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

Average Error: 17.6 → 0.0

Time: 14.4s

Precision: binary64

Cost: 6784

Math

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

↓

\[\mathsf{fma}\left(y, x, \left(-z\right) \cdot y\right) \]

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Target

Original	17.6
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 17.6

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

2. Simplified 0.0

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

3. Applied egg-rr 0.0

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

Alternatives

Alternative 1
Error	15.6
Cost	520

\[\begin{array}{l} \mathbf{if}\;x \leq -8.3 \cdot 10^{+52}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+22}:\\ \;\;\;\;-z \cdot y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2
Error	0.0
Cost	320

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

Alternative 3
Error	29.3
Cost	192

\[y \cdot x \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, B"
  :precision binary64

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

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