Average Error: 6.3 → 2.1
Time: 6.2s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \left(z - x\right) \cdot \frac{y}{t}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \left(z - x\right) \cdot \frac{y}{t}
(FPCore (x y z t) :precision binary64 (+ x (/ (* y (- z x)) t)))
↓
(FPCore (x y z t) :precision binary64 (+ x (* (- z x) (/ y t))))
double code(double x, double y, double z, double t) {
	return x + ((y * (z - x)) / t);
}
↓
double code(double x, double y, double z, double t) {
	return x + ((z - x) * (y / t));
}

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

Original6.3
Target2.1
Herbie2.1
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.3

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

  3. Applied clear-num_binary64_99666.3

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

  4. Simplified6.3

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

  6. Applied *-un-lft-identity_binary64_99676.3

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

  7. Applied times-frac_binary64_99732.1

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

  8. Applied add-sqr-sqrt_binary64_99892.1

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

  9. Applied times-frac_binary64_99732.3

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

  10. Simplified2.3

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

  11. Simplified2.1

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

  12. Final simplification2.1

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

Reproduce

herbie shell --seed 2021047 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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