Average Error: 0.1 → 0.1
Time: 30.2s
Precision: binary64
Cost: 576
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - z \cdot \sin y
(FPCore (x y z) :precision binary64 (- (* x (cos y)) (* z (sin y))))
↓
(FPCore (x y z) :precision binary64 (- (* x (cos y)) (* z (sin y))))
double code(double x, double y, double z) {
	return (x * cos(y)) - (z * sin(y));
}
↓
double code(double x, double y, double z) {
	return (x * cos(y)) - (z * sin(y));
}

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
Accuracy0.6
Cost1024
\[x \cdot \cos y - \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]

Derivation

  1. Initial program 0.1

    \[x \cdot \cos y - z \cdot \sin y\]
  2. Using strategy rm

  3. Applied pow1_binary64_62770.1

    \[\leadsto x \cdot \color{blue}{{\cos y}^{1}} - z \cdot \sin y\]

  4. Applied pow1_binary64_62770.1

    \[\leadsto \color{blue}{{x}^{1}} \cdot {\cos y}^{1} - z \cdot \sin y\]

  5. Applied pow-prod-down_binary64_62870.1

    \[\leadsto \color{blue}{{\left(x \cdot \cos y\right)}^{1}} - z \cdot \sin y\]

  6. Final simplification0.1

    \[\leadsto x \cdot \cos y - z \cdot \sin y\]

Reproduce

herbie shell --seed 2020322 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))