Average Error: 0.1 → 0.1
Time: 6.9s
Precision: binary64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(\left(\left(y - 0.5 \cdot \log y\right) - y \cdot \log y\right) + x\right) - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(\left(\left(y - 0.5 \cdot \log y\right) - y \cdot \log y\right) + x\right) - z
(FPCore (x y z) :precision binary64 (- (+ (- x (* (+ y 0.5) (log y))) y) z))
↓
(FPCore (x y z)
 :precision binary64
 (- (+ (- (- y (* 0.5 (log y))) (* y (log y))) x) z))
double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * log(y))) + y) - z;
}
↓
double code(double x, double y, double z) {
	return (((y - (0.5 * log(y))) - (y * log(y))) + x) - z;
}

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

Target

Original0.1
Target0.1
Herbie0.1
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]

  2. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  5. Applied distribute-rgt-in_binary64_140090.1

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

  6. Applied associate--r+_binary64_139950.1

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

  7. Final simplification0.1

    \[\leadsto \left(\left(\left(y - 0.5 \cdot \log y\right) - y \cdot \log y\right) + x\right) - z\]

Reproduce

herbie shell --seed 2021050 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))