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

Average Error: 2.8 → 2.0

Time: 4.1s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+246}:\\ \;\;\;\;{\left(\frac{y}{x} - \frac{z}{\frac{x}{t}}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -2e+246)
   (pow (- (/ y x) (/ z (/ x t))) -1.0)
   (/ x (- y (* z t)))))

C

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

↓

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -2e+246) {
		tmp = pow(((y / x) - (z / (x / t))), -1.0);
	} else {
		tmp = x / (y - (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
    code = x / (y - (z * t))
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * t) <= (-2d+246)) then
        tmp = ((y / x) - (z / (x / t))) ** (-1.0d0)
    else
        tmp = x / (y - (z * t))
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -2e+246) {
		tmp = Math.pow(((y / x) - (z / (x / t))), -1.0);
	} else {
		tmp = x / (y - (z * t));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -2e+246:
		tmp = math.pow(((y / x) - (z / (x / t))), -1.0)
	else:
		tmp = x / (y - (z * t))
	return tmp

Julia

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

↓

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -2e+246)
		tmp = Float64(Float64(y / x) - Float64(z / Float64(x / t))) ^ -1.0;
	else
		tmp = Float64(x / Float64(y - Float64(z * t)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -2e+246)
		tmp = ((y / x) - (z / (x / t))) ^ -1.0;
	else
		tmp = x / (y - (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -2e+246], N[Power[N[(N[(y / x), $MachinePrecision] - N[(z / N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	2.8
Target	1.6
Herbie	2.0

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -2.00000000000000014e246

   1. Initial program 14.0

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

   2. Applied egg-rr 14.2

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

   3. Applied egg-rr 5.6

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

   if -2.00000000000000014e246 < (*.f64 z t)

   1. Initial program 1.6

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

   2. Applied egg-rr 1.7

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

   3. Taylor expanded in x around 0 1.6

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

4. Final simplification 2.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+246}:\\ \;\;\;\;{\left(\frac{y}{x} - \frac{z}{\frac{x}{t}}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \]

Reproduce

herbie shell --seed 2022185 
(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))))