SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.5s

Alternatives: 7

Speedup: 1.0×

• 20.5% 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: 61.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+242}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+196}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+124}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-50}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+89} \lor \neg \left(y \leq 1.2 \cdot 10^{+161}\right) \land y \leq 7.5 \cdot 10^{+278}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= y -9.5e+242)
     t_0
     (if (<= y -3.5e+196)
       (* y z)
       (if (<= y -1.6e+124)
         t_0
         (if (<= y -4e-50)
           (* y z)
           (if (<= y 1.65e-24)
             x
             (if (or (<= y 1.06e+89)
                     (and (not (<= y 1.2e+161)) (<= y 7.5e+278)))
               (* y z)
               t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -y;
	double tmp;
	if (y <= -9.5e+242) {
		tmp = t_0;
	} else if (y <= -3.5e+196) {
		tmp = y * z;
	} else if (y <= -1.6e+124) {
		tmp = t_0;
	} else if (y <= -4e-50) {
		tmp = y * z;
	} else if (y <= 1.65e-24) {
		tmp = x;
	} else if ((y <= 1.06e+89) || (!(y <= 1.2e+161) && (y <= 7.5e+278))) {
		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 = x * -y
    if (y <= (-9.5d+242)) then
        tmp = t_0
    else if (y <= (-3.5d+196)) then
        tmp = y * z
    else if (y <= (-1.6d+124)) then
        tmp = t_0
    else if (y <= (-4d-50)) then
        tmp = y * z
    else if (y <= 1.65d-24) then
        tmp = x
    else if ((y <= 1.06d+89) .or. (.not. (y <= 1.2d+161)) .and. (y <= 7.5d+278)) 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 = x * -y;
	double tmp;
	if (y <= -9.5e+242) {
		tmp = t_0;
	} else if (y <= -3.5e+196) {
		tmp = y * z;
	} else if (y <= -1.6e+124) {
		tmp = t_0;
	} else if (y <= -4e-50) {
		tmp = y * z;
	} else if (y <= 1.65e-24) {
		tmp = x;
	} else if ((y <= 1.06e+89) || (!(y <= 1.2e+161) && (y <= 7.5e+278))) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -y
	tmp = 0
	if y <= -9.5e+242:
		tmp = t_0
	elif y <= -3.5e+196:
		tmp = y * z
	elif y <= -1.6e+124:
		tmp = t_0
	elif y <= -4e-50:
		tmp = y * z
	elif y <= 1.65e-24:
		tmp = x
	elif (y <= 1.06e+89) or (not (y <= 1.2e+161) and (y <= 7.5e+278)):
		tmp = y * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -9.5e+242)
		tmp = t_0;
	elseif (y <= -3.5e+196)
		tmp = Float64(y * z);
	elseif (y <= -1.6e+124)
		tmp = t_0;
	elseif (y <= -4e-50)
		tmp = Float64(y * z);
	elseif (y <= 1.65e-24)
		tmp = x;
	elseif ((y <= 1.06e+89) || (!(y <= 1.2e+161) && (y <= 7.5e+278)))
		tmp = Float64(y * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -y;
	tmp = 0.0;
	if (y <= -9.5e+242)
		tmp = t_0;
	elseif (y <= -3.5e+196)
		tmp = y * z;
	elseif (y <= -1.6e+124)
		tmp = t_0;
	elseif (y <= -4e-50)
		tmp = y * z;
	elseif (y <= 1.65e-24)
		tmp = x;
	elseif ((y <= 1.06e+89) || (~((y <= 1.2e+161)) && (y <= 7.5e+278)))
		tmp = y * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -9.5e+242], t$95$0, If[LessEqual[y, -3.5e+196], N[(y * z), $MachinePrecision], If[LessEqual[y, -1.6e+124], t$95$0, If[LessEqual[y, -4e-50], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.65e-24], x, If[Or[LessEqual[y, 1.06e+89], And[N[Not[LessEqual[y, 1.2e+161]], $MachinePrecision], LessEqual[y, 7.5e+278]]], N[(y * z), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.49999999999999995e242 or -3.4999999999999998e196 < y < -1.59999999999999996e124 or 1.05999999999999997e89 < y < 1.1999999999999999e161 or 7.49999999999999949e278 < y

   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 81.0%

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

      1. associate-*r* 81.0%

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

      2. mul-1-neg 81.0%

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

   5. Simplified 81.0%

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

   if -9.49999999999999995e242 < y < -3.4999999999999998e196 or -1.59999999999999996e124 < y < -4.00000000000000003e-50 or 1.64999999999999992e-24 < y < 1.05999999999999997e89 or 1.1999999999999999e161 < y < 7.49999999999999949e278

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 73.6%

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

   if -4.00000000000000003e-50 < y < 1.64999999999999992e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+242}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+196}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+124}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-50}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+89} \lor \neg \left(y \leq 1.2 \cdot 10^{+161}\right) \land y \leq 7.5 \cdot 10^{+278}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-49} \lor \neg \left(y \leq 8.8 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.6e-49) (not (<= y 8.8e-16))) (* y (- z x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.6e-49) || !(y <= 8.8e-16)) {
		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 <= (-4.6d-49)) .or. (.not. (y <= 8.8d-16))) 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 <= -4.6e-49) || !(y <= 8.8e-16)) {
		tmp = y * (z - x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.6e-49) or not (y <= 8.8e-16):
		tmp = y * (z - x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.6e-49) || !(y <= 8.8e-16))
		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 <= -4.6e-49) || ~((y <= 8.8e-16)))
		tmp = y * (z - x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.6e-49], N[Not[LessEqual[y, 8.8e-16]], $MachinePrecision]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.5999999999999998e-49 or 8.80000000000000001e-16 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 98.7%

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

   if -4.5999999999999998e-49 < y < 8.80000000000000001e-16

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.6%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-49} \lor \neg \left(y \leq 8.8 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -48000000000 \lor \neg \left(y \leq 7.5 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -48000000000.0) (not (<= y 7.5e-12)))
   (* y (- z x))
   (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -48000000000.0) || !(y <= 7.5e-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 <= (-48000000000.0d0)) .or. (.not. (y <= 7.5d-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 <= -48000000000.0) || !(y <= 7.5e-12)) {
		tmp = y * (z - x);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -48000000000.0) or not (y <= 7.5e-12):
		tmp = y * (z - x)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -48000000000.0) || !(y <= 7.5e-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 <= -48000000000.0) || ~((y <= 7.5e-12)))
		tmp = y * (z - x);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -48000000000.0], N[Not[LessEqual[y, 7.5e-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 < -4.8e10 or 7.5e-12 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 100.0%

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

   if -4.8e10 < y < 7.5e-12

   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/ 59.9%

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

      3. +-commutative 59.9%

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

   3. Applied egg-rr 59.9%

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

      1. associate-/l* 59.9%

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

      2. difference-of-squares 60.2%

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

      3. +-commutative 60.2%

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

      4. associate-/r* 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around inf 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -48000000000 \lor \neg \left(y \leq 7.5 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 5: 62.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-48}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.25e-48) (* y z) (if (<= y 1.05e-14) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.25e-48) {
		tmp = y * z;
	} else if (y <= 1.05e-14) {
		tmp = x;
	} 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 (y <= (-2.25d-48)) then
        tmp = y * z
    else if (y <= 1.05d-14) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.25e-48) {
		tmp = y * z;
	} else if (y <= 1.05e-14) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.25e-48:
		tmp = y * z
	elif y <= 1.05e-14:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.25e-48)
		tmp = Float64(y * z);
	elseif (y <= 1.05e-14)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.25e-48)
		tmp = y * z;
	elseif (y <= 1.05e-14)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.25e-48], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.05e-14], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.24999999999999994e-48 or 1.0499999999999999e-14 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 58.1%

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

   if -2.24999999999999994e-48 < y < 1.0499999999999999e-14

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.6%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-48}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

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: 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. Taylor expanded in y around 0 38.5%

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

3. Final simplification 38.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023173 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))