SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.0s

Alternatives: 8

Speedup: 1.0×

• 20.6% 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: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.72 \cdot 10^{+267}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-23} \lor \neg \left(y \leq -2.7 \cdot 10^{-49}\right) \land \left(y \leq -2.06 \cdot 10^{-97} \lor \neg \left(y \leq 6.5 \cdot 10^{-52}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.72e+267)
   (* y z)
   (if (<= y -1e+63)
     (* y (- x))
     (if (or (<= y -1.18e-23)
             (and (not (<= y -2.7e-49))
                  (or (<= y -2.06e-97) (not (<= y 6.5e-52)))))
       (* y z)
       x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.72e+267) {
		tmp = y * z;
	} else if (y <= -1e+63) {
		tmp = y * -x;
	} else if ((y <= -1.18e-23) || (!(y <= -2.7e-49) && ((y <= -2.06e-97) || !(y <= 6.5e-52)))) {
		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 <= (-1.72d+267)) then
        tmp = y * z
    else if (y <= (-1d+63)) then
        tmp = y * -x
    else if ((y <= (-1.18d-23)) .or. (.not. (y <= (-2.7d-49))) .and. (y <= (-2.06d-97)) .or. (.not. (y <= 6.5d-52))) 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 <= -1.72e+267) {
		tmp = y * z;
	} else if (y <= -1e+63) {
		tmp = y * -x;
	} else if ((y <= -1.18e-23) || (!(y <= -2.7e-49) && ((y <= -2.06e-97) || !(y <= 6.5e-52)))) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.72e+267:
		tmp = y * z
	elif y <= -1e+63:
		tmp = y * -x
	elif (y <= -1.18e-23) or (not (y <= -2.7e-49) and ((y <= -2.06e-97) or not (y <= 6.5e-52))):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.72e+267)
		tmp = Float64(y * z);
	elseif (y <= -1e+63)
		tmp = Float64(y * Float64(-x));
	elseif ((y <= -1.18e-23) || (!(y <= -2.7e-49) && ((y <= -2.06e-97) || !(y <= 6.5e-52))))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.72e+267)
		tmp = y * z;
	elseif (y <= -1e+63)
		tmp = y * -x;
	elseif ((y <= -1.18e-23) || (~((y <= -2.7e-49)) && ((y <= -2.06e-97) || ~((y <= 6.5e-52)))))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.72e+267], N[(y * z), $MachinePrecision], If[LessEqual[y, -1e+63], N[(y * (-x)), $MachinePrecision], If[Or[LessEqual[y, -1.18e-23], And[N[Not[LessEqual[y, -2.7e-49]], $MachinePrecision], Or[LessEqual[y, -2.06e-97], N[Not[LessEqual[y, 6.5e-52]], $MachinePrecision]]]], N[(y * z), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7200000000000001e267 or -1.00000000000000006e63 < y < -1.18e-23 or -2.7e-49 < y < -2.0600000000000001e-97 or 6.5e-52 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 65.8%

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

   if -1.7200000000000001e267 < y < -1.00000000000000006e63

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 100.0%

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

   3. Taylor expanded in z around 0 61.1%

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

      1. mul-1-neg 61.1%

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

      2. distribute-lft-neg-out 61.1%

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

      3. *-commutative 61.1%

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

   5. Simplified 61.1%

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

   if -1.18e-23 < y < -2.7e-49 or -2.0600000000000001e-97 < y < 6.5e-52

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.6%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.72 \cdot 10^{+267}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-23} \lor \neg \left(y \leq -2.7 \cdot 10^{-49}\right) \land \left(y \leq -2.06 \cdot 10^{-97} \lor \neg \left(y \leq 6.5 \cdot 10^{-52}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 83.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -1.48 \cdot 10^{-24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-97}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z x))))
   (if (<= y -1.48e-24)
     t_0
     (if (<= y -2.85e-49)
       x
       (if (<= y -5.5e-97) (* y z) (if (<= y 1.18e-51) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z - x);
	double tmp;
	if (y <= -1.48e-24) {
		tmp = t_0;
	} else if (y <= -2.85e-49) {
		tmp = x;
	} else if (y <= -5.5e-97) {
		tmp = y * z;
	} else if (y <= 1.18e-51) {
		tmp = x;
	} 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 <= (-1.48d-24)) then
        tmp = t_0
    else if (y <= (-2.85d-49)) then
        tmp = x
    else if (y <= (-5.5d-97)) then
        tmp = y * z
    else if (y <= 1.18d-51) then
        tmp = x
    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 <= -1.48e-24) {
		tmp = t_0;
	} else if (y <= -2.85e-49) {
		tmp = x;
	} else if (y <= -5.5e-97) {
		tmp = y * z;
	} else if (y <= 1.18e-51) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z - x)
	tmp = 0
	if y <= -1.48e-24:
		tmp = t_0
	elif y <= -2.85e-49:
		tmp = x
	elif y <= -5.5e-97:
		tmp = y * z
	elif y <= 1.18e-51:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z - x))
	tmp = 0.0
	if (y <= -1.48e-24)
		tmp = t_0;
	elseif (y <= -2.85e-49)
		tmp = x;
	elseif (y <= -5.5e-97)
		tmp = Float64(y * z);
	elseif (y <= 1.18e-51)
		tmp = x;
	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 <= -1.48e-24)
		tmp = t_0;
	elseif (y <= -2.85e-49)
		tmp = x;
	elseif (y <= -5.5e-97)
		tmp = y * z;
	elseif (y <= 1.18e-51)
		tmp = x;
	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, -1.48e-24], t$95$0, If[LessEqual[y, -2.85e-49], x, If[LessEqual[y, -5.5e-97], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.18e-51], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.48000000000000003e-24 or 1.18000000000000004e-51 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 96.9%

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

   if -1.48000000000000003e-24 < y < -2.8500000000000002e-49 or -5.49999999999999948e-97 < y < 1.18000000000000004e-51

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.6%

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

   if -2.8500000000000002e-49 < y < -5.49999999999999948e-97

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 87.1%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.48 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-97}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \end{array} \]

Alternative 4: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-24} \lor \neg \left(y \leq -5.2 \cdot 10^{-46}\right) \land \left(y \leq -5.5 \cdot 10^{-97} \lor \neg \left(y \leq 1.25 \cdot 10^{-51}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.3e-24)
         (and (not (<= y -5.2e-46))
              (or (<= y -5.5e-97) (not (<= y 1.25e-51)))))
   (* y z)
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.3e-24) || (!(y <= -5.2e-46) && ((y <= -5.5e-97) || !(y <= 1.25e-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 <= (-3.3d-24)) .or. (.not. (y <= (-5.2d-46))) .and. (y <= (-5.5d-97)) .or. (.not. (y <= 1.25d-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 <= -3.3e-24) || (!(y <= -5.2e-46) && ((y <= -5.5e-97) || !(y <= 1.25e-51)))) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.3e-24) or (not (y <= -5.2e-46) and ((y <= -5.5e-97) or not (y <= 1.25e-51))):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.3e-24) || (!(y <= -5.2e-46) && ((y <= -5.5e-97) || !(y <= 1.25e-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 <= -3.3e-24) || (~((y <= -5.2e-46)) && ((y <= -5.5e-97) || ~((y <= 1.25e-51)))))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.3e-24], And[N[Not[LessEqual[y, -5.2e-46]], $MachinePrecision], Or[LessEqual[y, -5.5e-97], N[Not[LessEqual[y, 1.25e-51]], $MachinePrecision]]]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.29999999999999984e-24 or -5.2000000000000004e-46 < y < -5.49999999999999948e-97 or 1.25000000000000001e-51 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 57.4%

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

   if -3.29999999999999984e-24 < y < -5.2000000000000004e-46 or -5.49999999999999948e-97 < y < 1.25000000000000001e-51

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.6%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-24} \lor \neg \left(y \leq -5.2 \cdot 10^{-46}\right) \land \left(y \leq -5.5 \cdot 10^{-97} \lor \neg \left(y \leq 1.25 \cdot 10^{-51}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-12} \lor \neg \left(x \leq 1.06 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.65e-12) (not (<= x 1.06e-32))) (* x (- 1.0 y)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.65e-12) || !(x <= 1.06e-32)) {
		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 <= (-1.65d-12)) .or. (.not. (x <= 1.06d-32))) 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 <= -1.65e-12) || !(x <= 1.06e-32)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.65e-12) or not (x <= 1.06e-32):
		tmp = x * (1.0 - y)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.65e-12) || !(x <= 1.06e-32))
		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 <= -1.65e-12) || ~((x <= 1.06e-32)))
		tmp = x * (1.0 - y);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.65e-12], N[Not[LessEqual[x, 1.06e-32]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65e-12 or 1.05999999999999994e-32 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 82.8%

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

      1. mul-1-neg 82.8%

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

      2. unsub-neg 82.8%

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

   4. Simplified 82.8%

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

   if -1.65e-12 < x < 1.05999999999999994e-32

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 69.8%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-12} \lor \neg \left(x \leq 1.06 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 6: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 3.4 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 3.4e-12))) (* y (- z x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 3.4e-12)) {
		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 <= 3.4d-12))) 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 <= 3.4e-12)) {
		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 <= 3.4e-12):
		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 <= 3.4e-12))
		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 <= 3.4e-12)))
		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, 3.4e-12]], $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 3.4000000000000001e-12 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.5%

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

   if -1 < y < 3.4000000000000001e-12

   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. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around inf 99.4%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 3.4 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

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: 36.0% 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. Taylor expanded in y around 0 35.4%

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

3. Final simplification 35.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023332 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))