SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.8s

Alternatives: 8

Speedup: 1.0×

• 20.8% 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

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

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. +-commutative N/A

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

   2. *-commutative N/A

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

   3. fma-define N/A

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

   4. fma-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\left(z - x\right), \color{blue}{y}, x\right) \]

   5. --lowering--.f64 100.0%

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{\_.f64}\left(z, x\right), y, x\right) \]

4. Applied egg-rr 100.0%

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

Alternative 2: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z - x\right) \cdot y\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-12}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z x) y)))
   (if (<= y -1.0) t_0 (if (<= y 5.2e-12) (+ 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 <= 5.2e-12) {
		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 <= 5.2d-12) 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 <= 5.2e-12) {
		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 <= 5.2e-12:
		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 <= 5.2e-12)
		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 <= 5.2e-12)
		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, 5.2e-12], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 5.19999999999999965e-12 < 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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(z - x\right)}\right) \]

      2. --lowering--.f64 96.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{x}\right)\right) \]

   5. Simplified 96.8%

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

   if -1 < y < 5.19999999999999965e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 98.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 98.9%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\left(z - x\right) \cdot y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-12}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(z - x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z - x\right) \cdot y\\ \mathbf{if}\;y \leq -38000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z x) y)))
   (if (<= y -38000000.0) t_0 (if (<= y 1.6e-82) (* x (- 1.0 y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z - x) * y;
	double tmp;
	if (y <= -38000000.0) {
		tmp = t_0;
	} else if (y <= 1.6e-82) {
		tmp = x * (1.0 - 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 <= (-38000000.0d0)) then
        tmp = t_0
    else if (y <= 1.6d-82) then
        tmp = x * (1.0d0 - 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 <= -38000000.0) {
		tmp = t_0;
	} else if (y <= 1.6e-82) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z - x) * y
	tmp = 0
	if y <= -38000000.0:
		tmp = t_0
	elif y <= 1.6e-82:
		tmp = x * (1.0 - 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 <= -38000000.0)
		tmp = t_0;
	elseif (y <= 1.6e-82)
		tmp = Float64(x * Float64(1.0 - 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 <= -38000000.0)
		tmp = t_0;
	elseif (y <= 1.6e-82)
		tmp = x * (1.0 - 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, -38000000.0], t$95$0, If[LessEqual[y, 1.6e-82], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8e7 or 1.6000000000000001e-82 < 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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(z - x\right)}\right) \]

      2. --lowering--.f64 92.4%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{x}\right)\right) \]

   5. Simplified 92.4%

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

   if -3.8e7 < y < 1.6000000000000001e-82

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot y\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{y}\right)\right) \]

      4. --lowering--.f64 83.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   5. Simplified 83.2%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -38000000:\\ \;\;\;\;\left(z - x\right) \cdot y\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{-30}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-241}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 y))))
   (if (<= x -8.5e-30) t_0 (if (<= x 9.2e-241) (* z y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - y);
	double tmp;
	if (x <= -8.5e-30) {
		tmp = t_0;
	} else if (x <= 9.2e-241) {
		tmp = 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 = x * (1.0d0 - y)
    if (x <= (-8.5d-30)) then
        tmp = t_0
    else if (x <= 9.2d-241) then
        tmp = 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 = x * (1.0 - y);
	double tmp;
	if (x <= -8.5e-30) {
		tmp = t_0;
	} else if (x <= 9.2e-241) {
		tmp = z * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - y)
	tmp = 0
	if x <= -8.5e-30:
		tmp = t_0
	elif x <= 9.2e-241:
		tmp = z * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (x <= -8.5e-30)
		tmp = t_0;
	elseif (x <= 9.2e-241)
		tmp = Float64(z * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - y);
	tmp = 0.0;
	if (x <= -8.5e-30)
		tmp = t_0;
	elseif (x <= 9.2e-241)
		tmp = z * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e-30], t$95$0, If[LessEqual[x, 9.2e-241], N[(z * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.49999999999999931e-30 or 9.1999999999999997e-241 < 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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot y\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{y}\right)\right) \]

      4. --lowering--.f64 80.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   5. Simplified 80.8%

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

   if -8.49999999999999931e-30 < x < 9.1999999999999997e-241

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 70.5%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{z}\right) \]

   5. Simplified 70.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-241}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 100.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. flip-- N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\frac{z \cdot z - x \cdot x}{\color{blue}{z + x}}\right)\right)\right) \]

   2. difference-of-squares N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\frac{\left(z + x\right) \cdot \left(z - x\right)}{\color{blue}{z} + x}\right)\right)\right) \]

   3. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(z + x\right) \cdot \color{blue}{\frac{z - x}{z + x}}\right)\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\left(z + x\right), \color{blue}{\left(\frac{z - x}{z + x}\right)}\right)\right)\right) \]

   5. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\left(x + z\right), \left(\frac{\color{blue}{z - x}}{z + x}\right)\right)\right)\right) \]

   6. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, z\right), \left(\frac{\color{blue}{z - x}}{z + x}\right)\right)\right)\right) \]

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, z\right), \mathsf{/.f64}\left(\left(z - x\right), \color{blue}{\left(z + x\right)}\right)\right)\right)\right) \]

   8. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, x\right), \left(\color{blue}{z} + x\right)\right)\right)\right)\right) \]

   9. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, x\right), \left(x + \color{blue}{z}\right)\right)\right)\right)\right) \]

   10. +-lowering-+.f64 100.0%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, x\right), \mathsf{+.f64}\left(x, \color{blue}{z}\right)\right)\right)\right)\right) \]

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

   \[\leadsto x + y \cdot \left(\left(z + x\right) \cdot \frac{z - x}{z + x}\right) \]
6. Add Preprocessing

Alternative 6: 60.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-23}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.2e-23) (* z y) (if (<= y 1.6e-82) x (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.2e-23) {
		tmp = z * y;
	} else if (y <= 1.6e-82) {
		tmp = 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 <= (-3.2d-23)) then
        tmp = z * y
    else if (y <= 1.6d-82) then
        tmp = 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 <= -3.2e-23) {
		tmp = z * y;
	} else if (y <= 1.6e-82) {
		tmp = x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.2e-23:
		tmp = z * y
	elif y <= 1.6e-82:
		tmp = x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.2e-23)
		tmp = Float64(z * y);
	elseif (y <= 1.6e-82)
		tmp = x;
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.2e-23)
		tmp = z * y;
	elseif (y <= 1.6e-82)
		tmp = x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.2e-23], N[(z * y), $MachinePrecision], If[LessEqual[y, 1.6e-82], x, N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999976e-23 or 1.6000000000000001e-82 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 50.8%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{z}\right) \]

   5. Simplified 50.8%

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

   if -3.19999999999999976e-23 < y < 1.6000000000000001e-82

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 85.1%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-23}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 8: 35.9% 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

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

5. Simplified 39.4%

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

Reproduce

herbie shell --seed 2024140 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))