Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3

Average Error: 0.0 → 0.0

Time: 4.6s

Precision: binary64

Cost: 6848

Math

\[x \cdot y + \left(x - 1\right) \cdot z \]

↓

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

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* (- x 1.0) z)))

↓

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

C

double code(double x, double y, double z) {
	return (x * y) + ((x - 1.0) * z);
}

↓

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

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(Float64(x - 1.0) * z))
end

↓

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

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(x - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

↓

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

Derivation

1. Initial program 0.0

   \[x \cdot y + \left(x - 1\right) \cdot z \]

2. Simplified 0.0

   \[\leadsto \color{blue}{x \cdot \left(y + z\right) - z} \]
   Proof
   (-.f64 (*.f64 x (+.f64 y z)) z): 0 points increase in error, 0 points decrease in error
   (-.f64 (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 x y) (*.f64 x z))) z): 2 points increase in error, 3 points decrease in error
   (Rewrite<= unsub-neg_binary64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (neg.f64 z))): 0 points increase in error, 0 points decrease in error
   (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 z))): 0 points increase in error, 0 points decrease in error
   (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 (Rewrite<= metadata-eval (neg.f64 1)) z)): 0 points increase in error, 0 points decrease in error
   (Rewrite<= associate-+r+_binary64 (+.f64 (*.f64 x y) (+.f64 (*.f64 x z) (*.f64 (neg.f64 1) z)))): 0 points increase in error, 1 points decrease in error
   (+.f64 (*.f64 x y) (Rewrite<= distribute-rgt-in_binary64 (*.f64 z (+.f64 x (neg.f64 1))))): 4 points increase in error, 2 points decrease in error
   (+.f64 (*.f64 x y) (*.f64 z (Rewrite<= sub-neg_binary64 (-.f64 x 1)))): 0 points increase in error, 0 points decrease in error
   (+.f64 (*.f64 x y) (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 x 1) z))): 0 points increase in error, 0 points decrease in error

3. Applied egg-rr 0.0

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	24.1
Cost	984

\[\begin{array}{l} \mathbf{if}\;x \leq -3.35 \cdot 10^{+189}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+134}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -5.867747587884991 \cdot 10^{-19}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -9.717088850848691 \cdot 10^{-141}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -1.8598063871050298 \cdot 10^{-174}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 7.437725542128105 \cdot 10^{-10}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2
Error	13.2
Cost	848

\[\begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -9.713037785339045 \cdot 10^{-43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -9.717088850848691 \cdot 10^{-141}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -1.8598063871050298 \cdot 10^{-174}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 7.437725542128105 \cdot 10^{-10}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	24.2
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -5.867747587884991 \cdot 10^{-19}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -9.717088850848691 \cdot 10^{-141}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -1.8598063871050298 \cdot 10^{-174}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 7.437725542128105 \cdot 10^{-10}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4
Error	1.0
Cost	584

\[\begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -76.55260091418698:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7.437725542128105 \cdot 10^{-10}:\\ \;\;\;\;y \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	1.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -76.55260091418698:\\ \;\;\;\;x \cdot z + y \cdot x\\ \mathbf{elif}\;x \leq 7.437725542128105 \cdot 10^{-10}:\\ \;\;\;\;y \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]

Alternative 6
Error	0.0
Cost	576

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

Alternative 7
Error	0.0
Cost	448

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

Alternative 8
Error	34.7
Cost	128

\[-z \]

Reproduce

herbie shell --seed 2022300 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))