SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.2s

Alternatives: 7

Speedup: 1.2×

• 21.6% 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, 1.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z - x, y, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- z x) y x))

C

double code(double x, double y, double z) {
	return fma((z - x), y, x);
}

Julia

function code(x, y, z)
	return fma(Float64(z - x), y, x)
end

Wolfram

code[x_, y_, z_] := N[(N[(z - x), $MachinePrecision] * y + x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + y \cdot \left(z - x\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-x\right) \cdot y\\ \mathbf{if}\;y \leq -3 \cdot 10^{+152}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-12}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+254}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- x) y)))
   (if (<= y -3e+152)
     (* y z)
     (if (<= y -2.3e+19)
       t_0
       (if (<= y 3e-12) (* 1.0 x) (if (<= y 7.2e+254) (* y z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -x * y;
	double tmp;
	if (y <= -3e+152) {
		tmp = y * z;
	} else if (y <= -2.3e+19) {
		tmp = t_0;
	} else if (y <= 3e-12) {
		tmp = 1.0 * x;
	} else if (y <= 7.2e+254) {
		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 <= (-3d+152)) then
        tmp = y * z
    else if (y <= (-2.3d+19)) then
        tmp = t_0
    else if (y <= 3d-12) then
        tmp = 1.0d0 * x
    else if (y <= 7.2d+254) 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 <= -3e+152) {
		tmp = y * z;
	} else if (y <= -2.3e+19) {
		tmp = t_0;
	} else if (y <= 3e-12) {
		tmp = 1.0 * x;
	} else if (y <= 7.2e+254) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x * y
	tmp = 0
	if y <= -3e+152:
		tmp = y * z
	elif y <= -2.3e+19:
		tmp = t_0
	elif y <= 3e-12:
		tmp = 1.0 * x
	elif y <= 7.2e+254:
		tmp = y * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) * y)
	tmp = 0.0
	if (y <= -3e+152)
		tmp = Float64(y * z);
	elseif (y <= -2.3e+19)
		tmp = t_0;
	elseif (y <= 3e-12)
		tmp = Float64(1.0 * x);
	elseif (y <= 7.2e+254)
		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 <= -3e+152)
		tmp = y * z;
	elseif (y <= -2.3e+19)
		tmp = t_0;
	elseif (y <= 3e-12)
		tmp = 1.0 * x;
	elseif (y <= 7.2e+254)
		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, -3e+152], N[(y * z), $MachinePrecision], If[LessEqual[y, -2.3e+19], t$95$0, If[LessEqual[y, 3e-12], N[(1.0 * x), $MachinePrecision], If[LessEqual[y, 7.2e+254], N[(y * z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.99999999999999991e152 or 3.0000000000000001e-12 < y < 7.19999999999999954e254

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{y \cdot z} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 65.1

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

   5. Applied rewrites 65.1%

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

   if -2.99999999999999991e152 < y < -2.3e19 or 7.19999999999999954e254 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 66.4%

      \[\leadsto \left(-x\right) \cdot y \]

   if -2.3e19 < y < 3.0000000000000001e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt1-in N/A

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

      6. +-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 73.6

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

   5. Applied rewrites 73.6%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 73.4%

      \[\leadsto 1 \cdot x \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+152}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+19}:\\ \;\;\;\;\left(-x\right) \cdot y\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-12}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+254}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-8}:\\ \;\;\;\;y \cdot z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z x))))
   (if (<= y -2.3e+19) t_0 (if (<= y 2.3e-8) (+ (* y z) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z - x);
	double tmp;
	if (y <= -2.3e+19) {
		tmp = t_0;
	} else if (y <= 2.3e-8) {
		tmp = (y * z) + 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 <= (-2.3d+19)) then
        tmp = t_0
    else if (y <= 2.3d-8) then
        tmp = (y * z) + 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 <= -2.3e+19) {
		tmp = t_0;
	} else if (y <= 2.3e-8) {
		tmp = (y * z) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z - x)
	tmp = 0
	if y <= -2.3e+19:
		tmp = t_0
	elif y <= 2.3e-8:
		tmp = (y * z) + 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 <= -2.3e+19)
		tmp = t_0;
	elseif (y <= 2.3e-8)
		tmp = Float64(Float64(y * z) + 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 <= -2.3e+19)
		tmp = t_0;
	elseif (y <= 2.3e-8)
		tmp = (y * z) + 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, -2.3e+19], t$95$0, If[LessEqual[y, 2.3e-8], N[(N[(y * z), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e19 or 2.3000000000000001e-8 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if -2.3e19 < y < 2.3000000000000001e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 99.8

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

   5. Applied rewrites 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-8}:\\ \;\;\;\;y \cdot z + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{-14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-12}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z x))))
   (if (<= y -4.3e-14) t_0 (if (<= y 6.8e-12) (* (- 1.0 y) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z - x);
	double tmp;
	if (y <= -4.3e-14) {
		tmp = t_0;
	} else if (y <= 6.8e-12) {
		tmp = (1.0 - y) * 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 <= (-4.3d-14)) then
        tmp = t_0
    else if (y <= 6.8d-12) then
        tmp = (1.0d0 - y) * 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 <= -4.3e-14) {
		tmp = t_0;
	} else if (y <= 6.8e-12) {
		tmp = (1.0 - y) * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z - x)
	tmp = 0
	if y <= -4.3e-14:
		tmp = t_0
	elif y <= 6.8e-12:
		tmp = (1.0 - y) * 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 <= -4.3e-14)
		tmp = t_0;
	elseif (y <= 6.8e-12)
		tmp = Float64(Float64(1.0 - y) * 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 <= -4.3e-14)
		tmp = t_0;
	elseif (y <= 6.8e-12)
		tmp = (1.0 - y) * 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, -4.3e-14], t$95$0, If[LessEqual[y, 6.8e-12], N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.29999999999999998e-14 or 6.8000000000000001e-12 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 99.3

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

   5. Applied rewrites 99.3%

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

   if -4.29999999999999998e-14 < y < 6.8000000000000001e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt1-in N/A

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

      6. +-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 75.8

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

   5. Applied rewrites 75.8%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-12}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+82}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+39}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.6e+82) (* y z) (if (<= z 3e+39) (* (- 1.0 y) x) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.6e+82) {
		tmp = y * z;
	} else if (z <= 3e+39) {
		tmp = (1.0 - y) * 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 (z <= (-6.6d+82)) then
        tmp = y * z
    else if (z <= 3d+39) then
        tmp = (1.0d0 - y) * 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 (z <= -6.6e+82) {
		tmp = y * z;
	} else if (z <= 3e+39) {
		tmp = (1.0 - y) * x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.6e+82:
		tmp = y * z
	elif z <= 3e+39:
		tmp = (1.0 - y) * x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.6e+82)
		tmp = Float64(y * z);
	elseif (z <= 3e+39)
		tmp = Float64(Float64(1.0 - y) * x);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.6e+82)
		tmp = y * z;
	elseif (z <= 3e+39)
		tmp = (1.0 - y) * x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.6e+82], N[(y * z), $MachinePrecision], If[LessEqual[z, 3e+39], N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5999999999999997e82 or 3e39 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{y \cdot z} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 73.4

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

   5. Applied rewrites 73.4%

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

   if -6.5999999999999997e82 < z < 3e39

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt1-in N/A

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

      6. +-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 89.1

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

   5. Applied rewrites 89.1%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+82}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+39}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-14}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-12}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.3e-14) (* y z) (if (<= y 3e-12) (* 1.0 x) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.3e-14) {
		tmp = y * z;
	} else if (y <= 3e-12) {
		tmp = 1.0 * 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 <= (-4.3d-14)) then
        tmp = y * z
    else if (y <= 3d-12) then
        tmp = 1.0d0 * 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 <= -4.3e-14) {
		tmp = y * z;
	} else if (y <= 3e-12) {
		tmp = 1.0 * x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.3e-14:
		tmp = y * z
	elif y <= 3e-12:
		tmp = 1.0 * x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.3e-14)
		tmp = Float64(y * z);
	elseif (y <= 3e-12)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.3e-14)
		tmp = y * z;
	elseif (y <= 3e-12)
		tmp = 1.0 * x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.3e-14], N[(y * z), $MachinePrecision], If[LessEqual[y, 3e-12], N[(1.0 * x), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.29999999999999998e-14 or 3.0000000000000001e-12 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{y \cdot z} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 57.0

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

   5. Applied rewrites 57.0%

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

   if -4.29999999999999998e-14 < y < 3.0000000000000001e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt1-in N/A

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

      6. +-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 75.8

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

   5. Applied rewrites 75.8%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 75.7%

      \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-14}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-12}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ y \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* y z))

C

double code(double x, double y, double z) {
	return y * z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y * z
end function

Java

public static double code(double x, double y, double z) {
	return y * z;
}

Python

def code(x, y, z):
	return y * z

Julia

function code(x, y, z)
	return Float64(y * z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = y * z;
end

Wolfram

code[x_, y_, z_] := N[(y * z), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{y \cdot z} \]
4. Step-by-step derivation

   1. *-commutative N/A

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

   2. lower-*.f64 42.9

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

5. Applied rewrites 42.9%

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

6. Final simplification 42.9%

   \[\leadsto y \cdot z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024277 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))