Average Error: 3.6 → 0.5
Time: 9.7s
Precision: binary64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4.388929419357894 \cdot 10^{+57}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{\frac{\left(z \cdot 3\right) \cdot y}{t}}\\ \mathbf{elif}\;z \cdot 3 \leq 2.0555027465377215 \cdot 10^{-40}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t \cdot \frac{0.3333333333333333}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{1}{z \cdot 3}}{y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot 3 \leq -4.388929419357894 \cdot 10^{+57}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{\frac{\left(z \cdot 3\right) \cdot y}{t}}\\

\mathbf{elif}\;z \cdot 3 \leq 2.0555027465377215 \cdot 10^{-40}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t \cdot \frac{0.3333333333333333}{y}}{z}\\

\mathbf{else}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{1}{z \cdot 3}}{y}\\

\end{array}
(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -4.388929419357894e+57)
   (+ (- x (/ y (* z 3.0))) (/ 1.0 (/ (* (* z 3.0) y) t)))
   (if (<= (* z 3.0) 2.0555027465377215e-40)
     (+ (- x (/ y (* z 3.0))) (/ (* t (/ 0.3333333333333333 y)) z))
     (+ (- x (/ y (* z 3.0))) (* t (/ (/ 1.0 (* z 3.0)) y))))))
double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -4.388929419357894e+57) {
		tmp = (x - (y / (z * 3.0))) + (1.0 / (((z * 3.0) * y) / t));
	} else if ((z * 3.0) <= 2.0555027465377215e-40) {
		tmp = (x - (y / (z * 3.0))) + ((t * (0.3333333333333333 / y)) / z);
	} else {
		tmp = (x - (y / (z * 3.0))) + (t * ((1.0 / (z * 3.0)) / y));
	}
	return tmp;
}

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

Original3.6
Target1.6
Herbie0.5
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 z 3) < -4.38892941935789372e57

    1. Initial program 0.6

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    2. Using strategy rm

    3. Applied clear-num_binary64_184910.6

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{1}{\frac{\left(z \cdot 3\right) \cdot y}{t}}}\]

    if -4.38892941935789372e57 < (*.f64 z 3) < 2.05550274653772154e-40

    1. Initial program 9.2

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    2. Using strategy rm

    3. Applied associate-/r*_binary64_184362.4

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}}\]
    4. Using strategy rm

    5. Applied associate-/r*_binary64_184362.4

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{\frac{t}{z}}{3}}}{y}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity_binary64_184922.4

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{\frac{t}{z}}{3}}{\color{blue}{1 \cdot y}}\]

    8. Applied div-inv_binary64_184892.5

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{t}{z} \cdot \frac{1}{3}}}{1 \cdot y}\]

    9. Applied times-frac_binary64_184982.5

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z}}{1} \cdot \frac{\frac{1}{3}}{y}}\]

    10. Simplified2.5

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{t}{z}} \cdot \frac{\frac{1}{3}}{y}\]

    11. Simplified2.5

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z} \cdot \color{blue}{\frac{0.3333333333333333}{y}}\]
    12. Using strategy rm

    13. Applied associate-*l/_binary64_184350.5

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

    if 2.05550274653772154e-40 < (*.f64 z 3)

    1. Initial program 0.5

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    2. Using strategy rm

    3. Applied associate-/r*_binary64_184361.0

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity_binary64_184921.0

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{\color{blue}{1 \cdot y}}\]

    6. Applied div-inv_binary64_184891.0

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{t \cdot \frac{1}{z \cdot 3}}}{1 \cdot y}\]

    7. Applied times-frac_binary64_184980.5

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{t}{1} \cdot \frac{\frac{1}{z \cdot 3}}{y}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4.388929419357894 \cdot 10^{+57}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{\frac{\left(z \cdot 3\right) \cdot y}{t}}\\ \mathbf{elif}\;z \cdot 3 \leq 2.0555027465377215 \cdot 10^{-40}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t \cdot \frac{0.3333333333333333}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{1}{z \cdot 3}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2021015 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))