Average Error: 0.2 → 0.2
Time: 38.6s
Precision: binary64
Cost: 512
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[0.5 \cdot \left(y \cdot \sqrt{z} + x\right)\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
0.5 \cdot \left(y \cdot \sqrt{z} + x\right)
(FPCore (x y z) :precision binary64 (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))
↓
(FPCore (x y z) :precision binary64 (* 0.5 (+ (* y (sqrt z)) x)))
double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * sqrt(z)));
}
↓
double code(double x, double y, double z) {
	return 0.5 * ((y * sqrt(z)) + x);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs
Alternative 1
Accuracy0.7
Cost1344
\[0.5 \cdot \left(x + \sqrt[3]{y \cdot \sqrt{z}} \cdot \left(\sqrt[3]{y \cdot \sqrt{z}} \cdot \sqrt[3]{y \cdot \sqrt{z}}\right)\right)\]
Alternative 2
Accuracy1.4
Cost1856
\[\sqrt[3]{0.5 \cdot \left(y \cdot \sqrt{z} + x\right)} \cdot \left(\sqrt[3]{0.5 \cdot \left(y \cdot \sqrt{z} + x\right)} \cdot \sqrt[3]{0.5 \cdot \left(y \cdot \sqrt{z} + x\right)}\right)\]
Alternative 3
Accuracy41.0
Cost704
\[\sqrt[3]{{\left(0.5 \cdot \left(y \cdot \sqrt{z} + x\right)\right)}^{3}}\]

Derivation

  1. Initial program 0.2

    \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]

  2. Simplified0.2

    \[\leadsto \color{blue}{0.5 \cdot \left(x + y \cdot \sqrt{z}\right)}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity_binary64_72390.2

    \[\leadsto \color{blue}{1 \cdot \left(0.5 \cdot \left(x + y \cdot \sqrt{z}\right)\right)}\]
  5. Using strategy rm

  6. Applied *-un-lft-identity_binary64_72390.2

    \[\leadsto 1 \cdot \left(\color{blue}{\left(1 \cdot 0.5\right)} \cdot \left(x + y \cdot \sqrt{z}\right)\right)\]

  7. Applied associate-*l*_binary64_71800.2

    \[\leadsto 1 \cdot \color{blue}{\left(1 \cdot \left(0.5 \cdot \left(x + y \cdot \sqrt{z}\right)\right)\right)}\]

  8. Simplified0.2

    \[\leadsto 1 \cdot \left(1 \cdot \color{blue}{\left(0.5 \cdot \left(y \cdot \sqrt{z} + x\right)\right)}\right)\]

  9. Final simplification0.2

    \[\leadsto 0.5 \cdot \left(y \cdot \sqrt{z} + x\right)\]

Reproduce

herbie shell --seed 2020322 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))