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

Average Error: 0.3 → 0.2

Time: 10.1s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 * (6.0d0 + ((-9.0d0) * x))
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 * (6.0 + (-9.0 * x));
}

Python

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

↓

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

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(6.0 + Float64(-9.0 * x)))
end

MATLAB

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

↓

function tmp = code(x)
	tmp = x * (6.0 + (-9.0 * x));
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[(6.0 + N[(-9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	0.3
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.3

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

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

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

Alternatives

Alternative 1
Error	1.7
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -2.323917429247241:\\ \;\;\;\;x \cdot \left(-9 \cdot x\right)\\ \mathbf{elif}\;x \leq 1.3738252580529614 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{0.16666666666666666 + x \cdot 0.25}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-0.1111111111111111}{x}}\\ \end{array} \]

Alternative 2
Error	2.0
Cost	584

\[\begin{array}{l} t_0 := \frac{x}{\frac{-0.1111111111111111}{x}}\\ \mathbf{if}\;x \leq -2.323917429247241:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.3738252580529614 \cdot 10^{-6}:\\ \;\;\;\;x \cdot 6\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	1.9
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -2.323917429247241:\\ \;\;\;\;x \cdot \left(-9 \cdot x\right)\\ \mathbf{elif}\;x \leq 1.3738252580529614 \cdot 10^{-6}:\\ \;\;\;\;x \cdot 6\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-0.1111111111111111}{x}}\\ \end{array} \]

Alternative 4
Error	21.0
Cost	192

\[\frac{x}{0.16666666666666666} \]

Alternative 5
Error	20.9
Cost	192

\[x \cdot 6 \]

Reproduce

herbie shell --seed 2022290 
(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))