Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E

Average Error: 0.2 → 0.2

Time: 11.9s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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 * (((-9.0d0) * x) + 6.0d0)
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.2
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.2

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

2. Taylor expanded in x around 0 0.2

   \[\leadsto \color{blue}{\left(-9 \cdot x + 6\right)} \cdot x \]

3. Final simplification 0.2

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

Alternatives

Alternative 1
Error	2.3
Cost	584

\[\begin{array}{l} t_0 := x \cdot \left(-9 \cdot x\right)\\ \mathbf{if}\;x \leq -26.66547093116212:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.878002767758079 \cdot 10^{-10}:\\ \;\;\;\;x \cdot 6\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	21.4
Cost	192

\[x \cdot 6 \]

Reproduce

herbie shell --seed 2022311 
(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))