Average Error: 2.7 → 2.7
Time: 9.7s
Precision: binary64
\[\frac{x}{y - z \cdot t}\]
↓
\[\frac{x}{y - t \cdot z}\]
\frac{x}{y - z \cdot t}
↓
\frac{x}{y - t \cdot z}
(FPCore (x y z t) :precision binary64 (/ x (- y (* z t))))
↓
(FPCore (x y z t) :precision binary64 (/ x (- y (* t z))))
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 / (y - (t * z));
}

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
Target1.8
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;x < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x < 2.1378306434876444 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Initial program 2.7

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

  3. Applied div-inv_binary64_123512.8

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

  4. Simplified2.8

    \[\leadsto x \cdot \color{blue}{\frac{1}{y - t \cdot z}}\]
  5. Using strategy rm

  6. Applied pow1_binary64_124152.8

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

  7. Applied pow1_binary64_124152.8

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

  8. Applied pow-prod-down_binary64_124252.8

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

  9. Simplified2.7

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

  10. Final simplification2.7

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

Reproduce

herbie shell --seed 2021075 
(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))))