Average Error: 10.2 → 0.3
Time: 4.8s
Precision: binary64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \leq -\infty:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \mathbf{elif}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \leq 4.457413215179628 \cdot 10^{-99}:\\ \;\;\;\;\left(\frac{x}{z} + \frac{x \cdot y}{z}\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \leq -\infty:\\
\;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\

\mathbf{elif}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \leq 4.457413215179628 \cdot 10^{-99}:\\
\;\;\;\;\left(\frac{x}{z} + \frac{x \cdot y}{z}\right) - x\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (+ (- y z) 1.0)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* x (+ (- y z) 1.0)) z) (- INFINITY))
   (* x (/ (+ (- y z) 1.0) z))
   (if (<= (/ (* x (+ (- y z) 1.0)) z) 4.457413215179628e-99)
     (- (+ (/ x z) (/ (* x y) z)) x)
     (- (* (/ x z) (+ y 1.0)) x))))
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 * ((y - z) + 1.0)) / z) <= -((double) INFINITY)) {
		tmp = x * (((y - z) + 1.0) / z);
	} else if (((x * ((y - z) + 1.0)) / z) <= 4.457413215179628e-99) {
		tmp = ((x / z) + ((x * y) / z)) - x;
	} else {
		tmp = ((x / z) * (y + 1.0)) - 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

Original10.2
Target0.5
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;x < -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x < 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z) < -inf.0

    1. Initial program 64.0

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

    3. Applied *-un-lft-identity_binary64_1405964.0

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

    4. Applied times-frac_binary64_140650.0

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

    if -inf.0 < (/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z) < 4.4574132151796279e-99

    1. Initial program 0.1

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

    2. Taylor expanded around 0 0.1

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

    if 4.4574132151796279e-99 < (/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

    1. Initial program 13.0

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

    2. Taylor expanded around 0 4.6

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

    3. Simplified0.7

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

    4. Taylor expanded around 0 4.3

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

    5. Simplified0.7

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \leq -\infty:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \mathbf{elif}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \leq 4.457413215179628 \cdot 10^{-99}:\\ \;\;\;\;\left(\frac{x}{z} + \frac{x \cdot y}{z}\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\ \end{array}\]

Reproduce

herbie shell --seed 2021059 
(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))