Average Error: 0.1 → 0.1
Time: 31.4s
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

Derivation

  1. Initial program 0.1

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

  3. Applied *-un-lft-identity_binary64_58750.1

    \[\leadsto \color{blue}{1 \cdot \left(x \cdot \cos y + z \cdot \sin y\right)}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity_binary64_58750.1

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

  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:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))