Diagrams.Color.HSV:lerp from diagrams-contrib-1.3.0.5

Average Error: 0.0 → 0.0

Time: 5.0s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	16.1
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-131} \lor \neg \left(y \leq 2.05 \cdot 10^{-60}\right):\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 2
Error	13.3
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-55} \lor \neg \left(y \leq 9.5 \cdot 10^{-49}\right):\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 3
Error	0.9
Cost	585

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

Alternative 4
Error	24.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-93}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 10^{-48}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5
Error	0.0
Cost	448

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

Alternative 6
Error	34.4
Cost	64

\[y \]

Reproduce

herbie shell --seed 2023027 
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

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

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