Average Error: 10.0 → 9.3
Time: 3.8s
Precision: binary64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -2.606579495399084 \cdot 10^{+208}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \leq -4.11761413583795 \cdot 10^{+154}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;x \leq -2.01574423849711:\\ \;\;\;\;-1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array} \]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -2.606579495399084 \cdot 10^{+208}:\\
\;\;\;\;-1 \cdot x\\

\mathbf{elif}\;x \leq -4.11761413583795 \cdot 10^{+154}:\\
\;\;\;\;\frac{y \cdot x}{z}\\

\mathbf{elif}\;x \leq -2.01574423849711:\\
\;\;\;\;-1 \cdot x\\

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


\end{array}

(FPCore (x y z) :precision binary64 (/ (* x (+ (- y z) 1.0)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= x -2.606579495399084e+208)
   (* -1.0 x)
   (if (<= x -4.11761413583795e+154)
     (/ (* y x) z)
     (if (<= x -2.01574423849711) (* -1.0 x) (/ x (/ z (+ (- y z) 1.0)))))))
double code(double x, double y, double z) {
	return (x * ((y - z) + 1.0)) / z;
}
↓
double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.606579495399084e+208) {
		tmp = -1.0 * x;
	} else if (x <= -4.11761413583795e+154) {
		tmp = (y * x) / z;
	} else if (x <= -2.01574423849711) {
		tmp = -1.0 * x;
	} else {
		tmp = x / (z / ((y - z) + 1.0));
	}
	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

Original10.0
Target0.5
Herbie9.3
\[\begin{array}{l} \mathbf{if}\;x < -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x < 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array} \]

Derivation

  1. Split input into 3 regimes

  2. if x < -2.606579495399084e208 or -4.11761413583794979e154 < x < -2.0157442384971098

    1. Initial program 24.1

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

    2. Taylor expanded in z around inf 26.8

      \[\leadsto \color{blue}{-1 \cdot x} \]

    if -2.606579495399084e208 < x < -4.11761413583794979e154

    1. Initial program 32.0

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

    2. Taylor expanded in y around inf 58.0

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]

    if -2.0157442384971098 < x

    1. Initial program 6.3

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

    2. Applied egg-rr11.0

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

    3. Applied egg-rr3.9

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

  4. Final simplification9.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.606579495399084 \cdot 10^{+208}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \leq -4.11761413583795 \cdot 10^{+154}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;x \leq -2.01574423849711:\\ \;\;\;\;-1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022127 
(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))