Average Error: 0.1 → 0.1
Time: 7.9s
Precision: binary64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\sqrt[3]{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)\right) + \left(z + \left(t + \left(a + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)\right)\right)\right)\]
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\sqrt[3]{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)\right) + \left(z + \left(t + \left(a + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)\right)\right)\right)
(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))
↓
(FPCore (x y z t a b c i)
 :precision binary64
 (+
  (+
   (* x (* 2.0 (log (cbrt y))))
   (* x (log (* (cbrt (pow (cbrt y) 2.0)) (cbrt (cbrt y))))))
  (+ z (+ t (+ a (+ (* (- b 0.5) (log c)) (* y i)))))))
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (x * ((double) log(y)))) + z)) + t)) + a)) + ((double) (((double) (b - 0.5)) * ((double) log(c)))))) + ((double) (y * i))));
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((double) (((double) (((double) (x * ((double) (2.0 * ((double) log(((double) cbrt(y)))))))) + ((double) (x * ((double) log(((double) (((double) cbrt(((double) pow(((double) cbrt(y)), 2.0)))) * ((double) cbrt(((double) cbrt(y)))))))))))) + ((double) (z + ((double) (t + ((double) (a + ((double) (((double) (((double) (b - 0.5)) * ((double) log(c)))) + ((double) (y * i))))))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  2. Simplified0.1

    \[\leadsto \color{blue}{x \cdot \log y + \left(z + \left(t + \left(a + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)\right)\right)\right)}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt0.1

    \[\leadsto x \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} + \left(z + \left(t + \left(a + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)\right)\right)\right)\]

  5. Applied log-prod0.1

    \[\leadsto x \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)} + \left(z + \left(t + \left(a + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)\right)\right)\right)\]

  6. Applied distribute-lft-in0.1

    \[\leadsto \color{blue}{\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right)} + \left(z + \left(t + \left(a + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)\right)\right)\right)\]

  7. Simplified0.1

    \[\leadsto \left(\color{blue}{x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right)} + x \cdot \log \left(\sqrt[3]{y}\right)\right) + \left(z + \left(t + \left(a + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)\right)\right)\right)\]
  8. Using strategy rm

  9. Applied add-cube-cbrt0.1

    \[\leadsto \left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\sqrt[3]{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}\right)\right) + \left(z + \left(t + \left(a + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)\right)\right)\right)\]

  10. Applied cbrt-prod0.1

    \[\leadsto \left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \color{blue}{\left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)}\right) + \left(z + \left(t + \left(a + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)\right)\right)\right)\]

  11. Simplified0.1

    \[\leadsto \left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\color{blue}{\sqrt[3]{{\left(\sqrt[3]{y}\right)}^{2}}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)\right) + \left(z + \left(t + \left(a + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)\right)\right)\right)\]

  12. Final simplification0.1

    \[\leadsto \left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\sqrt[3]{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)\right) + \left(z + \left(t + \left(a + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)\right)\right)\right)\]

Reproduce

herbie shell --seed 2020198 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))