SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Average Accuracy: 100.0% → 100.0%

Time: 5.7s

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 100.0%

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

2. Applied egg-rr 100.0%

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

   [Start] 100.0	\[ x + y \cdot \left(z - x\right) \]
   sub-neg [=>] 100.0	\[ x + y \cdot \color{blue}{\left(z + \left(-x\right)\right)} \]
   distribute-rgt-in [=>] 100.0	\[ x + \color{blue}{\left(z \cdot y + \left(-x\right) \cdot y\right)} \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	63.2%
Cost	916

\[\begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+63}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq -108000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-39}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+129}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Accuracy	80.9%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-63} \lor \neg \left(y \leq 3.1 \cdot 10^{-10}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Accuracy	98.7%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -5.4 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]

Alternative 4
Accuracy	100.0%
Cost	576

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

Alternative 5
Accuracy	55.5%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-45}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 6
Accuracy	100.0%
Cost	448

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

Alternative 7
Accuracy	46.1%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023151 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))