Average Error: 10.3 → 1.7
Time: 3.0s
Precision: binary64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq 2592826044157362.5:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y + 1\right) \cdot \frac{1}{z}\right) - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \leq 2592826044157362.5:\\
\;\;\;\;\frac{x \cdot \left(y + 1\right)}{z} - x\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (+ (- y z) 1.0)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= x 2592826044157362.5)
   (- (/ (* x (+ y 1.0)) z) x)
   (- (* x (* (+ y 1.0) (/ 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 tmp;
	if ((x <= 2592826044157362.5)) {
		tmp = ((double) ((((double) (x * ((double) (y + 1.0)))) / z) - x));
	} else {
		tmp = ((double) (((double) (x * ((double) (((double) (y + 1.0)) * (1.0 / z))))) - x));
	}
	return tmp;
}

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

Original10.3
Target0.5
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;x < -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x < 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < 2592826044157362.5

    1. Initial program Error: 6.4 bits

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

    2. SimplifiedError: 4.2 bits

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

    4. Applied associate-*r/Error: 2.1 bits

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

    if 2592826044157362.5 < x

    1. Initial program Error: 27.3 bits

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

    2. SimplifiedError: 0.1 bits

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

    4. Applied div-invError: 0.1 bits

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

  4. Final simplificationError: 1.7 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2592826044157362.5:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y + 1\right) \cdot \frac{1}{z}\right) - x\\ \end{array}\]

Reproduce

herbie shell --seed 2020204 
(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))