SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 4.5s

Alternatives: 8

Speedup: 1.0×

• 21.2% 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: 60.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-76}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+68} \lor \neg \left(y \leq 6.6 \cdot 10^{+150} \lor \neg \left(y \leq 4 \cdot 10^{+255}\right) \land y \leq 1.25 \cdot 10^{+278}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -1.0)
     t_0
     (if (<= y 1e-105)
       x
       (if (<= y 6.5e-76)
         (* y z)
         (if (<= y 6.5e-19)
           x
           (if (or (<= y 2e+68)
                   (not
                    (or (<= y 6.6e+150)
                        (and (not (<= y 4e+255)) (<= y 1.25e+278)))))
             (* y z)
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 1e-105) {
		tmp = x;
	} else if (y <= 6.5e-76) {
		tmp = y * z;
	} else if (y <= 6.5e-19) {
		tmp = x;
	} else if ((y <= 2e+68) || !((y <= 6.6e+150) || (!(y <= 4e+255) && (y <= 1.25e+278)))) {
		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 = y * -x
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 1d-105) then
        tmp = x
    else if (y <= 6.5d-76) then
        tmp = y * z
    else if (y <= 6.5d-19) then
        tmp = x
    else if ((y <= 2d+68) .or. (.not. (y <= 6.6d+150) .or. (.not. (y <= 4d+255)) .and. (y <= 1.25d+278))) 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 = y * -x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 1e-105) {
		tmp = x;
	} else if (y <= 6.5e-76) {
		tmp = y * z;
	} else if (y <= 6.5e-19) {
		tmp = x;
	} else if ((y <= 2e+68) || !((y <= 6.6e+150) || (!(y <= 4e+255) && (y <= 1.25e+278)))) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 1e-105:
		tmp = x
	elif y <= 6.5e-76:
		tmp = y * z
	elif y <= 6.5e-19:
		tmp = x
	elif (y <= 2e+68) or not ((y <= 6.6e+150) or (not (y <= 4e+255) and (y <= 1.25e+278))):
		tmp = y * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 1e-105)
		tmp = x;
	elseif (y <= 6.5e-76)
		tmp = Float64(y * z);
	elseif (y <= 6.5e-19)
		tmp = x;
	elseif ((y <= 2e+68) || !((y <= 6.6e+150) || (!(y <= 4e+255) && (y <= 1.25e+278))))
		tmp = Float64(y * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -x;
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 1e-105)
		tmp = x;
	elseif (y <= 6.5e-76)
		tmp = y * z;
	elseif (y <= 6.5e-19)
		tmp = x;
	elseif ((y <= 2e+68) || ~(((y <= 6.6e+150) || (~((y <= 4e+255)) && (y <= 1.25e+278)))))
		tmp = y * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 1e-105], x, If[LessEqual[y, 6.5e-76], N[(y * z), $MachinePrecision], If[LessEqual[y, 6.5e-19], x, If[Or[LessEqual[y, 2e+68], N[Not[Or[LessEqual[y, 6.6e+150], And[N[Not[LessEqual[y, 4e+255]], $MachinePrecision], LessEqual[y, 1.25e+278]]]], $MachinePrecision]], N[(y * z), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1.99999999999999991e68 < y < 6.59999999999999962e150 or 3.99999999999999995e255 < y < 1.25000000000000007e278

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 98.6%

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

   3. Taylor expanded in z around 0 63.4%

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

      1. mul-1-neg 63.4%

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

      2. distribute-lft-neg-out 63.4%

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

      3. *-commutative 63.4%

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

   5. Simplified 63.4%

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

   if -1 < y < 9.99999999999999965e-106 or 6.5e-76 < y < 6.5000000000000001e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.0%

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

   if 9.99999999999999965e-106 < y < 6.5e-76 or 6.5000000000000001e-19 < y < 1.99999999999999991e68 or 6.59999999999999962e150 < y < 3.99999999999999995e255 or 1.25000000000000007e278 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 74.4%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-76}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+68} \lor \neg \left(y \leq 6.6 \cdot 10^{+150} \lor \neg \left(y \leq 4 \cdot 10^{+255}\right) \land y \leq 1.25 \cdot 10^{+278}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+71} \lor \neg \left(z \leq -3.8 \cdot 10^{+31}\right) \land \left(z \leq -1.2 \cdot 10^{-14} \lor \neg \left(z \leq 2.1 \cdot 10^{+38}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.9e+71)
         (and (not (<= z -3.8e+31)) (or (<= z -1.2e-14) (not (<= z 2.1e+38)))))
   (* y z)
   (* x (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9e+71) || (!(z <= -3.8e+31) && ((z <= -1.2e-14) || !(z <= 2.1e+38)))) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - 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 <= (-1.9d+71)) .or. (.not. (z <= (-3.8d+31))) .and. (z <= (-1.2d-14)) .or. (.not. (z <= 2.1d+38))) then
        tmp = y * z
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9e+71) || (!(z <= -3.8e+31) && ((z <= -1.2e-14) || !(z <= 2.1e+38)))) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.9e+71) or (not (z <= -3.8e+31) and ((z <= -1.2e-14) or not (z <= 2.1e+38))):
		tmp = y * z
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.9e+71) || (!(z <= -3.8e+31) && ((z <= -1.2e-14) || !(z <= 2.1e+38))))
		tmp = Float64(y * z);
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.9e+71) || (~((z <= -3.8e+31)) && ((z <= -1.2e-14) || ~((z <= 2.1e+38)))))
		tmp = y * z;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.9e+71], And[N[Not[LessEqual[z, -3.8e+31]], $MachinePrecision], Or[LessEqual[z, -1.2e-14], N[Not[LessEqual[z, 2.1e+38]], $MachinePrecision]]]], N[(y * z), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e71 or -3.8000000000000001e31 < z < -1.2e-14 or 2.1e38 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.5%

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

   if -1.9e71 < z < -3.8000000000000001e31 or -1.2e-14 < z < 2.1e38

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 86.5%

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

      1. mul-1-neg 86.5%

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

      2. unsub-neg 86.5%

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

   4. Simplified 86.5%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+71} \lor \neg \left(z \leq -3.8 \cdot 10^{+31}\right) \land \left(z \leq -1.2 \cdot 10^{-14} \lor \neg \left(z \leq 2.1 \cdot 10^{+38}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 4: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{-48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-75}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z x))))
   (if (<= y -4.1e-48)
     t_0
     (if (<= y 3.1e-105)
       x
       (if (<= y 6.8e-75) (* y z) (if (<= y 4.6e-15) (* x (- 1.0 y)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z - x);
	double tmp;
	if (y <= -4.1e-48) {
		tmp = t_0;
	} else if (y <= 3.1e-105) {
		tmp = x;
	} else if (y <= 6.8e-75) {
		tmp = y * z;
	} else if (y <= 4.6e-15) {
		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 = y * (z - x)
    if (y <= (-4.1d-48)) then
        tmp = t_0
    else if (y <= 3.1d-105) then
        tmp = x
    else if (y <= 6.8d-75) then
        tmp = y * z
    else if (y <= 4.6d-15) 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 = y * (z - x);
	double tmp;
	if (y <= -4.1e-48) {
		tmp = t_0;
	} else if (y <= 3.1e-105) {
		tmp = x;
	} else if (y <= 6.8e-75) {
		tmp = y * z;
	} else if (y <= 4.6e-15) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z - x)
	tmp = 0
	if y <= -4.1e-48:
		tmp = t_0
	elif y <= 3.1e-105:
		tmp = x
	elif y <= 6.8e-75:
		tmp = y * z
	elif y <= 4.6e-15:
		tmp = x * (1.0 - y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z - x))
	tmp = 0.0
	if (y <= -4.1e-48)
		tmp = t_0;
	elseif (y <= 3.1e-105)
		tmp = x;
	elseif (y <= 6.8e-75)
		tmp = Float64(y * z);
	elseif (y <= 4.6e-15)
		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 = y * (z - x);
	tmp = 0.0;
	if (y <= -4.1e-48)
		tmp = t_0;
	elseif (y <= 3.1e-105)
		tmp = x;
	elseif (y <= 6.8e-75)
		tmp = y * z;
	elseif (y <= 4.6e-15)
		tmp = x * (1.0 - y);
	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, -4.1e-48], t$95$0, If[LessEqual[y, 3.1e-105], x, If[LessEqual[y, 6.8e-75], N[(y * z), $MachinePrecision], If[LessEqual[y, 4.6e-15], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.10000000000000014e-48 or 4.59999999999999981e-15 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 97.4%

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

   if -4.10000000000000014e-48 < y < 3.10000000000000014e-105

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.7%

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

   if 3.10000000000000014e-105 < y < 6.8000000000000003e-75

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 88.3%

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

   if 6.8000000000000003e-75 < y < 4.59999999999999981e-15

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 91.3%

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

      1. mul-1-neg 91.3%

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

      2. unsub-neg 91.3%

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

   4. Simplified 91.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-75}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \end{array} \]

Alternative 5: 60.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-14} \lor \neg \left(y \leq 9.5 \cdot 10^{-114} \lor \neg \left(y \leq 6.2 \cdot 10^{-76}\right) \land y \leq 1.25 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.7e-14)
         (not (or (<= y 9.5e-114) (and (not (<= y 6.2e-76)) (<= y 1.25e-17)))))
   (* y z)
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.7e-14) || !((y <= 9.5e-114) || (!(y <= 6.2e-76) && (y <= 1.25e-17)))) {
		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 <= (-3.7d-14)) .or. (.not. (y <= 9.5d-114) .or. (.not. (y <= 6.2d-76)) .and. (y <= 1.25d-17))) 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 <= -3.7e-14) || !((y <= 9.5e-114) || (!(y <= 6.2e-76) && (y <= 1.25e-17)))) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.7e-14) or not ((y <= 9.5e-114) or (not (y <= 6.2e-76) and (y <= 1.25e-17))):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.7e-14) || !((y <= 9.5e-114) || (!(y <= 6.2e-76) && (y <= 1.25e-17))))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.7e-14) || ~(((y <= 9.5e-114) || (~((y <= 6.2e-76)) && (y <= 1.25e-17)))))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.7e-14], N[Not[Or[LessEqual[y, 9.5e-114], And[N[Not[LessEqual[y, 6.2e-76]], $MachinePrecision], LessEqual[y, 1.25e-17]]]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.70000000000000001e-14 or 9.49999999999999958e-114 < y < 6.19999999999999939e-76 or 1.25e-17 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 52.6%

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

   if -3.70000000000000001e-14 < y < 9.49999999999999958e-114 or 6.19999999999999939e-76 < y < 1.25e-17

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.9%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-14} \lor \neg \left(y \leq 9.5 \cdot 10^{-114} \lor \neg \left(y \leq 6.2 \cdot 10^{-76}\right) \land y \leq 1.25 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 4.4 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 4.4e-13))) (* y (- z x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 4.4e-13)) {
		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 <= 4.4d-13))) 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 <= 4.4e-13)) {
		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 <= 4.4e-13):
		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 <= 4.4e-13))
		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 <= 4.4e-13)))
		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, 4.4e-13]], $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 4.39999999999999993e-13 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 98.5%

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

   if -1 < y < 4.39999999999999993e-13

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 100.0%

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

      3. fma-def 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around inf 99.5%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 4.4 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

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

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

3. Final simplification 34.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023331 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))