SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.6% → 97.9%

Time: 7.4s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((y * z) * (tanh((t / y)) - tanh((x / y))));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y * z) * (tanh((t / y)) - tanh((x / y))))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((y * z) * (Math.tanh((t / y)) - Math.tanh((x / y))));
}

Python

def code(x, y, z, t):
	return x + ((y * z) * (math.tanh((t / y)) - math.tanh((x / y))))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((y * z) * (tanh((t / y)) - tanh((x / y))));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y * z) * (tanh((t / y)) - tanh((x / y))))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((y * z) * (Math.tanh((t / y)) - Math.tanh((x / y))));
}

Python

def code(x, y, z, t):
	return x + ((y * z) * (math.tanh((t / y)) - math.tanh((x / y))))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (fma (* (- (tanh (/ t y)) (tanh (/ x y))) y) z x))

C

double code(double x, double y, double z, double t) {
	return fma(((tanh((t / y)) - tanh((x / y))) * y), z, x);
}

Julia

function code(x, y, z, t)
	return fma(Float64(Float64(tanh(Float64(t / y)) - tanh(Float64(x / y))) * y), z, x)
end

Wolfram

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

Derivation

1. Initial program 95.1%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lift-*.f64 N/A

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

   6. associate-*r* N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-*.f64 98.5

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

4. Applied rewrites 98.5%

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

Alternative 2: 79.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-5} \lor \neg \left(x \leq 5 \cdot 10^{+40}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right) \cdot z, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.7e-5) (not (<= x 5e+40)))
   (* 1.0 x)
   (fma (* (- (tanh (/ t y)) (/ x y)) z) y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.7e-5) || !(x <= 5e+40)) {
		tmp = 1.0 * x;
	} else {
		tmp = fma(((tanh((t / y)) - (x / y)) * z), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.7e-5) || !(x <= 5e+40))
		tmp = Float64(1.0 * x);
	else
		tmp = fma(Float64(Float64(tanh(Float64(t / y)) - Float64(x / y)) * z), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.7e-5], N[Not[LessEqual[x, 5e+40]], $MachinePrecision]], N[(1.0 * x), $MachinePrecision], N[(N[(N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.7000000000000003e-5 or 5.00000000000000003e40 < x

   1. Initial program 97.3%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 65.7

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

   5. Applied rewrites 65.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 67.3%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 86.2%

       \[\leadsto 1 \cdot x \]

   if -5.7000000000000003e-5 < x < 5.00000000000000003e40

   1. Initial program 92.4%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 85.1

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

   5. Applied rewrites 85.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 86.6

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

   7. Applied rewrites 86.6%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-5} \lor \neg \left(x \leq 5 \cdot 10^{+40}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right) \cdot z, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.3% accurate, 10.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+87} \lor \neg \left(y \leq 1.2 \cdot 10^{+41}\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.8e+87) (not (<= y 1.2e+41))) (fma (- t x) z x) (* 1.0 x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e+87) || !(y <= 1.2e+41)) {
		tmp = fma((t - x), z, x);
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.8e+87) || !(y <= 1.2e+41))
		tmp = fma(Float64(t - x), z, x);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.8e+87], N[Not[LessEqual[y, 1.2e+41]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * z + x), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000011e87 or 1.2000000000000001e41 < y

   1. Initial program 88.8%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 85.1

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

   5. Applied rewrites 85.1%

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

   if -3.80000000000000011e87 < y < 1.2000000000000001e41

   1. Initial program 99.3%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 48.5

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

   5. Applied rewrites 48.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 54.3%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 76.3%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+87} \lor \neg \left(y \leq 1.2 \cdot 10^{+41}\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.5% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+151} \lor \neg \left(y \leq 6.2 \cdot 10^{+46}\right):\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.02e+151) (not (<= y 6.2e+46))) (* (- 1.0 z) x) (* 1.0 x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e+151) || !(y <= 6.2e+46)) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.02d+151)) .or. (.not. (y <= 6.2d+46))) then
        tmp = (1.0d0 - z) * x
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e+151) || !(y <= 6.2e+46)) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.02e+151) or not (y <= 6.2e+46):
		tmp = (1.0 - z) * x
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.02e+151) || !(y <= 6.2e+46))
		tmp = Float64(Float64(1.0 - z) * x);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.02e+151) || ~((y <= 6.2e+46)))
		tmp = (1.0 - z) * x;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.02e+151], N[Not[LessEqual[y, 6.2e+46]], $MachinePrecision]], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02000000000000002e151 or 6.1999999999999995e46 < y

   1. Initial program 86.8%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 85.6

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

   5. Applied rewrites 85.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 60.0%

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

   if -1.02000000000000002e151 < y < 6.1999999999999995e46

   1. Initial program 99.3%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 51.7

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

   5. Applied rewrites 51.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 55.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 75.7%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+151} \lor \neg \left(y \leq 6.2 \cdot 10^{+46}\right):\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.9% accurate, 19.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4.4 \cdot 10^{+169}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= z 4.4e+169) (* 1.0 x) (* z t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 4.4e+169) {
		tmp = 1.0 * x;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 4.4d+169) then
        tmp = 1.0d0 * x
    else
        tmp = z * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 4.4e+169) {
		tmp = 1.0 * x;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 4.4e+169:
		tmp = 1.0 * x
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 4.4e+169)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 4.4e+169)
		tmp = 1.0 * x;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 4.4e+169], N[(1.0 * x), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.4e169

   1. Initial program 97.1%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 62.6

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

   5. Applied rewrites 62.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 60.5%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 70.3%

       \[\leadsto 1 \cdot x \]

   if 4.4e169 < z

   1. Initial program 76.6%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 68.8

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

   5. Applied rewrites 68.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 45.9%

      \[\leadsto z \cdot \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 17.0% accurate, 39.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.1%

   \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
2. Add Preprocessing

3. Taylor expanded in y around inf

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lower--.f64 63.2

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

5. Applied rewrites 63.2%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 17.1%

   \[\leadsto z \cdot \color{blue}{t} \]
9. Add Preprocessing

Developer Target 1: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + (y * (z * (tanh((t / y)) - tanh((x / y)))));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + (y * (z * (tanh((t / y)) - tanh((x / y)))))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + (y * (z * (Math.tanh((t / y)) - Math.tanh((x / y)))));
}

Python

def code(x, y, z, t):
	return x + (y * (z * (math.tanh((t / y)) - math.tanh((x / y)))))

Julia

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

MATLAB

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

Wolfram

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

Reproduce

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

  :alt
  (! :herbie-platform default (+ x (* y (* z (- (tanh (/ t y)) (tanh (/ x y)))))))

  (+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))))