SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Average Error: 0.02% → 0.02%

Time: 4.1s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

Python

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.02

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

2. Applied egg-rr 0.02

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

3. Applied egg-rr 0.02

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

4. Final simplification 0.02

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

Alternatives

Alternative 1
Error	36.28%
Cost	1313

\[\begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+226}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+144}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+85}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-24}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+54} \lor \neg \left(y \leq 4.9 \cdot 10^{+150}\right) \land y \leq 2.15 \cdot 10^{+215}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	18.98%
Cost	1049

\[\begin{array}{l} t_0 := x \cdot \left(-y\right)\\ t_1 := x + z \cdot y\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+233}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+97}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+151} \lor \neg \left(y \leq 2 \cdot 10^{+221}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 3
Error	10.82%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-94} \lor \neg \left(z \leq 1.35 \cdot 10^{-127}\right):\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \]

Alternative 4
Error	36.31%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-24}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 5
Error	0.02%
Cost	448

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

Alternative 6
Error	54.41%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023089 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))