Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3

Average Accuracy: 78.7% → 78.7%

Time: 5.6s

Precision: binary64

Cost: 576

Math

\[x \cdot y + z \cdot \left(1 - y\right) \]

↓

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

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* z (- 1.0 y))))

↓

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

C

double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - y));
}

↓

double code(double x, double y, double z) {
	return (z + (y * x)) - (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 * y) + (z * (1.0d0 - y))
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)) - (y * z)
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - y));
}

↓

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

Python

def code(x, y, z):
	return (x * y) + (z * (1.0 - y))

↓

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

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(z * Float64(1.0 - y)))
end

↓

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

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + (z * (1.0 - y));
end

↓

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

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

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

Target

Original	78.7%
Target	78.7%
Herbie	78.7%

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

Derivation

1. Initial program 81.6%

   \[x \cdot y + z \cdot \left(1 - y\right) \]

2. Simplified 81.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, x - z, z\right)} \]
   Step-by-step derivation

   [Start] 81.6	\[ x \cdot y + z \cdot \left(1 - y\right) \]
   +-commutative [=>] 81.6	\[ \color{blue}{z \cdot \left(1 - y\right) + x \cdot y} \]
   sub-neg [=>] 81.6	\[ z \cdot \color{blue}{\left(1 + \left(-y\right)\right)} + x \cdot y \]
   distribute-rgt-in [=>] 81.6	\[ \color{blue}{\left(1 \cdot z + \left(-y\right) \cdot z\right)} + x \cdot y \]
   *-lft-identity [=>] 81.6	\[ \left(\color{blue}{z} + \left(-y\right) \cdot z\right) + x \cdot y \]
   associate-+l+ [=>] 81.6	\[ \color{blue}{z + \left(\left(-y\right) \cdot z + x \cdot y\right)} \]
   +-commutative [=>] 81.6	\[ \color{blue}{\left(\left(-y\right) \cdot z + x \cdot y\right) + z} \]
   *-commutative [=>] 81.6	\[ \left(\color{blue}{z \cdot \left(-y\right)} + x \cdot y\right) + z \]
   neg-mul-1 [=>] 81.6	\[ \left(z \cdot \color{blue}{\left(-1 \cdot y\right)} + x \cdot y\right) + z \]
   associate-*r* [=>] 81.6	\[ \left(\color{blue}{\left(z \cdot -1\right) \cdot y} + x \cdot y\right) + z \]
   distribute-rgt-out [=>] 81.6	\[ \color{blue}{y \cdot \left(z \cdot -1 + x\right)} + z \]
   fma-def [=>] 81.6	\[ \color{blue}{\mathsf{fma}\left(y, z \cdot -1 + x, z\right)} \]
   +-commutative [=>] 81.6	\[ \mathsf{fma}\left(y, \color{blue}{x + z \cdot -1}, z\right) \]
   *-commutative [=>] 81.6	\[ \mathsf{fma}\left(y, x + \color{blue}{-1 \cdot z}, z\right) \]
   neg-mul-1 [<=] 81.6	\[ \mathsf{fma}\left(y, x + \color{blue}{\left(-z\right)}, z\right) \]
   unsub-neg [=>] 81.6	\[ \mathsf{fma}\left(y, \color{blue}{x - z}, z\right) \]

3. Taylor expanded in x around inf 81.6%

   \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right) + \left(y \cdot x + z\right)} \]

4. Final simplification 81.6%

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

Alternatives

Alternative 1
Accuracy	62.5%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-10} \lor \neg \left(y \leq 1.95 \cdot 10^{-75}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 2
Accuracy	77.6%
Cost	585

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

Alternative 3
Accuracy	78.7%
Cost	576

\[y \cdot x + z \cdot \left(1 - y\right) \]

Alternative 4
Accuracy	48.7%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-11}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-74}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 5
Accuracy	48.6%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-77}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 6
Accuracy	78.7%
Cost	448

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

Alternative 7
Accuracy	36.3%
Cost	64

\[z \]

Reproduce

herbie shell --seed 2023157 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

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

  (+ (* x y) (* z (- 1.0 y))))