SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 4.6s

Alternatives: 7

Speedup: 1.2×

• 21.2% 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: 61.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+226}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+128}:\\ \;\;\;\;\left(-y\right) \cdot x\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-31}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-56}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.45e+226)
   (* y z)
   (if (<= y -3.8e+128)
     (* (- y) x)
     (if (<= y -9e-31) (* y z) (if (<= y 7e-56) (* 1.0 x) (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.45e+226) {
		tmp = y * z;
	} else if (y <= -3.8e+128) {
		tmp = -y * x;
	} else if (y <= -9e-31) {
		tmp = y * z;
	} else if (y <= 7e-56) {
		tmp = 1.0 * x;
	} else {
		tmp = y * 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 (y <= (-1.45d+226)) then
        tmp = y * z
    else if (y <= (-3.8d+128)) then
        tmp = -y * x
    else if (y <= (-9d-31)) then
        tmp = y * z
    else if (y <= 7d-56) then
        tmp = 1.0d0 * x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.45e+226) {
		tmp = y * z;
	} else if (y <= -3.8e+128) {
		tmp = -y * x;
	} else if (y <= -9e-31) {
		tmp = y * z;
	} else if (y <= 7e-56) {
		tmp = 1.0 * x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.45e+226:
		tmp = y * z
	elif y <= -3.8e+128:
		tmp = -y * x
	elif y <= -9e-31:
		tmp = y * z
	elif y <= 7e-56:
		tmp = 1.0 * x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.45e+226)
		tmp = Float64(y * z);
	elseif (y <= -3.8e+128)
		tmp = Float64(Float64(-y) * x);
	elseif (y <= -9e-31)
		tmp = Float64(y * z);
	elseif (y <= 7e-56)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.45e+226)
		tmp = y * z;
	elseif (y <= -3.8e+128)
		tmp = -y * x;
	elseif (y <= -9e-31)
		tmp = y * z;
	elseif (y <= 7e-56)
		tmp = 1.0 * x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.45e+226], N[(y * z), $MachinePrecision], If[LessEqual[y, -3.8e+128], N[((-y) * x), $MachinePrecision], If[LessEqual[y, -9e-31], N[(y * z), $MachinePrecision], If[LessEqual[y, 7e-56], N[(1.0 * x), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.44999999999999987e226 or -3.7999999999999999e128 < y < -9.0000000000000008e-31 or 6.9999999999999996e-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 62.8

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

   5. Applied rewrites 62.8%

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

   if -1.44999999999999987e226 < y < -3.7999999999999999e128

   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 73.5

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

   5. Applied rewrites 73.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 73.5%

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

   if -9.0000000000000008e-31 < y < 6.9999999999999996e-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 77.1

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

   5. Applied rewrites 77.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 77.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+226}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+128}:\\ \;\;\;\;\left(-y\right) \cdot x\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-31}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-56}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -7.1 \cdot 10^{-31}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-55}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z x))))
   (if (<= y -7.1e-31) t_0 (if (<= y 1.3e-55) (* (- 1.0 y) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z - x);
	double tmp;
	if (y <= -7.1e-31) {
		tmp = t_0;
	} else if (y <= 1.3e-55) {
		tmp = (1.0 - 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 = y * (z - x)
    if (y <= (-7.1d-31)) then
        tmp = t_0
    else if (y <= 1.3d-55) then
        tmp = (1.0d0 - 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 = y * (z - x);
	double tmp;
	if (y <= -7.1e-31) {
		tmp = t_0;
	} else if (y <= 1.3e-55) {
		tmp = (1.0 - y) * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z - x)
	tmp = 0
	if y <= -7.1e-31:
		tmp = t_0
	elif y <= 1.3e-55:
		tmp = (1.0 - y) * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z - x))
	tmp = 0.0
	if (y <= -7.1e-31)
		tmp = t_0;
	elseif (y <= 1.3e-55)
		tmp = Float64(Float64(1.0 - y) * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z - x);
	tmp = 0.0;
	if (y <= -7.1e-31)
		tmp = t_0;
	elseif (y <= 1.3e-55)
		tmp = (1.0 - y) * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.1e-31], t$95$0, If[LessEqual[y, 1.3e-55], N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.0999999999999999e-31 or 1.2999999999999999e-55 < 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 96.0

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

   4. Applied rewrites 96.0%

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

   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 97.3

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

   7. Applied rewrites 97.3%

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

   if -7.0999999999999999e-31 < y < 1.2999999999999999e-55

   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 77.1

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

   5. Applied rewrites 77.1%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.1 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-55}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.24 \cdot 10^{-5}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(-y, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.24e-5) (* y z) (if (<= z 1e+142) (fma (- y) x x) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.24e-5) {
		tmp = y * z;
	} else if (z <= 1e+142) {
		tmp = fma(-y, x, x);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.24e-5)
		tmp = Float64(y * z);
	elseif (z <= 1e+142)
		tmp = fma(Float64(-y), x, x);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.24e-5], N[(y * z), $MachinePrecision], If[LessEqual[z, 1e+142], N[((-y) * x + x), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.24e-5 or 1.00000000000000005e142 < z

   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 74.2

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

   5. Applied rewrites 74.2%

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

   if -1.24e-5 < z < 1.00000000000000005e142

   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 82.3

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

   5. Applied rewrites 82.3%

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

   7. Applied rewrites 82.3%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.24 \cdot 10^{-5}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(-y, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.24 \cdot 10^{-5}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 10^{+142}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.24e-5) (* y z) (if (<= z 1e+142) (* (- 1.0 y) x) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.24e-5) {
		tmp = y * z;
	} else if (z <= 1e+142) {
		tmp = (1.0 - y) * x;
	} else {
		tmp = y * 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 (z <= (-1.24d-5)) then
        tmp = y * z
    else if (z <= 1d+142) then
        tmp = (1.0d0 - y) * x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.24e-5) {
		tmp = y * z;
	} else if (z <= 1e+142) {
		tmp = (1.0 - y) * x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.24e-5:
		tmp = y * z
	elif z <= 1e+142:
		tmp = (1.0 - y) * x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.24e-5)
		tmp = Float64(y * z);
	elseif (z <= 1e+142)
		tmp = Float64(Float64(1.0 - y) * x);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.24e-5)
		tmp = y * z;
	elseif (z <= 1e+142)
		tmp = (1.0 - y) * x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.24e-5], N[(y * z), $MachinePrecision], If[LessEqual[z, 1e+142], N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.24e-5 or 1.00000000000000005e142 < z

   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 74.2

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

   5. Applied rewrites 74.2%

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

   if -1.24e-5 < z < 1.00000000000000005e142

   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 82.3

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

   5. Applied rewrites 82.3%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.24 \cdot 10^{-5}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 10^{+142}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-31}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-56}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9e-31) (* y z) (if (<= y 7e-56) (* 1.0 x) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e-31) {
		tmp = y * z;
	} else if (y <= 7e-56) {
		tmp = 1.0 * x;
	} else {
		tmp = y * 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 (y <= (-9d-31)) then
        tmp = y * z
    else if (y <= 7d-56) then
        tmp = 1.0d0 * x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e-31) {
		tmp = y * z;
	} else if (y <= 7e-56) {
		tmp = 1.0 * x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9e-31:
		tmp = y * z
	elif y <= 7e-56:
		tmp = 1.0 * x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9e-31)
		tmp = Float64(y * z);
	elseif (y <= 7e-56)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9e-31)
		tmp = y * z;
	elseif (y <= 7e-56)
		tmp = 1.0 * x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9e-31], N[(y * z), $MachinePrecision], If[LessEqual[y, 7e-56], N[(1.0 * x), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.0000000000000008e-31 or 6.9999999999999996e-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 57.0

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

   5. Applied rewrites 57.0%

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

   if -9.0000000000000008e-31 < y < 6.9999999999999996e-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 77.1

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

   5. Applied rewrites 77.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 77.1%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-31}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-56}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.0% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(y * z), $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 44.3

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

5. Applied rewrites 44.3%

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

6. Final simplification 44.3%

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

Reproduce

herbie shell --seed 2024295 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))