SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

Alternatives: 8

Speedup: 1.0×

• 20.9% 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: 60.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-64}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-111}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+68}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.65e-64)
   (* y z)
   (if (<= y -2.35e-90)
     x
     (if (<= y -4.1e-111)
       (* y z)
       (if (<= y 1.18e-49) x (if (<= y 4.8e+68) (* y z) (* y (- x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e-64) {
		tmp = y * z;
	} else if (y <= -2.35e-90) {
		tmp = x;
	} else if (y <= -4.1e-111) {
		tmp = y * z;
	} else if (y <= 1.18e-49) {
		tmp = x;
	} else if (y <= 4.8e+68) {
		tmp = y * z;
	} else {
		tmp = y * -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 <= (-1.65d-64)) then
        tmp = y * z
    else if (y <= (-2.35d-90)) then
        tmp = x
    else if (y <= (-4.1d-111)) then
        tmp = y * z
    else if (y <= 1.18d-49) then
        tmp = x
    else if (y <= 4.8d+68) then
        tmp = y * z
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e-64) {
		tmp = y * z;
	} else if (y <= -2.35e-90) {
		tmp = x;
	} else if (y <= -4.1e-111) {
		tmp = y * z;
	} else if (y <= 1.18e-49) {
		tmp = x;
	} else if (y <= 4.8e+68) {
		tmp = y * z;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.65e-64:
		tmp = y * z
	elif y <= -2.35e-90:
		tmp = x
	elif y <= -4.1e-111:
		tmp = y * z
	elif y <= 1.18e-49:
		tmp = x
	elif y <= 4.8e+68:
		tmp = y * z
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.65e-64)
		tmp = Float64(y * z);
	elseif (y <= -2.35e-90)
		tmp = x;
	elseif (y <= -4.1e-111)
		tmp = Float64(y * z);
	elseif (y <= 1.18e-49)
		tmp = x;
	elseif (y <= 4.8e+68)
		tmp = Float64(y * z);
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.65e-64)
		tmp = y * z;
	elseif (y <= -2.35e-90)
		tmp = x;
	elseif (y <= -4.1e-111)
		tmp = y * z;
	elseif (y <= 1.18e-49)
		tmp = x;
	elseif (y <= 4.8e+68)
		tmp = y * z;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.65e-64], N[(y * z), $MachinePrecision], If[LessEqual[y, -2.35e-90], x, If[LessEqual[y, -4.1e-111], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.18e-49], x, If[LessEqual[y, 4.8e+68], N[(y * z), $MachinePrecision], N[(y * (-x)), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65e-64 or -2.35e-90 < y < -4.09999999999999968e-111 or 1.18e-49 < y < 4.80000000000000016e68

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 75.0%

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

   4. Taylor expanded in y around inf 74.2%

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

   5. Taylor expanded in y around inf 65.1%

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

   if -1.65e-64 < y < -2.35e-90 or -4.09999999999999968e-111 < y < 1.18e-49

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.8%

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

   if 4.80000000000000016e68 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in z around inf 100.0%

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

   5. Taylor expanded in z around 0 57.5%

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

      1. mul-1-neg 57.5%

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

      2. distribute-lft-neg-out 57.5%

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

      3. *-commutative 57.5%

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

   7. Simplified 57.5%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-64}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-111}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+68}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{-65}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-112} \lor \neg \left(y \leq 1.55 \cdot 10^{-50}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z x))))
   (if (<= y -6.8e-65)
     t_0
     (if (<= y -3.6e-88)
       (* x (- 1.0 y))
       (if (or (<= y -3.7e-112) (not (<= y 1.55e-50))) t_0 x)))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z - x);
	double tmp;
	if (y <= -6.8e-65) {
		tmp = t_0;
	} else if (y <= -3.6e-88) {
		tmp = x * (1.0 - y);
	} else if ((y <= -3.7e-112) || !(y <= 1.55e-50)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = y * (z - x)
    if (y <= (-6.8d-65)) then
        tmp = t_0
    else if (y <= (-3.6d-88)) then
        tmp = x * (1.0d0 - y)
    else if ((y <= (-3.7d-112)) .or. (.not. (y <= 1.55d-50))) then
        tmp = t_0
    else
        tmp = x
    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 <= -6.8e-65) {
		tmp = t_0;
	} else if (y <= -3.6e-88) {
		tmp = x * (1.0 - y);
	} else if ((y <= -3.7e-112) || !(y <= 1.55e-50)) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z - x)
	tmp = 0
	if y <= -6.8e-65:
		tmp = t_0
	elif y <= -3.6e-88:
		tmp = x * (1.0 - y)
	elif (y <= -3.7e-112) or not (y <= 1.55e-50):
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z - x))
	tmp = 0.0
	if (y <= -6.8e-65)
		tmp = t_0;
	elseif (y <= -3.6e-88)
		tmp = Float64(x * Float64(1.0 - y));
	elseif ((y <= -3.7e-112) || !(y <= 1.55e-50))
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z - x);
	tmp = 0.0;
	if (y <= -6.8e-65)
		tmp = t_0;
	elseif (y <= -3.6e-88)
		tmp = x * (1.0 - y);
	elseif ((y <= -3.7e-112) || ~((y <= 1.55e-50)))
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e-65], t$95$0, If[LessEqual[y, -3.6e-88], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.7e-112], N[Not[LessEqual[y, 1.55e-50]], $MachinePrecision]], t$95$0, x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.79999999999999973e-65 or -3.5999999999999999e-88 < y < -3.6999999999999998e-112 or 1.5500000000000001e-50 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.4%

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

   4. Taylor expanded in z around inf 93.1%

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

   if -6.79999999999999973e-65 < y < -3.5999999999999999e-88

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.1%

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

      1. mul-1-neg 86.1%

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

      2. unsub-neg 86.1%

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

   5. Simplified 86.1%

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

   if -3.6999999999999998e-112 < y < 1.5500000000000001e-50

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.2%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-112} \lor \neg \left(y \leq 1.55 \cdot 10^{-50}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-64} \lor \neg \left(y \leq -5.5 \cdot 10^{-89} \lor \neg \left(y \leq -8.4 \cdot 10^{-111}\right) \land y \leq 8 \cdot 10^{-51}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.35e-64)
         (not (or (<= y -5.5e-89) (and (not (<= y -8.4e-111)) (<= y 8e-51)))))
   (* y z)
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.35e-64) || !((y <= -5.5e-89) || (!(y <= -8.4e-111) && (y <= 8e-51)))) {
		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 <= (-1.35d-64)) .or. (.not. (y <= (-5.5d-89)) .or. (.not. (y <= (-8.4d-111))) .and. (y <= 8d-51))) 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 <= -1.35e-64) || !((y <= -5.5e-89) || (!(y <= -8.4e-111) && (y <= 8e-51)))) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.35e-64) or not ((y <= -5.5e-89) or (not (y <= -8.4e-111) and (y <= 8e-51))):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.35e-64) || !((y <= -5.5e-89) || (!(y <= -8.4e-111) && (y <= 8e-51))))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.35e-64) || ~(((y <= -5.5e-89) || (~((y <= -8.4e-111)) && (y <= 8e-51)))))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.35e-64], N[Not[Or[LessEqual[y, -5.5e-89], And[N[Not[LessEqual[y, -8.4e-111]], $MachinePrecision], LessEqual[y, 8e-51]]]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.34999999999999993e-64 or -5.50000000000000012e-89 < y < -8.3999999999999995e-111 or 8.0000000000000001e-51 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 65.4%

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

   4. Taylor expanded in y around inf 64.9%

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

   5. Taylor expanded in y around inf 58.9%

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

   if -1.34999999999999993e-64 < y < -5.50000000000000012e-89 or -8.3999999999999995e-111 < y < 8.0000000000000001e-51

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.8%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-64} \lor \neg \left(y \leq -5.5 \cdot 10^{-89} \lor \neg \left(y \leq -8.4 \cdot 10^{-111}\right) \land y \leq 8 \cdot 10^{-51}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -450000000000 \lor \neg \left(z \leq 4.8 \cdot 10^{+69}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -450000000000.0) (not (<= z 4.8e+69))) (* y z) (* x (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -450000000000.0) || !(z <= 4.8e+69)) {
		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 <= (-450000000000.0d0)) .or. (.not. (z <= 4.8d+69))) 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 <= -450000000000.0) || !(z <= 4.8e+69)) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -450000000000.0) or not (z <= 4.8e+69):
		tmp = y * z
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -450000000000.0) || !(z <= 4.8e+69))
		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 <= -450000000000.0) || ~((z <= 4.8e+69)))
		tmp = y * z;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -450000000000.0], N[Not[LessEqual[z, 4.8e+69]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e11 or 4.8000000000000003e69 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 96.2%

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

   4. Taylor expanded in y around inf 92.9%

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

   5. Taylor expanded in y around inf 77.6%

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

   if -4.5e11 < z < 4.8000000000000003e69

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.7%

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

      1. mul-1-neg 82.7%

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

      2. unsub-neg 82.7%

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

   5. Simplified 82.7%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -450000000000 \lor \neg \left(z \leq 4.8 \cdot 10^{+69}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1400000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1400000.0) (not (<= y 1.0))) (* y (- z x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1400000.0) || !(y <= 1.0)) {
		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 <= (-1400000.0d0)) .or. (.not. (y <= 1.0d0))) 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 <= -1400000.0) || !(y <= 1.0)) {
		tmp = y * (z - x);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1400000.0) or not (y <= 1.0):
		tmp = y * (z - x)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1400000.0) || !(y <= 1.0))
		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 <= -1400000.0) || ~((y <= 1.0)))
		tmp = y * (z - x);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1400000.0], N[Not[LessEqual[y, 1.0]], $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 < -1.4e6 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in z around inf 99.4%

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

   if -1.4e6 < y < 1

   1. Initial program 100.0%

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

   3. 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 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1400000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
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: 36.6% 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 37.6%

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

4. Final simplification 37.6%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024095 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))