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

Average Accuracy: 73.3% → 100.0%

Time: 7.8s

Precision: binary64

Cost: 320

Math

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

↓

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

FPCore

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

↓

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

Python

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

↓

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 * z)) - Float64(y * y))
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 * z)) - (y * y);
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 * z), $MachinePrecision]), $MachinePrecision] - N[(y * y), $MachinePrecision]), $MachinePrecision]

↓

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

Target

Original	73.3%
Target	100.0%
Herbie	100.0%

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

Derivation

1. Initial program 73.3%

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

2. Simplified 100.0%

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

   [Start] 73.3	\[ \left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y \]
   associate--l- [=>] 73.3	\[ \color{blue}{\left(x \cdot y + y \cdot y\right) - \left(y \cdot z + y \cdot y\right)} \]
   +-commutative [=>] 73.3	\[ \left(x \cdot y + y \cdot y\right) - \color{blue}{\left(y \cdot y + y \cdot z\right)} \]
   associate--r+ [=>] 80.6	\[ \color{blue}{\left(\left(x \cdot y + y \cdot y\right) - y \cdot y\right) - y \cdot z} \]
   associate--l+ [=>] 88.1	\[ \color{blue}{\left(x \cdot y + \left(y \cdot y - y \cdot y\right)\right)} - y \cdot z \]
   +-inverses [=>] 100.0	\[ \left(x \cdot y + \color{blue}{0}\right) - y \cdot z \]
   +-rgt-identity [=>] 100.0	\[ \color{blue}{x \cdot y} - y \cdot z \]
   *-commutative [=>] 100.0	\[ x \cdot y - \color{blue}{z \cdot y} \]
   distribute-rgt-out-- [=>] 100.0	\[ \color{blue}{y \cdot \left(x - z\right)} \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	75.4%
Cost	1050

\[\begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-8}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-55} \lor \neg \left(x \leq -6.9 \cdot 10^{-102}\right) \land \left(x \leq 3.3 \cdot 10^{-51} \lor \neg \left(x \leq 6.4 \cdot 10^{-18}\right) \land x \leq 1.18 \cdot 10^{+33}\right):\\ \;\;\;\;-y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2
Accuracy	52.9%
Cost	192

\[y \cdot x \]

Reproduce

herbie shell --seed 2023137 
(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)))