Average Error: 1.9 → 2.2
Time: 10.7s
Precision: binary64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot \left({\left(\sqrt{{e}^{\left(\sqrt[3]{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \sqrt[3]{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}\right)}}\right)}^{\left(\sqrt[3]{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}\right)} \cdot {\left(\sqrt{{e}^{\left(\sqrt[3]{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \sqrt[3]{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}\right)}}\right)}^{\left(\sqrt[3]{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}\right)}\right)}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{x \cdot \left({\left(\sqrt{{e}^{\left(\sqrt[3]{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \sqrt[3]{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}\right)}}\right)}^{\left(\sqrt[3]{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}\right)} \cdot {\left(\sqrt{{e}^{\left(\sqrt[3]{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \sqrt[3]{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}\right)}}\right)}^{\left(\sqrt[3]{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}\right)}\right)}{y}
(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))
↓
(FPCore (x y z t a b)
 :precision binary64
 (/
  (*
   x
   (*
    (pow
     (sqrt
      (pow
       E
       (*
        (cbrt (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
        (cbrt (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))))
     (cbrt (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))
    (pow
     (sqrt
      (pow
       E
       (*
        (cbrt (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
        (cbrt (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))))
     (cbrt (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))))
  y))
double code(double x, double y, double z, double t, double a, double b) {
	return (((double) (x * ((double) exp(((double) (((double) (((double) (y * ((double) log(z)))) + ((double) (((double) (t - 1.0)) * ((double) log(a)))))) - b)))))) / y);
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return (((double) (x * ((double) (((double) pow(((double) sqrt(((double) pow(((double) M_E), ((double) (((double) cbrt(((double) (((double) (((double) (y * ((double) log(z)))) + ((double) (((double) (t - 1.0)) * ((double) log(a)))))) - b)))) * ((double) cbrt(((double) (((double) (((double) (y * ((double) log(z)))) + ((double) (((double) (t - 1.0)) * ((double) log(a)))))) - b)))))))))), ((double) cbrt(((double) (((double) (((double) (y * ((double) log(z)))) + ((double) (((double) (t - 1.0)) * ((double) log(a)))))) - b)))))) * ((double) pow(((double) sqrt(((double) pow(((double) M_E), ((double) (((double) cbrt(((double) (((double) (((double) (y * ((double) log(z)))) + ((double) (((double) (t - 1.0)) * ((double) log(a)))))) - b)))) * ((double) cbrt(((double) (((double) (((double) (y * ((double) log(z)))) + ((double) (((double) (t - 1.0)) * ((double) log(a)))))) - b)))))))))), ((double) cbrt(((double) (((double) (((double) (y * ((double) log(z)))) + ((double) (((double) (t - 1.0)) * ((double) log(a)))))) - b)))))))))) / y);
}

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

Original1.9
Target11.1
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Initial program 1.9

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity_binary641.9

    \[\leadsto \frac{x \cdot e^{\color{blue}{1 \cdot \left(\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b\right)}}}{y}\]

  4. Applied exp-prod_binary641.9

    \[\leadsto \frac{x \cdot \color{blue}{{\left(e^{1}\right)}^{\left(\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b\right)}}}{y}\]

  5. Simplified1.9

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

  7. Applied add-cube-cbrt_binary642.2

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

  8. Applied pow-unpow_binary642.2

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

  10. Applied add-sqr-sqrt_binary642.2

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

  11. Applied unpow-prod-down_binary642.2

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

  12. Final simplification2.2

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

Reproduce

herbie shell --seed 2020210 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))