SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Average Error: 0.0 → 0.0

Time: 6.0s

Precision: binary64

Cost: 576

Math

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

↓

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

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 - 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. Final simplification 0.0

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

Alternatives

Alternative 1
Error	24.4
Cost	916

\[\begin{array}{l} t_0 := -y \cdot x\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{+127}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+27}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+31}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	12.5
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-17} \lor \neg \left(y \leq 3.9 \cdot 10^{-36}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	0.8
Cost	585

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

Alternative 4
Error	0.0
Cost	576

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

Alternative 5
Error	23.6
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-18}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 6
Error	0.0
Cost	448

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

Alternative 7
Error	35.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023060 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))