SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 8

Speedup: 1.0×

• 21.4% 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, 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-define 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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 60.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-40}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-137}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+151} \lor \neg \left(y \leq 1.1 \cdot 10^{+207}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3e-40)
   (* y z)
   (if (<= y 1.35e-193)
     x
     (if (<= y 2.8e-137)
       (* y z)
       (if (<= y 1.6e-23)
         x
         (if (or (<= y 7e+151) (not (<= y 1.1e+207))) (* y z) (* y (- x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3e-40) {
		tmp = y * z;
	} else if (y <= 1.35e-193) {
		tmp = x;
	} else if (y <= 2.8e-137) {
		tmp = y * z;
	} else if (y <= 1.6e-23) {
		tmp = x;
	} else if ((y <= 7e+151) || !(y <= 1.1e+207)) {
		tmp = y * z;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3d-40)) then
        tmp = y * z
    else if (y <= 1.35d-193) then
        tmp = x
    else if (y <= 2.8d-137) then
        tmp = y * z
    else if (y <= 1.6d-23) then
        tmp = x
    else if ((y <= 7d+151) .or. (.not. (y <= 1.1d+207))) then
        tmp = y * z
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3e-40) {
		tmp = y * z;
	} else if (y <= 1.35e-193) {
		tmp = x;
	} else if (y <= 2.8e-137) {
		tmp = y * z;
	} else if (y <= 1.6e-23) {
		tmp = x;
	} else if ((y <= 7e+151) || !(y <= 1.1e+207)) {
		tmp = y * z;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3e-40:
		tmp = y * z
	elif y <= 1.35e-193:
		tmp = x
	elif y <= 2.8e-137:
		tmp = y * z
	elif y <= 1.6e-23:
		tmp = x
	elif (y <= 7e+151) or not (y <= 1.1e+207):
		tmp = y * z
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3e-40)
		tmp = Float64(y * z);
	elseif (y <= 1.35e-193)
		tmp = x;
	elseif (y <= 2.8e-137)
		tmp = Float64(y * z);
	elseif (y <= 1.6e-23)
		tmp = x;
	elseif ((y <= 7e+151) || !(y <= 1.1e+207))
		tmp = Float64(y * z);
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3e-40)
		tmp = y * z;
	elseif (y <= 1.35e-193)
		tmp = x;
	elseif (y <= 2.8e-137)
		tmp = y * z;
	elseif (y <= 1.6e-23)
		tmp = x;
	elseif ((y <= 7e+151) || ~((y <= 1.1e+207)))
		tmp = y * z;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3e-40], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.35e-193], x, If[LessEqual[y, 2.8e-137], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.6e-23], x, If[Or[LessEqual[y, 7e+151], N[Not[LessEqual[y, 1.1e+207]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(y * (-x)), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0000000000000002e-40 or 1.35e-193 < y < 2.7999999999999999e-137 or 1.59999999999999988e-23 < y < 7.0000000000000006e151 or 1.10000000000000004e207 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 97.0%

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

   4. Applied egg-rr 97.0%

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

      1. associate-+r+ 97.0%

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

      2. distribute-lft-neg-out 97.0%

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

      3. unsub-neg 97.0%

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

      4. +-commutative 97.0%

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

      5. *-commutative 97.0%

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

   6. Applied egg-rr 97.0%

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

   7. Taylor expanded in z around inf 62.9%

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

   if -3.0000000000000002e-40 < y < 1.35e-193 or 2.7999999999999999e-137 < y < 1.59999999999999988e-23

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.8%

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

   if 7.0000000000000006e151 < y < 1.10000000000000004e207

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.0%

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

      1. mul-1-neg 87.0%

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

      2. unsub-neg 87.0%

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

   5. Simplified 87.0%

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

      1. sub-neg 87.0%

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

      2. distribute-rgt-in 87.0%

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

      3. *-un-lft-identity 87.0%

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

      4. distribute-lft-neg-in 87.0%

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

      5. unsub-neg 87.0%

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

   7. Applied egg-rr 87.0%

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

   8. Taylor expanded in y around inf 87.0%

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

      1. mul-1-neg 87.0%

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

      2. distribute-rgt-neg-out 87.0%

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

   10. Simplified 87.0%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-40}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-137}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+151} \lor \neg \left(y \leq 1.1 \cdot 10^{+207}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{-34}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-142}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z x))))
   (if (<= y -8.5e-34)
     t_0
     (if (<= y 1.35e-193)
       x
       (if (<= y 1.36e-142) (* y z) (if (<= y 5000.0) (* x (- 1.0 y)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z - x);
	double tmp;
	if (y <= -8.5e-34) {
		tmp = t_0;
	} else if (y <= 1.35e-193) {
		tmp = x;
	} else if (y <= 1.36e-142) {
		tmp = y * z;
	} else if (y <= 5000.0) {
		tmp = x * (1.0 - y);
	} 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 <= (-8.5d-34)) then
        tmp = t_0
    else if (y <= 1.35d-193) then
        tmp = x
    else if (y <= 1.36d-142) then
        tmp = y * z
    else if (y <= 5000.0d0) then
        tmp = x * (1.0d0 - y)
    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 <= -8.5e-34) {
		tmp = t_0;
	} else if (y <= 1.35e-193) {
		tmp = x;
	} else if (y <= 1.36e-142) {
		tmp = y * z;
	} else if (y <= 5000.0) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z - x)
	tmp = 0
	if y <= -8.5e-34:
		tmp = t_0
	elif y <= 1.35e-193:
		tmp = x
	elif y <= 1.36e-142:
		tmp = y * z
	elif y <= 5000.0:
		tmp = x * (1.0 - y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z - x))
	tmp = 0.0
	if (y <= -8.5e-34)
		tmp = t_0;
	elseif (y <= 1.35e-193)
		tmp = x;
	elseif (y <= 1.36e-142)
		tmp = Float64(y * z);
	elseif (y <= 5000.0)
		tmp = Float64(x * Float64(1.0 - y));
	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 <= -8.5e-34)
		tmp = t_0;
	elseif (y <= 1.35e-193)
		tmp = x;
	elseif (y <= 1.36e-142)
		tmp = y * z;
	elseif (y <= 5000.0)
		tmp = x * (1.0 - y);
	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, -8.5e-34], t$95$0, If[LessEqual[y, 1.35e-193], x, If[LessEqual[y, 1.36e-142], N[(y * z), $MachinePrecision], If[LessEqual[y, 5000.0], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.5000000000000001e-34 or 5e3 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 96.8%

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

   4. Applied egg-rr 96.8%

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

      1. associate-+r+ 96.8%

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

      2. distribute-lft-neg-out 96.8%

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

      3. unsub-neg 96.8%

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

      4. +-commutative 96.8%

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

      5. *-commutative 96.8%

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

   6. Applied egg-rr 96.8%

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

   7. Taylor expanded in y around inf 97.6%

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

   if -8.5000000000000001e-34 < y < 1.35e-193

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 79.7%

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

   if 1.35e-193 < y < 1.35999999999999993e-142

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. associate-+r+ 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. unsub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. *-commutative 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around inf 72.6%

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

   if 1.35999999999999993e-142 < y < 5e3

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 66.5%

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

      1. mul-1-neg 66.5%

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

      2. unsub-neg 66.5%

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

   5. Simplified 66.5%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-142}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-38} \lor \neg \left(y \leq 1.2 \cdot 10^{-193} \lor \neg \left(y \leq 9.2 \cdot 10^{-143}\right) \land y \leq 8 \cdot 10^{-24}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.05e-38)
         (not (or (<= y 1.2e-193) (and (not (<= y 9.2e-143)) (<= y 8e-24)))))
   (* y z)
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.05e-38) || !((y <= 1.2e-193) || (!(y <= 9.2e-143) && (y <= 8e-24)))) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.05d-38)) .or. (.not. (y <= 1.2d-193) .or. (.not. (y <= 9.2d-143)) .and. (y <= 8d-24))) then
        tmp = y * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.05e-38) || !((y <= 1.2e-193) || (!(y <= 9.2e-143) && (y <= 8e-24)))) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.05e-38) or not ((y <= 1.2e-193) or (not (y <= 9.2e-143) and (y <= 8e-24))):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.05e-38) || !((y <= 1.2e-193) || (!(y <= 9.2e-143) && (y <= 8e-24))))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.05e-38) || ~(((y <= 1.2e-193) || (~((y <= 9.2e-143)) && (y <= 8e-24)))))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.05e-38], N[Not[Or[LessEqual[y, 1.2e-193], And[N[Not[LessEqual[y, 9.2e-143]], $MachinePrecision], LessEqual[y, 8e-24]]]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.05000000000000006e-38 or 1.2e-193 < y < 9.20000000000000045e-143 or 7.99999999999999939e-24 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 97.2%

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

   4. Applied egg-rr 97.2%

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

      1. associate-+r+ 97.2%

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

      2. distribute-lft-neg-out 97.2%

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

      3. unsub-neg 97.2%

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

      4. +-commutative 97.2%

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

      5. *-commutative 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in z around inf 60.3%

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

   if -1.05000000000000006e-38 < y < 1.2e-193 or 9.20000000000000045e-143 < y < 7.99999999999999939e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.8%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-38} \lor \neg \left(y \leq 1.2 \cdot 10^{-193} \lor \neg \left(y \leq 9.2 \cdot 10^{-143}\right) \land y \leq 8 \cdot 10^{-24}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+24} \lor \neg \left(z \leq 2.55 \cdot 10^{+92}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1e+24) (not (<= z 2.55e+92))) (* y z) (* x (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e+24) || !(z <= 2.55e+92)) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - 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 <= (-1d+24)) .or. (.not. (z <= 2.55d+92))) then
        tmp = y * z
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e+24) || !(z <= 2.55e+92)) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1e+24) or not (z <= 2.55e+92):
		tmp = y * z
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1e+24) || !(z <= 2.55e+92))
		tmp = Float64(y * z);
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1e+24) || ~((z <= 2.55e+92)))
		tmp = y * z;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1e+24], N[Not[LessEqual[z, 2.55e+92]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999998e23 or 2.5500000000000001e92 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 96.5%

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

   4. Applied egg-rr 96.5%

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

      1. associate-+r+ 96.5%

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

      2. distribute-lft-neg-out 96.5%

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

      3. unsub-neg 96.5%

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

      4. +-commutative 96.5%

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

      5. *-commutative 96.5%

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

   6. Applied egg-rr 96.5%

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

   7. Taylor expanded in z around inf 76.6%

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

   if -9.9999999999999998e23 < z < 2.5500000000000001e92

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.2%

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

      1. mul-1-neg 80.2%

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

      2. unsub-neg 80.2%

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

   5. Simplified 80.2%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+24} \lor \neg \left(z \leq 2.55 \cdot 10^{+92}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -96 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -96.0) (not (<= y 1.0))) (* y (- z x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -96.0) || !(y <= 1.0)) {
		tmp = y * (z - x);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-96.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * (z - x)
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -96.0) || !(y <= 1.0)) {
		tmp = y * (z - x);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -96.0) or not (y <= 1.0):
		tmp = y * (z - x)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -96.0) || !(y <= 1.0))
		tmp = Float64(y * Float64(z - x));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -96.0) || ~((y <= 1.0)))
		tmp = y * (z - x);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -96.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -96 or 1 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 96.6%

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

   4. Applied egg-rr 96.6%

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

      1. associate-+r+ 96.6%

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

      2. distribute-lft-neg-out 96.6%

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

      3. unsub-neg 96.6%

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

      4. +-commutative 96.6%

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

      5. *-commutative 96.6%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in y around inf 98.2%

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

   if -96 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 97.6%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -96 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 8: 36.6% 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. Add Preprocessing

3. Taylor expanded in y around 0 37.0%

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

4. Final simplification 37.0%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024080 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))