SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

Alternatives: 7

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-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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 61.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+228}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+50}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -600000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-18}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-102}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+61}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -1.2e+228)
     t_0
     (if (<= y -5.5e+50)
       (* y z)
       (if (<= y -600000.0)
         t_0
         (if (<= y -2.45e-18)
           (* y z)
           (if (<= y -3.2e-64)
             x
             (if (<= y -6.2e-102)
               (* y z)
               (if (<= y 2e-53) x (if (<= y 1.35e+61) (* y z) t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -1.2e+228) {
		tmp = t_0;
	} else if (y <= -5.5e+50) {
		tmp = y * z;
	} else if (y <= -600000.0) {
		tmp = t_0;
	} else if (y <= -2.45e-18) {
		tmp = y * z;
	} else if (y <= -3.2e-64) {
		tmp = x;
	} else if (y <= -6.2e-102) {
		tmp = y * z;
	} else if (y <= 2e-53) {
		tmp = x;
	} else if (y <= 1.35e+61) {
		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 <= (-1.2d+228)) then
        tmp = t_0
    else if (y <= (-5.5d+50)) then
        tmp = y * z
    else if (y <= (-600000.0d0)) then
        tmp = t_0
    else if (y <= (-2.45d-18)) then
        tmp = y * z
    else if (y <= (-3.2d-64)) then
        tmp = x
    else if (y <= (-6.2d-102)) then
        tmp = y * z
    else if (y <= 2d-53) then
        tmp = x
    else if (y <= 1.35d+61) 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 <= -1.2e+228) {
		tmp = t_0;
	} else if (y <= -5.5e+50) {
		tmp = y * z;
	} else if (y <= -600000.0) {
		tmp = t_0;
	} else if (y <= -2.45e-18) {
		tmp = y * z;
	} else if (y <= -3.2e-64) {
		tmp = x;
	} else if (y <= -6.2e-102) {
		tmp = y * z;
	} else if (y <= 2e-53) {
		tmp = x;
	} else if (y <= 1.35e+61) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -1.2e+228:
		tmp = t_0
	elif y <= -5.5e+50:
		tmp = y * z
	elif y <= -600000.0:
		tmp = t_0
	elif y <= -2.45e-18:
		tmp = y * z
	elif y <= -3.2e-64:
		tmp = x
	elif y <= -6.2e-102:
		tmp = y * z
	elif y <= 2e-53:
		tmp = x
	elif y <= 1.35e+61:
		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 <= -1.2e+228)
		tmp = t_0;
	elseif (y <= -5.5e+50)
		tmp = Float64(y * z);
	elseif (y <= -600000.0)
		tmp = t_0;
	elseif (y <= -2.45e-18)
		tmp = Float64(y * z);
	elseif (y <= -3.2e-64)
		tmp = x;
	elseif (y <= -6.2e-102)
		tmp = Float64(y * z);
	elseif (y <= 2e-53)
		tmp = x;
	elseif (y <= 1.35e+61)
		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 <= -1.2e+228)
		tmp = t_0;
	elseif (y <= -5.5e+50)
		tmp = y * z;
	elseif (y <= -600000.0)
		tmp = t_0;
	elseif (y <= -2.45e-18)
		tmp = y * z;
	elseif (y <= -3.2e-64)
		tmp = x;
	elseif (y <= -6.2e-102)
		tmp = y * z;
	elseif (y <= 2e-53)
		tmp = x;
	elseif (y <= 1.35e+61)
		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, -1.2e+228], t$95$0, If[LessEqual[y, -5.5e+50], N[(y * z), $MachinePrecision], If[LessEqual[y, -600000.0], t$95$0, If[LessEqual[y, -2.45e-18], N[(y * z), $MachinePrecision], If[LessEqual[y, -3.2e-64], x, If[LessEqual[y, -6.2e-102], N[(y * z), $MachinePrecision], If[LessEqual[y, 2e-53], x, If[LessEqual[y, 1.35e+61], N[(y * z), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.19999999999999994e228 or -5.4999999999999998e50 < y < -6e5 or 1.3500000000000001e61 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 71.7%

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

      1. mul-1-neg 71.7%

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

      2. unsub-neg 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in y around inf 70.3%

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

      1. associate-*r* 70.3%

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

      2. mul-1-neg 70.3%

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

   8. Simplified 70.3%

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

   if -1.19999999999999994e228 < y < -5.4999999999999998e50 or -6e5 < y < -2.4500000000000001e-18 or -3.19999999999999975e-64 < y < -6.20000000000000026e-102 or 2.00000000000000006e-53 < y < 1.3500000000000001e61

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 68.1%

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

   if -2.4500000000000001e-18 < y < -3.19999999999999975e-64 or -6.20000000000000026e-102 < y < 2.00000000000000006e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.4%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+228}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+50}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -600000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-18}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-102}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+61}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-20} \lor \neg \left(y \leq -4.8 \cdot 10^{-66}\right) \land \left(y \leq -4.3 \cdot 10^{-102} \lor \neg \left(y \leq 8 \cdot 10^{-43}\right)\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.05e-20)
         (and (not (<= y -4.8e-66)) (or (<= y -4.3e-102) (not (<= y 8e-43)))))
   (* y (- z x))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.05e-20) || (!(y <= -4.8e-66) && ((y <= -4.3e-102) || !(y <= 8e-43)))) {
		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 <= (-1.05d-20)) .or. (.not. (y <= (-4.8d-66))) .and. (y <= (-4.3d-102)) .or. (.not. (y <= 8d-43))) 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 <= -1.05e-20) || (!(y <= -4.8e-66) && ((y <= -4.3e-102) || !(y <= 8e-43)))) {
		tmp = y * (z - x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.05e-20) or (not (y <= -4.8e-66) and ((y <= -4.3e-102) or not (y <= 8e-43))):
		tmp = y * (z - x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.05e-20) || (!(y <= -4.8e-66) && ((y <= -4.3e-102) || !(y <= 8e-43))))
		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 <= -1.05e-20) || (~((y <= -4.8e-66)) && ((y <= -4.3e-102) || ~((y <= 8e-43)))))
		tmp = y * (z - x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.05e-20], And[N[Not[LessEqual[y, -4.8e-66]], $MachinePrecision], Or[LessEqual[y, -4.3e-102], N[Not[LessEqual[y, 8e-43]], $MachinePrecision]]]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.0499999999999999e-20 or -4.80000000000000052e-66 < y < -4.2999999999999997e-102 or 8.00000000000000062e-43 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 94.6%

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

   if -1.0499999999999999e-20 < y < -4.80000000000000052e-66 or -4.2999999999999997e-102 < y < 8.00000000000000062e-43

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.9%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-20} \lor \neg \left(y \leq -4.8 \cdot 10^{-66}\right) \land \left(y \leq -4.3 \cdot 10^{-102} \lor \neg \left(y \leq 8 \cdot 10^{-43}\right)\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-21} \lor \neg \left(y \leq -7.8 \cdot 10^{-58} \lor \neg \left(y \leq -6.2 \cdot 10^{-102}\right) \land y \leq 1.45 \cdot 10^{-53}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.6e-21)
         (not
          (or (<= y -7.8e-58) (and (not (<= y -6.2e-102)) (<= y 1.45e-53)))))
   (* y z)
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.6e-21) || !((y <= -7.8e-58) || (!(y <= -6.2e-102) && (y <= 1.45e-53)))) {
		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 <= (-1.6d-21)) .or. (.not. (y <= (-7.8d-58)) .or. (.not. (y <= (-6.2d-102))) .and. (y <= 1.45d-53))) 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 <= -1.6e-21) || !((y <= -7.8e-58) || (!(y <= -6.2e-102) && (y <= 1.45e-53)))) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.6e-21) or not ((y <= -7.8e-58) or (not (y <= -6.2e-102) and (y <= 1.45e-53))):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.6e-21) || !((y <= -7.8e-58) || (!(y <= -6.2e-102) && (y <= 1.45e-53))))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.6e-21) || ~(((y <= -7.8e-58) || (~((y <= -6.2e-102)) && (y <= 1.45e-53)))))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.6e-21], N[Not[Or[LessEqual[y, -7.8e-58], And[N[Not[LessEqual[y, -6.2e-102]], $MachinePrecision], LessEqual[y, 1.45e-53]]]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.6000000000000001e-21 or -7.79999999999999985e-58 < y < -6.20000000000000026e-102 or 1.4499999999999999e-53 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 50.0%

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

   if -1.6000000000000001e-21 < y < -7.79999999999999985e-58 or -6.20000000000000026e-102 < y < 1.4499999999999999e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.4%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-21} \lor \neg \left(y \leq -7.8 \cdot 10^{-58} \lor \neg \left(y \leq -6.2 \cdot 10^{-102}\right) \land y \leq 1.45 \cdot 10^{-53}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+47} \lor \neg \left(z \leq 10^{+83}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1e+47) (not (<= z 1e+83))) (* y z) (* x (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e+47) || !(z <= 1e+83)) {
		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 <= (-1d+47)) .or. (.not. (z <= 1d+83))) 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 <= -1e+47) || !(z <= 1e+83)) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1e+47) or not (z <= 1e+83):
		tmp = y * z
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1e+47) || !(z <= 1e+83))
		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 <= -1e+47) || ~((z <= 1e+83)))
		tmp = y * z;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1e+47], N[Not[LessEqual[z, 1e+83]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e47 or 1.00000000000000003e83 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 72.0%

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

   if -1e47 < z < 1.00000000000000003e83

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.7%

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

      1. mul-1-neg 83.7%

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

      2. unsub-neg 83.7%

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

   5. Simplified 83.7%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+47} \lor \neg \left(z \leq 10^{+83}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

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. Add Preprocessing

3. Final simplification 100.0%

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

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. Add Preprocessing

3. Taylor expanded in y around 0 40.0%

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

4. Final simplification 40.0%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024026 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))