SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 4.5s

Alternatives: 7

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

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

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: 57.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-147}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+136}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -3.2e+57)
     t_0
     (if (<= y -1.02e-147)
       (* y z)
       (if (<= y 3.3e-90) x (if (<= y 3.1e+136) (* y z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -3.2e+57) {
		tmp = t_0;
	} else if (y <= -1.02e-147) {
		tmp = y * z;
	} else if (y <= 3.3e-90) {
		tmp = x;
	} else if (y <= 3.1e+136) {
		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 <= (-3.2d+57)) then
        tmp = t_0
    else if (y <= (-1.02d-147)) then
        tmp = y * z
    else if (y <= 3.3d-90) then
        tmp = x
    else if (y <= 3.1d+136) 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 <= -3.2e+57) {
		tmp = t_0;
	} else if (y <= -1.02e-147) {
		tmp = y * z;
	} else if (y <= 3.3e-90) {
		tmp = x;
	} else if (y <= 3.1e+136) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -3.2e+57:
		tmp = t_0
	elif y <= -1.02e-147:
		tmp = y * z
	elif y <= 3.3e-90:
		tmp = x
	elif y <= 3.1e+136:
		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 <= -3.2e+57)
		tmp = t_0;
	elseif (y <= -1.02e-147)
		tmp = Float64(y * z);
	elseif (y <= 3.3e-90)
		tmp = x;
	elseif (y <= 3.1e+136)
		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 <= -3.2e+57)
		tmp = t_0;
	elseif (y <= -1.02e-147)
		tmp = y * z;
	elseif (y <= 3.3e-90)
		tmp = x;
	elseif (y <= 3.1e+136)
		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, -3.2e+57], t$95$0, If[LessEqual[y, -1.02e-147], N[(y * z), $MachinePrecision], If[LessEqual[y, 3.3e-90], x, If[LessEqual[y, 3.1e+136], N[(y * z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.20000000000000029e57 or 3.09999999999999983e136 < y

   1. Initial program 100.0%

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

      1. flip-- 93.1%

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

      2. associate-*r/ 82.3%

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

   3. Applied egg-rr 82.3%

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

      1. associate-/l* 92.9%

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

      2. +-commutative 92.9%

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

   5. Simplified 92.9%

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

   6. Taylor expanded in z around inf 95.3%

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

   7. Taylor expanded in y around inf 100.0%

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

   8. Taylor expanded in z around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. distribute-rgt-neg-out 62.1%

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

   10. Simplified 62.1%

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

   if -3.20000000000000029e57 < y < -1.02e-147 or 3.3e-90 < y < 3.09999999999999983e136

   1. Initial program 100.0%

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

      1. flip-- 59.9%

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

      2. associate-*r/ 50.6%

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

   3. Applied egg-rr 50.6%

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

      1. associate-/l* 59.8%

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

      2. +-commutative 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in z around inf 100.0%

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

   7. Taylor expanded in z around inf 62.0%

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

   if -1.02e-147 < y < 3.3e-90

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 70.4%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-147}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+136}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 81.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-147} \lor \neg \left(y \leq 3.7 \cdot 10^{-90}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.02e-147) (not (<= y 3.7e-90))) (* y (- z x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.02e-147) || !(y <= 3.7e-90)) {
		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 <= (-1.02d-147)) .or. (.not. (y <= 3.7d-90))) 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 <= -1.02e-147) || !(y <= 3.7e-90)) {
		tmp = y * (z - x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.02e-147) or not (y <= 3.7e-90):
		tmp = y * (z - x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.02e-147) || !(y <= 3.7e-90))
		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 <= -1.02e-147) || ~((y <= 3.7e-90)))
		tmp = y * (z - x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.02e-147], N[Not[LessEqual[y, 3.7e-90]], $MachinePrecision]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.02e-147 or 3.70000000000000018e-90 < y

   1. Initial program 100.0%

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

      1. flip-- 76.9%

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

      2. associate-*r/ 66.9%

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

   3. Applied egg-rr 66.9%

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

      1. associate-/l* 76.7%

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

      2. +-commutative 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in z around inf 97.6%

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

   7. Taylor expanded in y around inf 87.8%

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

   if -1.02e-147 < y < 3.70000000000000018e-90

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 70.4%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-147} \lor \neg \left(y \leq 3.7 \cdot 10^{-90}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.8\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.8))) (* y (- z x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.8)) {
		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 <= 0.8d0))) 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 <= 0.8)) {
		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 <= 0.8):
		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 <= 0.8))
		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 <= 0.8)))
		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, 0.8]], $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 0.80000000000000004 < y

   1. Initial program 100.0%

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

      1. flip-- 89.9%

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

      2. associate-*r/ 76.6%

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

   3. Applied egg-rr 76.6%

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

      1. associate-/l* 89.7%

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

      2. +-commutative 89.7%

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

   5. Simplified 89.7%

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

   6. Taylor expanded in z around inf 96.6%

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

   7. Taylor expanded in y around inf 99.2%

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

   if -1 < y < 0.80000000000000004

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.1%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.8\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 5: 52.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+187}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+25}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.6e+187) x (if (<= x 1.7e+25) (* y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.6e+187) {
		tmp = x;
	} else if (x <= 1.7e+25) {
		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 (x <= (-5.6d+187)) then
        tmp = x
    else if (x <= 1.7d+25) 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 (x <= -5.6e+187) {
		tmp = x;
	} else if (x <= 1.7e+25) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.6e+187:
		tmp = x
	elif x <= 1.7e+25:
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.6e+187)
		tmp = x;
	elseif (x <= 1.7e+25)
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.6e+187)
		tmp = x;
	elseif (x <= 1.7e+25)
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.6e+187], x, If[LessEqual[x, 1.7e+25], N[(y * z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.59999999999999979e187 or 1.69999999999999992e25 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 51.6%

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

   if -5.59999999999999979e187 < x < 1.69999999999999992e25

   1. Initial program 100.0%

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

      1. flip-- 75.5%

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

      2. associate-*r/ 66.7%

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

   3. Applied egg-rr 66.7%

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

      1. associate-/l* 75.3%

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

      2. +-commutative 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in z around inf 100.0%

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

   7. Taylor expanded in z around inf 63.8%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+187}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+25}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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: 36.4% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around 0 33.2%

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

3. Final simplification 33.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023182 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))