Average Error: 0.3 → 0.2

Time: 7.4s

Precision: binary64

Cost: 448

\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x \]

↓

\[x \cdot \left(6 + x \cdot -9\right) \]

(FPCore (x) :precision binary64 (* (* 3.0 (- 2.0 (* x 3.0))) x))

↓

(FPCore (x) :precision binary64 (* x (+ 6.0 (* x -9.0))))

double code(double x) {
	return (3.0 * (2.0 - (x * 3.0))) * x;
}

↓

double code(double x) {
	return x * (6.0 + (x * -9.0));
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = (3.0d0 * (2.0d0 - (x * 3.0d0))) * x
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = x * (6.0d0 + (x * (-9.0d0)))
end function

public static double code(double x) {
	return (3.0 * (2.0 - (x * 3.0))) * x;
}

↓

public static double code(double x) {
	return x * (6.0 + (x * -9.0));
}

def code(x):
	return (3.0 * (2.0 - (x * 3.0))) * x

↓

def code(x):
	return x * (6.0 + (x * -9.0))

function code(x)
	return Float64(Float64(3.0 * Float64(2.0 - Float64(x * 3.0))) * x)
end

↓

function code(x)
	return Float64(x * Float64(6.0 + Float64(x * -9.0)))
end

function tmp = code(x)
	tmp = (3.0 * (2.0 - (x * 3.0))) * x;
end

↓

function tmp = code(x)
	tmp = x * (6.0 + (x * -9.0));
end

code[x_] := N[(N[(3.0 * N[(2.0 - N[(x * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]

↓

code[x_] := N[(x * N[(6.0 + N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x

↓

x \cdot \left(6 + x \cdot -9\right)

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	0.3
Target	0.2
Herbie	0.2

\[6 \cdot x - 9 \cdot \left(x \cdot x\right) \]

Derivation

Initial program 0.3
\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x \]
Simplified0.2
\[\leadsto \color{blue}{x \cdot \left(6 + x \cdot -9\right)} \]
Proof
(*.f64 x (+.f64 6 (*.f64 x -9))): 0 points increase in error, 0 points decrease in error
(*.f64 x (+.f64 (Rewrite<= metadata-eval (*.f64 2 3)) (*.f64 x -9))): 0 points increase in error, 0 points decrease in error
(*.f64 x (+.f64 (*.f64 2 3) (*.f64 x (Rewrite<= metadata-eval (*.f64 -3 3))))): 0 points increase in error, 0 points decrease in error
(*.f64 x (+.f64 (*.f64 2 3) (*.f64 x (*.f64 (Rewrite<= metadata-eval (neg.f64 3)) 3)))): 0 points increase in error, 0 points decrease in error
(*.f64 x (+.f64 (*.f64 2 3) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x (neg.f64 3)) 3)))): 14 points increase in error, 3 points decrease in error
(*.f64 x (+.f64 (*.f64 2 3) (*.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 x 3))) 3))): 0 points increase in error, 0 points decrease in error
(*.f64 x (+.f64 (*.f64 2 3) (*.f64 (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 x) 3)) 3))): 0 points increase in error, 0 points decrease in error
(*.f64 x (Rewrite<= distribute-rgt-in_binary64 (*.f64 3 (+.f64 2 (*.f64 (neg.f64 x) 3))))): 1 points increase in error, 0 points decrease in error
(*.f64 x (*.f64 3 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 2 (*.f64 x 3))))): 0 points increase in error, 0 points decrease in error
(Rewrite<= *-commutative_binary64 (*.f64 (*.f64 3 (-.f64 2 (*.f64 x 3))) x)): 0 points increase in error, 0 points decrease in error
Final simplification0.2
\[\leadsto x \cdot \left(6 + x \cdot -9\right) \]

Alternatives

Alternative 1
Error	1.9
Cost	584

\[\begin{array}{l} t_0 := -9 \cdot \left(x \cdot x\right)\\ \mathbf{if}\;x \leq -0.66:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.68:\\ \;\;\;\;x \cdot 6\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	1.9
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -0.66:\\ \;\;\;\;x \cdot \left(x \cdot -9\right)\\ \mathbf{elif}\;x \leq 0.68:\\ \;\;\;\;x \cdot 6\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(x \cdot x\right)\\ \end{array} \]

Alternative 3
Error	21.2
Cost	192

\[x \cdot 6 \]

Reproduce

herbie shell --seed 2022325 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E"
  :precision binary64

  :herbie-target
  (- (* 6.0 x) (* 9.0 (* x x)))

  (* (* 3.0 (- 2.0 (* x 3.0))) x))