Average Error: 3.7 → 0.8
Time: 4.4s
Precision: binary64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -4.833879571757204 \cdot 10^{+31}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;t \leq 1.664154512901837 \cdot 10^{-124}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \leq -4.833879571757204 \cdot 10^{+31}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\

\mathbf{elif}\;t \leq 1.664154512901837 \cdot 10^{-124}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\

\mathbf{else}:\\
\;\;\;\;\left(x - \frac{\frac{y}{z}}{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 -4.833879571757204e+31)
   (+ (- x (/ y (* z 3.0))) (* 0.3333333333333333 (/ t (* y z))))
   (if (<= t 1.664154512901837e-124)
     (+ (- x (/ y (* z 3.0))) (* (/ 1.0 (* z 3.0)) (/ t y)))
     (+ (- 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 <= -4.833879571757204e+31)) {
		tmp = ((double) (((double) (x - (y / ((double) (z * 3.0))))) + ((double) (0.3333333333333333 * (t / ((double) (y * z)))))));
	} else {
		double tmp_1;
		if ((t <= 1.664154512901837e-124)) {
			tmp_1 = ((double) (((double) (x - (y / ((double) (z * 3.0))))) + ((double) ((1.0 / ((double) (z * 3.0))) * (t / y)))));
		} else {
			tmp_1 = ((double) (((double) (x - ((y / z) / 3.0))) + (t / ((double) (y * ((double) (z * 3.0)))))));
		}
		tmp = tmp_1;
	}
	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

Original3.7
Target1.8
Herbie0.8
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -4.8338795717572036e31

    1. Initial program 0.6

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

    2. Taylor expanded around 0 0.7

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

    if -4.8338795717572036e31 < t < 1.66415451290183694e-124

    1. Initial program 6.2

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

    3. Applied *-un-lft-identity_binary646.2

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

    4. Applied times-frac_binary640.3

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

    if 1.66415451290183694e-124 < t

    1. Initial program 1.6

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

    3. Applied associate-/r*_binary641.6

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.833879571757204 \cdot 10^{+31}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;t \leq 1.664154512901837 \cdot 10^{-124}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020205 
(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))))