Average Error: 0.1 → 0.1
Time: 5.7s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(x + y\right) + \left(z - \left(z \cdot \log \left(\sqrt{t}\right) + z \cdot \log \left(\sqrt{t}\right)\right)\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(x + y\right) + \left(z - \left(z \cdot \log \left(\sqrt{t}\right) + z \cdot \log \left(\sqrt{t}\right)\right)\right)\right) + \left(a - 0.5\right) \cdot 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 (((x + y) + (z - ((z * log(sqrt(t))) + (z * log(sqrt(t)))))) + ((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
\[\left(\left(x + y\right) + \frac{\left(1 - {\left(\log t\right)}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b\]

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 associate--l+0.1

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

  5. Applied add-sqr-sqrt0.1

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

  6. Applied log-prod0.1

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

  7. Applied distribute-lft-in0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020060 
(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 (pow (log t) 2)) z) (+ 1 (log t)))) (* (- a 0.5) b))

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