Average Error: 0.1 → 0.1
Time: 13.2s
Precision: binary64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(\left(z + y\right) + x\right) - z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right)\right) - z \cdot \log \left({t}^{0.3333333333333333}\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(\left(z + y\right) + x\right) - z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right)\right) - z \cdot \log \left({t}^{0.3333333333333333}\right)\right) + \left(a - 0.5\right) \cdot b
(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
 (+
  (-
   (- (+ (+ z y) x) (* z (* 2.0 (log (cbrt t)))))
   (* z (log (pow t 0.3333333333333333))))
  (* (- a 0.5) b)))
double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return ((((z + y) + x) - (z * (2.0 * log(cbrt(t))))) - (z * log(pow(t, 0.3333333333333333)))) + ((a - 0.5) * b);
}

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
Target0.4
Herbie0.1
\[\left(\left(x + y\right) + \frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b\]

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
  2. Using strategy rm

  3. Applied add-cube-cbrt_binary64_89790.1

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

  4. Applied log-prod_binary64_90300.1

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

  5. Applied distribute-rgt-in_binary64_88940.1

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

  6. Applied associate--r+_binary64_88800.1

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

  7. Simplified0.1

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

  9. Applied pow1/3_binary64_90260.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2021098 
(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)))