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

Average Error: 0.3 → 0.1

Time: 1.8min

Precision: binary64

Cost: 6848

Math

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

↓

\[\mathsf{fma}\left(x, 6, \left(-9 \cdot x\right) \cdot x\right) \]

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

function code(x)
	return fma(x, 6.0, Float64(Float64(-9.0 * x) * 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 * 6.0 + N[(N[(-9.0 * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Target

Original	0.3
Target	0.2
Herbie	0.1

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

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. Applied egg-rr 0.1

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

Alternatives

Alternative 1
Error	2.0
Cost	584

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

Alternative 2
Error	2.0
Cost	584

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

Alternative 3
Error	0.2
Cost	448

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

Alternative 4
Error	21.1
Cost	192

\[6 \cdot x \]

Reproduce

herbie shell --seed 2023033 
(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))