Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3

Percentage Accurate: 97.9% → 100.0%

Time: 5.7s

Alternatives: 6

Speedup: 1.7×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * y) + ((1.0 - 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 * y) + ((1.0d0 - x) * z)
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(Float64(1.0 - x) * z))
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * y) + ((1.0 - 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 * y) + ((1.0d0 - x) * z)
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(Float64(1.0 - x) * z))
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. mul-1-neg N/A

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

   3. remove-double-neg N/A

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

   4. mul-1-neg N/A

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

   5. distribute-neg-in N/A

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

   6. +-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. +-commutative N/A

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

   9. distribute-neg-in N/A

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

   10. mul-1-neg N/A

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

   11. remove-double-neg N/A

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

   12. unsub-neg N/A

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

   13. lower--.f64 100.0

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

5. Applied rewrites 100.0%

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

Alternative 2: 78.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y - z\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-32}:\\ \;\;\;\;\mathsf{fma}\left(-z, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y z))))
   (if (<= y -1.9e+73) t_0 (if (<= y 7.4e-32) (fma (- z) x z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y - z);
	double tmp;
	if (y <= -1.9e+73) {
		tmp = t_0;
	} else if (y <= 7.4e-32) {
		tmp = fma(-z, x, z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y - z))
	tmp = 0.0
	if (y <= -1.9e+73)
		tmp = t_0;
	elseif (y <= 7.4e-32)
		tmp = fma(Float64(-z), x, z);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+73], t$95$0, If[LessEqual[y, 7.4e-32], N[((-z) * x + z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000011e73 or 7.4e-32 < y

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 85.0

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

   5. Applied rewrites 85.0%

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

   if -1.90000000000000011e73 < y < 7.4e-32

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

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

         \[\leadsto \color{blue}{1 \cdot z - x \cdot z} \]

      2. *-lft-identity N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 86.2

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

   5. Applied rewrites 86.2%

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

   7. Applied rewrites 86.3%

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

Alternative 3: 78.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y - z\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-32}:\\ \;\;\;\;z - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y z))))
   (if (<= y -1.9e+73) t_0 (if (<= y 7.4e-32) (- z (* x z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y - z);
	double tmp;
	if (y <= -1.9e+73) {
		tmp = t_0;
	} else if (y <= 7.4e-32) {
		tmp = z - (x * z);
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x * (y - z)
    if (y <= (-1.9d+73)) then
        tmp = t_0
    else if (y <= 7.4d-32) then
        tmp = z - (x * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y - z);
	double tmp;
	if (y <= -1.9e+73) {
		tmp = t_0;
	} else if (y <= 7.4e-32) {
		tmp = z - (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y - z)
	tmp = 0
	if y <= -1.9e+73:
		tmp = t_0
	elif y <= 7.4e-32:
		tmp = z - (x * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y - z))
	tmp = 0.0
	if (y <= -1.9e+73)
		tmp = t_0;
	elseif (y <= 7.4e-32)
		tmp = Float64(z - Float64(x * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y - z);
	tmp = 0.0;
	if (y <= -1.9e+73)
		tmp = t_0;
	elseif (y <= 7.4e-32)
		tmp = z - (x * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+73], t$95$0, If[LessEqual[y, 7.4e-32], N[(z - N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000011e73 or 7.4e-32 < y

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 85.0

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

   5. Applied rewrites 85.0%

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

   if -1.90000000000000011e73 < y < 7.4e-32

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

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

         \[\leadsto \color{blue}{1 \cdot z - x \cdot z} \]

      2. *-lft-identity N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 86.2

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

   5. Applied rewrites 86.2%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-32}:\\ \;\;\;\;z - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{-61}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.26e-61) (* x y) (if (<= y 3.8e-7) (* x (- z)) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.26e-61) {
		tmp = x * y;
	} else if (y <= 3.8e-7) {
		tmp = x * -z;
	} else {
		tmp = 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 (y <= (-1.26d-61)) then
        tmp = x * y
    else if (y <= 3.8d-7) then
        tmp = x * -z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.26e-61) {
		tmp = x * y;
	} else if (y <= 3.8e-7) {
		tmp = x * -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.26e-61:
		tmp = x * y
	elif y <= 3.8e-7:
		tmp = x * -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.26e-61)
		tmp = Float64(x * y);
	elseif (y <= 3.8e-7)
		tmp = Float64(x * Float64(-z));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.26e-61)
		tmp = x * y;
	elseif (y <= 3.8e-7)
		tmp = x * -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.26e-61], N[(x * y), $MachinePrecision], If[LessEqual[y, 3.8e-7], N[(x * (-z)), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2599999999999999e-61 or 3.80000000000000015e-7 < y

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 68.7

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

   5. Applied rewrites 68.7%

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

   if -1.2599999999999999e-61 < y < 3.80000000000000015e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 51.4

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

   5. Applied rewrites 51.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 44.9%

      \[\leadsto x \cdot \left(-z\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 64.9% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in x around inf

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

   1. mul-1-neg N/A

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

   2. remove-double-neg N/A

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

   3. mul-1-neg N/A

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

   4. distribute-neg-in N/A

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

   5. +-commutative N/A

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

   6. lower-*.f64 N/A

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

   7. +-commutative N/A

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

   8. distribute-neg-in N/A

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

   9. mul-1-neg N/A

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

   10. remove-double-neg N/A

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

   11. unsub-neg N/A

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

   12. lower--.f64 66.3

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

5. Applied rewrites 66.3%

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

Alternative 6: 41.7% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

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 * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in y around inf

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

   1. lower-*.f64 41.5

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

5. Applied rewrites 41.5%

   \[\leadsto \color{blue}{x \cdot y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024223 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))