Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2

Average Error: 0.2 → 0.2

Time: 9.6s

Precision: binary64

Cost: 832

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.2
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.2

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

2. Simplified 0.2

   \[\leadsto \color{blue}{x \cdot \left(x \cdot \left(3 - \left(x + x\right)\right)\right)} \]
   Proof

   [Start] 0.2	\[ \left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.2	\[ \color{blue}{\left(3 - x \cdot 2\right) \cdot \left(x \cdot x\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-89 [=>] 0.2	\[ \left(3 - x \cdot 2\right) \cdot \color{blue}{\left(x \cdot \left(x \cdot \frac{x}{x}\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-89 [=>] 0.2	\[ \left(3 - x \cdot 2\right) \cdot \color{blue}{\left(x \cdot \left(\left(x \cdot \frac{x}{x}\right) \cdot \frac{x}{x}\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-7 [=>] 0.2	\[ \color{blue}{x \cdot \left(\left(3 - x \cdot 2\right) \cdot \left(\left(x \cdot \frac{x}{x}\right) \cdot \frac{x}{x}\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.2	\[ x \cdot \left(\left(3 - x \cdot 2\right) \cdot \color{blue}{\left(\frac{x}{x} \cdot \left(x \cdot \frac{x}{x}\right)\right)}\right) \]
   rational_best_oopsla_all_46_json_45_simplify-7 [<=] 0.2	\[ x \cdot \left(\left(3 - x \cdot 2\right) \cdot \color{blue}{\left(x \cdot \left(\frac{x}{x} \cdot \frac{x}{x}\right)\right)}\right) \]
   rational_best_oopsla_all_46_json_45_simplify-89 [<=] 0.2	\[ x \cdot \left(\left(3 - x \cdot 2\right) \cdot \color{blue}{\left(x \cdot \frac{x}{x}\right)}\right) \]
   rational_best_oopsla_all_46_json_45_simplify-7 [=>] 0.2	\[ x \cdot \color{blue}{\left(x \cdot \left(\left(3 - x \cdot 2\right) \cdot \frac{x}{x}\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-6 [=>] 0.2	\[ x \cdot \color{blue}{\left(x \cdot \left(3 - x \cdot 2\right)\right)} \]
   metadata-eval [<=] 0.2	\[ x \cdot \left(x \cdot \left(3 - x \cdot \color{blue}{\left(1 + 1\right)}\right)\right) \]
   metadata-eval [<=] 0.2	\[ x \cdot \left(x \cdot \left(3 - x \cdot \left(\color{blue}{\frac{2}{2}} + 1\right)\right)\right) \]
   metadata-eval [<=] 0.2	\[ x \cdot \left(x \cdot \left(3 - x \cdot \left(\frac{2}{2} + \color{blue}{\frac{2}{2}}\right)\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-23 [<=] 0.2	\[ x \cdot \left(x \cdot \left(3 - \color{blue}{\left(\frac{2}{2} \cdot x + x \cdot \frac{2}{2}\right)}\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-74 [<=] 0.2	\[ x \cdot \left(x \cdot \left(3 - \left(\color{blue}{x \cdot \frac{2}{2}} + x \cdot \frac{2}{2}\right)\right)\right) \]
   metadata-eval [=>] 0.2	\[ x \cdot \left(x \cdot \left(3 - \left(x \cdot \color{blue}{1} + x \cdot \frac{2}{2}\right)\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-52 [=>] 0.2	\[ x \cdot \left(x \cdot \left(3 - \left(\color{blue}{x} + x \cdot \frac{2}{2}\right)\right)\right) \]
   metadata-eval [=>] 0.2	\[ x \cdot \left(x \cdot \left(3 - \left(x + x \cdot \color{blue}{1}\right)\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-52 [=>] 0.2	\[ x \cdot \left(x \cdot \left(3 - \left(x + \color{blue}{x}\right)\right)\right) \]

3. Applied egg-rr 0.2

   \[\leadsto \color{blue}{\left(x \cdot \left(-x\right)\right) \cdot x + x \cdot \left(x \cdot \left(3 - x\right)\right)} \]

4. Applied egg-rr 0.2

   \[\leadsto \color{blue}{x \cdot \left(x \cdot \left(3 - x\right)\right) - x \cdot \left(x \cdot x\right)} \]

5. Final simplification 0.2

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

Alternatives

Alternative 1
Error	0.2
Cost	832

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

Alternative 2
Error	2.3
Cost	712

\[\begin{array}{l} t_0 := \left(x \cdot -2\right) \cdot \left(x \cdot x\right)\\ \mathbf{if}\;x \leq -1.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.5:\\ \;\;\;\;x \cdot \left(3 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	0.2
Cost	576

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

Alternative 4
Error	16.2
Cost	320

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

Alternative 5
Error	16.2
Cost	320

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

Reproduce

herbie shell --seed 2023090 
(FPCore (x)
  :name "Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2"
  :precision binary64

  :herbie-target
  (* x (* x (- 3.0 (* x 2.0))))

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