SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.2s

Alternatives: 7

Speedup: 1.2×

• 21.1% 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: 58.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-x\right) \cdot y\\ \mathbf{if}\;y \leq -1.28 \cdot 10^{-51}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-176}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;y \leq 80:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+170}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+276}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- x) y)))
   (if (<= y -1.28e-51)
     (* y z)
     (if (<= y 2.9e-176)
       (* 1.0 x)
       (if (<= y 80.0)
         (* y z)
         (if (<= y 6.5e+170) t_0 (if (<= y 1.75e+276) (* y z) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -x * y;
	double tmp;
	if (y <= -1.28e-51) {
		tmp = y * z;
	} else if (y <= 2.9e-176) {
		tmp = 1.0 * x;
	} else if (y <= 80.0) {
		tmp = y * z;
	} else if (y <= 6.5e+170) {
		tmp = t_0;
	} else if (y <= 1.75e+276) {
		tmp = y * 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
    if (y <= (-1.28d-51)) then
        tmp = y * z
    else if (y <= 2.9d-176) then
        tmp = 1.0d0 * x
    else if (y <= 80.0d0) then
        tmp = y * z
    else if (y <= 6.5d+170) then
        tmp = t_0
    else if (y <= 1.75d+276) then
        tmp = y * 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;
	double tmp;
	if (y <= -1.28e-51) {
		tmp = y * z;
	} else if (y <= 2.9e-176) {
		tmp = 1.0 * x;
	} else if (y <= 80.0) {
		tmp = y * z;
	} else if (y <= 6.5e+170) {
		tmp = t_0;
	} else if (y <= 1.75e+276) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x * y
	tmp = 0
	if y <= -1.28e-51:
		tmp = y * z
	elif y <= 2.9e-176:
		tmp = 1.0 * x
	elif y <= 80.0:
		tmp = y * z
	elif y <= 6.5e+170:
		tmp = t_0
	elif y <= 1.75e+276:
		tmp = y * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) * y)
	tmp = 0.0
	if (y <= -1.28e-51)
		tmp = Float64(y * z);
	elseif (y <= 2.9e-176)
		tmp = Float64(1.0 * x);
	elseif (y <= 80.0)
		tmp = Float64(y * z);
	elseif (y <= 6.5e+170)
		tmp = t_0;
	elseif (y <= 1.75e+276)
		tmp = Float64(y * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -x * y;
	tmp = 0.0;
	if (y <= -1.28e-51)
		tmp = y * z;
	elseif (y <= 2.9e-176)
		tmp = 1.0 * x;
	elseif (y <= 80.0)
		tmp = y * z;
	elseif (y <= 6.5e+170)
		tmp = t_0;
	elseif (y <= 1.75e+276)
		tmp = y * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) * y), $MachinePrecision]}, If[LessEqual[y, -1.28e-51], N[(y * z), $MachinePrecision], If[LessEqual[y, 2.9e-176], N[(1.0 * x), $MachinePrecision], If[LessEqual[y, 80.0], N[(y * z), $MachinePrecision], If[LessEqual[y, 6.5e+170], t$95$0, If[LessEqual[y, 1.75e+276], N[(y * z), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.28000000000000004e-51 or 2.90000000000000006e-176 < y < 80 or 6.5e170 < y < 1.74999999999999991e276

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 63.5

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

   5. Applied rewrites 63.5%

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

   if -1.28000000000000004e-51 < y < 2.90000000000000006e-176

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt1-in N/A

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

      6. +-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 80.7

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

   5. Applied rewrites 80.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 80.7%

      \[\leadsto 1 \cdot x \]

   if 80 < y < 6.5e170 or 1.74999999999999991e276 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 95.0

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

   5. Applied rewrites 95.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 66.6%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{-51}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-176}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;y \leq 80:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+170}:\\ \;\;\;\;\left(-x\right) \cdot y\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+276}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -75:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.0008:\\ \;\;\;\;y \cdot z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z x))))
   (if (<= y -75.0) t_0 (if (<= y 0.0008) (+ (* y z) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z - x);
	double tmp;
	if (y <= -75.0) {
		tmp = t_0;
	} else if (y <= 0.0008) {
		tmp = (y * z) + 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 <= (-75.0d0)) then
        tmp = t_0
    else if (y <= 0.0008d0) then
        tmp = (y * z) + 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 <= -75.0) {
		tmp = t_0;
	} else if (y <= 0.0008) {
		tmp = (y * z) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z - x)
	tmp = 0
	if y <= -75.0:
		tmp = t_0
	elif y <= 0.0008:
		tmp = (y * z) + 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 <= -75.0)
		tmp = t_0;
	elseif (y <= 0.0008)
		tmp = Float64(Float64(y * z) + 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 <= -75.0)
		tmp = t_0;
	elseif (y <= 0.0008)
		tmp = (y * z) + 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, -75.0], t$95$0, If[LessEqual[y, 0.0008], N[(N[(y * z), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -75 or 8.00000000000000038e-4 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 97.7

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

   5. Applied rewrites 97.7%

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

   if -75 < y < 8.00000000000000038e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 99.4

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

   5. Applied rewrites 99.4%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -75:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{elif}\;y \leq 0.0008:\\ \;\;\;\;y \cdot z + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot x\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{-73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.45 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) x)))
   (if (<= x -5.6e-73) t_0 (if (<= x 3.45e+50) (* y (- z x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * x;
	double tmp;
	if (x <= -5.6e-73) {
		tmp = t_0;
	} else if (x <= 3.45e+50) {
		tmp = y * (z - 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 = (1.0d0 - y) * x
    if (x <= (-5.6d-73)) then
        tmp = t_0
    else if (x <= 3.45d+50) then
        tmp = y * (z - 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 = (1.0 - y) * x;
	double tmp;
	if (x <= -5.6e-73) {
		tmp = t_0;
	} else if (x <= 3.45e+50) {
		tmp = y * (z - x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - y) * x
	tmp = 0
	if x <= -5.6e-73:
		tmp = t_0
	elif x <= 3.45e+50:
		tmp = y * (z - x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * x)
	tmp = 0.0
	if (x <= -5.6e-73)
		tmp = t_0;
	elseif (x <= 3.45e+50)
		tmp = Float64(y * Float64(z - x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * x;
	tmp = 0.0;
	if (x <= -5.6e-73)
		tmp = t_0;
	elseif (x <= 3.45e+50)
		tmp = y * (z - x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -5.6e-73], t$95$0, If[LessEqual[x, 3.45e+50], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.60000000000000023e-73 or 3.45000000000000016e50 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt1-in N/A

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

      6. +-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 87.6

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

   5. Applied rewrites 87.6%

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

   if -5.60000000000000023e-73 < x < 3.45000000000000016e50

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.1

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

   5. Applied rewrites 83.1%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-73}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{elif}\;x \leq 3.45 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot x\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{-73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+44}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) x)))
   (if (<= x -4.6e-73) t_0 (if (<= x 1.25e+44) (* y z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * x;
	double tmp;
	if (x <= -4.6e-73) {
		tmp = t_0;
	} else if (x <= 1.25e+44) {
		tmp = y * 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 = (1.0d0 - y) * x
    if (x <= (-4.6d-73)) then
        tmp = t_0
    else if (x <= 1.25d+44) then
        tmp = y * 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 = (1.0 - y) * x;
	double tmp;
	if (x <= -4.6e-73) {
		tmp = t_0;
	} else if (x <= 1.25e+44) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - y) * x
	tmp = 0
	if x <= -4.6e-73:
		tmp = t_0
	elif x <= 1.25e+44:
		tmp = y * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * x)
	tmp = 0.0
	if (x <= -4.6e-73)
		tmp = t_0;
	elseif (x <= 1.25e+44)
		tmp = Float64(y * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * x;
	tmp = 0.0;
	if (x <= -4.6e-73)
		tmp = t_0;
	elseif (x <= 1.25e+44)
		tmp = y * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -4.6e-73], t$95$0, If[LessEqual[x, 1.25e+44], N[(y * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.59999999999999977e-73 or 1.2499999999999999e44 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt1-in N/A

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

      6. +-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 87.6

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

   5. Applied rewrites 87.6%

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

   if -4.59999999999999977e-73 < x < 1.2499999999999999e44

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 75.1

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

   5. Applied rewrites 75.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-73}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+44}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{-51}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-176}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.28e-51) (* y z) (if (<= y 2.9e-176) (* 1.0 x) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.28e-51) {
		tmp = y * z;
	} else if (y <= 2.9e-176) {
		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 <= (-1.28d-51)) then
        tmp = y * z
    else if (y <= 2.9d-176) 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 <= -1.28e-51) {
		tmp = y * z;
	} else if (y <= 2.9e-176) {
		tmp = 1.0 * x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.28e-51:
		tmp = y * z
	elif y <= 2.9e-176:
		tmp = 1.0 * x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.28e-51)
		tmp = Float64(y * z);
	elseif (y <= 2.9e-176)
		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 <= -1.28e-51)
		tmp = y * z;
	elseif (y <= 2.9e-176)
		tmp = 1.0 * x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.28e-51], N[(y * z), $MachinePrecision], If[LessEqual[y, 2.9e-176], N[(1.0 * x), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.28000000000000004e-51 or 2.90000000000000006e-176 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 56.6

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

   5. Applied rewrites 56.6%

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

   if -1.28000000000000004e-51 < y < 2.90000000000000006e-176

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt1-in N/A

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

      6. +-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 80.7

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

   5. Applied rewrites 80.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 80.7%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{-51}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-176}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.2% 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 z around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 46.4

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

5. Applied rewrites 46.4%

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

6. Final simplification 46.4%

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

Reproduce

herbie shell --seed 2024276 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))