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

Average Error: 0.1 → 0.1

Time: 8.6s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = ((x * 3.0d0) * y) - z
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 ((x * 3.0) * y) - z;
}

Python

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

↓

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

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.1
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Alternatives

Alternative 1
Error	17.2
Cost	1112

\[\begin{array}{l} t_0 := 3 \cdot \left(y \cdot x\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+72}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-19}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-54}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-55}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+20}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+41}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 2
Error	17.3
Cost	1112

\[\begin{array}{l} t_0 := 3 \cdot \left(y \cdot x\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+72}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-55}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+19}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+41}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 3
Error	17.3
Cost	1112

\[\begin{array}{l} t_0 := y \cdot \left(x \cdot 3\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+72}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -105000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.55 \cdot 10^{-53}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+20}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+40}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4
Error	0.1
Cost	448

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

Alternative 5
Error	0.1
Cost	448

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

Alternative 6
Error	27.0
Cost	128

\[-z \]

Reproduce

herbie shell --seed 2023075 
(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))