SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.2s

Alternatives: 6

Speedup: 1.2×

• 20.7% 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: 98.9% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z x) y)))
   (if (<= y -1.0) t_0 (if (<= y 1.0) (+ x (* z y)) t_0))))

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   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. lower-*.f64 N/A

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

      2. lower--.f64 99.5

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

   5. Applied rewrites 99.5%

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

   if -1 < y < 1

   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. lower-*.f64 98.0

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

   5. Applied rewrites 98.0%

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

4. Final simplification 98.7%

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

Alternative 3: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z - x\right) \cdot y\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{-94}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4400:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z x) y)))
   (if (<= y -1.65e-94) t_0 (if (<= y 4400.0) (- x (* x y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z - x) * y;
	double tmp;
	if (y <= -1.65e-94) {
		tmp = t_0;
	} else if (y <= 4400.0) {
		tmp = x - (x * y);
	} 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) * y
    if (y <= (-1.65d-94)) then
        tmp = t_0
    else if (y <= 4400.0d0) then
        tmp = x - (x * y)
    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) * y;
	double tmp;
	if (y <= -1.65e-94) {
		tmp = t_0;
	} else if (y <= 4400.0) {
		tmp = x - (x * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z - x) * y
	tmp = 0
	if y <= -1.65e-94:
		tmp = t_0
	elif y <= 4400.0:
		tmp = x - (x * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z - x) * y)
	tmp = 0.0
	if (y <= -1.65e-94)
		tmp = t_0;
	elseif (y <= 4400.0)
		tmp = Float64(x - Float64(x * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z - x) * y;
	tmp = 0.0;
	if (y <= -1.65e-94)
		tmp = t_0;
	elseif (y <= 4400.0)
		tmp = x - (x * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.65e-94], t$95$0, If[LessEqual[y, 4400.0], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6500000000000001e-94 or 4400 < y

   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. lower-*.f64 N/A

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

      2. lower--.f64 93.3

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

   5. Applied rewrites 93.3%

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

   if -1.6500000000000001e-94 < y < 4400

   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. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. distribute-lft-out-- N/A

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

      4. *-rgt-identity N/A

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

      5. lower--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 75.7

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

   5. Applied rewrites 75.7%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-94}:\\ \;\;\;\;\left(z - x\right) \cdot y\\ \mathbf{elif}\;y \leq 4400:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(z - x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-57}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.8e-57) (* z y) (if (<= z 6.4e-41) (* y (- x)) (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.8e-57) {
		tmp = z * y;
	} else if (z <= 6.4e-41) {
		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 (z <= (-4.8d-57)) then
        tmp = z * y
    else if (z <= 6.4d-41) 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 (z <= -4.8e-57) {
		tmp = z * y;
	} else if (z <= 6.4e-41) {
		tmp = y * -x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.8e-57:
		tmp = z * y
	elif z <= 6.4e-41:
		tmp = y * -x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.8e-57)
		tmp = Float64(z * y);
	elseif (z <= 6.4e-41)
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.8e-57)
		tmp = z * y;
	elseif (z <= 6.4e-41)
		tmp = y * -x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.8e-57], N[(z * y), $MachinePrecision], If[LessEqual[z, 6.4e-41], N[(y * (-x)), $MachinePrecision], N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.80000000000000012e-57 or 6.40000000000000024e-41 < 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. lower-*.f64 65.5

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

   5. Applied rewrites 65.5%

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

   if -4.80000000000000012e-57 < z < 6.40000000000000024e-41

   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. lower-*.f64 N/A

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

      2. lower--.f64 49.8

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

   5. Applied rewrites 49.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 46.2%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-57}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.3% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. lower-*.f64 N/A

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

   2. lower--.f64 64.3

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

5. Applied rewrites 64.3%

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

6. Final simplification 64.3%

   \[\leadsto \left(z - x\right) \cdot y \]
7. Add Preprocessing

Alternative 6: 42.3% 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. lower-*.f64 41.4

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

5. Applied rewrites 41.4%

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

6. Final simplification 41.4%

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

Reproduce

herbie shell --seed 2024221 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))