Average Error: 0.1 → 0.1
Time: 15.1s
Precision: binary64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[x + \left(y + \left(\left(a - 0.5\right) \cdot b + z \cdot \left(\left(1 - 2 \cdot \log \left({t}^{0.3333333333333333}\right)\right) - \log \left(\sqrt[3]{t}\right)\right)\right)\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
x + \left(y + \left(\left(a - 0.5\right) \cdot b + z \cdot \left(\left(1 - 2 \cdot \log \left({t}^{0.3333333333333333}\right)\right) - \log \left(\sqrt[3]{t}\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
   (+
    (* (- a 0.5) b)
    (*
     z
     (- (- 1.0 (* 2.0 (log (pow t 0.3333333333333333)))) (log (cbrt 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 + (((a - 0.5) * b) + (z * ((1.0 - (2.0 * log(pow(t, 0.3333333333333333)))) - log(cbrt(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
Target0.4
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. Simplified0.1

    \[\leadsto \color{blue}{x + \left(y + \left(\left(a - 0.5\right) \cdot b + z \cdot \left(1 - \log t\right)\right)\right)}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt_binary64_175040.1

    \[\leadsto x + \left(y + \left(\left(a - 0.5\right) \cdot b + z \cdot \left(1 - \log \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\right)\right)\right)\]

  5. Applied log-prod_binary64_175550.1

    \[\leadsto x + \left(y + \left(\left(a - 0.5\right) \cdot b + z \cdot \left(1 - \color{blue}{\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)}\right)\right)\right)\]

  6. Applied associate--r+_binary64_174050.1

    \[\leadsto x + \left(y + \left(\left(a - 0.5\right) \cdot b + z \cdot \color{blue}{\left(\left(1 - \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) - \log \left(\sqrt[3]{t}\right)\right)}\right)\right)\]

  7. Simplified0.1

    \[\leadsto x + \left(y + \left(\left(a - 0.5\right) \cdot b + z \cdot \left(\color{blue}{\left(1 - 2 \cdot \log \left(\sqrt[3]{t}\right)\right)} - \log \left(\sqrt[3]{t}\right)\right)\right)\right)\]
  8. Using strategy rm

  9. Applied pow1/3_binary64_175510.1

    \[\leadsto x + \left(y + \left(\left(a - 0.5\right) \cdot b + z \cdot \left(\left(1 - 2 \cdot \log \color{blue}{\left({t}^{0.3333333333333333}\right)}\right) - \log \left(\sqrt[3]{t}\right)\right)\right)\right)\]

  10. Final simplification0.1

    \[\leadsto x + \left(y + \left(\left(a - 0.5\right) \cdot b + z \cdot \left(\left(1 - 2 \cdot \log \left({t}^{0.3333333333333333}\right)\right) - \log \left(\sqrt[3]{t}\right)\right)\right)\right)\]

Reproduce

herbie shell --seed 2021176 
(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)))