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

Average Error: 0.0 → 0.0

Time: 4.3s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

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 ((1.0 - x) * 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 = ((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 = ((1.0d0 - x) * y) + (x * z)
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 ((1.0 - x) * y) + (x * z);
}

Python

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

↓

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

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(Float64(1.0 - x) * y) + Float64(x * z))
end

MATLAB

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

↓

function tmp = code(x, y, z)
	tmp = ((1.0 - x) * y) + (x * z);
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[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] + N[(x * z), $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

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

Alternatives

Alternative 1
Error	20.1
Cost	1640

\[\begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ t_1 := \left(1 - x\right) \cdot y\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+110}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.3913275494901846 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1047950.1430179984:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.930199504377719 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.561049246352538 \cdot 10^{-141}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.8189436965995737 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5446062651144353 \cdot 10^{-98}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 530670849.2173305:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4383819344127384 \cdot 10^{+91}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+139}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	30.6
Cost	1512

\[\begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+104}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.3913275494901846 \cdot 10^{+81}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -1047950.1430179984:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -6.930199504377719 \cdot 10^{-42}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -2.3003523306639402 \cdot 10^{-84}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 4.8189436965995737 \cdot 10^{-166}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.5446062651144353 \cdot 10^{-98}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 530670849.2173305:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.4383819344127384 \cdot 10^{+91}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+139}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3
Error	20.0
Cost	1376

\[\begin{array}{l} t_0 := \left(1 - x\right) \cdot y\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+110}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.3913275494901846 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1047950.1430179984:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -6.930199504377719 \cdot 10^{-42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.3003523306639402 \cdot 10^{-84}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 530670849.2173305:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.3340297276112976 \cdot 10^{+31}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+139}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 4
Error	0.0
Cost	448

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

Alternative 5
Error	35.0
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022312 
(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)))