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

Average Accuracy: 100.0% → 100.0%

Time: 4.0s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (- (* x (+ y 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 (x * (y + z)) - 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) + ((x - 1.0d0) * 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 + z)) - z
end function

Java

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

↓

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

Python

def code(x, y, z):
	return (x * y) + ((x - 1.0) * z)

↓

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

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + ((x - 1.0) * z);
end

↓

function tmp = code(x, y, z)
	tmp = (x * (y + 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[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

2. Simplified 100.0%

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

   [Start] 100.0	\[ x \cdot y + \left(x - 1\right) \cdot z \]
   *-commutative [=>] 100.0	\[ x \cdot y + \color{blue}{z \cdot \left(x - 1\right)} \]
   sub-neg [=>] 100.0	\[ x \cdot y + z \cdot \color{blue}{\left(x + \left(-1\right)\right)} \]
   distribute-rgt-in [=>] 100.0	\[ x \cdot y + \color{blue}{\left(x \cdot z + \left(-1\right) \cdot z\right)} \]
   metadata-eval [=>] 100.0	\[ x \cdot y + \left(x \cdot z + \color{blue}{-1} \cdot z\right) \]
   mul-1-neg [=>] 100.0	\[ x \cdot y + \left(x \cdot z + \color{blue}{\left(-z\right)}\right) \]
   unsub-neg [=>] 100.0	\[ x \cdot y + \color{blue}{\left(x \cdot z - z\right)} \]
   associate-+r- [=>] 100.0	\[ \color{blue}{\left(x \cdot y + x \cdot z\right) - z} \]
   distribute-lft-out [=>] 100.0	\[ \color{blue}{x \cdot \left(y + z\right)} - z \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	62.4%
Cost	588

\[\begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+149}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-91}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-28}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 2
Accuracy	80.2%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-92} \lor \neg \left(x \leq 6 \cdot 10^{-28}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 3
Accuracy	98.2%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -250000 \lor \neg \left(x \leq 4.2 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - z\\ \end{array} \]

Alternative 4
Accuracy	98.2%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -250000:\\ \;\;\;\;x \cdot z + x \cdot y\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-15}:\\ \;\;\;\;x \cdot y - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]

Alternative 5
Accuracy	62.3%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-92}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-29}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6
Accuracy	45.0%
Cost	128

\[-z \]

Reproduce

herbie shell --seed 2023141 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))