Average Error: 0.1 → 0.1
Time: 10.1s
Precision: binary64
Cost: 26688
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log t + \left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log y \cdot \left(x \cdot 0.3333333333333333\right)\right) - y\right) - z\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log t + \left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log y \cdot \left(x \cdot 0.3333333333333333\right)\right) - y\right) - z\right)
(FPCore (x y z t) :precision binary64 (+ (- (- (* x (log y)) y) z) (log t)))
↓
(FPCore (x y z t)
 :precision binary64
 (+
  (log t)
  (-
   (- (+ (* x (* 2.0 (log (cbrt y)))) (* (log y) (* x 0.3333333333333333))) y)
   z)))
double code(double x, double y, double z, double t) {
	return (((x * log(y)) - y) - z) + log(t);
}
↓
double code(double x, double y, double z, double t) {
	return log(t) + ((((x * (2.0 * log(cbrt(y)))) + (log(y) * (x * 0.3333333333333333))) - y) - z);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.1
Cost26560
\[\log t + \left(\left(\left(x \cdot \log \left(\sqrt[3]{y}\right) + x \cdot \left(\log y \cdot 0.6666666666666666\right)\right) - y\right) - z\right)\]
Alternative 2
Error0.1
Cost26496
\[\log t + \left(\left(3 \cdot \left(x \cdot \log \left(\sqrt[3]{-y} \cdot \sqrt[3]{-1}\right)\right) - y\right) - z\right)\]
Alternative 3
Error0.1
Cost13376
\[\log t + \left(\left(x \cdot \log y - y\right) - z\right)\]
Alternative 4
Error6.6
Cost14211
\[\begin{array}{l} \mathbf{if}\;x \leq -7.969374254347619 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \log y + \left(\log t - z\right)\\ \mathbf{elif}\;x \leq -1.8863645764484405 \cdot 10^{+40}:\\ \;\;\;\;\log t + \left(x \cdot \log y - y\right)\\ \mathbf{elif}\;x \leq 5.668703090593301 \cdot 10^{+27}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + \left(\log t - z\right)\\ \end{array}\]
Alternative 5
Error6.9
Cost13576
\[\begin{array}{l} \mathbf{if}\;x \leq -7.382329161334326 \cdot 10^{+37} \lor \neg \left(x \leq 7.295452747192458 \cdot 10^{+31}\right):\\ \;\;\;\;\log t + \left(x \cdot \log y - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array}\]
Alternative 6
Error10.9
Cost7048
\[\begin{array}{l} \mathbf{if}\;x \leq -1.7379731327875018 \cdot 10^{+113} \lor \neg \left(x \leq 2.4784889808443074 \cdot 10^{+68}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array}\]
Alternative 7
Error24.9
Cost8197
\[\begin{array}{l} \mathbf{if}\;x \leq -1.4008379546812208 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -2.0265368381009863 \cdot 10^{-95}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 2.7365996940462594 \cdot 10^{-159}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 2.427510472541674 \cdot 10^{-102}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 9.947727666082691 \cdot 10^{+33}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array}\]
Alternative 8
Error24.9
Cost7234
\[\begin{array}{l} \mathbf{if}\;z \leq -5.102848052255118 \cdot 10^{+54}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 5.8438619760370475 \cdot 10^{+28}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;\log t - z\\ \end{array}\]
Alternative 9
Error26.3
Cost6913
\[\begin{array}{l} \mathbf{if}\;y \leq 3.1980678212088143 \cdot 10^{+119}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array}\]
Alternative 10
Error32.5
Cost456
\[\begin{array}{l} \mathbf{if}\;z \leq -2.294749219137473 \cdot 10^{+54} \lor \neg \left(z \leq 1.8744169494846408 \cdot 10^{+52}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array}\]
Alternative 11
Error44.3
Cost128
\[-z\]
Alternative 12
Error61.5
Cost64
\[-1\]
Alternative 13
Error62.1
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.1

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

  3. Applied add-cube-cbrt_binary64_11360.1

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

  4. Applied log-prod_binary64_11870.1

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

  5. Applied distribute-rgt-in_binary64_10510.1

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

  6. Simplified0.1

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

  7. Simplified0.1

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

  9. Applied pow1/3_binary64_11830.1

    \[\leadsto \left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \color{blue}{\left({y}^{0.3333333333333333}\right)}\right) - y\right) - z\right) + \log t\]
  10. Using strategy rm

  11. Applied log-pow_binary64_11900.1

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

  12. Applied associate-*r*_binary64_10410.1

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

  13. Simplified0.1

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

  14. Simplified0.1

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

  15. Final simplification0.1

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))