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

Average Error: 18.0 → 0.0

Time: 6.2s

Precision: binary64

Cost: 7296

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (- (+ (fma (- z) y (* z y)) (* 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(-z, y, (z * y)) + (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 Float64(Float64(fma(Float64(-z), y, Float64(z * y)) + Float64(y * x)) - 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[(N[(N[((-z) * y + N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]

Target

Original	18.0
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 18.0

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

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	17.4
Cost	1051

\[\begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+33} \lor \neg \left(z \leq -3.1 \cdot 10^{-59}\right) \land \left(z \leq -2.3 \cdot 10^{-124} \lor \neg \left(z \leq 3300\right) \land \left(z \leq 8 \cdot 10^{+36} \lor \neg \left(z \leq 1.3 \cdot 10^{+78}\right)\right)\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2
Error	0.0
Cost	448

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

Alternative 3
Error	0.0
Cost	320

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

Alternative 4
Error	30.9
Cost	192

\[y \cdot x \]

Reproduce

herbie shell --seed 2023039 
(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)))