Average Error: 3.6 → 2.1
Time: 4.6s
Precision: binary64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq 6.264993903807226 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{y} - y}{z}}{3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \leq 6.264993903807226 \cdot 10^{-26}:\\
\;\;\;\;x + \frac{\frac{\frac{t}{y} - y}{z}}{3}\\

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

\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 (<= t 6.264993903807226e-26)
   (+ x (/ (/ (- (/ t y) y) z) 3.0))
   (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))))
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x - (y / ((double) (z * 3.0))))) + (t / ((double) (((double) (z * 3.0)) * y)))));
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= 6.264993903807226e-26)) {
		tmp = ((double) (x + ((((double) ((t / y) - y)) / z) / 3.0)));
	} else {
		tmp = ((double) (((double) (x - (y / ((double) (z * 3.0))))) + (t / ((double) (y * ((double) (z * 3.0)))))));
	}
	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
Target1.8
Herbie2.1
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if t < 6.26499390380722575e-26

    1. Initial program Error: 4.4 bits

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

    2. SimplifiedError: 2.6 bits

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

    4. Applied associate-/r*Error: 2.6 bits

      \[\leadsto x + \color{blue}{\frac{\frac{\frac{t}{y} - y}{z}}{3}}\]

    if 6.26499390380722575e-26 < t

    1. Initial program Error: 0.6 bits

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
  3. Recombined 2 regimes into one program.

  4. Final simplificationError: 2.1 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.264993903807226 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{y} - y}{z}}{3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020204 
(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))))