Average Error: 0.1 → 0.1
Time: 5.8s
Precision: binary64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[x + \left(y + \left(z + \left(\left(a - 0.5\right) \cdot b - \left(z \cdot \left(\log \left(\sqrt[3]{t}\right) \cdot 2\right) + z \cdot \log \left({t}^{0.3333333333333333}\right)\right)\right)\right)\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
x + \left(y + \left(z + \left(\left(a - 0.5\right) \cdot b - \left(z \cdot \left(\log \left(\sqrt[3]{t}\right) \cdot 2\right) + z \cdot \log \left({t}^{0.3333333333333333}\right)\right)\right)\right)\right)
(FPCore (x y z t a b)
 :precision binary64
 (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))
↓
(FPCore (x y z t a b)
 :precision binary64
 (+
  x
  (+
   y
   (+
    z
    (-
     (* (- a 0.5) b)
     (+
      (* z (* (log (cbrt t)) 2.0))
      (* z (log (pow t 0.3333333333333333)))))))))
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (((double) (((double) (x + y)) + z)) - ((double) (z * ((double) log(t)))))) + ((double) (((double) (a - 0.5)) * b))));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (x + ((double) (y + ((double) (z + ((double) (((double) (((double) (a - 0.5)) * b)) - ((double) (((double) (z * ((double) (((double) log(((double) cbrt(t)))) * 2.0)))) + ((double) (z * ((double) log(((double) pow(t, 0.3333333333333333))))))))))))))));
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.3
Herbie0.1
\[\left(\left(x + y\right) + \frac{\left(1 - {\left(\log t\right)}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b\]

Derivation

  1. Initial program Error: 0.1 bits

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

  2. SimplifiedError: 0.1 bits

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

  4. Applied add-cube-cbrtError: 0.1 bits

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

  5. Applied log-prodError: 0.1 bits

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

  6. Applied distribute-lft-inError: 0.1 bits

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

  7. SimplifiedError: 0.1 bits

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

  9. Applied pow1/3Error: 0.1 bits

    \[\leadsto x + \left(y + \left(z + \left(\left(a - 0.5\right) \cdot b - \left(z \cdot \left(\log \left(\sqrt[3]{t}\right) \cdot 2\right) + z \cdot \log \color{blue}{\left({t}^{0.3333333333333333}\right)}\right)\right)\right)\right)\]

  10. Final simplificationError: 0.1 bits

    \[\leadsto x + \left(y + \left(z + \left(\left(a - 0.5\right) \cdot b - \left(z \cdot \left(\log \left(\sqrt[3]{t}\right) \cdot 2\right) + z \cdot \log \left({t}^{0.3333333333333333}\right)\right)\right)\right)\right)\]

Reproduce

herbie shell --seed 2020203 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))