Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, B

Average Error: 0.1 → 0.3

Time: 6.7s

Precision: binary64

Cost: 960

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

Math

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

↓

\[\frac{\frac{\left(z - y \cdot \left(x \cdot 12\right)\right) + z \cdot 3}{2}}{-2} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (/ (/ (+ (- z (* y (* x 12.0))) (* z 3.0)) 2.0) -2.0))

C

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

↓

double code(double x, double y, double z) {
	return (((z - (y * (x * 12.0))) + (z * 3.0)) / 2.0) / -2.0;
}

Fortran

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

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (((z - (y * (x * 12.0d0))) + (z * 3.0d0)) / 2.0d0) / (-2.0d0)
end function

Java

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

↓

public static double code(double x, double y, double z) {
	return (((z - (y * (x * 12.0))) + (z * 3.0)) / 2.0) / -2.0;
}

Python

def code(x, y, z):
	return ((x * 3.0) * y) - z

↓

def code(x, y, z):
	return (((z - (y * (x * 12.0))) + (z * 3.0)) / 2.0) / -2.0

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * 3.0) * y) - z)
end

↓

function code(x, y, z)
	return Float64(Float64(Float64(Float64(z - Float64(y * Float64(x * 12.0))) + Float64(z * 3.0)) / 2.0) / -2.0)
end

MATLAB

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

↓

function tmp = code(x, y, z)
	tmp = (((z - (y * (x * 12.0))) + (z * 3.0)) / 2.0) / -2.0;
end

Wolfram

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

↓

code[x_, y_, z_] := N[(N[(N[(N[(z - N[(y * N[(x * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision] / -2.0), $MachinePrecision]

Target

Original	0.1
Target	0.1
Herbie	0.3

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

Derivation

1. Initial program 0.1

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

2. Applied egg-rr 0.2

   \[\leadsto \color{blue}{\frac{z + \left(z - x \cdot \left(y \cdot 6\right)\right)}{-2}} \]

3. Simplified 0.2

   \[\leadsto \color{blue}{\frac{z + \left(z - y \cdot \left(x \cdot 6\right)\right)}{-2}} \]
   Proof

   [Start] 0.2	\[ \frac{z + \left(z - x \cdot \left(y \cdot 6\right)\right)}{-2} \]
   rational.json-simplify-43 [=>] 0.2	\[ \frac{z + \left(z - \color{blue}{y \cdot \left(6 \cdot x\right)}\right)}{-2} \]
   rational.json-simplify-2 [=>] 0.2	\[ \frac{z + \left(z - y \cdot \color{blue}{\left(x \cdot 6\right)}\right)}{-2} \]

4. Applied egg-rr 0.2

   \[\leadsto \frac{z + \color{blue}{\frac{z + \left(z - x \cdot \left(y \cdot 12\right)\right)}{2}}}{-2} \]

5. Simplified 0.2

   \[\leadsto \frac{z + \color{blue}{\frac{z + \left(z - y \cdot \left(x \cdot 12\right)\right)}{2}}}{-2} \]
   Proof

   [Start] 0.2	\[ \frac{z + \frac{z + \left(z - x \cdot \left(y \cdot 12\right)\right)}{2}}{-2} \]
   rational.json-simplify-43 [=>] 0.2	\[ \frac{z + \frac{z + \left(z - \color{blue}{y \cdot \left(12 \cdot x\right)}\right)}{2}}{-2} \]
   rational.json-simplify-2 [=>] 0.2	\[ \frac{z + \frac{z + \left(z - y \cdot \color{blue}{\left(x \cdot 12\right)}\right)}{2}}{-2} \]

6. Applied egg-rr 0.3

   \[\leadsto \frac{\color{blue}{\frac{\left(z - y \cdot \left(x \cdot 12\right)\right) + z \cdot 3}{2}}}{-2} \]

7. Final simplification 0.3

   \[\leadsto \frac{\frac{\left(z - y \cdot \left(x \cdot 12\right)\right) + z \cdot 3}{2}}{-2} \]

Alternatives

Alternative 1
Error	0.2
Cost	960

\[\frac{z + \frac{z + \left(z - y \cdot \left(x \cdot 12\right)\right)}{2}}{-2} \]

Alternative 2
Error	16.8
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-65}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 0.0195:\\ \;\;\;\;3 \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 3
Error	16.8
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-65}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 0.00192:\\ \;\;\;\;y \cdot \left(x \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4
Error	0.1
Cost	448

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

Alternative 5
Error	0.1
Cost	448

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

Alternative 6
Error	26.4
Cost	128

\[-z \]

Reproduce

herbie shell --seed 2023074 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (* x (* 3.0 y)) z)

  (- (* (* x 3.0) y) z))