SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.2s

Alternatives: 7

Speedup: 1.0×

• 20.0% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+94} \lor \neg \left(x \leq 1.15 \cdot 10^{+90}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.6e+94) (not (<= x 1.15e+90))) (* x (- 1.0 y)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.6e+94) || !(x <= 1.15e+90)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = x + (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 ((x <= (-2.6d+94)) .or. (.not. (x <= 1.15d+90))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.6e+94) || !(x <= 1.15e+90)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.6e+94) or not (x <= 1.15e+90):
		tmp = x * (1.0 - y)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.6e+94) || !(x <= 1.15e+90))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.6e+94) || ~((x <= 1.15e+90)))
		tmp = x * (1.0 - y);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.6e+94], N[Not[LessEqual[x, 1.15e+90]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5999999999999999e94 or 1.15e90 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 93.8%

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

      1. mul-1-neg 93.8%

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

      2. unsub-neg 93.8%

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

   5. Simplified 93.8%

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

   if -2.5999999999999999e94 < x < 1.15e90

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 89.1%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+94} \lor \neg \left(x \leq 1.15 \cdot 10^{+90}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-54} \lor \neg \left(x \leq 5.5 \cdot 10^{-113}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.2e-54) (not (<= x 5.5e-113))) (* x (- 1.0 y)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.2e-54) || !(x <= 5.5e-113)) {
		tmp = x * (1.0 - y);
	} 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 ((x <= (-1.2d-54)) .or. (.not. (x <= 5.5d-113))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.2e-54) || !(x <= 5.5e-113)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.2e-54) or not (x <= 5.5e-113):
		tmp = x * (1.0 - y)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.2e-54) || !(x <= 5.5e-113))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.2e-54) || ~((x <= 5.5e-113)))
		tmp = x * (1.0 - y);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.2e-54], N[Not[LessEqual[x, 5.5e-113]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.20000000000000007e-54 or 5.50000000000000053e-113 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.4%

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

      1. mul-1-neg 78.4%

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

      2. unsub-neg 78.4%

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

   5. Simplified 78.4%

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

   if -1.20000000000000007e-54 < x < 5.50000000000000053e-113

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 94.8%

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

   4. Taylor expanded in z around inf 94.8%

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

   5. Taylor expanded in y around inf 74.2%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-54} \lor \neg \left(x \leq 5.5 \cdot 10^{-113}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+91}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9e+92)
   (* x (- 1.0 y))
   (if (<= x 1.8e+91) (+ x (* y z)) (- x (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9e+92) {
		tmp = x * (1.0 - y);
	} else if (x <= 1.8e+91) {
		tmp = x + (y * z);
	} else {
		tmp = x - (y * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-9d+92)) then
        tmp = x * (1.0d0 - y)
    else if (x <= 1.8d+91) then
        tmp = x + (y * z)
    else
        tmp = x - (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -9e+92) {
		tmp = x * (1.0 - y);
	} else if (x <= 1.8e+91) {
		tmp = x + (y * z);
	} else {
		tmp = x - (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9e+92:
		tmp = x * (1.0 - y)
	elif x <= 1.8e+91:
		tmp = x + (y * z)
	else:
		tmp = x - (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9e+92)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (x <= 1.8e+91)
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x - Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9e+92)
		tmp = x * (1.0 - y);
	elseif (x <= 1.8e+91)
		tmp = x + (y * z);
	else
		tmp = x - (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9e+92], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e+91], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.9999999999999998e92

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 93.5%

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

      1. mul-1-neg 93.5%

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

      2. unsub-neg 93.5%

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

   5. Simplified 93.5%

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

   if -8.9999999999999998e92 < x < 1.8e91

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 89.1%

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

   if 1.8e91 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 94.0%

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

      1. mul-1-neg 94.0%

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

      2. unsub-neg 94.0%

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

   5. Simplified 94.0%

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

      1. sub-neg 94.0%

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

      2. distribute-rgt-in 94.1%

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

      3. *-un-lft-identity 94.1%

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

      4. distribute-lft-neg-in 94.1%

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

      5. unsub-neg 94.1%

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

   7. Applied egg-rr 94.1%

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

Alternative 5: 62.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-51} \lor \neg \left(y \leq 7.5 \cdot 10^{-32}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.8e-51) (not (<= y 7.5e-32))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e-51) || !(y <= 7.5e-32)) {
		tmp = y * z;
	} else {
		tmp = 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 <= (-4.8d-51)) .or. (.not. (y <= 7.5d-32))) then
        tmp = y * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e-51) || !(y <= 7.5e-32)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.8e-51) or not (y <= 7.5e-32):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.8e-51) || !(y <= 7.5e-32))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.8e-51) || ~((y <= 7.5e-32)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.8e-51], N[Not[LessEqual[y, 7.5e-32]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.8e-51 or 7.49999999999999953e-32 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 64.3%

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

   4. Taylor expanded in z around inf 67.2%

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

   5. Taylor expanded in y around inf 59.5%

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

   if -4.8e-51 < y < 7.49999999999999953e-32

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.9%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-51} \lor \neg \left(y \leq 7.5 \cdot 10^{-32}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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]

Derivation

1. Initial program 100.0%

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

Alternative 7: 38.4% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0 38.7%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024163 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))