Average Error: 2.6 → 2.6
Time: 8.9s
Precision: binary64
\[\frac{x}{y - z \cdot t} \]
↓
\[\frac{x}{y - z \cdot t} \]
\frac{x}{y - z \cdot t}
↓
\frac{x}{y - z \cdot t}

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

Original2.6
Target1.7
Herbie2.6
\[\begin{array}{l} \mathbf{if}\;x < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x < 2.1378306434876444 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array} \]

Derivation

  1. Initial program 2.6

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

  2. Applied add-cube-cbrt_binary643.5

    \[\leadsto \frac{x}{\color{blue}{\left(\sqrt[3]{y - z \cdot t} \cdot \sqrt[3]{y - z \cdot t}\right) \cdot \sqrt[3]{y - z \cdot t}}} \]

  3. Applied pow1/3_binary6432.3

    \[\leadsto \frac{x}{\left(\sqrt[3]{y - z \cdot t} \cdot \sqrt[3]{y - z \cdot t}\right) \cdot \color{blue}{{\left(y - z \cdot t\right)}^{0.3333333333333333}}} \]

  4. Applied pow1/3_binary6432.6

    \[\leadsto \frac{x}{\left(\sqrt[3]{y - z \cdot t} \cdot \color{blue}{{\left(y - z \cdot t\right)}^{0.3333333333333333}}\right) \cdot {\left(y - z \cdot t\right)}^{0.3333333333333333}} \]

  5. Applied pow1/3_binary6432.8

    \[\leadsto \frac{x}{\left(\color{blue}{{\left(y - z \cdot t\right)}^{0.3333333333333333}} \cdot {\left(y - z \cdot t\right)}^{0.3333333333333333}\right) \cdot {\left(y - z \cdot t\right)}^{0.3333333333333333}} \]

  6. Applied pow-sqr_binary6432.8

    \[\leadsto \frac{x}{\color{blue}{{\left(y - z \cdot t\right)}^{\left(2 \cdot 0.3333333333333333\right)}} \cdot {\left(y - z \cdot t\right)}^{0.3333333333333333}} \]

  7. Applied pow-prod-up_binary642.6

    \[\leadsto \frac{x}{\color{blue}{{\left(y - z \cdot t\right)}^{\left(2 \cdot 0.3333333333333333 + 0.3333333333333333\right)}}} \]

  8. Final simplification2.6

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

Reproduce

herbie shell --seed 2021280 
(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))))