Average Error: 33.2 → 0.4
Time: 8.3s
Precision: binary64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\left|\frac{z}{t}\right|\right)}^{2}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
{\left(\frac{x}{y}\right)}^{2} + {\left(\left|\frac{z}{t}\right|\right)}^{2}
(FPCore (x y z t)
 :precision binary64
 (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))
↓
(FPCore (x y z t)
 :precision binary64
 (+ (pow (/ x y) 2.0) (pow (fabs (/ z t)) 2.0)))
double code(double x, double y, double z, double t) {
	return ((x * x) / (y * y)) + ((z * z) / (t * t));
}
↓
double code(double x, double y, double z, double t) {
	return pow((x / y), 2.0) + pow(fabs(z / t), 2.0);
}

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

Original33.2
Target0.4
Herbie0.4
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.2

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

  3. Applied add-sqr-sqrt_binary64_1680933.3

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

  4. Simplified33.3

    \[\leadsto \frac{x \cdot x}{y \cdot y} + \color{blue}{\left|\frac{z}{t}\right|} \cdot \sqrt{\frac{z \cdot z}{t \cdot t}}\]

  5. Simplified18.8

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

  6. Taylor expanded around 0 18.8

    \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|\]

  7. Simplified0.4

    \[\leadsto \color{blue}{{\left(\frac{x}{y}\right)}^{2}} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|\]
  8. Using strategy rm

  9. Applied pow2_binary64_168680.4

    \[\leadsto {\left(\frac{x}{y}\right)}^{2} + \color{blue}{{\left(\left|\frac{z}{t}\right|\right)}^{2}}\]

  10. Final simplification0.4

    \[\leadsto {\left(\frac{x}{y}\right)}^{2} + {\left(\left|\frac{z}{t}\right|\right)}^{2}\]

Reproduce

herbie shell --seed 2021098 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
  :precision binary64

  :herbie-target
  (+ (pow (/ x y) 2.0) (pow (/ z t) 2.0))

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