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

Average Accuracy: 99.8% → 99.8%

Time: 7.1s

Precision: binary64

Cost: 704

Math

\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]

↓

\[3 + 3 \cdot \left(x \cdot \left(3 \cdot x + -4\right)\right) \]

FPCore

(FPCore (x) :precision binary64 (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))

↓

(FPCore (x) :precision binary64 (+ 3.0 (* 3.0 (* x (+ (* 3.0 x) -4.0)))))

C

double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

↓

double code(double x) {
	return 3.0 + (3.0 * (x * ((3.0 * x) + -4.0)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 * ((((x * 3.0d0) * x) - (x * 4.0d0)) + 1.0d0)
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 + (3.0d0 * (x * ((3.0d0 * x) + (-4.0d0))))
end function

Java

public static double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

↓

public static double code(double x) {
	return 3.0 + (3.0 * (x * ((3.0 * x) + -4.0)));
}

Python

def code(x):
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0)

↓

def code(x):
	return 3.0 + (3.0 * (x * ((3.0 * x) + -4.0)))

Julia

function code(x)
	return Float64(3.0 * Float64(Float64(Float64(Float64(x * 3.0) * x) - Float64(x * 4.0)) + 1.0))
end

↓

function code(x)
	return Float64(3.0 + Float64(3.0 * Float64(x * Float64(Float64(3.0 * x) + -4.0))))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
end

↓

function tmp = code(x)
	tmp = 3.0 + (3.0 * (x * ((3.0 * x) + -4.0)));
end

Wolfram

code[x_] := N[(3.0 * N[(N[(N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision] - N[(x * 4.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]

↓

code[x_] := N[(3.0 + N[(3.0 * N[(x * N[(N[(3.0 * x), $MachinePrecision] + -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	99.8%
Target	99.9%
Herbie	99.8%

\[3 + \left(\left(9 \cdot x\right) \cdot x - 12 \cdot x\right) \]

Derivation

1. Initial program 99.8%

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]

2. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{3 \cdot \left(x \cdot \left(x \cdot 3 - 4\right)\right) + 3} \]
   Proof

   [Start] 99.8	\[ 3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   distribute-lft-in [=>] 99.8	\[ \color{blue}{3 \cdot \left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 3 \cdot 1} \]
   *-commutative [=>] 99.8	\[ 3 \cdot \left(\color{blue}{x \cdot \left(x \cdot 3\right)} - x \cdot 4\right) + 3 \cdot 1 \]
   distribute-lft-out-- [=>] 99.8	\[ 3 \cdot \color{blue}{\left(x \cdot \left(x \cdot 3 - 4\right)\right)} + 3 \cdot 1 \]
   metadata-eval [=>] 99.8	\[ 3 \cdot \left(x \cdot \left(x \cdot 3 - 4\right)\right) + \color{blue}{3} \]

3. Final simplification 99.8%

   \[\leadsto 3 + 3 \cdot \left(x \cdot \left(3 \cdot x + -4\right)\right) \]

Alternatives

Alternative 1
Accuracy	98.5%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -0.58 \lor \neg \left(x \leq 0.58\right):\\ \;\;\;\;x \cdot \left(x \cdot 9 + -12\right)\\ \mathbf{else}:\\ \;\;\;\;3 + x \cdot -12\\ \end{array} \]

Alternative 2
Accuracy	96.9%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -0.58 \lor \neg \left(x \leq 1.7\right):\\ \;\;\;\;9 \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;3\\ \end{array} \]

Alternative 3
Accuracy	97.7%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -1.55 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;9 \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;3 + x \cdot -12\\ \end{array} \]

Alternative 4
Accuracy	99.9%
Cost	576

\[3 + x \cdot \left(x \cdot 9 + -12\right) \]

Alternative 5
Accuracy	67.2%
Cost	64

\[3 \]

Reproduce

herbie shell --seed 2023135 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (+ 3.0 (- (* (* 9.0 x) x) (* 12.0 x)))

  (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))