Average Error: 3.0 → 1.8
Time: 3.9s
Precision: binary64
\[ \begin{array}{c}[z, t] = \mathsf{sort}([z, t])\\ \end{array} \]
\[\frac{x}{y - z \cdot t} \]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq 2 \cdot 10^{+201}:\\ \;\;\;\;\frac{-x}{z \cdot t - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \end{array} \]
(FPCore (x y z t) :precision binary64 (/ x (- y (* z t))))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) 2e+201) (/ (- x) (- (* z t) y)) (/ (/ (- x) z) t)))
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+201) {
		tmp = -x / ((z * t) - y);
	} else {
		tmp = (-x / z) / t;
	}
	return tmp;
}

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+201) then
        tmp = -x / ((z * t) - y)
    else
        tmp = (-x / z) / t
    end if
    code = tmp
end function

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+201) {
		tmp = -x / ((z * t) - y);
	} else {
		tmp = (-x / z) / t;
	}
	return tmp;
}

def code(x, y, z, t):
	return x / (y - (z * t))
↓
def code(x, y, z, t):
	tmp = 0
	if (z * t) <= 2e+201:
		tmp = -x / ((z * t) - y)
	else:
		tmp = (-x / z) / t
	return tmp

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+201)
		tmp = Float64(Float64(-x) / Float64(Float64(z * t) - y));
	else
		tmp = Float64(Float64(Float64(-x) / z) / t);
	end
	return tmp
end

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+201)
		tmp = -x / ((z * t) - y);
	else
		tmp = (-x / z) / t;
	end
	tmp_2 = tmp;
end

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+201], N[((-x) / N[(N[(z * t), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(N[((-x) / z), $MachinePrecision] / t), $MachinePrecision]]

\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot t \leq 2 \cdot 10^{+201}:\\
\;\;\;\;\frac{-x}{z \cdot t - y}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{-x}{z}}{t}\\


\end{array}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.0
Target1.6
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;x < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x < 2.1378306434876444 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array} \]

Derivation

  1. Split input into 2 regimes

  2. if (*.f64 z t) < 2.00000000000000008e201

    1. Initial program 1.7

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

    2. Applied egg-rr2.2

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

    3. Taylor expanded in x around -inf 1.7

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

    4. Simplified1.7

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

    if 2.00000000000000008e201 < (*.f64 z t)

    1. Initial program 11.8

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

    2. Taylor expanded in y around 0 13.1

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

    3. Simplified2.0

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq 2 \cdot 10^{+201}:\\ \;\;\;\;\frac{-x}{z \cdot t - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \end{array} \]

Reproduce

herbie shell --seed 2022156 
(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))))