Average Error: 2.9 → 3.0
Time: 2.6s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[x \cdot \frac{1}{y - z \cdot t}\]
\frac{x}{y - z \cdot t}
↓
x \cdot \frac{1}{y - z \cdot 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) {
	return (x * (1.0 / (y - (z * t))));
}

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

Original2.9
Target1.7
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.13783064348764444 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Initial program 2.9

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

  3. Applied div-inv3.0

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

  4. Final simplification3.0

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

Reproduce

herbie shell --seed 2020057 +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))))