \cdot t}\right)} - 1 \]

   7. Applied egg-rr 36.5%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 32.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)\right)} \]

      2. expm1-log1p 32.4%

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

      3. associate-/r* 32.3%

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

   9. Simplified 32.3%

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

   10. Taylor expanded in x around 0 32.4%

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

   if -2.9000000000000003e-48 < t < 2.7000000000000001e216

   1. Initial program 97.6%

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

   3. Taylor expanded in y around inf 61.2%

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

   if 2.7000000000000001e216 < t

   1. Initial program 87.5%

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

   3. Taylor expanded in y around 0 74.0%

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

      1. associate-*r/ 74.0%

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

      2. neg-mul-1 74.0%

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

   5. Simplified 74.0%

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

      1. neg-mul-1 74.0%

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

      2. *-commutative 74.0%

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

      3. times-frac 86.3%

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

   7. Applied egg-rr 86.3%

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

      1. associate-*l/ 86.4%

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

      2. associate-*r/ 86.4%

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

      3. associate-*l/ 86.2%

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

      4. frac-2neg 86.2%

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

      5. metadata-eval 86.2%

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

      6. associate-*l/ 86.4%

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

      7. *-un-lft-identity 86.4%

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

   9. Applied egg-rr 86.4%

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

       1. associate-/l/ 74.0%

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

       2. associate-/r* 77.1%

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

       3. add-sqr-sqrt 0.0%

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

       4. sqrt-unprod 50.6%

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

       5. sqr-neg 50.6%

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

       6. sqrt-unprod 50.4%

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

       7. add-sqr-sqrt 50.4%

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

       8. associate-/r* 50.7%

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

       9. *-commutative 50.7%

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

       10. expm1-log1p-u 50.6%

           \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{t \cdot z}\right)\right)} \]

       11. expm1-udef 50.7%

           \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{t \cdot z}\right)} - 1} \]

   11. Applied egg-rr 50.7%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{t \cdot z}\right)} - 1} \]
   12. Step-by-step derivation

       1. expm1-def 50.6%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{t \cdot z}\right)\right)} \]

       2. expm1-log1p 50.7%

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

       3. associate-/r* 50.5%

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

   13. Simplified 50.5%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+216}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.8% 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 95.7%

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

3. Taylor expanded in y around inf 51.3%

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

4. Final simplification 51.3%

   \[\leadsto \frac{x}{y} \]
5. Add Preprocessing

Developer target: 96.9% 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 2024031 
(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))))