SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 4.9s

Alternatives: 7

Speedup: 1.0×

• 21.3% 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-def 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. Final simplification 100.0%

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

Alternative 2: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-96}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+36}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+90} \lor \neg \left(y \leq 5 \cdot 10^{+119}\right) \land y \leq 3 \cdot 10^{+226}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -9.5e+105)
     t_0
     (if (<= y -2.8e-96)
       (* y z)
       (if (<= y 7.8e-70)
         x
         (if (<= y 7.2e+36)
           (* y z)
           (if (or (<= y 2.05e+90) (and (not (<= y 5e+119)) (<= y 3e+226)))
             t_0
             (* y z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -9.5e+105) {
		tmp = t_0;
	} else if (y <= -2.8e-96) {
		tmp = y * z;
	} else if (y <= 7.8e-70) {
		tmp = x;
	} else if (y <= 7.2e+36) {
		tmp = y * z;
	} else if ((y <= 2.05e+90) || (!(y <= 5e+119) && (y <= 3e+226))) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = y * -x
    if (y <= (-9.5d+105)) then
        tmp = t_0
    else if (y <= (-2.8d-96)) then
        tmp = y * z
    else if (y <= 7.8d-70) then
        tmp = x
    else if (y <= 7.2d+36) then
        tmp = y * z
    else if ((y <= 2.05d+90) .or. (.not. (y <= 5d+119)) .and. (y <= 3d+226)) then
        tmp = t_0
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -9.5e+105) {
		tmp = t_0;
	} else if (y <= -2.8e-96) {
		tmp = y * z;
	} else if (y <= 7.8e-70) {
		tmp = x;
	} else if (y <= 7.2e+36) {
		tmp = y * z;
	} else if ((y <= 2.05e+90) || (!(y <= 5e+119) && (y <= 3e+226))) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -9.5e+105:
		tmp = t_0
	elif y <= -2.8e-96:
		tmp = y * z
	elif y <= 7.8e-70:
		tmp = x
	elif y <= 7.2e+36:
		tmp = y * z
	elif (y <= 2.05e+90) or (not (y <= 5e+119) and (y <= 3e+226)):
		tmp = t_0
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -9.5e+105)
		tmp = t_0;
	elseif (y <= -2.8e-96)
		tmp = Float64(y * z);
	elseif (y <= 7.8e-70)
		tmp = x;
	elseif (y <= 7.2e+36)
		tmp = Float64(y * z);
	elseif ((y <= 2.05e+90) || (!(y <= 5e+119) && (y <= 3e+226)))
		tmp = t_0;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -x;
	tmp = 0.0;
	if (y <= -9.5e+105)
		tmp = t_0;
	elseif (y <= -2.8e-96)
		tmp = y * z;
	elseif (y <= 7.8e-70)
		tmp = x;
	elseif (y <= 7.2e+36)
		tmp = y * z;
	elseif ((y <= 2.05e+90) || (~((y <= 5e+119)) && (y <= 3e+226)))
		tmp = t_0;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -9.5e+105], t$95$0, If[LessEqual[y, -2.8e-96], N[(y * z), $MachinePrecision], If[LessEqual[y, 7.8e-70], x, If[LessEqual[y, 7.2e+36], N[(y * z), $MachinePrecision], If[Or[LessEqual[y, 2.05e+90], And[N[Not[LessEqual[y, 5e+119]], $MachinePrecision], LessEqual[y, 3e+226]]], t$95$0, N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.4999999999999995e105 or 7.1999999999999995e36 < y < 2.05000000000000021e90 or 4.9999999999999999e119 < y < 2.99999999999999975e226

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 98.7%

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

      1. fma-def 100.0%

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

      2. +-commutative 100.0%

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

      3. metadata-eval 100.0%

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

      4. distribute-lft-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-*r* 100.0%

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

      8. mul-1-neg 100.0%

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

      9. *-commutative 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-neg-in 100.0%

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

      15. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. mul-1-neg 100.0%

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

      3. +-commutative 100.0%

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

      4. mul-1-neg 100.0%

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

      5. sub-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 72.1%

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

      1. mul-1-neg 72.1%

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

      2. distribute-rgt-neg-in 72.1%

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

   10. Simplified 72.1%

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

   if -9.4999999999999995e105 < y < -2.80000000000000015e-96 or 7.80000000000000038e-70 < y < 7.1999999999999995e36 or 2.05000000000000021e90 < y < 4.9999999999999999e119 or 2.99999999999999975e226 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 81.7%

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

   3. Taylor expanded in x around 0 68.9%

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

   if -2.80000000000000015e-96 < y < 7.80000000000000038e-70

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.3%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-96}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+36}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+90} \lor \neg \left(y \leq 5 \cdot 10^{+119}\right) \land y \leq 3 \cdot 10^{+226}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{-96} \lor \neg \left(y \leq 1.9 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.65e-96) (not (<= y 1.9e-19))) (* y (- z x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.65e-96) || !(y <= 1.9e-19)) {
		tmp = y * (z - x);
	} 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 <= (-2.65d-96)) .or. (.not. (y <= 1.9d-19))) then
        tmp = y * (z - x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.65e-96) || !(y <= 1.9e-19)) {
		tmp = y * (z - x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.65e-96) or not (y <= 1.9e-19):
		tmp = y * (z - x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.65e-96) || !(y <= 1.9e-19))
		tmp = Float64(y * Float64(z - x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.65e-96) || ~((y <= 1.9e-19)))
		tmp = y * (z - x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.65e-96], N[Not[LessEqual[y, 1.9e-19]], $MachinePrecision]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.6500000000000001e-96 or 1.9e-19 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 98.0%

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

      1. fma-def 99.3%

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

      2. +-commutative 99.3%

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

      3. metadata-eval 99.3%

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

      4. distribute-lft-in 99.3%

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

      5. metadata-eval 99.3%

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

      6. sub-neg 99.3%

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

      7. associate-*r* 99.3%

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

      8. mul-1-neg 99.3%

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

      9. *-commutative 99.3%

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

      10. distribute-rgt-neg-in 99.3%

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

      11. sub-neg 99.3%

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

      12. metadata-eval 99.3%

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

      13. +-commutative 99.3%

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

      14. distribute-neg-in 99.3%

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

      15. metadata-eval 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in y around -inf 94.7%

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

      1. associate-*r* 94.7%

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

      2. mul-1-neg 94.7%

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

      3. +-commutative 94.7%

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

      4. mul-1-neg 94.7%

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

      5. sub-neg 94.7%

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

   7. Simplified 94.7%

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

   8. Taylor expanded in x around 0 92.6%

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

      1. mul-1-neg 92.6%

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

      2. distribute-rgt-neg-in 92.6%

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

      3. distribute-lft-in 94.7%

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

      4. sub-neg 94.7%

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

   10. Simplified 94.7%

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

   if -2.6500000000000001e-96 < y < 1.9e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 72.6%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{-96} \lor \neg \left(y \leq 1.9 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2.3 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 2.3e-19))) (* y (- z x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 2.3e-19)) {
		tmp = y * (z - x);
	} 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 ((y <= (-1.0d0)) .or. (.not. (y <= 2.3d-19))) then
        tmp = y * (z - x)
    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 ((y <= -1.0) || !(y <= 2.3e-19)) {
		tmp = y * (z - x);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 2.3e-19):
		tmp = y * (z - x)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 2.3e-19))
		tmp = Float64(y * Float64(z - x));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 2.3e-19)))
		tmp = y * (z - x);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 2.3e-19]], $MachinePrecision]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 2.2999999999999998e-19 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 97.6%

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

      1. fma-def 99.2%

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

      2. +-commutative 99.2%

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

      3. metadata-eval 99.2%

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

      4. distribute-lft-in 99.2%

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

      5. metadata-eval 99.2%

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

      6. sub-neg 99.2%

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

      7. associate-*r* 99.2%

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

      8. mul-1-neg 99.2%

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

      9. *-commutative 99.2%

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

      10. distribute-rgt-neg-in 99.2%

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

      11. sub-neg 99.2%

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

      12. metadata-eval 99.2%

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

      13. +-commutative 99.2%

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

      14. distribute-neg-in 99.2%

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

      15. metadata-eval 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in y around -inf 99.5%

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

      1. associate-*r* 99.5%

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

      2. mul-1-neg 99.5%

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

      3. +-commutative 99.5%

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

      4. mul-1-neg 99.5%

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

      5. sub-neg 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in x around 0 97.1%

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

      1. mul-1-neg 97.1%

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

      2. distribute-rgt-neg-in 97.1%

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

      3. distribute-lft-in 99.5%

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

      4. sub-neg 99.5%

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

   10. Simplified 99.5%

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

   if -1 < y < 2.2999999999999998e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 98.6%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2.3 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 5: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-96}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.65e-96) (* y z) (if (<= y 4.7e-70) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e-96) {
		tmp = y * z;
	} else if (y <= 4.7e-70) {
		tmp = 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 <= (-1.65d-96)) then
        tmp = y * z
    else if (y <= 4.7d-70) then
        tmp = 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 <= -1.65e-96) {
		tmp = y * z;
	} else if (y <= 4.7e-70) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.65e-96:
		tmp = y * z
	elif y <= 4.7e-70:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.65e-96)
		tmp = Float64(y * z);
	elseif (y <= 4.7e-70)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.65e-96)
		tmp = y * z;
	elseif (y <= 4.7e-70)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.65e-96], N[(y * z), $MachinePrecision], If[LessEqual[y, 4.7e-70], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.64999999999999995e-96 or 4.6999999999999998e-70 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 58.1%

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

   3. Taylor expanded in x around 0 51.5%

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

   if -1.64999999999999995e-96 < y < 4.6999999999999998e-70

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.3%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-96}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

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. Final simplification 100.0%

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

Alternative 7: 36.7% 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. Taylor expanded in y around 0 34.9%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 34.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023194 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))