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

Percentage Accurate: 98.1% → 100.0%

Time: 4.4s

Precision: binary64

Cost: 448

• 20.3% of points produce a very large (infinite) output. You may want to add a precondition.

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 99.6%

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

2. Simplified 100.0%

   \[\leadsto \color{blue}{x \cdot \left(y + z\right) - z} \]
   Step-by-step derivation

   [Start] 99.6%	\[ x \cdot y + \left(x - 1\right) \cdot z \]
   *-commutative [=>] 99.6%	\[ x \cdot y + \color{blue}{z \cdot \left(x - 1\right)} \]
   sub-neg [=>] 99.6%	\[ x \cdot y + z \cdot \color{blue}{\left(x + \left(-1\right)\right)} \]
   distribute-rgt-in [=>] 99.6%	\[ x \cdot y + \color{blue}{\left(x \cdot z + \left(-1\right) \cdot z\right)} \]
   associate-+r+ [=>] 99.6%	\[ \color{blue}{\left(x \cdot y + x \cdot z\right) + \left(-1\right) \cdot z} \]
   metadata-eval [=>] 99.6%	\[ \left(x \cdot y + x \cdot z\right) + \color{blue}{-1} \cdot z \]
   mul-1-neg [=>] 99.6%	\[ \left(x \cdot y + x \cdot z\right) + \color{blue}{\left(-z\right)} \]
   unsub-neg [=>] 99.6%	\[ \color{blue}{\left(x \cdot y + x \cdot z\right) - z} \]
   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	100.0%
Cost	448

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

Alternative 2
Accuracy	61.3%
Cost	853

\[\begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-12}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-20}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+80} \lor \neg \left(x \leq 3 \cdot 10^{+143}\right) \land x \leq 1.9 \cdot 10^{+186}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3
Accuracy	84.4%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-13} \lor \neg \left(x \leq 7 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4
Accuracy	80.1%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+25} \lor \neg \left(z \leq 3.5 \cdot 10^{+59}\right):\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]

Alternative 5
Accuracy	80.1%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+26}:\\ \;\;\;\;x \cdot z - z\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 6
Accuracy	61.0%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -2.06 \cdot 10^{-13}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 8.1 \cdot 10^{-22}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7
Accuracy	36.5%
Cost	128

\[-z \]

Reproduce

herbie shell --seed 2023272 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))