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

Average Accuracy: 63.3% → 78.7%

Time: 3.2s

Precision: binary64

Cost: 448

Math

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

↓

\[x \cdot y - y \cdot z \]

FPCore

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

↓

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

Python

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

↓

def code(x, y, z):
	return (x * y) - (y * 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(Float64(x * y) - Float64(y * 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 = (x * y) - (y * 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[(N[(x * y), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]

Target

Original	63.3%
Target	78.7%
Herbie	78.7%

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

Derivation

1. Initial program 68.6%

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

2. Simplified 81.6%

   \[\leadsto \color{blue}{x \cdot y - y \cdot z} \]
   Step-by-step derivation

   [Start] 68.6	\[ \left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z \]
   associate-+l- [=>] 75.4	\[ \color{blue}{\left(x \cdot y - \left(y \cdot y - y \cdot y\right)\right)} - y \cdot z \]
   +-inverses [=>] 81.6	\[ \left(x \cdot y - \color{blue}{0}\right) - y \cdot z \]
   associate--l- [=>] 81.6	\[ \color{blue}{x \cdot y - \left(0 + y \cdot z\right)} \]
   +-lft-identity [=>] 81.6	\[ x \cdot y - \color{blue}{y \cdot z} \]

3. Final simplification 81.6%

   \[\leadsto x \cdot y - y \cdot z \]

Alternatives

Alternative 1
Accuracy	59.6%
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+34} \lor \neg \left(z \leq 1.35 \cdot 10^{-70}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 2
Accuracy	78.7%
Cost	320

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

Alternative 3
Accuracy	41.8%
Cost	192

\[x \cdot y \]

Reproduce

herbie shell --seed 2023157 
(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)))