SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.7% → 98.7%

Time: 11.2s

Alternatives: 7

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: 93.7% 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: 98.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 8.2 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(y\_m \cdot \left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 8.2e+215)
   (fma (* y_m (- (tanh (/ t y_m)) (tanh (/ x y_m)))) z x)
   (fma z (- t x) x)))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 8.2e+215) {
		tmp = fma((y_m * (tanh((t / y_m)) - tanh((x / y_m)))), z, x);
	} else {
		tmp = fma(z, (t - x), x);
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 8.2e+215)
		tmp = fma(Float64(y_m * Float64(tanh(Float64(t / y_m)) - tanh(Float64(x / y_m)))), z, x);
	else
		tmp = fma(z, Float64(t - x), x);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 8.2e+215], N[(N[(y$95$m * N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision], N[(z * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.2000000000000007e215

   1. Initial program 96.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. tanh-lowering-tanh.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. tanh-lowering-tanh.f64 N/A

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

      10. /-lowering-/.f64 97.3

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

   4. Applied egg-rr 97.3%

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

   if 8.2000000000000007e215 < y

   1. Initial program 74.2%

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

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

      3. --lowering--.f64 95.2

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

   5. Simplified 95.2%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.2 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 65.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_1 := x + \left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right) \cdot \left(y\_m \cdot z\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- (tanh (/ t y_m)) (tanh (/ x y_m))) (* y_m z)))))
   (if (<= t_1 (- INFINITY)) (* t z) (if (<= t_1 5e+306) x (* t z)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double t_1 = x + ((tanh((t / y_m)) - tanh((x / y_m))) * (y_m * z));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t * z;
	} else if (t_1 <= 5e+306) {
		tmp = x;
	} else {
		tmp = t * z;
	}
	return tmp;
}

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double t_1 = x + ((Math.tanh((t / y_m)) - Math.tanh((x / y_m))) * (y_m * z));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t * z;
	} else if (t_1 <= 5e+306) {
		tmp = x;
	} else {
		tmp = t * z;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	t_1 = x + ((math.tanh((t / y_m)) - math.tanh((x / y_m))) * (y_m * z))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t * z
	elif t_1 <= 5e+306:
		tmp = x
	else:
		tmp = t * z
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	t_1 = Float64(x + Float64(Float64(tanh(Float64(t / y_m)) - tanh(Float64(x / y_m))) * Float64(y_m * z)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t * z);
	elseif (t_1 <= 5e+306)
		tmp = x;
	else
		tmp = Float64(t * z);
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	t_1 = x + ((tanh((t / y_m)) - tanh((x / y_m))) * (y_m * z));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t * z;
	elseif (t_1 <= 5e+306)
		tmp = x;
	else
		tmp = t * z;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(y$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t * z), $MachinePrecision], If[LessEqual[t$95$1, 5e+306], x, N[(t * z), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < -inf.0 or 4.99999999999999993e306 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

   1. Initial program 58.7%

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

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

      3. --lowering--.f64 100.0

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 54.2

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

   8. Simplified 54.2%

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

   if -inf.0 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < 4.99999999999999993e306

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 66.1%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right) \leq -\infty:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;x\\ \mathbf{elif}\;y\_m \leq 1.35 \cdot 10^{-36}:\\ \;\;\;\;\mathsf{fma}\left(y\_m \cdot \left(\tanh \left(\frac{t}{y\_m}\right) - \frac{x}{y\_m}\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(t, 1, \tanh \left(\frac{x}{y\_m}\right) \cdot \left(-y\_m\right)\right), z, x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 1.6e-97)
   x
   (if (<= y_m 1.35e-36)
     (fma (* y_m (- (tanh (/ t y_m)) (/ x y_m))) z x)
     (fma (fma t 1.0 (* (tanh (/ x y_m)) (- y_m))) z x))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 1.6e-97) {
		tmp = x;
	} else if (y_m <= 1.35e-36) {
		tmp = fma((y_m * (tanh((t / y_m)) - (x / y_m))), z, x);
	} else {
		tmp = fma(fma(t, 1.0, (tanh((x / y_m)) * -y_m)), z, x);
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 1.6e-97)
		tmp = x;
	elseif (y_m <= 1.35e-36)
		tmp = fma(Float64(y_m * Float64(tanh(Float64(t / y_m)) - Float64(x / y_m))), z, x);
	else
		tmp = fma(fma(t, 1.0, Float64(tanh(Float64(x / y_m)) * Float64(-y_m))), z, x);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 1.6e-97], x, If[LessEqual[y$95$m, 1.35e-36], N[(N[(y$95$m * N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - N[(x / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(t * 1.0 + N[(N[Tanh[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision] * (-y$95$m)), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.5999999999999999e-97

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 66.5%

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

   if 1.5999999999999999e-97 < y < 1.35000000000000004e-36

   1. Initial program 100.0%

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

   3. Taylor expanded in 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. /-lowering-/.f64 85.4

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

   5. Simplified 85.4%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. tanh-lowering-tanh.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. /-lowering-/.f64 85.4

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

   7. Applied egg-rr 85.4%

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

   if 1.35000000000000004e-36 < y

   1. Initial program 86.3%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. tanh-lowering-tanh.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. tanh-lowering-tanh.f64 N/A

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

      10. /-lowering-/.f64 92.1

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

   4. Applied egg-rr 92.1%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 83.7

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

   7. Simplified 83.7%

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-rgt-in N/A

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

      4. div-inv N/A

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

      5. associate-*l* N/A

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

      6. lft-mult-inverse N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. neg-lowering-neg.f64 N/A

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

      10. tanh-lowering-tanh.f64 N/A

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

      11. /-lowering-/.f64 89.3

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

   9. Applied egg-rr 89.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(t, 1, \left(-\tanh \left(\frac{x}{y}\right)\right) \cdot y\right)}, z, x\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-36}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(t, 1, \tanh \left(\frac{x}{y}\right) \cdot \left(-y\right)\right), z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 4.4 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(t, 1, \tanh \left(\frac{x}{y\_m}\right) \cdot \left(-y\_m\right)\right), z, x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 4.4e-36) x (fma (fma t 1.0 (* (tanh (/ x y_m)) (- y_m))) z x)))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 4.4e-36) {
		tmp = x;
	} else {
		tmp = fma(fma(t, 1.0, (tanh((x / y_m)) * -y_m)), z, x);
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 4.4e-36)
		tmp = x;
	else
		tmp = fma(fma(t, 1.0, Float64(tanh(Float64(x / y_m)) * Float64(-y_m))), z, x);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 4.4e-36], x, N[(N[(t * 1.0 + N[(N[Tanh[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision] * (-y$95$m)), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.3999999999999999e-36

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 65.4%

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

   if 4.3999999999999999e-36 < y

   1. Initial program 86.1%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. tanh-lowering-tanh.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. tanh-lowering-tanh.f64 N/A

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

      10. /-lowering-/.f64 92.0

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

   4. Applied egg-rr 92.0%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 83.6

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

   7. Simplified 83.6%

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-rgt-in N/A

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

      4. div-inv N/A

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

      5. associate-*l* N/A

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

      6. lft-mult-inverse N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. neg-lowering-neg.f64 N/A

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

      10. tanh-lowering-tanh.f64 N/A

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

      11. /-lowering-/.f64 89.3

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

   9. Applied egg-rr 89.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(t, 1, \left(-\tanh \left(\frac{x}{y}\right)\right) \cdot y\right)}, z, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.4 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(t, 1, \tanh \left(\frac{x}{y}\right) \cdot \left(-y\right)\right), z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.4% accurate, 14.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 5.5 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 5.5e-33) x (fma z (- t x) x)))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 5.5e-33) {
		tmp = x;
	} else {
		tmp = fma(z, (t - x), x);
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 5.5e-33)
		tmp = x;
	else
		tmp = fma(z, Float64(t - x), x);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 5.5e-33], x, N[(z * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.5e-33

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 65.4%

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

   if 5.5e-33 < y

   1. Initial program 86.1%

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

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

      3. --lowering--.f64 80.7

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

   5. Simplified 80.7%

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

Alternative 6: 70.6% accurate, 18.4× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 8.5 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t, x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t) :precision binary64 (if (<= y_m 8.5e-32) x (fma z t x)))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 8.5e-32) {
		tmp = x;
	} else {
		tmp = fma(z, t, x);
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 8.5e-32)
		tmp = x;
	else
		tmp = fma(z, t, x);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 8.5e-32], x, N[(z * t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.5000000000000003e-32

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 65.4%

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

   if 8.5000000000000003e-32 < y

   1. Initial program 86.1%

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

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

      3. --lowering--.f64 80.7

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

   5. Simplified 80.7%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 66.3%

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

Alternative 7: 60.2% accurate, 239.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t) :precision binary64 x)

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	return x;
}

Fortran

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

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	return x;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	return x

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	return x
end

MATLAB

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

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := x

Derivation

1. Initial program 94.4%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 59.7%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 97.2% 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 2024198 
(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))))))