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

Percentage Accurate: 98.0% → 100.0%

Time: 3.5s

Alternatives: 5

Speedup: 1.7×

• 21.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(1 - x\right) \cdot y + x \cdot z \end{array} \]

FPCore

(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);
}

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

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]

Initial Program: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - x\right) \cdot y + x \cdot z \end{array} \]

FPCore

(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);
}

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

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]

Alternative 1: 100.0% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

   \[\left(1 - x\right) \cdot y + x \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{y + x \cdot \left(z + -1 \cdot y\right)} \]
4. Step-by-step derivation

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. fp-cancel-sign-sub-inv N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{z - \left(\mathsf{neg}\left(-1\right)\right) \cdot y}, x, y\right) \]

   5. metadata-eval N/A

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

   6. *-lft-identity N/A

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

   7. lower--.f64 100.0

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

5. Applied rewrites 100.0%

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

Alternative 2: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-186} \lor \neg \left(x \leq 1.05 \cdot 10^{-37}\right):\\ \;\;\;\;\left(z - y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, x, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.4e-186) (not (<= x 1.05e-37)))
   (* (- z y) x)
   (fma (- y) x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.4e-186) || !(x <= 1.05e-37)) {
		tmp = (z - y) * x;
	} else {
		tmp = fma(-y, x, y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.4e-186) || !(x <= 1.05e-37))
		tmp = Float64(Float64(z - y) * x);
	else
		tmp = fma(Float64(-y), x, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.4e-186], N[Not[LessEqual[x, 1.05e-37]], $MachinePrecision]], N[(N[(z - y), $MachinePrecision] * x), $MachinePrecision], N[((-y) * x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.40000000000000003e-186 or 1.05e-37 < x

   1. Initial program 97.1%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(z + -1 \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. lower--.f64 91.8

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

   5. Applied rewrites 91.8%

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

   if -2.40000000000000003e-186 < x < 1.05e-37

   1. Initial program 100.0%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y + x \cdot \left(z + -1 \cdot y\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{z - \left(\mathsf{neg}\left(-1\right)\right) \cdot y}, x, y\right) \]

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot y, x, y\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 87.2%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-186} \lor \neg \left(x \leq 1.05 \cdot 10^{-37}\right):\\ \;\;\;\;\left(z - y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, x, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-54} \lor \neg \left(y \leq 2.12 \cdot 10^{-16}\right):\\ \;\;\;\;\left(-y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3e-54) (not (<= y 2.12e-16))) (* (- y) x) (* z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e-54) || !(y <= 2.12e-16)) {
		tmp = -y * x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3d-54)) .or. (.not. (y <= 2.12d-16))) then
        tmp = -y * x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e-54) || !(y <= 2.12e-16)) {
		tmp = -y * x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3e-54) or not (y <= 2.12e-16):
		tmp = -y * x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3e-54) || !(y <= 2.12e-16))
		tmp = Float64(Float64(-y) * x);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3e-54) || ~((y <= 2.12e-16)))
		tmp = -y * x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3e-54], N[Not[LessEqual[y, 2.12e-16]], $MachinePrecision]], N[((-y) * x), $MachinePrecision], N[(z * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.00000000000000009e-54 or 2.1199999999999999e-16 < y

   1. Initial program 96.7%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(z + -1 \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. lower--.f64 57.0

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

   5. Applied rewrites 57.0%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot y\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 48.0%

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

   if -3.00000000000000009e-54 < y < 2.1199999999999999e-16

   1. Initial program 100.0%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(z + -1 \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. lower--.f64 81.8

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

   5. Applied rewrites 81.8%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x \cdot z} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot x} \]

      2. lower-*.f64 73.7

         \[\leadsto \color{blue}{z \cdot x} \]

   8. Applied rewrites 73.7%

      \[\leadsto \color{blue}{z \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-54} \lor \neg \left(y \leq 2.12 \cdot 10^{-16}\right):\\ \;\;\;\;\left(-y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \left(z - y\right) \cdot x \end{array} \]

FPCore

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

C

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

Fortran

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

   \[\left(1 - x\right) \cdot y + x \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(z + -1 \cdot y\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. fp-cancel-sign-sub-inv N/A

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

   4. metadata-eval N/A

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

   5. *-lft-identity N/A

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

   6. lower--.f64 67.2

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

5. Applied rewrites 67.2%

   \[\leadsto \color{blue}{\left(z - y\right) \cdot x} \]
6. Add Preprocessing

Alternative 5: 42.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ z \cdot x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

   \[\left(1 - x\right) \cdot y + x \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(z + -1 \cdot y\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. fp-cancel-sign-sub-inv N/A

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

   4. metadata-eval N/A

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

   5. *-lft-identity N/A

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

   6. lower--.f64 67.2

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

5. Applied rewrites 67.2%

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

6. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x \cdot z} \]
7. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{z \cdot x} \]

   2. lower-*.f64 39.2

      \[\leadsto \color{blue}{z \cdot x} \]

8. Applied rewrites 39.2%

   \[\leadsto \color{blue}{z \cdot x} \]
9. Add Preprocessing

Developer Target 1: 100.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ y - x \cdot \left(y - z\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = y - (x * (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024327 
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

  :alt
  (! :herbie-platform default (- y (* x (- y z))))

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