Average Error: 1.8 → 1.3
Time: 3.1s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -1.13227931900744647 \cdot 10^{-179} \lor \neg \left(\frac{x - y}{z - y} \le 1.2264097927151126 \cdot 10^{-151}\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - y\right) \cdot 1\right) \cdot \frac{t}{z - y}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{z - y} \le -1.13227931900744647 \cdot 10^{-179} \lor \neg \left(\frac{x - y}{z - y} \le 1.2264097927151126 \cdot 10^{-151}\right):\\
\;\;\;\;\frac{x - y}{z - y} \cdot t\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (x - y)) / ((double) (z - y)))) * t));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((((double) (((double) (x - y)) / ((double) (z - y)))) <= -1.1322793190074465e-179) || !(((double) (((double) (x - y)) / ((double) (z - y)))) <= 1.2264097927151126e-151))) {
		VAR = ((double) (((double) (((double) (x - y)) / ((double) (z - y)))) * t));
	} else {
		VAR = ((double) (((double) (((double) (x - y)) * 1.0)) * ((double) (t / ((double) (z - y))))));
	}
	return VAR;
}

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

Original1.8
Target1.9
Herbie1.3
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (- x y) (- z y)) < -1.1322793190074465e-179 or 1.2264097927151126e-151 < (/ (- x y) (- z y))

    1. Initial program 1.2

      \[\frac{x - y}{z - y} \cdot t\]

    if -1.1322793190074465e-179 < (/ (- x y) (- z y)) < 1.2264097927151126e-151

    1. Initial program 5.3

      \[\frac{x - y}{z - y} \cdot t\]
    2. Using strategy rm

    3. Applied div-inv5.3

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

    5. Applied *-un-lft-identity5.3

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

    6. Applied associate-*r*5.3

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

    7. Applied associate-*l*1.7

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

    8. Simplified1.6

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -1.13227931900744647 \cdot 10^{-179} \lor \neg \left(\frac{x - y}{z - y} \le 1.2264097927151126 \cdot 10^{-151}\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - y\right) \cdot 1\right) \cdot \frac{t}{z - y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020114 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

  (* (/ (- x y) (- z y)) t))