Average Error: 10.1 → 2.1
Time: 2.8s
Precision: binary64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -7.973597288859605 \cdot 10^{+99}:\\ \;\;\;\;\frac{x}{\frac{z}{y + 1}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z} - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -7.973597288859605 \cdot 10^{+99}:\\
\;\;\;\;\frac{x}{\frac{z}{y + 1}} - x\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (+ (- y z) 1.0)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= x -7.973597288859605e+99)
   (- (/ x (/ z (+ y 1.0))) x)
   (- (/ (* x (+ y 1.0)) z) x)))
double code(double x, double y, double z) {
	return (((double) (x * ((double) (((double) (y - z)) + 1.0)))) / z);
}
↓
double code(double x, double y, double z) {
	double VAR;
	if ((x <= -7.973597288859605e+99)) {
		VAR = ((double) ((x / (z / ((double) (y + 1.0)))) - x));
	} else {
		VAR = ((double) ((((double) (x * ((double) (y + 1.0)))) / z) - x));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.1
Target0.4
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;x < -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x < 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -7.9735972888596052e99

    1. Initial program 37.3

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]

    2. Simplified0.1

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

    4. Applied associate-*r/12.6

      \[\leadsto \color{blue}{\frac{x \cdot \left(y + 1\right)}{z}} - x\]
    5. Using strategy rm

    6. Applied associate-/l*0.1

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

    if -7.9735972888596052e99 < x

    1. Initial program 6.6

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]

    2. Simplified4.1

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

    4. Applied associate-*r/2.3

      \[\leadsto \color{blue}{\frac{x \cdot \left(y + 1\right)}{z}} - x\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.973597288859605 \cdot 10^{+99}:\\ \;\;\;\;\frac{x}{\frac{z}{y + 1}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z} - x\\ \end{array}\]

Reproduce

herbie shell --seed 2020198 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))