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

Percentage Accurate: 98.3% → 100.0%

Time: 5.9s

Alternatives: 6

Speedup: 1.7×

• 20.5% 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: 98.3% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

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

   3. mul-1-neg N/A

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

   4. remove-double-neg N/A

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

   5. mul-1-neg N/A

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

   6. distribute-neg-in N/A

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

   7. +-commutative N/A

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

   8. lower-fma.f64 N/A

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

   9. +-commutative N/A

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

   10. distribute-neg-in N/A

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

   11. mul-1-neg N/A

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

   12. remove-double-neg N/A

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

   13. unsub-neg N/A

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

   14. lower--.f64 100.0

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

5. Applied rewrites 100.0%

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

Alternative 2: 58.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-z\right) \cdot x\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+175}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+57}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-43}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-167}:\\ \;\;\;\;1 \cdot z\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+84}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z) x)))
   (if (<= x -1.35e+175)
     (* y x)
     (if (<= x -1.05e+57)
       t_0
       (if (<= x -8e-43)
         (* y x)
         (if (<= x 2.35e-167) (* 1.0 z) (if (<= x 1.4e+84) (* y x) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -z * x;
	double tmp;
	if (x <= -1.35e+175) {
		tmp = y * x;
	} else if (x <= -1.05e+57) {
		tmp = t_0;
	} else if (x <= -8e-43) {
		tmp = y * x;
	} else if (x <= 2.35e-167) {
		tmp = 1.0 * z;
	} else if (x <= 1.4e+84) {
		tmp = y * x;
	} 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 = -z * x
    if (x <= (-1.35d+175)) then
        tmp = y * x
    else if (x <= (-1.05d+57)) then
        tmp = t_0
    else if (x <= (-8d-43)) then
        tmp = y * x
    else if (x <= 2.35d-167) then
        tmp = 1.0d0 * z
    else if (x <= 1.4d+84) then
        tmp = y * x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -z * x;
	double tmp;
	if (x <= -1.35e+175) {
		tmp = y * x;
	} else if (x <= -1.05e+57) {
		tmp = t_0;
	} else if (x <= -8e-43) {
		tmp = y * x;
	} else if (x <= 2.35e-167) {
		tmp = 1.0 * z;
	} else if (x <= 1.4e+84) {
		tmp = y * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z * x
	tmp = 0
	if x <= -1.35e+175:
		tmp = y * x
	elif x <= -1.05e+57:
		tmp = t_0
	elif x <= -8e-43:
		tmp = y * x
	elif x <= 2.35e-167:
		tmp = 1.0 * z
	elif x <= 1.4e+84:
		tmp = y * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-z) * x)
	tmp = 0.0
	if (x <= -1.35e+175)
		tmp = Float64(y * x);
	elseif (x <= -1.05e+57)
		tmp = t_0;
	elseif (x <= -8e-43)
		tmp = Float64(y * x);
	elseif (x <= 2.35e-167)
		tmp = Float64(1.0 * z);
	elseif (x <= 1.4e+84)
		tmp = Float64(y * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -z * x;
	tmp = 0.0;
	if (x <= -1.35e+175)
		tmp = y * x;
	elseif (x <= -1.05e+57)
		tmp = t_0;
	elseif (x <= -8e-43)
		tmp = y * x;
	elseif (x <= 2.35e-167)
		tmp = 1.0 * z;
	elseif (x <= 1.4e+84)
		tmp = y * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-z) * x), $MachinePrecision]}, If[LessEqual[x, -1.35e+175], N[(y * x), $MachinePrecision], If[LessEqual[x, -1.05e+57], t$95$0, If[LessEqual[x, -8e-43], N[(y * x), $MachinePrecision], If[LessEqual[x, 2.35e-167], N[(1.0 * z), $MachinePrecision], If[LessEqual[x, 1.4e+84], N[(y * x), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35e175 or -1.04999999999999995e57 < x < -8.00000000000000062e-43 or 2.34999999999999985e-167 < x < 1.39999999999999991e84

   1. Initial program 95.3%

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

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 42.3

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

   5. Applied rewrites 42.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 20.0%

      \[\leadsto 1 \cdot z \]

   9. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 61.2

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

   11. Applied rewrites 61.2%

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

   if -1.35e175 < x < -1.04999999999999995e57 or 1.39999999999999991e84 < x

   1. Initial program 97.0%

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

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. +-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. unsub-neg N/A

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

      13. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 65.8%

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

   if -8.00000000000000062e-43 < x < 2.34999999999999985e-167

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 76.3%

      \[\leadsto 1 \cdot z \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-44} \lor \neg \left(x \leq 2.35 \cdot 10^{-167}\right):\\ \;\;\;\;\left(y - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.3e-44) (not (<= x 2.35e-167))) (* (- y z) x) (* 1.0 z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.3e-44) || !(x <= 2.35e-167)) {
		tmp = (y - z) * x;
	} else {
		tmp = 1.0 * z;
	}
	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 <= (-4.3d-44)) .or. (.not. (x <= 2.35d-167))) then
        tmp = (y - z) * x
    else
        tmp = 1.0d0 * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.3e-44) || !(x <= 2.35e-167)) {
		tmp = (y - z) * x;
	} else {
		tmp = 1.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.3e-44) or not (x <= 2.35e-167):
		tmp = (y - z) * x
	else:
		tmp = 1.0 * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.3e-44) || !(x <= 2.35e-167))
		tmp = Float64(Float64(y - z) * x);
	else
		tmp = Float64(1.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.3e-44) || ~((x <= 2.35e-167)))
		tmp = (y - z) * x;
	else
		tmp = 1.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.3e-44], N[Not[LessEqual[x, 2.35e-167]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision], N[(1.0 * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.30000000000000013e-44 or 2.34999999999999985e-167 < x

   1. Initial program 96.0%

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

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. +-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. unsub-neg N/A

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

      13. lower--.f64 88.9

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

   5. Applied rewrites 88.9%

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

   if -4.30000000000000013e-44 < x < 2.34999999999999985e-167

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 76.3%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-44} \lor \neg \left(x \leq 2.35 \cdot 10^{-167}\right):\\ \;\;\;\;\left(y - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-95} \lor \neg \left(z \leq 540000000000\right):\\ \;\;\;\;\left(1 - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.1e-95) (not (<= z 540000000000.0))) (* (- 1.0 x) z) (* y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.1e-95) || !(z <= 540000000000.0)) {
		tmp = (1.0 - 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 ((z <= (-2.1d-95)) .or. (.not. (z <= 540000000000.0d0))) then
        tmp = (1.0d0 - 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 ((z <= -2.1e-95) || !(z <= 540000000000.0)) {
		tmp = (1.0 - x) * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.1e-95) or not (z <= 540000000000.0):
		tmp = (1.0 - x) * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.1e-95) || !(z <= 540000000000.0))
		tmp = Float64(Float64(1.0 - x) * z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.1e-95) || ~((z <= 540000000000.0)))
		tmp = (1.0 - x) * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.1e-95], N[Not[LessEqual[z, 540000000000.0]], $MachinePrecision]], N[(N[(1.0 - x), $MachinePrecision] * z), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1e-95 or 5.4e11 < z

   1. Initial program 94.8%

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

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 86.6

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

   5. Applied rewrites 86.6%

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

   if -2.1e-95 < z < 5.4e11

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 29.6

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

   5. Applied rewrites 29.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 23.4%

      \[\leadsto 1 \cdot z \]

   9. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 71.9

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

   11. Applied rewrites 71.9%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-95} \lor \neg \left(z \leq 540000000000\right):\\ \;\;\;\;\left(1 - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-43} \lor \neg \left(x \leq 2.35 \cdot 10^{-167}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8e-43) (not (<= x 2.35e-167))) (* y x) (* 1.0 z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8e-43) || !(x <= 2.35e-167)) {
		tmp = y * x;
	} else {
		tmp = 1.0 * z;
	}
	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 <= (-8d-43)) .or. (.not. (x <= 2.35d-167))) then
        tmp = y * x
    else
        tmp = 1.0d0 * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8e-43) || !(x <= 2.35e-167)) {
		tmp = y * x;
	} else {
		tmp = 1.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8e-43) or not (x <= 2.35e-167):
		tmp = y * x
	else:
		tmp = 1.0 * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8e-43) || !(x <= 2.35e-167))
		tmp = Float64(y * x);
	else
		tmp = Float64(1.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8e-43) || ~((x <= 2.35e-167)))
		tmp = y * x;
	else
		tmp = 1.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8e-43], N[Not[LessEqual[x, 2.35e-167]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(1.0 * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.00000000000000062e-43 or 2.34999999999999985e-167 < x

   1. Initial program 96.0%

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

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.3

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

   5. Applied rewrites 51.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 13.4%

      \[\leadsto 1 \cdot z \]

   9. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 52.7

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

   11. Applied rewrites 52.7%

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

   if -8.00000000000000062e-43 < x < 2.34999999999999985e-167

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 76.3%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-43} \lor \neg \left(x \leq 2.35 \cdot 10^{-167}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.7% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 59.4

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

5. Applied rewrites 59.4%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 33.8%

   \[\leadsto 1 \cdot z \]

9. Taylor expanded in y around inf

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

    1. *-commutative N/A

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

    2. lower-*.f64 43.8

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

11. Applied rewrites 43.8%

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

Reproduce

herbie shell --seed 2024323 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))