Average Error: 0.1 → 0.1
Time: 4.8s
Precision: binary64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(x + y\right) + z\right) + \left(\left(\left(a - 0.5\right) \cdot b - z \cdot \log \left(\sqrt{t}\right)\right) - z \cdot \log \left(\sqrt{t}\right)\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(x + y\right) + z\right) + \left(\left(\left(a - 0.5\right) \cdot b - z \cdot \log \left(\sqrt{t}\right)\right) - z \cdot \log \left(\sqrt{t}\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 (sqrt t)))) (* z (log (sqrt t))))))
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 ((x + y) + z) + ((((a - 0.5) * b) - (z * log(sqrt(t)))) - (z * log(sqrt(t))));
}

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

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 sub-neg_binary640.1

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

  4. Applied associate-+l+_binary640.1

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

  5. Simplified0.1

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

  7. Applied add-sqr-sqrt_binary640.1

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

  8. Applied log-prod_binary640.1

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

  9. Applied distribute-lft-in_binary640.1

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

  10. Applied associate--r+_binary640.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020220 
(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)))