SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.3s

Alternatives: 7

Speedup: 1.2×

• 21.1% 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: 61.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-y\right) \cdot x\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-53}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+254}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y) x)))
   (if (<= y -1.0)
     t_0
     (if (<= y 1.55e-53) (* 1.0 x) (if (<= y 1.45e+254) (* y z) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -y * x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 1.55e-53) {
		tmp = 1.0 * x;
	} else if (y <= 1.45e+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 = -y * x
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 1.55d-53) then
        tmp = 1.0d0 * x
    else if (y <= 1.45d+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 = -y * x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 1.55e-53) {
		tmp = 1.0 * x;
	} else if (y <= 1.45e+254) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -y * x
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 1.55e-53:
		tmp = 1.0 * x
	elif y <= 1.45e+254:
		tmp = y * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-y) * x)
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 1.55e-53)
		tmp = Float64(1.0 * x);
	elseif (y <= 1.45e+254)
		tmp = Float64(y * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -y * x;
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 1.55e-53)
		tmp = 1.0 * x;
	elseif (y <= 1.45e+254)
		tmp = y * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-y) * x), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 1.55e-53], N[(1.0 * x), $MachinePrecision], If[LessEqual[y, 1.45e+254], N[(y * z), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1.45e254 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 63.8

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

   5. Applied rewrites 63.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 63.1%

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

   if -1 < y < 1.55000000000000008e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 78.3

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

   5. Applied rewrites 78.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 77.8%

      \[\leadsto 1 \cdot x \]

   if 1.55000000000000008e-53 < y < 1.45e254

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 57.8

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

   5. Applied rewrites 57.8%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\left(-y\right) \cdot x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-53}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+254}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -850000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.48:\\ \;\;\;\;\mathsf{fma}\left(-y, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z x))))
   (if (<= y -850000.0) t_0 (if (<= y 0.48) (fma (- y) x x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z - x);
	double tmp;
	if (y <= -850000.0) {
		tmp = t_0;
	} else if (y <= 0.48) {
		tmp = fma(-y, x, 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 <= -850000.0)
		tmp = t_0;
	elseif (y <= 0.48)
		tmp = fma(Float64(-y), x, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -850000.0], t$95$0, If[LessEqual[y, 0.48], N[((-y) * x + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5e5 or 0.47999999999999998 < y

   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. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. distribute-rgt-in N/A

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

      7. associate-+l+ N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 97.8

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.7

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

   7. Applied rewrites 99.7%

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

   if -8.5e5 < y < 0.47999999999999998

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 76.7

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

   5. Applied rewrites 76.7%

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

   7. Applied rewrites 76.7%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -850000:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{elif}\;y \leq 0.48:\\ \;\;\;\;\mathsf{fma}\left(-y, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-60}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-80}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.8e-60)
   (* (- 1.0 y) x)
   (if (<= x 2.35e-80) (* y z) (fma (- y) x x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.8e-60) {
		tmp = (1.0 - y) * x;
	} else if (x <= 2.35e-80) {
		tmp = y * z;
	} else {
		tmp = fma(-y, x, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.8e-60)
		tmp = Float64(Float64(1.0 - y) * x);
	elseif (x <= 2.35e-80)
		tmp = Float64(y * z);
	else
		tmp = fma(Float64(-y), x, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.8e-60], N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 2.35e-80], N[(y * z), $MachinePrecision], N[((-y) * x + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.80000000000000013e-60

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 85.2

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

   5. Applied rewrites 85.2%

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

   if -6.80000000000000013e-60 < x < 2.34999999999999986e-80

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 76.5

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

   5. Applied rewrites 76.5%

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

   if 2.34999999999999986e-80 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 91.8

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

   5. Applied rewrites 91.8%

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

   7. Applied rewrites 91.8%

      \[\leadsto \mathsf{fma}\left(-y, \color{blue}{x}, x\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-60}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-80}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot x\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{-60}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-80}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) x)))
   (if (<= x -6.8e-60) t_0 (if (<= x 2.35e-80) (* y z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * x;
	double tmp;
	if (x <= -6.8e-60) {
		tmp = t_0;
	} else if (x <= 2.35e-80) {
		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 = (1.0d0 - y) * x
    if (x <= (-6.8d-60)) then
        tmp = t_0
    else if (x <= 2.35d-80) 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 = (1.0 - y) * x;
	double tmp;
	if (x <= -6.8e-60) {
		tmp = t_0;
	} else if (x <= 2.35e-80) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - y) * x
	tmp = 0
	if x <= -6.8e-60:
		tmp = t_0
	elif x <= 2.35e-80:
		tmp = y * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * x)
	tmp = 0.0
	if (x <= -6.8e-60)
		tmp = t_0;
	elseif (x <= 2.35e-80)
		tmp = Float64(y * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * x;
	tmp = 0.0;
	if (x <= -6.8e-60)
		tmp = t_0;
	elseif (x <= 2.35e-80)
		tmp = y * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -6.8e-60], t$95$0, If[LessEqual[x, 2.35e-80], N[(y * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.80000000000000013e-60 or 2.34999999999999986e-80 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 88.5

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

   5. Applied rewrites 88.5%

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

   if -6.80000000000000013e-60 < x < 2.34999999999999986e-80

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 76.5

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

   5. Applied rewrites 76.5%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-60}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-80}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-12}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-53}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.6e-12) (* y z) (if (<= y 1.55e-53) (* 1.0 x) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.6e-12) {
		tmp = y * z;
	} else if (y <= 1.55e-53) {
		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 <= (-2.6d-12)) then
        tmp = y * z
    else if (y <= 1.55d-53) 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 <= -2.6e-12) {
		tmp = y * z;
	} else if (y <= 1.55e-53) {
		tmp = 1.0 * x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.6e-12:
		tmp = y * z
	elif y <= 1.55e-53:
		tmp = 1.0 * x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.6e-12)
		tmp = Float64(y * z);
	elseif (y <= 1.55e-53)
		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 <= -2.6e-12)
		tmp = y * z;
	elseif (y <= 1.55e-53)
		tmp = 1.0 * x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.6e-12], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.55e-53], N[(1.0 * x), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.59999999999999983e-12 or 1.55000000000000008e-53 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 49.8

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

   5. Applied rewrites 49.8%

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

   if -2.59999999999999983e-12 < y < 1.55000000000000008e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 78.8

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

   5. Applied rewrites 78.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 78.8%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-12}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-53}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 41.3% 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 x around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 38.6

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

5. Applied rewrites 38.6%

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

6. Final simplification 38.6%

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

Reproduce

herbie shell --seed 2024327 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))