Linear.Quaternion:$c/ from linear-1.19.1.3, D

Average Error: 12.7 → 0.0

Time: 4.5s

Precision: binary64

Cost: 320

Math

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

↓

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

FPCore

(FPCore (x y z)
 :precision binary64
 (- (+ (- (* x y) (* y y)) (* y y)) (* y z)))

↓

(FPCore (x y z) :precision binary64 (* y (- x z)))

C

double code(double x, double y, double z) {
	return (((x * y) - (y * y)) + (y * y)) - (y * z);
}

↓

double code(double x, double y, double z) {
	return y * (x - z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (((x * y) - (y * y)) + (y * y)) - (y * z)
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y * (x - z)
end function

Java

public static double code(double x, double y, double z) {
	return (((x * y) - (y * y)) + (y * y)) - (y * z);
}

↓

public static double code(double x, double y, double z) {
	return y * (x - z);
}

Python

def code(x, y, z):
	return (((x * y) - (y * y)) + (y * y)) - (y * z)

↓

def code(x, y, z):
	return y * (x - z)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(x * y) - Float64(y * y)) + Float64(y * y)) - Float64(y * z))
end

↓

function code(x, y, z)
	return Float64(y * Float64(x - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (((x * y) - (y * y)) + (y * y)) - (y * z);
end

↓

function tmp = code(x, y, z)
	tmp = y * (x - z);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(x * y), $MachinePrecision] - N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]

Target

Original	12.7
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 12.7

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

2. Simplified 0.0

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

   [Start] 12.7	\[ \left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z \]
   associate-+l- [=>] 8.2	\[ \color{blue}{\left(x \cdot y - \left(y \cdot y - y \cdot y\right)\right)} - y \cdot z \]
   associate--l- [=>] 8.2	\[ \color{blue}{x \cdot y - \left(\left(y \cdot y - y \cdot y\right) + y \cdot z\right)} \]
   +-inverses [=>] 0.0	\[ x \cdot y - \left(\color{blue}{0} + y \cdot z\right) \]
   +-lft-identity [=>] 0.0	\[ x \cdot y - \color{blue}{y \cdot z} \]
   *-commutative [=>] 0.0	\[ x \cdot y - \color{blue}{z \cdot y} \]
   distribute-rgt-out-- [=>] 0.0	\[ \color{blue}{y \cdot \left(x - z\right)} \]

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	15.2
Cost	521

\[\begin{array}{l} \mathbf{if}\;x \leq -29500000000000 \lor \neg \left(x \leq 3.6 \cdot 10^{-102}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 2
Error	30.3
Cost	192

\[y \cdot x \]

Reproduce

herbie shell --seed 2022356 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"
  :precision binary64

  :herbie-target
  (* (- x z) y)

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