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

Average Error: 17.4 → 0.0

Time: 4.8s

Precision: binary64

Cost: 512

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	17.4
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 17.4

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

2. Simplified 17.4

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

   [Start] 17.4	\[ \left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y \]
   rational_best-simplify-2 [=>] 17.4	\[ \left(\left(\color{blue}{y \cdot x} + y \cdot y\right) - y \cdot z\right) - y \cdot y \]
   rational_best-simplify-47 [=>] 17.4	\[ \left(\color{blue}{y \cdot \left(y + x\right)} - y \cdot z\right) - y \cdot y \]

3. Applied egg-rr 0.0

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	15.1
Cost	520

\[\begin{array}{l} t_0 := z \cdot \left(-y\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{-83}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-21}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.0
Cost	320

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

Alternative 3
Error	29.6
Cost	192

\[y \cdot x \]

Reproduce

herbie shell --seed 2023094 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

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

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