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

Percentage Accurate: 98.0% → 100.0%

Time: 1.9s

Alternatives: 4

Speedup: 1.4×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    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);
}

Python

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

MATLAB

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]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(((1) - x) * y) + (x * z)
END code

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    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);
}

Python

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

MATLAB

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]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(((1) - x) * y) + (x * z)
END code

Alternative 1: 100.0% accurate, 1.4× speedup

Math

\[\mathsf{fma}\left(x, z - y, y\right) \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (fma x (- z y) y))

C

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

Julia

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * (z - y)) + y
END code

Derivation

1. Initial program 98.0%

   \[\left(1 - x\right) \cdot y + x \cdot z \]
2. Step-by-step derivation

3. Applied rewrites 100.0%

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

5. Applied rewrites 100.0%

   \[\leadsto \mathsf{fma}\left(x, z - y, y\right) \]
6. Add Preprocessing

Alternative 2: 98.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -771.6157302664199:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 857.8504450292068:\\ \;\;\;\;\mathsf{fma}\left(x, z, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* x (- z y))))
  (if (<= x -771.6157302664199)
    t_0
    (if (<= x 857.8504450292068) (fma x z y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (x <= -771.6157302664199) {
		tmp = t_0;
	} else if (x <= 857.8504450292068) {
		tmp = fma(x, z, y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z - y))
	tmp = 0.0
	if (x <= -771.6157302664199)
		tmp = t_0;
	elseif (x <= 857.8504450292068)
		tmp = fma(x, z, y);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -771.6157302664199], t$95$0, If[LessEqual[x, 857.8504450292068], N[(x * z + y), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (x * (z - y)) IN
		LET tmp_1 = IF (x <= (8578504450292067531336215324699878692626953125e-43)) THEN ((x * z) + y) ELSE t_0 ENDIF IN
		LET tmp = IF (x <= (-771615730266419859617599286139011383056640625e-42)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -771.61573026641986 or 857.85044502920675 < x

   1. Initial program 98.0%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Step-by-step derivation

   3. Applied rewrites 100.0%

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

   5. Applied rewrites 100.0%

      \[\leadsto \mathsf{fma}\left(x, z - y, y\right) \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(z - y\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 65.2%

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

   if -771.61573026641986 < x < 857.85044502920675

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0

      \[\leadsto y + x \cdot z \]
   3. Step-by-step derivation

   4. Applied rewrites 76.2%

      \[\leadsto y + x \cdot z \]
   5. Step-by-step derivation

   6. Applied rewrites 76.2%

      \[\leadsto \mathsf{fma}\left(x, z, y\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 76.2% accurate, 2.0× speedup

Math

\[\mathsf{fma}\left(x, z, y\right) \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (fma x z y))

C

double code(double x, double y, double z) {
	return fma(x, z, y);
}

Julia

function code(x, y, z)
	return fma(x, z, y)
end

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * z) + y
END code

Derivation

1. Initial program 98.0%

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

2. Taylor expanded in x around 0

   \[\leadsto y + x \cdot z \]
3. Step-by-step derivation

4. Applied rewrites 76.2%

   \[\leadsto y + x \cdot z \]
5. Step-by-step derivation

6. Applied rewrites 76.2%

   \[\leadsto \mathsf{fma}\left(x, z, y\right) \]
7. Add Preprocessing

Alternative 4: 42.2% accurate, 3.0× speedup

Math

\[x \cdot z \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (* x z))

C

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

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	x * z
END code

Derivation

1. Initial program 98.0%

   \[\left(1 - x\right) \cdot y + x \cdot z \]
2. Step-by-step derivation

3. Applied rewrites 100.0%

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

5. Applied rewrites 100.0%

   \[\leadsto \mathsf{fma}\left(x, z - y, y\right) \]

6. Taylor expanded in y around 0

   \[\leadsto x \cdot z \]
7. Step-by-step derivation

8. Applied rewrites 42.2%

   \[\leadsto x \cdot z \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64
  (+ (* (- 1.0 x) y) (* x z)))