SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.9s

Alternatives: 7

Speedup: 1.0×

• 20.4% 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, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(z - x\right) \cdot y + x \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return ((z - x) * y) + 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 = ((z - x) * y) + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+147}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+16}:\\ \;\;\;\;\left(-x\right) \cdot y\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-100}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-57}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.2e+147)
   (* z y)
   (if (<= y -5.6e+16)
     (* (- x) y)
     (if (<= y -3.6e-100) (* z y) (if (<= y 4.6e-57) (* 1.0 x) (* z y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.2e+147) {
		tmp = z * y;
	} else if (y <= -5.6e+16) {
		tmp = -x * y;
	} else if (y <= -3.6e-100) {
		tmp = z * y;
	} else if (y <= 4.6e-57) {
		tmp = 1.0 * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-7.2d+147)) then
        tmp = z * y
    else if (y <= (-5.6d+16)) then
        tmp = -x * y
    else if (y <= (-3.6d-100)) then
        tmp = z * y
    else if (y <= 4.6d-57) then
        tmp = 1.0d0 * x
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.2e+147) {
		tmp = z * y;
	} else if (y <= -5.6e+16) {
		tmp = -x * y;
	} else if (y <= -3.6e-100) {
		tmp = z * y;
	} else if (y <= 4.6e-57) {
		tmp = 1.0 * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.2e+147:
		tmp = z * y
	elif y <= -5.6e+16:
		tmp = -x * y
	elif y <= -3.6e-100:
		tmp = z * y
	elif y <= 4.6e-57:
		tmp = 1.0 * x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.2e+147)
		tmp = Float64(z * y);
	elseif (y <= -5.6e+16)
		tmp = Float64(Float64(-x) * y);
	elseif (y <= -3.6e-100)
		tmp = Float64(z * y);
	elseif (y <= 4.6e-57)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.2e+147)
		tmp = z * y;
	elseif (y <= -5.6e+16)
		tmp = -x * y;
	elseif (y <= -3.6e-100)
		tmp = z * y;
	elseif (y <= 4.6e-57)
		tmp = 1.0 * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.2e+147], N[(z * y), $MachinePrecision], If[LessEqual[y, -5.6e+16], N[((-x) * y), $MachinePrecision], If[LessEqual[y, -3.6e-100], N[(z * y), $MachinePrecision], If[LessEqual[y, 4.6e-57], N[(1.0 * x), $MachinePrecision], N[(z * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.20000000000000041e147 or -5.6e16 < y < -3.5999999999999999e-100 or 4.6e-57 < 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 61.2

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

   5. Applied rewrites 61.2%

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

   if -7.20000000000000041e147 < y < -5.6e16

   1. Initial program 99.9%

      \[x + y \cdot \left(z - x\right) \]
   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 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 74.5%

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

   if -3.5999999999999999e-100 < y < 4.6e-57

   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 75.6

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

   5. Applied rewrites 75.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 75.6%

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

Alternative 3: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z - x\right) \cdot y\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-15}:\\ \;\;\;\;z \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z x) y)))
   (if (<= y -1.0) t_0 (if (<= y 4e-15) (+ (* z y) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z - x) * y;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 4e-15) {
		tmp = (z * 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 = (z - x) * y
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 4d-15) then
        tmp = (z * 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 = (z - x) * y;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 4e-15) {
		tmp = (z * y) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z - x) * y
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 4e-15:
		tmp = (z * y) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z - x) * y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 4e-15)
		tmp = Float64(Float64(z * y) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z - x) * y;
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 4e-15)
		tmp = (z * y) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 4e-15], N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 4.0000000000000003e-15 < 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 98.9

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

   5. Applied rewrites 98.9%

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

   if -1 < y < 4.0000000000000003e-15

   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 100.0

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

   5. Applied rewrites 100.0%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\left(z - x\right) \cdot y\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-15}:\\ \;\;\;\;z \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;\left(z - x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z - x\right) \cdot y\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{-100}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-56}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z x) y)))
   (if (<= y -3.6e-100) t_0 (if (<= y 1.65e-56) (* 1.0 x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z - x) * y;
	double tmp;
	if (y <= -3.6e-100) {
		tmp = t_0;
	} else if (y <= 1.65e-56) {
		tmp = 1.0 * 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 = (z - x) * y
    if (y <= (-3.6d-100)) then
        tmp = t_0
    else if (y <= 1.65d-56) then
        tmp = 1.0d0 * 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 = (z - x) * y;
	double tmp;
	if (y <= -3.6e-100) {
		tmp = t_0;
	} else if (y <= 1.65e-56) {
		tmp = 1.0 * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z - x) * y
	tmp = 0
	if y <= -3.6e-100:
		tmp = t_0
	elif y <= 1.65e-56:
		tmp = 1.0 * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z - x) * y)
	tmp = 0.0
	if (y <= -3.6e-100)
		tmp = t_0;
	elseif (y <= 1.65e-56)
		tmp = Float64(1.0 * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z - x) * y;
	tmp = 0.0;
	if (y <= -3.6e-100)
		tmp = t_0;
	elseif (y <= 1.65e-56)
		tmp = 1.0 * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -3.6e-100], t$95$0, If[LessEqual[y, 1.65e-56], N[(1.0 * x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5999999999999999e-100 or 1.64999999999999992e-56 < 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 95.8

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

   5. Applied rewrites 95.8%

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

   if -3.5999999999999999e-100 < y < 1.64999999999999992e-56

   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 75.6

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

   5. Applied rewrites 75.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 75.6%

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

Alternative 5: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+64}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+47}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.8e+64) (* z y) (if (<= z 9.5e+47) (* (- 1.0 y) x) (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.8e+64) {
		tmp = z * y;
	} else if (z <= 9.5e+47) {
		tmp = (1.0 - y) * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-8.8d+64)) then
        tmp = z * y
    else if (z <= 9.5d+47) then
        tmp = (1.0d0 - y) * x
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.8e+64) {
		tmp = z * y;
	} else if (z <= 9.5e+47) {
		tmp = (1.0 - y) * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.8e+64:
		tmp = z * y
	elif z <= 9.5e+47:
		tmp = (1.0 - y) * x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.8e+64)
		tmp = Float64(z * y);
	elseif (z <= 9.5e+47)
		tmp = Float64(Float64(1.0 - y) * x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.8e+64)
		tmp = z * y;
	elseif (z <= 9.5e+47)
		tmp = (1.0 - y) * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.8e+64], N[(z * y), $MachinePrecision], If[LessEqual[z, 9.5e+47], N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision], N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.80000000000000007e64 or 9.50000000000000001e47 < 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 75.5

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

   5. Applied rewrites 75.5%

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

   if -8.80000000000000007e64 < z < 9.50000000000000001e47

   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 79.7

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

   5. Applied rewrites 79.7%

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

Alternative 6: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-100}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-57}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.6e-100) (* z y) (if (<= y 4.6e-57) (* 1.0 x) (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e-100) {
		tmp = z * y;
	} else if (y <= 4.6e-57) {
		tmp = 1.0 * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.6d-100)) then
        tmp = z * y
    else if (y <= 4.6d-57) then
        tmp = 1.0d0 * x
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e-100) {
		tmp = z * y;
	} else if (y <= 4.6e-57) {
		tmp = 1.0 * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.6e-100:
		tmp = z * y
	elif y <= 4.6e-57:
		tmp = 1.0 * x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.6e-100)
		tmp = Float64(z * y);
	elseif (y <= 4.6e-57)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.6e-100)
		tmp = z * y;
	elseif (y <= 4.6e-57)
		tmp = 1.0 * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.6e-100], N[(z * y), $MachinePrecision], If[LessEqual[y, 4.6e-57], N[(1.0 * x), $MachinePrecision], N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5999999999999999e-100 or 4.6e-57 < 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 57.1

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

   5. Applied rewrites 57.1%

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

   if -3.5999999999999999e-100 < y < 4.6e-57

   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 75.6

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

   5. Applied rewrites 75.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 75.6%

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

Alternative 7: 41.2% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(z * y), $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 46.4

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

5. Applied rewrites 46.4%

   \[\leadsto \color{blue}{z \cdot y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024268 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))