Average Error: 0.0 → 0.2
Time: 6.9s
Precision: binary64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\left(\left(x - \left(\sqrt[3]{y - 1} \cdot \sqrt[3]{y - 1}\right) \cdot \left(\sqrt[3]{y - 1} \cdot z\right)\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b
↓
\left(\left(x - \left(\sqrt[3]{y - 1} \cdot \sqrt[3]{y - 1}\right) \cdot \left(\sqrt[3]{y - 1} \cdot z\right)\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b
(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))
↓
(FPCore (x y z t a b)
 :precision binary64
 (+
  (-
   (- x (* (* (cbrt (- y 1.0)) (cbrt (- y 1.0))) (* (cbrt (- y 1.0)) z)))
   (* (- t 1.0) a))
  (* (- (+ y t) 2.0) b)))
double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((cbrt(y - 1.0) * cbrt(y - 1.0)) * (cbrt(y - 1.0) * z))) - ((t - 1.0) * a)) + (((y + t) - 2.0) * 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

Derivation

  1. Initial program 0.0

    \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
  2. Using strategy rm

  3. Applied add-cube-cbrt_binary64_4460.2

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

  4. Applied associate-*l*_binary64_3570.2

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

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020280 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))