Average Error: 2.7 → 2.7
Time: 2.7s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\frac{-x}{\mathsf{fma}\left(t, z, -y\right)}\]
\frac{x}{y - z \cdot t}
↓
\frac{-x}{\mathsf{fma}\left(t, z, -y\right)}
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) {
	return (-x / fma(t, z, -y));
}

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

Original2.7
Target1.6
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.13783064348764444 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Initial program 2.7

    \[\frac{x}{y - z \cdot t}\]
  2. Using strategy rm

  3. Applied frac-2neg2.7

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

  4. Simplified2.7

    \[\leadsto \frac{-x}{\color{blue}{\mathsf{fma}\left(t, z, -y\right)}}\]

  5. Final simplification2.7

    \[\leadsto \frac{-x}{\mathsf{fma}\left(t, z, -y\right)}\]

Reproduce

herbie shell --seed 2020102 +o rules:numerics
(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 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1 (- (/ y x) (* (/ z x) t)))))

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