Average Error: 0.1 → 0.1
Time: 8.3s
Precision: binary64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\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
 (+ (- (+ (+ 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(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(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
\[\left(\left(x + y\right) + \frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b\]

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_binary640.1

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

  4. Applied log-prod_binary640.1

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

  5. Applied distribute-rgt-in_binary640.1

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

  6. Simplified0.1

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

  7. Simplified0.1

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

  9. Applied add-sqr-sqrt_binary640.1

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

  10. Applied log-prod_binary640.1

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

  11. Applied distribute-rgt-in_binary640.1

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

  12. Applied associate-+r+_binary640.1

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

  13. Simplified0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(\color{blue}{z \cdot \left(\log t \cdot 0.8333333333333334\right)} + \log \left(\sqrt{\sqrt[3]{t}}\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b\]

  14. Taylor expanded around 0 0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{z \cdot \left(\log \left({t}^{0.16666666666666666}\right) + 0.8333333333333334 \cdot \log t\right)}\right) + \left(a - 0.5\right) \cdot b\]

  15. Simplified0.1

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

  16. Final simplification0.1

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

Alternatives

Reproduce

herbie shell --seed 2021118 
(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)))