SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Average Error: 0.0 → 0.0

Time: 5.8s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 * (z - x))
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)) - (x * y)
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

3. Applied egg-rr 0.0

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	23.8
Cost	652

\[\begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-15}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+50}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 2
Error	12.1
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-16} \lor \neg \left(y \leq 6.9 \cdot 10^{-37}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	0.8
Cost	585

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

Alternative 4
Error	24.0
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-17}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5
Error	0.0
Cost	448

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

Alternative 6
Error	35.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023066 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))