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

Percentage Accurate: 97.9% → 100.0%

Time: 10.7s

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: 97.9% 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

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

FPCore

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

Derivation

1. Initial program 97.2%

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

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

   2. distribute-lft-in N/A

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

   3. mul-1-neg N/A

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

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

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

   5. mul-1-neg N/A

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

   6. associate-+r+ N/A

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

   7. mul-1-neg N/A

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

   8. unsub-neg N/A

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

   9. associate-+l- N/A

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

   10. distribute-lft-out-- N/A

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

   11. unsub-neg N/A

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

   12. mul-1-neg N/A

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

   13. sub-neg N/A

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

   14. mul-1-neg N/A

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

   15. +-commutative N/A

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

   16. mul-1-neg N/A

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

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

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

   18. lower-fma.f64 N/A

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

5. Applied rewrites 100.0%

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

Alternative 2: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -14500000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\mathsf{fma}\left(z, x, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z y))))
   (if (<= x -14500000.0) t_0 (if (<= x 1.0) (fma z x y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (x <= -14500000.0) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = fma(z, x, 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 <= -14500000.0)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = fma(z, x, 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, -14500000.0], t$95$0, If[LessEqual[x, 1.0], N[(z * x + y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45e7 or 1 < 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

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if -1.45e7 < x < 1

   1. Initial program 100.0%

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

      1. lift--.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-lft-in N/A

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

      6. *-rgt-identity N/A

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

      7. lift-*.f64 N/A

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

      8. associate-+l+ N/A

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

      9. lower-+.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 98.8

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

   7. Applied rewrites 98.8%

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

      1. lift-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 98.8

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

   9. Applied rewrites 98.8%

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

Alternative 3: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-170}:\\ \;\;\;\;\mathsf{fma}\left(z, x, y\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.2e-170)
   (fma z x y)
   (if (<= z 1.7e-159) (* x (- y)) (fma z x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.2e-170) {
		tmp = fma(z, x, y);
	} else if (z <= 1.7e-159) {
		tmp = x * -y;
	} else {
		tmp = fma(z, x, y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.2e-170)
		tmp = fma(z, x, y);
	elseif (z <= 1.7e-159)
		tmp = Float64(x * Float64(-y));
	else
		tmp = fma(z, x, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.2e-170], N[(z * x + y), $MachinePrecision], If[LessEqual[z, 1.7e-159], N[(x * (-y)), $MachinePrecision], N[(z * x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.19999999999999948e-170 or 1.69999999999999992e-159 < z

   1. Initial program 96.4%

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

      1. lift--.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-lft-in N/A

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

      6. *-rgt-identity N/A

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

      7. lift-*.f64 N/A

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

      8. associate-+l+ N/A

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

      9. lower-+.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 98.0

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

   4. Applied rewrites 98.0%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 85.3

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

   7. Applied rewrites 85.3%

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

      1. lift-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 85.3

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

   9. Applied rewrites 85.3%

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

   if -9.19999999999999948e-170 < z < 1.69999999999999992e-159

   1. Initial program 99.9%

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

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 72.3

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

   5. Applied rewrites 72.3%

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

   6. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 65.9

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

   8. Applied rewrites 65.9%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-170}:\\ \;\;\;\;\mathsf{fma}\left(z, x, y\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.9% accurate, 2.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. lift--.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-neg N/A

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

   5. distribute-lft-in N/A

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

   6. *-rgt-identity N/A

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

   7. lift-*.f64 N/A

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

   8. associate-+l+ N/A

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

   9. lower-+.f64 N/A

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

   10. lower-fma.f64 N/A

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

   11. lower-neg.f64 98.4

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

4. Applied rewrites 98.4%

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

5. Taylor expanded in y around 0

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

   1. lower-*.f64 73.3

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

7. Applied rewrites 73.3%

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

   1. lift-*.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 73.3

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

9. Applied rewrites 73.3%

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

Alternative 5: 42.1% 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 97.2%

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

3. Taylor expanded in y around 0

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

   1. lower-*.f64 41.2

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

5. Applied rewrites 41.2%

   \[\leadsto \color{blue}{x \cdot z} \]
6. 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 2024219 
(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)))