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

Average Error: 13.2 → 0.0

Time: 3.1s

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	13.2
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 13.2

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

2. Simplified 0.0

   \[\leadsto \color{blue}{y \cdot \left(x - z\right)} \]
   Proof
   (*.f64 y (-.f64 x z)): 0 points increase in error, 0 points decrease in error
   (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 x y) (*.f64 z y))): 1 points increase in error, 0 points decrease in error
   (-.f64 (*.f64 x y) (Rewrite<= *-commutative_binary64 (*.f64 y z))): 0 points increase in error, 1 points decrease in error
   (-.f64 (*.f64 x y) (Rewrite<= +-lft-identity_binary64 (+.f64 0 (*.f64 y z)))): 0 points increase in error, 0 points decrease in error
   (-.f64 (*.f64 x y) (+.f64 (Rewrite<= +-inverses_binary64 (-.f64 (*.f64 y y) (*.f64 y y))) (*.f64 y z))): 0 points increase in error, 0 points decrease in error
   (Rewrite<= associate--l-_binary64 (-.f64 (-.f64 (*.f64 x y) (-.f64 (*.f64 y y) (*.f64 y y))) (*.f64 y z))): 0 points increase in error, 0 points decrease in error
   (-.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 (*.f64 x y) (*.f64 y y)) (*.f64 y y))) (*.f64 y z)): 0 points increase in error, 0 points decrease in error

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	16.4
Cost	1050

\[\begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{+84}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+21} \lor \neg \left(x \leq -1.18 \cdot 10^{-14}\right) \land \left(x \leq 9.2 \cdot 10^{-21} \lor \neg \left(x \leq 3.9 \cdot 10^{+45}\right) \land x \leq 5.6 \cdot 10^{+60}\right):\\ \;\;\;\;-y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2
Error	30.0
Cost	192

\[y \cdot x \]

Reproduce

herbie shell --seed 2022343 
(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)))