SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.4% → 96.8%

Time: 14.0s

Alternatives: 10

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: 93.4% 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: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.6%

   \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
2. Add Preprocessing
3. 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. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-*.f64 98.0

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

4. Applied rewrites 98.0%

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

   1. lift-*.f64 N/A

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

   2. lift--.f64 N/A

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

   3. sub-neg N/A

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

   4. distribute-rgt-in N/A

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

   5. lower-fma.f64 N/A

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

   6. lower-*.f64 N/A

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

   7. lower-neg.f64 98.1

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

6. Applied rewrites 98.1%

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

7. Final simplification 98.1%

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

Alternative 2: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.6%

   \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
2. Add Preprocessing
3. 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. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-*.f64 98.0

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

4. Applied rewrites 98.0%

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

Alternative 3: 71.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{-129}:\\ \;\;\;\;\frac{1}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right), z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.4e-129)
   (/ 1.0 (/ 1.0 x))
   (fma (* y (- (tanh (/ t y)) (/ x y))) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.4e-129) {
		tmp = 1.0 / (1.0 / x);
	} else {
		tmp = fma((y * (tanh((t / y)) - (x / y))), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.4e-129)
		tmp = Float64(1.0 / Float64(1.0 / x));
	else
		tmp = fma(Float64(y * Float64(tanh(Float64(t / y)) - Float64(x / y))), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.4e-129], N[(1.0 / N[(1.0 / x), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.39999999999999989e-129

   1. Initial program 94.1%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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. lower-fma.f64 N/A

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

      3. lower--.f64 55.3

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

   5. Applied rewrites 55.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, t - x, x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 10.0%

      \[\leadsto \frac{1}{\color{blue}{\frac{\mathsf{fma}\left(x, x - z \cdot \left(t - x\right), z \cdot \left(\left(t - x\right) \cdot \left(z \cdot \left(t - x\right)\right)\right)\right)}{\mathsf{fma}\left(x, x \cdot x, \left(z \cdot \left(z \cdot z\right)\right) \cdot \left(\left(t - x\right) \cdot \left(\left(t - x\right) \cdot \left(t - x\right)\right)\right)\right)}}} \]

   8. Taylor expanded in z around 0

      \[\leadsto \frac{1}{\frac{1}{\color{blue}{x}}} \]
   9. Step-by-step derivation

   10. Applied rewrites 64.0%

       \[\leadsto \frac{1}{\frac{1}{\color{blue}{x}}} \]

   if 2.39999999999999989e-129 < y

   1. Initial program 92.8%

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

   3. Taylor expanded in 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 81.8

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

   5. Applied rewrites 81.8%

      \[\leadsto x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \color{blue}{\frac{x}{y}}\right) \]
   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. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 85.8

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

   7. Applied rewrites 85.8%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{-129}:\\ \;\;\;\;\frac{1}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right), z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{-65}:\\ \;\;\;\;\frac{1}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right), y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.85e-65)
   (/ 1.0 (/ 1.0 x))
   (fma (* z (- (/ t y) (tanh (/ x y)))) y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.85e-65) {
		tmp = 1.0 / (1.0 / x);
	} else {
		tmp = fma((z * ((t / y) - tanh((x / y)))), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.85e-65)
		tmp = Float64(1.0 / Float64(1.0 / x));
	else
		tmp = fma(Float64(z * Float64(Float64(t / y) - tanh(Float64(x / y)))), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.85e-65], N[(1.0 / N[(1.0 / x), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(N[(t / y), $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.85e-65

   1. Initial program 94.5%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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. lower-fma.f64 N/A

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

      3. lower--.f64 55.1

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

   5. Applied rewrites 55.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, t - x, x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 9.4%

      \[\leadsto \frac{1}{\color{blue}{\frac{\mathsf{fma}\left(x, x - z \cdot \left(t - x\right), z \cdot \left(\left(t - x\right) \cdot \left(z \cdot \left(t - x\right)\right)\right)\right)}{\mathsf{fma}\left(x, x \cdot x, \left(z \cdot \left(z \cdot z\right)\right) \cdot \left(\left(t - x\right) \cdot \left(\left(t - x\right) \cdot \left(t - x\right)\right)\right)\right)}}} \]

   8. Taylor expanded in z around 0

      \[\leadsto \frac{1}{\frac{1}{\color{blue}{x}}} \]
   9. Step-by-step derivation

   10. Applied rewrites 63.2%

       \[\leadsto \frac{1}{\frac{1}{\color{blue}{x}}} \]

   if 1.85e-65 < y

   1. Initial program 91.8%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   2. Add Preprocessing
   3. 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. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 96.3

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

   4. Applied rewrites 96.3%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 80.0

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

   7. Applied rewrites 80.0%

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

Alternative 5: 68.5% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.15 \cdot 10^{-67}:\\ \;\;\;\;\frac{1}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.15e-67) (/ 1.0 (/ 1.0 x)) (fma z (- t x) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.15e-67) {
		tmp = 1.0 / (1.0 / x);
	} else {
		tmp = fma(z, (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.15e-67)
		tmp = Float64(1.0 / Float64(1.0 / x));
	else
		tmp = fma(z, Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.15e-67], N[(1.0 / N[(1.0 / x), $MachinePrecision]), $MachinePrecision], N[(z * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.15000000000000013e-67

   1. Initial program 94.5%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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. lower-fma.f64 N/A

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

      3. lower--.f64 54.8

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

   5. Applied rewrites 54.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, t - x, x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 9.5%

      \[\leadsto \frac{1}{\color{blue}{\frac{\mathsf{fma}\left(x, x - z \cdot \left(t - x\right), z \cdot \left(\left(t - x\right) \cdot \left(z \cdot \left(t - x\right)\right)\right)\right)}{\mathsf{fma}\left(x, x \cdot x, \left(z \cdot \left(z \cdot z\right)\right) \cdot \left(\left(t - x\right) \cdot \left(\left(t - x\right) \cdot \left(t - x\right)\right)\right)\right)}}} \]

   8. Taylor expanded in z around 0

      \[\leadsto \frac{1}{\frac{1}{\color{blue}{x}}} \]
   9. Step-by-step derivation

   10. Applied rewrites 63.5%

       \[\leadsto \frac{1}{\frac{1}{\color{blue}{x}}} \]

   if 2.15000000000000013e-67 < y

   1. Initial program 91.8%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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. lower-fma.f64 N/A

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

      3. lower--.f64 77.0

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

   5. Applied rewrites 77.0%

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

Alternative 6: 62.7% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 48000:\\ \;\;\;\;\mathsf{fma}\left(z, -x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t x))))
   (if (<= z -6.2e-11) t_1 (if (<= z 48000.0) (fma z (- x) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (t - x);
	double tmp;
	if (z <= -6.2e-11) {
		tmp = t_1;
	} else if (z <= 48000.0) {
		tmp = fma(z, -x, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(t - x))
	tmp = 0.0
	if (z <= -6.2e-11)
		tmp = t_1;
	elseif (z <= 48000.0)
		tmp = fma(z, Float64(-x), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e-11], t$95$1, If[LessEqual[z, 48000.0], N[(z * (-x) + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000056e-11 or 48000 < z

   1. Initial program 88.6%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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. lower-fma.f64 N/A

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

      3. lower--.f64 46.7

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

   5. Applied rewrites 46.7%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 46.4%

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

   if -6.20000000000000056e-11 < z < 48000

   1. Initial program 99.2%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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. lower-fma.f64 N/A

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

      3. lower--.f64 78.7

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

   5. Applied rewrites 78.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 86.1%

      \[\leadsto \mathsf{fma}\left(z, -x, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 20.7% accurate, 11.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-155}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-135}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7e-155) (* t z) (if (<= t 3.1e-135) (* z (- x)) (* t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7e-155) {
		tmp = t * z;
	} else if (t <= 3.1e-135) {
		tmp = z * -x;
	} else {
		tmp = t * z;
	}
	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 (t <= (-7d-155)) then
        tmp = t * z
    else if (t <= 3.1d-135) then
        tmp = z * -x
    else
        tmp = t * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7e-155) {
		tmp = t * z;
	} else if (t <= 3.1e-135) {
		tmp = z * -x;
	} else {
		tmp = t * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7e-155:
		tmp = t * z
	elif t <= 3.1e-135:
		tmp = z * -x
	else:
		tmp = t * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7e-155)
		tmp = Float64(t * z);
	elseif (t <= 3.1e-135)
		tmp = Float64(z * Float64(-x));
	else
		tmp = Float64(t * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -7e-155)
		tmp = t * z;
	elseif (t <= 3.1e-135)
		tmp = z * -x;
	else
		tmp = t * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7e-155], N[(t * z), $MachinePrecision], If[LessEqual[t, 3.1e-135], N[(z * (-x)), $MachinePrecision], N[(t * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.00000000000000031e-155 or 3.1000000000000001e-135 < t

   1. Initial program 95.4%

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

   3. Taylor expanded in 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. lower-fma.f64 N/A

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

      3. lower--.f64 53.6

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

   5. Applied rewrites 53.6%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 23.8%

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

   if -7.00000000000000031e-155 < t < 3.1000000000000001e-135

   1. Initial program 89.0%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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. lower-fma.f64 N/A

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

      3. lower--.f64 84.1

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

   5. Applied rewrites 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, t - x, x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 46.5%

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

   8. Taylor expanded in z around -inf

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

   10. Applied rewrites 38.3%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 30.3%

       \[\leadsto z \cdot \left(-x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-155}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-135}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.1% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(z, -x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.85e-67) (fma z (- x) x) (fma z (- t x) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.85e-67) {
		tmp = fma(z, -x, x);
	} else {
		tmp = fma(z, (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.85e-67)
		tmp = fma(z, Float64(-x), x);
	else
		tmp = fma(z, Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.85e-67], N[(z * (-x) + x), $MachinePrecision], N[(z * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.85e-67

   1. Initial program 94.5%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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. lower-fma.f64 N/A

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

      3. lower--.f64 54.8

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 49.6%

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

   if 1.85e-67 < y

   1. Initial program 91.8%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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. lower-fma.f64 N/A

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

      3. lower--.f64 77.0

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

   5. Applied rewrites 77.0%

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

Alternative 9: 26.4% accurate, 26.6× speedup

Math

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

FPCore

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

C

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

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 - x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

   \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
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. lower-fma.f64 N/A

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

   3. lower--.f64 62.0

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

5. Applied rewrites 62.0%

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

6. Taylor expanded in z around inf

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

8. Applied rewrites 28.7%

   \[\leadsto z \cdot \color{blue}{\left(t - x\right)} \]
9. Add Preprocessing

Alternative 10: 17.1% accurate, 39.8× speedup

Math

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

FPCore

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

C

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

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 = t * z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

   \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
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. lower-fma.f64 N/A

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

   3. lower--.f64 62.0

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

5. Applied rewrites 62.0%

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

6. Taylor expanded in t around inf

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

8. Applied rewrites 20.2%

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

9. Final simplification 20.2%

   \[\leadsto t \cdot z \]
10. Add Preprocessing

Developer Target 1: 96.8% 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 2024219 
(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))))))