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

Average Error: 0.0 → 0.0

Time: 5.8s

Precision: binary64

Cost: 512

Math

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

↓

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

FPCore

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

↓

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

Python

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

↓

def code(x, y, z):
	return z + (y * (x + -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(z + Float64(y * Float64(x + Float64(-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 + -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[(z + N[(y * N[(x + (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 0.0

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

2. Taylor expanded in y around 0 0.0

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

3. Simplified 0.0

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

   [Start] 0.0	\[ z + y \cdot \left(-1 \cdot z + x\right) \]
   rational_best-simplify-1 [=>] 0.0	\[ z + y \cdot \color{blue}{\left(x + -1 \cdot z\right)} \]
   rational_best-simplify-2 [=>] 0.0	\[ z + y \cdot \left(x + \color{blue}{z \cdot -1}\right) \]
   rational_best-simplify-12 [=>] 0.0	\[ z + y \cdot \left(x + \color{blue}{\left(-z\right)}\right) \]

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	24.1
Cost	984

\[\begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+140}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{+78}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-17}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-109}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-130}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-19}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2
Error	12.7
Cost	848

\[\begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{-15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-105}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-130}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.85 \cdot 10^{-16}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	13.2
Cost	584

\[\begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{-66}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	1.0
Cost	584

\[\begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	24.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-66}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-114}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 6
Error	35.1
Cost	64

\[z \]

Reproduce

herbie shell --seed 2023092 
(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))))