SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.2s

Alternatives: 7

Speedup: 1.0×

• 20.3% 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: 61.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+253}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+111}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+22} \lor \neg \left(y \leq 3.5 \cdot 10^{+177}\right) \land \left(y \leq 1.1 \cdot 10^{+186} \lor \neg \left(y \leq 4.1 \cdot 10^{+207}\right) \land y \leq 5.4 \cdot 10^{+223}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= y -3.9e+253)
     t_0
     (if (<= y -8.5e+111)
       (* y z)
       (if (<= y -1.0)
         t_0
         (if (<= y 3.3e-24)
           x
           (if (or (<= y 9e+22)
                   (and (not (<= y 3.5e+177))
                        (or (<= y 1.1e+186)
                            (and (not (<= y 4.1e+207)) (<= y 5.4e+223)))))
             (* y z)
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -y;
	double tmp;
	if (y <= -3.9e+253) {
		tmp = t_0;
	} else if (y <= -8.5e+111) {
		tmp = y * z;
	} else if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 3.3e-24) {
		tmp = x;
	} else if ((y <= 9e+22) || (!(y <= 3.5e+177) && ((y <= 1.1e+186) || (!(y <= 4.1e+207) && (y <= 5.4e+223))))) {
		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 <= (-3.9d+253)) then
        tmp = t_0
    else if (y <= (-8.5d+111)) then
        tmp = y * z
    else if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 3.3d-24) then
        tmp = x
    else if ((y <= 9d+22) .or. (.not. (y <= 3.5d+177)) .and. (y <= 1.1d+186) .or. (.not. (y <= 4.1d+207)) .and. (y <= 5.4d+223)) 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 <= -3.9e+253) {
		tmp = t_0;
	} else if (y <= -8.5e+111) {
		tmp = y * z;
	} else if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 3.3e-24) {
		tmp = x;
	} else if ((y <= 9e+22) || (!(y <= 3.5e+177) && ((y <= 1.1e+186) || (!(y <= 4.1e+207) && (y <= 5.4e+223))))) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -y
	tmp = 0
	if y <= -3.9e+253:
		tmp = t_0
	elif y <= -8.5e+111:
		tmp = y * z
	elif y <= -1.0:
		tmp = t_0
	elif y <= 3.3e-24:
		tmp = x
	elif (y <= 9e+22) or (not (y <= 3.5e+177) and ((y <= 1.1e+186) or (not (y <= 4.1e+207) and (y <= 5.4e+223)))):
		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 <= -3.9e+253)
		tmp = t_0;
	elseif (y <= -8.5e+111)
		tmp = Float64(y * z);
	elseif (y <= -1.0)
		tmp = t_0;
	elseif (y <= 3.3e-24)
		tmp = x;
	elseif ((y <= 9e+22) || (!(y <= 3.5e+177) && ((y <= 1.1e+186) || (!(y <= 4.1e+207) && (y <= 5.4e+223)))))
		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 <= -3.9e+253)
		tmp = t_0;
	elseif (y <= -8.5e+111)
		tmp = y * z;
	elseif (y <= -1.0)
		tmp = t_0;
	elseif (y <= 3.3e-24)
		tmp = x;
	elseif ((y <= 9e+22) || (~((y <= 3.5e+177)) && ((y <= 1.1e+186) || (~((y <= 4.1e+207)) && (y <= 5.4e+223)))))
		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, -3.9e+253], t$95$0, If[LessEqual[y, -8.5e+111], N[(y * z), $MachinePrecision], If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 3.3e-24], x, If[Or[LessEqual[y, 9e+22], And[N[Not[LessEqual[y, 3.5e+177]], $MachinePrecision], Or[LessEqual[y, 1.1e+186], And[N[Not[LessEqual[y, 4.1e+207]], $MachinePrecision], LessEqual[y, 5.4e+223]]]]], N[(y * z), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9000000000000001e253 or -8.49999999999999983e111 < y < -1 or 8.9999999999999996e22 < y < 3.49999999999999991e177 or 1.0999999999999999e186 < y < 4.1e207 or 5.4000000000000001e223 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 73.1%

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

      1. +-commutative 73.1%

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

      2. distribute-rgt1-in 73.1%

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

      3. mul-1-neg 73.1%

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

      4. cancel-sign-sub-inv 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in y around inf 71.9%

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

      1. mul-1-neg 71.9%

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

      2. distribute-rgt-neg-in 71.9%

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

   7. Simplified 71.9%

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

   if -3.9000000000000001e253 < y < -8.49999999999999983e111 or 3.29999999999999984e-24 < y < 8.9999999999999996e22 or 3.49999999999999991e177 < y < 1.0999999999999999e186 or 4.1e207 < y < 5.4000000000000001e223

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 73.9%

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

   3. Taylor expanded in x around 0 69.6%

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

   if -1 < y < 3.29999999999999984e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.1%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+111}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+22} \lor \neg \left(y \leq 3.5 \cdot 10^{+177}\right) \land \left(y \leq 1.1 \cdot 10^{+186} \lor \neg \left(y \leq 4.1 \cdot 10^{+207}\right) \land y \leq 5.4 \cdot 10^{+223}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 76.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ t_1 := x + y \cdot z\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+254}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+38}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+173} \lor \neg \left(y \leq 1.1 \cdot 10^{+186}\right) \land \left(y \leq 2.05 \cdot 10^{+207} \lor \neg \left(y \leq 4 \cdot 10^{+223}\right)\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y))) (t_1 (+ x (* y z))))
   (if (<= y -4.3e+254)
     t_0
     (if (<= y -2.8e+112)
       t_1
       (if (<= y -1.35e+38)
         t_0
         (if (<= y 6.4e+29)
           t_1
           (if (or (<= y 2.9e+173)
                   (and (not (<= y 1.1e+186))
                        (or (<= y 2.05e+207) (not (<= y 4e+223)))))
             t_0
             (* y z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -y;
	double t_1 = x + (y * z);
	double tmp;
	if (y <= -4.3e+254) {
		tmp = t_0;
	} else if (y <= -2.8e+112) {
		tmp = t_1;
	} else if (y <= -1.35e+38) {
		tmp = t_0;
	} else if (y <= 6.4e+29) {
		tmp = t_1;
	} else if ((y <= 2.9e+173) || (!(y <= 1.1e+186) && ((y <= 2.05e+207) || !(y <= 4e+223)))) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * -y
    t_1 = x + (y * z)
    if (y <= (-4.3d+254)) then
        tmp = t_0
    else if (y <= (-2.8d+112)) then
        tmp = t_1
    else if (y <= (-1.35d+38)) then
        tmp = t_0
    else if (y <= 6.4d+29) then
        tmp = t_1
    else if ((y <= 2.9d+173) .or. (.not. (y <= 1.1d+186)) .and. (y <= 2.05d+207) .or. (.not. (y <= 4d+223))) then
        tmp = t_0
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -y;
	double t_1 = x + (y * z);
	double tmp;
	if (y <= -4.3e+254) {
		tmp = t_0;
	} else if (y <= -2.8e+112) {
		tmp = t_1;
	} else if (y <= -1.35e+38) {
		tmp = t_0;
	} else if (y <= 6.4e+29) {
		tmp = t_1;
	} else if ((y <= 2.9e+173) || (!(y <= 1.1e+186) && ((y <= 2.05e+207) || !(y <= 4e+223)))) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -y
	t_1 = x + (y * z)
	tmp = 0
	if y <= -4.3e+254:
		tmp = t_0
	elif y <= -2.8e+112:
		tmp = t_1
	elif y <= -1.35e+38:
		tmp = t_0
	elif y <= 6.4e+29:
		tmp = t_1
	elif (y <= 2.9e+173) or (not (y <= 1.1e+186) and ((y <= 2.05e+207) or not (y <= 4e+223))):
		tmp = t_0
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-y))
	t_1 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (y <= -4.3e+254)
		tmp = t_0;
	elseif (y <= -2.8e+112)
		tmp = t_1;
	elseif (y <= -1.35e+38)
		tmp = t_0;
	elseif (y <= 6.4e+29)
		tmp = t_1;
	elseif ((y <= 2.9e+173) || (!(y <= 1.1e+186) && ((y <= 2.05e+207) || !(y <= 4e+223))))
		tmp = t_0;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -y;
	t_1 = x + (y * z);
	tmp = 0.0;
	if (y <= -4.3e+254)
		tmp = t_0;
	elseif (y <= -2.8e+112)
		tmp = t_1;
	elseif (y <= -1.35e+38)
		tmp = t_0;
	elseif (y <= 6.4e+29)
		tmp = t_1;
	elseif ((y <= 2.9e+173) || (~((y <= 1.1e+186)) && ((y <= 2.05e+207) || ~((y <= 4e+223)))))
		tmp = t_0;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e+254], t$95$0, If[LessEqual[y, -2.8e+112], t$95$1, If[LessEqual[y, -1.35e+38], t$95$0, If[LessEqual[y, 6.4e+29], t$95$1, If[Or[LessEqual[y, 2.9e+173], And[N[Not[LessEqual[y, 1.1e+186]], $MachinePrecision], Or[LessEqual[y, 2.05e+207], N[Not[LessEqual[y, 4e+223]], $MachinePrecision]]]], t$95$0, N[(y * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.30000000000000012e254 or -2.8000000000000001e112 < y < -1.34999999999999998e38 or 6.39999999999999973e29 < y < 2.90000000000000007e173 or 1.0999999999999999e186 < y < 2.05e207 or 4.00000000000000019e223 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.1%

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

      1. +-commutative 75.1%

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

      2. distribute-rgt1-in 75.1%

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

      3. mul-1-neg 75.1%

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

      4. cancel-sign-sub-inv 75.1%

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

   4. Simplified 75.1%

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

   5. Taylor expanded in y around inf 75.1%

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

      1. mul-1-neg 75.1%

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

      2. distribute-rgt-neg-in 75.1%

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

   7. Simplified 75.1%

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

   if -4.30000000000000012e254 < y < -2.8000000000000001e112 or -1.34999999999999998e38 < y < 6.39999999999999973e29

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 89.9%

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

   if 2.90000000000000007e173 < y < 1.0999999999999999e186 or 2.05e207 < y < 4.00000000000000019e223

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.4%

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

   3. Taylor expanded in x around 0 99.4%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+254}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+112}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+173} \lor \neg \left(y \leq 1.1 \cdot 10^{+186}\right) \land \left(y \leq 2.05 \cdot 10^{+207} \lor \neg \left(y \leq 4 \cdot 10^{+223}\right)\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-49} \lor \neg \left(x \leq 7 \cdot 10^{-118} \lor \neg \left(x \leq 6.2 \cdot 10^{-30}\right) \land x \leq 2.6 \cdot 10^{+55}\right):\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.15e-49)
         (not (or (<= x 7e-118) (and (not (<= x 6.2e-30)) (<= x 2.6e+55)))))
   (- x (* y x))
   (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.15e-49) || !((x <= 7e-118) || (!(x <= 6.2e-30) && (x <= 2.6e+55)))) {
		tmp = x - (y * 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 ((x <= (-1.15d-49)) .or. (.not. (x <= 7d-118) .or. (.not. (x <= 6.2d-30)) .and. (x <= 2.6d+55))) then
        tmp = x - (y * 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 ((x <= -1.15e-49) || !((x <= 7e-118) || (!(x <= 6.2e-30) && (x <= 2.6e+55)))) {
		tmp = x - (y * x);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.15e-49) or not ((x <= 7e-118) or (not (x <= 6.2e-30) and (x <= 2.6e+55))):
		tmp = x - (y * x)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.15e-49) || !((x <= 7e-118) || (!(x <= 6.2e-30) && (x <= 2.6e+55))))
		tmp = Float64(x - Float64(y * x));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.15e-49) || ~(((x <= 7e-118) || (~((x <= 6.2e-30)) && (x <= 2.6e+55)))))
		tmp = x - (y * x);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.15e-49], N[Not[Or[LessEqual[x, 7e-118], And[N[Not[LessEqual[x, 6.2e-30]], $MachinePrecision], LessEqual[x, 2.6e+55]]]], $MachinePrecision]], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15e-49 or 7e-118 < x < 6.19999999999999982e-30 or 2.6e55 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 90.5%

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

      1. +-commutative 90.5%

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

      2. distribute-rgt1-in 90.5%

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

      3. mul-1-neg 90.5%

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

      4. cancel-sign-sub-inv 90.5%

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

   4. Simplified 90.5%

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

   if -1.15e-49 < x < 7e-118 or 6.19999999999999982e-30 < x < 2.6e55

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 91.8%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-49} \lor \neg \left(x \leq 7 \cdot 10^{-118} \lor \neg \left(x \leq 6.2 \cdot 10^{-30}\right) \land x \leq 2.6 \cdot 10^{+55}\right):\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 5: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-18}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-18) (* y z) (if (<= y 2.6e-24) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-18) {
		tmp = y * z;
	} else if (y <= 2.6e-24) {
		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 <= (-5d-18)) then
        tmp = y * z
    else if (y <= 2.6d-24) 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 <= -5e-18) {
		tmp = y * z;
	} else if (y <= 2.6e-24) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5e-18:
		tmp = y * z
	elif y <= 2.6e-24:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-18)
		tmp = Float64(y * z);
	elseif (y <= 2.6e-24)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5e-18)
		tmp = y * z;
	elseif (y <= 2.6e-24)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-18], N[(y * z), $MachinePrecision], If[LessEqual[y, 2.6e-24], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.00000000000000036e-18 or 2.6e-24 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 48.6%

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

   3. Taylor expanded in x around 0 46.4%

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

   if -5.00000000000000036e-18 < y < 2.6e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.4%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-18}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

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: 36.2% 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 36.4%

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

3. Final simplification 36.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023230 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))