SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.9s

Alternatives: 8

Speedup: 1.0×

• 20.3% 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-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. Final simplification 100.0%

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

Alternative 2: 59.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-47}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1650000 \lor \neg \left(y \leq 9 \cdot 10^{+117}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -1.0)
     t_0
     (if (<= y 2.4e-143)
       x
       (if (<= y 7.4e-47)
         (* y z)
         (if (<= y 1.15e-14)
           x
           (if (or (<= y 1650000.0) (not (<= y 9e+117))) (* 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 <= 2.4e-143) {
		tmp = x;
	} else if (y <= 7.4e-47) {
		tmp = y * z;
	} else if (y <= 1.15e-14) {
		tmp = x;
	} else if ((y <= 1650000.0) || !(y <= 9e+117)) {
		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 <= 2.4d-143) then
        tmp = x
    else if (y <= 7.4d-47) then
        tmp = y * z
    else if (y <= 1.15d-14) then
        tmp = x
    else if ((y <= 1650000.0d0) .or. (.not. (y <= 9d+117))) 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 <= 2.4e-143) {
		tmp = x;
	} else if (y <= 7.4e-47) {
		tmp = y * z;
	} else if (y <= 1.15e-14) {
		tmp = x;
	} else if ((y <= 1650000.0) || !(y <= 9e+117)) {
		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 <= 2.4e-143:
		tmp = x
	elif y <= 7.4e-47:
		tmp = y * z
	elif y <= 1.15e-14:
		tmp = x
	elif (y <= 1650000.0) or not (y <= 9e+117):
		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 <= 2.4e-143)
		tmp = x;
	elseif (y <= 7.4e-47)
		tmp = Float64(y * z);
	elseif (y <= 1.15e-14)
		tmp = x;
	elseif ((y <= 1650000.0) || !(y <= 9e+117))
		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 <= 2.4e-143)
		tmp = x;
	elseif (y <= 7.4e-47)
		tmp = y * z;
	elseif (y <= 1.15e-14)
		tmp = x;
	elseif ((y <= 1650000.0) || ~((y <= 9e+117)))
		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, 2.4e-143], x, If[LessEqual[y, 7.4e-47], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.15e-14], x, If[Or[LessEqual[y, 1650000.0], N[Not[LessEqual[y, 9e+117]], $MachinePrecision]], N[(y * z), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1.65e6 < y < 9e117

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 64.0%

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

      1. mul-1-neg 64.0%

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

      2. unsub-neg 64.0%

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

   5. Simplified 64.0%

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

      1. sub-neg 64.0%

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

      2. distribute-rgt-in 64.0%

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

      3. *-un-lft-identity 64.0%

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

      4. distribute-lft-neg-in 64.0%

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

      5. unsub-neg 64.0%

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

   7. Applied egg-rr 64.0%

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

   8. Taylor expanded in y around inf 62.3%

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

      1. associate-*r* 62.3%

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

      2. neg-mul-1 62.3%

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

      3. *-commutative 62.3%

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

   10. Simplified 62.3%

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

   if -1 < y < 2.3999999999999999e-143 or 7.4000000000000001e-47 < y < 1.14999999999999999e-14

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.4%

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

   if 2.3999999999999999e-143 < y < 7.4000000000000001e-47 or 1.14999999999999999e-14 < y < 1.65e6 or 9e117 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 78.1%

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

   4. Taylor expanded in z around inf 73.5%

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

   5. Taylor expanded in y around inf 64.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-47}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1650000 \lor \neg \left(y \leq 9 \cdot 10^{+117}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{-61} \lor \neg \left(x \leq 2 \cdot 10^{-52}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.52e-61) (not (<= x 2e-52))) (* x (- 1.0 y)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.52e-61) || !(x <= 2e-52)) {
		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 <= (-1.52d-61)) .or. (.not. (x <= 2d-52))) 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 <= -1.52e-61) || !(x <= 2e-52)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.52e-61) or not (x <= 2e-52):
		tmp = x * (1.0 - y)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.52e-61) || !(x <= 2e-52))
		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 <= -1.52e-61) || ~((x <= 2e-52)))
		tmp = x * (1.0 - y);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.52e-61], N[Not[LessEqual[x, 2e-52]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.52000000000000003e-61 or 2e-52 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.6%

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

      1. mul-1-neg 84.6%

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

      2. unsub-neg 84.6%

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

   5. Simplified 84.6%

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

   if -1.52000000000000003e-61 < x < 2e-52

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 92.6%

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

   4. Taylor expanded in z around inf 92.6%

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

   5. Taylor expanded in y around inf 79.2%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{-61} \lor \neg \left(x \leq 2 \cdot 10^{-52}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+28} \lor \neg \left(x \leq 9.5 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.5e+28) (not (<= x 9.5e-8))) (* x (- 1.0 y)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.5e+28) || !(x <= 9.5e-8)) {
		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 <= (-2.5d+28)) .or. (.not. (x <= 9.5d-8))) 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 <= -2.5e+28) || !(x <= 9.5e-8)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.5e+28) or not (x <= 9.5e-8):
		tmp = x * (1.0 - y)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.5e+28) || !(x <= 9.5e-8))
		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 <= -2.5e+28) || ~((x <= 9.5e-8)))
		tmp = x * (1.0 - y);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.5e+28], N[Not[LessEqual[x, 9.5e-8]], $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 < -2.49999999999999979e28 or 9.50000000000000036e-8 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.0%

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

      1. mul-1-neg 88.0%

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

      2. unsub-neg 88.0%

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

   5. Simplified 88.0%

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

   if -2.49999999999999979e28 < x < 9.50000000000000036e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 91.6%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+28} \lor \neg \left(x \leq 9.5 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+28} \lor \neg \left(x \leq 1.05 \cdot 10^{-7}\right):\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.5e+28) (not (<= x 1.05e-7))) (- x (* y x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.5e+28) || !(x <= 1.05e-7)) {
		tmp = x - (y * 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 ((x <= (-2.5d+28)) .or. (.not. (x <= 1.05d-7))) then
        tmp = x - (y * 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 ((x <= -2.5e+28) || !(x <= 1.05e-7)) {
		tmp = x - (y * x);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.5e+28) or not (x <= 1.05e-7):
		tmp = x - (y * x)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.5e+28) || !(x <= 1.05e-7))
		tmp = Float64(x - Float64(y * x));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.5e+28) || ~((x <= 1.05e-7)))
		tmp = x - (y * x);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.5e+28], N[Not[LessEqual[x, 1.05e-7]], $MachinePrecision]], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.49999999999999979e28 or 1.05e-7 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.0%

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

      1. mul-1-neg 88.0%

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

      2. unsub-neg 88.0%

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

   5. Simplified 88.0%

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

      1. sub-neg 88.0%

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

      2. distribute-rgt-in 88.0%

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

      3. *-un-lft-identity 88.0%

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

      4. distribute-lft-neg-in 88.0%

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

      5. unsub-neg 88.0%

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

   7. Applied egg-rr 88.0%

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

   if -2.49999999999999979e28 < x < 1.05e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 91.6%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+28} \lor \neg \left(x \leq 1.05 \cdot 10^{-7}\right):\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-20} \lor \neg \left(z \leq 2.5 \cdot 10^{+18}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3e-20) (not (<= z 2.5e+18))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e-20) || !(z <= 2.5e+18)) {
		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 ((z <= (-3d-20)) .or. (.not. (z <= 2.5d+18))) 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 ((z <= -3e-20) || !(z <= 2.5e+18)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3e-20) or not (z <= 2.5e+18):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3e-20) || !(z <= 2.5e+18))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3e-20) || ~((z <= 2.5e+18)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3e-20], N[Not[LessEqual[z, 2.5e+18]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000029e-20 or 2.5e18 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 88.0%

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

   4. Taylor expanded in z around inf 88.0%

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

   5. Taylor expanded in y around inf 71.4%

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

   if -3.00000000000000029e-20 < z < 2.5e18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 50.5%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-20} \lor \neg \left(z \leq 2.5 \cdot 10^{+18}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 8: 37.0% 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 34.5%

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

4. Final simplification 34.5%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024076 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))