SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 4.7s

Alternatives: 7

Speedup: 1.2×

• 20.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 61.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-9}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+203}:\\ \;\;\;\;\left(-y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.8e-9)
   (* z y)
   (if (<= y 1.0) (* 1.0 x) (if (<= y 5.3e+203) (* (- y) x) (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.8e-9) {
		tmp = z * y;
	} else if (y <= 1.0) {
		tmp = 1.0 * x;
	} else if (y <= 5.3e+203) {
		tmp = -y * x;
	} else {
		tmp = z * 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 <= (-1.8d-9)) then
        tmp = z * y
    else if (y <= 1.0d0) then
        tmp = 1.0d0 * x
    else if (y <= 5.3d+203) then
        tmp = -y * x
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.8e-9) {
		tmp = z * y;
	} else if (y <= 1.0) {
		tmp = 1.0 * x;
	} else if (y <= 5.3e+203) {
		tmp = -y * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.8e-9:
		tmp = z * y
	elif y <= 1.0:
		tmp = 1.0 * x
	elif y <= 5.3e+203:
		tmp = -y * x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.8e-9)
		tmp = Float64(z * y);
	elseif (y <= 1.0)
		tmp = Float64(1.0 * x);
	elseif (y <= 5.3e+203)
		tmp = Float64(Float64(-y) * x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.8e-9)
		tmp = z * y;
	elseif (y <= 1.0)
		tmp = 1.0 * x;
	elseif (y <= 5.3e+203)
		tmp = -y * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.8e-9], N[(z * y), $MachinePrecision], If[LessEqual[y, 1.0], N[(1.0 * x), $MachinePrecision], If[LessEqual[y, 5.3e+203], N[((-y) * x), $MachinePrecision], N[(z * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8e-9 or 5.29999999999999987e203 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 67.7

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

   5. Applied rewrites 67.7%

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

   if -1.8e-9 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 75.5%

      \[\leadsto 1 \cdot x \]

   if 1 < y < 5.29999999999999987e203

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 68.0

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

   5. Applied rewrites 68.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 59.9%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-9}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+203}:\\ \;\;\;\;\left(-y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-7} \lor \neg \left(y \leq 5500000\right):\\ \;\;\;\;\left(z - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.1e-7) (not (<= y 5500000.0))) (* (- z x) y) (fma (- x) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.1e-7) || !(y <= 5500000.0)) {
		tmp = (z - x) * y;
	} else {
		tmp = fma(-x, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.1e-7) || !(y <= 5500000.0))
		tmp = Float64(Float64(z - x) * y);
	else
		tmp = fma(Float64(-x), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.1e-7], N[Not[LessEqual[y, 5500000.0]], $MachinePrecision]], N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision], N[((-x) * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1e-7 or 5.5e6 < y

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. distribute-rgt-in N/A

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

      7. associate-+l+ N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 97.0

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

   4. Applied rewrites 97.0%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.8

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

   7. Applied rewrites 99.8%

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

   if -2.1e-7 < y < 5.5e6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 77.3

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

   5. Applied rewrites 77.3%

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

   7. Applied rewrites 77.3%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-7} \lor \neg \left(y \leq 5500000\right):\\ \;\;\;\;\left(z - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -42 \lor \neg \left(x \leq 9 \cdot 10^{-44}\right):\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -42.0) (not (<= x 9e-44))) (* (- 1.0 y) x) (* z y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -42.0) || !(x <= 9e-44)) {
		tmp = (1.0 - y) * x;
	} else {
		tmp = z * 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 <= (-42.0d0)) .or. (.not. (x <= 9d-44))) then
        tmp = (1.0d0 - y) * x
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -42.0) || !(x <= 9e-44)) {
		tmp = (1.0 - y) * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -42.0) or not (x <= 9e-44):
		tmp = (1.0 - y) * x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -42.0) || !(x <= 9e-44))
		tmp = Float64(Float64(1.0 - y) * x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -42.0) || ~((x <= 9e-44)))
		tmp = (1.0 - y) * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -42.0], N[Not[LessEqual[x, 9e-44]], $MachinePrecision]], N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision], N[(z * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -42 or 8.9999999999999997e-44 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 86.5

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

   5. Applied rewrites 86.5%

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

   if -42 < x < 8.9999999999999997e-44

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 74.7

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

   5. Applied rewrites 74.7%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -42 \lor \neg \left(x \leq 9 \cdot 10^{-44}\right):\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -42:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-44}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -42.0) (* (- 1.0 y) x) (if (<= x 9e-44) (* z y) (fma (- x) y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -42.0) {
		tmp = (1.0 - y) * x;
	} else if (x <= 9e-44) {
		tmp = z * y;
	} else {
		tmp = fma(-x, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -42.0)
		tmp = Float64(Float64(1.0 - y) * x);
	elseif (x <= 9e-44)
		tmp = Float64(z * y);
	else
		tmp = fma(Float64(-x), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -42.0], N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 9e-44], N[(z * y), $MachinePrecision], N[((-x) * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -42

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 85.3

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

   5. Applied rewrites 85.3%

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

   if -42 < x < 8.9999999999999997e-44

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 74.7

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

   5. Applied rewrites 74.7%

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

   if 8.9999999999999997e-44 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 87.4

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

   5. Applied rewrites 87.4%

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

   7. Applied rewrites 87.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -42:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-44}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-9} \lor \neg \left(y \leq 7.5 \cdot 10^{-56}\right):\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.8e-9) (not (<= y 7.5e-56))) (* z y) (* 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e-9) || !(y <= 7.5e-56)) {
		tmp = z * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.8d-9)) .or. (.not. (y <= 7.5d-56))) then
        tmp = z * y
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e-9) || !(y <= 7.5e-56)) {
		tmp = z * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.8e-9) or not (y <= 7.5e-56):
		tmp = z * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.8e-9) || !(y <= 7.5e-56))
		tmp = Float64(z * y);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.8e-9) || ~((y <= 7.5e-56)))
		tmp = z * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.8e-9], N[Not[LessEqual[y, 7.5e-56]], $MachinePrecision]], N[(z * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e-9 or 7.50000000000000041e-56 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.0

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

   5. Applied rewrites 59.0%

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

   if -1.8e-9 < y < 7.50000000000000041e-56

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 78.8

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

   5. Applied rewrites 78.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 78.3%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-9} \lor \neg \left(y \leq 7.5 \cdot 10^{-56}\right):\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 41.5% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 43.5

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

5. Applied rewrites 43.5%

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

6. Final simplification 43.5%

   \[\leadsto z \cdot y \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024313 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))