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

Percentage Accurate: 97.7% → 100.0%

Time: 9.1s

Alternatives: 7

Speedup: 1.7×

• 21.2% 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: 97.7% 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 97.3%

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

3. Taylor expanded in z around 0

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

   1. distribute-rgt-out-- N/A

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

   2. unsub-neg N/A

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

   3. *-lft-identity N/A

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

   4. mul-1-neg N/A

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

   5. +-commutative N/A

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

   6. associate-+l+ N/A

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

   7. mul-1-neg N/A

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

   8. distribute-rgt-neg-in N/A

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

   9. mul-1-neg N/A

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

   10. distribute-lft-in N/A

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

   11. *-commutative N/A

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

   12. +-commutative N/A

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

   13. remove-double-neg N/A

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

   14. mul-1-neg N/A

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

   15. mul-1-neg N/A

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

   16. distribute-neg-in N/A

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

   17. lower-fma.f64 N/A

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

5. Applied rewrites 100.0%

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

Alternative 2: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-105}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-13}:\\ \;\;\;\;1 \cdot y\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+82}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6e-105)
   (* x z)
   (if (<= x 5e-13) (* 1.0 y) (if (<= x 8.8e+82) (* x z) (* (- y) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6e-105) {
		tmp = x * z;
	} else if (x <= 5e-13) {
		tmp = 1.0 * y;
	} else if (x <= 8.8e+82) {
		tmp = x * z;
	} else {
		tmp = -y * 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 (x <= (-6d-105)) then
        tmp = x * z
    else if (x <= 5d-13) then
        tmp = 1.0d0 * y
    else if (x <= 8.8d+82) then
        tmp = x * z
    else
        tmp = -y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6e-105) {
		tmp = x * z;
	} else if (x <= 5e-13) {
		tmp = 1.0 * y;
	} else if (x <= 8.8e+82) {
		tmp = x * z;
	} else {
		tmp = -y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6e-105:
		tmp = x * z
	elif x <= 5e-13:
		tmp = 1.0 * y
	elif x <= 8.8e+82:
		tmp = x * z
	else:
		tmp = -y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6e-105)
		tmp = Float64(x * z);
	elseif (x <= 5e-13)
		tmp = Float64(1.0 * y);
	elseif (x <= 8.8e+82)
		tmp = Float64(x * z);
	else
		tmp = Float64(Float64(-y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6e-105)
		tmp = x * z;
	elseif (x <= 5e-13)
		tmp = 1.0 * y;
	elseif (x <= 8.8e+82)
		tmp = x * z;
	else
		tmp = -y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6e-105], N[(x * z), $MachinePrecision], If[LessEqual[x, 5e-13], N[(1.0 * y), $MachinePrecision], If[LessEqual[x, 8.8e+82], N[(x * z), $MachinePrecision], N[((-y) * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.0000000000000002e-105 or 4.9999999999999999e-13 < x < 8.8000000000000005e82

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.3

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

   5. Applied rewrites 59.3%

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

   if -6.0000000000000002e-105 < x < 4.9999999999999999e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 77.9

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

   5. Applied rewrites 77.9%

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

   6. Taylor expanded in x around 0

      \[\leadsto 1 \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 77.9%

      \[\leadsto 1 \cdot y \]

   if 8.8000000000000005e82 < x

   1. Initial program 91.7%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. unsub-neg N/A

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

      13. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 68.3%

      \[\leadsto \left(-y\right) \cdot x \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-105}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-13}:\\ \;\;\;\;1 \cdot y\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+82}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.32 \lor \neg \left(x \leq 3400000000000\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, x, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.32) (not (<= x 3400000000000.0)))
   (* x (- z y))
   (fma (- y) x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.32) || !(x <= 3400000000000.0)) {
		tmp = x * (z - y);
	} else {
		tmp = fma(-y, x, y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.32) || !(x <= 3400000000000.0))
		tmp = Float64(x * Float64(z - y));
	else
		tmp = fma(Float64(-y), x, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.32], N[Not[LessEqual[x, 3400000000000.0]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], N[((-y) * x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.320000000000000007 or 3.4e12 < x

   1. Initial program 94.6%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. unsub-neg N/A

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

      13. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if -0.320000000000000007 < x < 3.4e12

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 74.6

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

   5. Applied rewrites 74.6%

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

   7. Applied rewrites 74.7%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.32 \lor \neg \left(x \leq 3400000000000\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, x, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.32 \lor \neg \left(x \leq 3400000000000\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.32) (not (<= x 3400000000000.0)))
   (* x (- z y))
   (* (- 1.0 x) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.32) || !(x <= 3400000000000.0)) {
		tmp = x * (z - y);
	} else {
		tmp = (1.0 - x) * y;
	}
	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 ((x <= (-0.32d0)) .or. (.not. (x <= 3400000000000.0d0))) then
        tmp = x * (z - y)
    else
        tmp = (1.0d0 - x) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.32) || !(x <= 3400000000000.0)) {
		tmp = x * (z - y);
	} else {
		tmp = (1.0 - x) * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.32) or not (x <= 3400000000000.0):
		tmp = x * (z - y)
	else:
		tmp = (1.0 - x) * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.32) || !(x <= 3400000000000.0))
		tmp = Float64(x * Float64(z - y));
	else
		tmp = Float64(Float64(1.0 - x) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.32) || ~((x <= 3400000000000.0)))
		tmp = x * (z - y);
	else
		tmp = (1.0 - x) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.32], N[Not[LessEqual[x, 3400000000000.0]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.320000000000000007 or 3.4e12 < x

   1. Initial program 94.6%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. unsub-neg N/A

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

      13. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if -0.320000000000000007 < x < 3.4e12

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 74.6

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

   5. Applied rewrites 74.6%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.32 \lor \neg \left(x \leq 3400000000000\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+20} \lor \neg \left(z \leq 3.05 \cdot 10^{+82}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.7e+20) (not (<= z 3.05e+82))) (* x z) (* (- 1.0 x) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e+20) || !(z <= 3.05e+82)) {
		tmp = x * z;
	} else {
		tmp = (1.0 - x) * y;
	}
	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 ((z <= (-1.7d+20)) .or. (.not. (z <= 3.05d+82))) then
        tmp = x * z
    else
        tmp = (1.0d0 - x) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e+20) || !(z <= 3.05e+82)) {
		tmp = x * z;
	} else {
		tmp = (1.0 - x) * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.7e+20) or not (z <= 3.05e+82):
		tmp = x * z
	else:
		tmp = (1.0 - x) * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.7e+20) || !(z <= 3.05e+82))
		tmp = Float64(x * z);
	else
		tmp = Float64(Float64(1.0 - x) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.7e+20) || ~((z <= 3.05e+82)))
		tmp = x * z;
	else
		tmp = (1.0 - x) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.7e+20], N[Not[LessEqual[z, 3.05e+82]], $MachinePrecision]], N[(x * z), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e20 or 3.0499999999999999e82 < z

   1. Initial program 94.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 75.6

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

   5. Applied rewrites 75.6%

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

   if -1.7e20 < z < 3.0499999999999999e82

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 84.3

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

   5. Applied rewrites 84.3%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+20} \lor \neg \left(z \leq 3.05 \cdot 10^{+82}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-105} \lor \neg \left(x \leq 5 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;1 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6e-105) (not (<= x 5e-13))) (* x z) (* 1.0 y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e-105) || !(x <= 5e-13)) {
		tmp = x * z;
	} else {
		tmp = 1.0 * y;
	}
	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 ((x <= (-6d-105)) .or. (.not. (x <= 5d-13))) then
        tmp = x * z
    else
        tmp = 1.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e-105) || !(x <= 5e-13)) {
		tmp = x * z;
	} else {
		tmp = 1.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6e-105) or not (x <= 5e-13):
		tmp = x * z
	else:
		tmp = 1.0 * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6e-105) || !(x <= 5e-13))
		tmp = Float64(x * z);
	else
		tmp = Float64(1.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6e-105) || ~((x <= 5e-13)))
		tmp = x * z;
	else
		tmp = 1.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6e-105], N[Not[LessEqual[x, 5e-13]], $MachinePrecision]], N[(x * z), $MachinePrecision], N[(1.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.0000000000000002e-105 or 4.9999999999999999e-13 < x

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 53.7

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

   5. Applied rewrites 53.7%

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

   if -6.0000000000000002e-105 < x < 4.9999999999999999e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 77.9

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

   5. Applied rewrites 77.9%

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

   6. Taylor expanded in x around 0

      \[\leadsto 1 \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 77.9%

      \[\leadsto 1 \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-105} \lor \neg \left(x \leq 5 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;1 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.2% accurate, 2.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 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 * 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]

Derivation

1. Initial program 97.3%

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

3. Taylor expanded in z around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 42.3

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

5. Applied rewrites 42.3%

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

6. Final simplification 42.3%

   \[\leadsto x \cdot z \]
7. 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 2024271 
(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)))