SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Average Error: 0.0 → 0.0

Time: 6.6s

Precision: binary64

Cost: 640

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = (y * z) + ((1.0d0 + -y) * x)
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 (y * z) + ((1.0 + -y) * x);
}

Python

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

↓

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

Julia

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

↓

function code(x, y, z)
	return Float64(Float64(y * z) + Float64(Float64(1.0 + Float64(-y)) * x))
end

MATLAB

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

↓

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

Wolfram

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

↓

code[x_, y_, z_] := N[(N[(y * z), $MachinePrecision] + N[(N[(1.0 + (-y)), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Taylor expanded in x around 0 0.0

   \[\leadsto \color{blue}{y \cdot z + \left(1 + -1 \cdot y\right) \cdot x} \]

3. Simplified 0.0

   \[\leadsto \color{blue}{y \cdot z + \left(1 + \left(-y\right)\right) \cdot x} \]
   Proof

   [Start] 0.0	\[ y \cdot z + \left(1 + -1 \cdot y\right) \cdot x \]
   rational_best.json-simplify-2 [=>] 0.0	\[ y \cdot z + \left(1 + \color{blue}{y \cdot -1}\right) \cdot x \]
   rational_best.json-simplify-12 [=>] 0.0	\[ y \cdot z + \left(1 + \color{blue}{\left(-y\right)}\right) \cdot x \]

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	24.6
Cost	916

\[\begin{array}{l} t_0 := \left(-y\right) \cdot x\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+72}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-36}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-125}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	13.0
Cost	848

\[\begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{-36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-126}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	12.6
Cost	848

\[\begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-126}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5.1:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	24.2
Cost	720

\[\begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-36}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-125}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5
Error	0.9
Cost	584

\[\begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -220:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y \cdot z + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	0.0
Cost	448

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

Alternative 7
Error	34.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))