SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.5% → 97.7%

Time: 13.3s

Alternatives: 12

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: 93.5% 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: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{+158}:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.3e+158)
   (fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
   (+ x (* z (- t x)))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.3e+158) {
		tmp = fma(y, (z * (tanh((t / y)) - tanh((x / y)))), x);
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.3e+158)
		tmp = fma(y, Float64(z * Float64(tanh(Float64(t / y)) - tanh(Float64(x / y)))), x);
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[y, 2.3e+158], N[(y * N[(z * N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.29999999999999986e158

   1. Initial program 94.8%

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

      1. +-commutative 94.8%

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

      2. associate-*l* 98.6%

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

      3. fma-def 98.6%

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

   3. Simplified 98.6%

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

   if 2.29999999999999986e158 < y

   1. Initial program 78.7%

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

      1. associate-*l* 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in y around inf 94.5%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{+158}:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 2: 87.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-26} \lor \neg \left(t \leq 2.8 \cdot 10^{-64}\right):\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot \left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right), x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.2e-26) (not (<= t 2.8e-64)))
   (+ x (* y (* z (tanh (/ t y)))))
   (fma y (* z (- (/ t y) (tanh (/ x y)))) x)))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.2e-26) || !(t <= 2.8e-64)) {
		tmp = x + (y * (z * tanh((t / y))));
	} else {
		tmp = fma(y, (z * ((t / y) - tanh((x / y)))), x);
	}
	return tmp;
}

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.2e-26) || !(t <= 2.8e-64))
		tmp = Float64(x + Float64(y * Float64(z * tanh(Float64(t / y)))));
	else
		tmp = fma(y, Float64(z * Float64(Float64(t / y) - tanh(Float64(x / y)))), x);
	end
	return tmp
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.2e-26], N[Not[LessEqual[t, 2.8e-64]], $MachinePrecision]], N[(x + N[(y * N[(z * N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * N[(N[(t / y), $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2000000000000001e-26 or 2.80000000000000004e-64 < t

   1. Initial program 95.7%

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

      1. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 12.0%

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

      1. associate-/r* 12.0%

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

      2. div-sub 12.0%

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

      3. rec-exp 12.0%

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

      4. rec-exp 12.0%

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

      5. tanh-def-a 92.1%

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

   6. Simplified 92.1%

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

   if -2.2000000000000001e-26 < t < 2.80000000000000004e-64

   1. Initial program 88.3%

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

      1. +-commutative 88.3%

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

      2. associate-*l* 92.9%

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

      3. fma-def 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in t around 0 87.2%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-26} \lor \neg \left(t \leq 2.8 \cdot 10^{-64}\right):\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot \left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right), x\right)\\ \end{array} \]

Alternative 3: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{+158}:\\ \;\;\;\;x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.85e+158)
   (+ x (* y (* z (- (tanh (/ t y)) (tanh (/ x y))))))
   (+ x (* z (- t x)))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.85e+158) {
		tmp = x + (y * (z * (tanh((t / y)) - tanh((x / y)))));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= 1.85d+158) then
        tmp = x + (y * (z * (tanh((t / y)) - tanh((x / y)))))
    else
        tmp = x + (z * (t - x))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.85e+158) {
		tmp = x + (y * (z * (Math.tanh((t / y)) - Math.tanh((x / y)))));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	tmp = 0
	if y <= 1.85e+158:
		tmp = x + (y * (z * (math.tanh((t / y)) - math.tanh((x / y)))))
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.85e+158)
		tmp = Float64(x + Float64(y * Float64(z * Float64(tanh(Float64(t / y)) - tanh(Float64(x / y))))));
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.85e+158)
		tmp = x + (y * (z * (tanh((t / y)) - tanh((x / y)))));
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[y, 1.85e+158], 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], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.85000000000000005e158

   1. Initial program 94.8%

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

      1. associate-*l* 98.6%

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

   3. Simplified 98.6%

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

   if 1.85000000000000005e158 < y

   1. Initial program 78.7%

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

      1. associate-*l* 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in y around inf 94.5%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{+158}:\\ \;\;\;\;x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4: 85.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-28} \lor \neg \left(t \leq 2.8 \cdot 10^{-63}\right):\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.2e-28) (not (<= t 2.8e-63)))
   (+ x (* y (* z (tanh (/ t y)))))
   (+ x (* (- (/ t y) (tanh (/ x y))) (* y z)))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.2e-28) || !(t <= 2.8e-63)) {
		tmp = x + (y * (z * tanh((t / y))));
	} else {
		tmp = x + (((t / y) - tanh((x / y))) * (y * z));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= (-4.2d-28)) .or. (.not. (t <= 2.8d-63))) then
        tmp = x + (y * (z * tanh((t / y))))
    else
        tmp = x + (((t / y) - tanh((x / y))) * (y * z))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.2e-28) || !(t <= 2.8e-63)) {
		tmp = x + (y * (z * Math.tanh((t / y))));
	} else {
		tmp = x + (((t / y) - Math.tanh((x / y))) * (y * z));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	tmp = 0
	if (t <= -4.2e-28) or not (t <= 2.8e-63):
		tmp = x + (y * (z * math.tanh((t / y))))
	else:
		tmp = x + (((t / y) - math.tanh((x / y))) * (y * z))
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.2e-28) || !(t <= 2.8e-63))
		tmp = Float64(x + Float64(y * Float64(z * tanh(Float64(t / y)))));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - tanh(Float64(x / y))) * Float64(y * z)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.2e-28) || ~((t <= 2.8e-63)))
		tmp = x + (y * (z * tanh((t / y))));
	else
		tmp = x + (((t / y) - tanh((x / y))) * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.2e-28], N[Not[LessEqual[t, 2.8e-63]], $MachinePrecision]], N[(x + N[(y * N[(z * N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.20000000000000013e-28 or 2.8000000000000002e-63 < t

   1. Initial program 95.7%

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

      1. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 12.0%

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

      1. associate-/r* 12.0%

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

      2. div-sub 12.0%

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

      3. rec-exp 12.0%

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

      4. rec-exp 12.0%

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

      5. tanh-def-a 92.1%

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

   6. Simplified 92.1%

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

   if -4.20000000000000013e-28 < t < 2.8000000000000002e-63

   1. Initial program 88.3%

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

   2. Taylor expanded in t around 0 83.6%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-28} \lor \neg \left(t \leq 2.8 \cdot 10^{-63}\right):\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 5: 82.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-136} \lor \neg \left(t \leq 2.85 \cdot 10^{-65}\right):\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.65e-136) (not (<= t 2.85e-65)))
   (+ x (* y (* z (tanh (/ t y)))))
   (+ x (* z (- t x)))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.65e-136) || !(t <= 2.85e-65)) {
		tmp = x + (y * (z * tanh((t / y))));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= (-1.65d-136)) .or. (.not. (t <= 2.85d-65))) then
        tmp = x + (y * (z * tanh((t / y))))
    else
        tmp = x + (z * (t - x))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.65e-136) || !(t <= 2.85e-65)) {
		tmp = x + (y * (z * Math.tanh((t / y))));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	tmp = 0
	if (t <= -1.65e-136) or not (t <= 2.85e-65):
		tmp = x + (y * (z * math.tanh((t / y))))
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.65e-136) || !(t <= 2.85e-65))
		tmp = Float64(x + Float64(y * Float64(z * tanh(Float64(t / y)))));
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.65e-136) || ~((t <= 2.85e-65)))
		tmp = x + (y * (z * tanh((t / y))));
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.65e-136], N[Not[LessEqual[t, 2.85e-65]], $MachinePrecision]], N[(x + N[(y * N[(z * N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.65000000000000009e-136 or 2.8500000000000001e-65 < t

   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. Step-by-step derivation

      1. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around 0 13.4%

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

      1. associate-/r* 13.4%

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

      2. div-sub 13.4%

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

      3. rec-exp 13.4%

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

      4. rec-exp 13.4%

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

      5. tanh-def-a 90.0%

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

   6. Simplified 90.0%

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

   if -1.65000000000000009e-136 < t < 2.8500000000000001e-65

   1. Initial program 89.4%

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

      1. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in y around inf 81.3%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-136} \lor \neg \left(t \leq 2.85 \cdot 10^{-65}\right):\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 6: 87.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} t_1 := \tanh \left(\frac{t}{y}\right)\\ \mathbf{if}\;y \leq 3.4 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot \left(z \cdot t_1\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot t_1 - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (tanh (/ t y))))
   (if (<= y 3.4e+42) (+ x (* y (* z t_1))) (+ x (* z (- (* y t_1) x))))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double t_1 = tanh((t / y));
	double tmp;
	if (y <= 3.4e+42) {
		tmp = x + (y * (z * t_1));
	} else {
		tmp = x + (z * ((y * t_1) - x));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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) :: t_1
    real(8) :: tmp
    t_1 = tanh((t / y))
    if (y <= 3.4d+42) then
        tmp = x + (y * (z * t_1))
    else
        tmp = x + (z * ((y * t_1) - x))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.tanh((t / y));
	double tmp;
	if (y <= 3.4e+42) {
		tmp = x + (y * (z * t_1));
	} else {
		tmp = x + (z * ((y * t_1) - x));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	t_1 = math.tanh((t / y))
	tmp = 0
	if y <= 3.4e+42:
		tmp = x + (y * (z * t_1))
	else:
		tmp = x + (z * ((y * t_1) - x))
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	t_1 = tanh(Float64(t / y))
	tmp = 0.0
	if (y <= 3.4e+42)
		tmp = Float64(x + Float64(y * Float64(z * t_1)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y * t_1) - x)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	t_1 = tanh((t / y));
	tmp = 0.0;
	if (y <= 3.4e+42)
		tmp = x + (y * (z * t_1));
	else
		tmp = x + (z * ((y * t_1) - x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, 3.4e+42], N[(x + N[(y * N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y * t$95$1), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 3.39999999999999975e42

   1. Initial program 94.8%

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

      1. associate-*l* 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in x around 0 23.9%

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

      1. associate-/r* 23.9%

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

      2. div-sub 23.9%

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

      3. rec-exp 23.9%

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

      4. rec-exp 23.9%

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

      5. tanh-def-a 82.3%

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

   6. Simplified 82.3%

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

   if 3.39999999999999975e42 < y

   1. Initial program 84.9%

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

      1. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in x around 0 45.4%

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

      1. +-commutative 45.4%

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

   6. Simplified 89.6%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.4 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot \tanh \left(\frac{t}{y}\right) - x\right)\\ \end{array} \]

Alternative 7: 64.1% accurate, 19.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 3.8 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+134} \lor \neg \left(y \leq 1.4 \cdot 10^{+200}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (<= y 3.8e+47)
   x
   (if (or (<= y 4e+134) (not (<= y 1.4e+200))) (* x (- 1.0 z)) (* z t))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.8e+47) {
		tmp = x;
	} else if ((y <= 4e+134) || !(y <= 1.4e+200)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * t;
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= 3.8d+47) then
        tmp = x
    else if ((y <= 4d+134) .or. (.not. (y <= 1.4d+200))) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * t
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.8e+47) {
		tmp = x;
	} else if ((y <= 4e+134) || !(y <= 1.4e+200)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	tmp = 0
	if y <= 3.8e+47:
		tmp = x
	elif (y <= 4e+134) or not (y <= 1.4e+200):
		tmp = x * (1.0 - z)
	else:
		tmp = z * t
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 3.8e+47)
		tmp = x;
	elseif ((y <= 4e+134) || !(y <= 1.4e+200))
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 3.8e+47)
		tmp = x;
	elseif ((y <= 4e+134) || ~((y <= 1.4e+200)))
		tmp = x * (1.0 - z);
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[y, 3.8e+47], x, If[Or[LessEqual[y, 4e+134], N[Not[LessEqual[y, 1.4e+200]], $MachinePrecision]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.8000000000000003e47

   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. Taylor expanded in x around inf 65.3%

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

   if 3.8000000000000003e47 < y < 3.99999999999999969e134 or 1.39999999999999992e200 < y

   1. Initial program 82.0%

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

      1. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in y around inf 78.9%

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

   5. Taylor expanded in x around inf 48.3%

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

      1. mul-1-neg 48.3%

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

      2. unsub-neg 48.3%

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

   7. Simplified 48.3%

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

   if 3.99999999999999969e134 < y < 1.39999999999999992e200

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*l* 99.6%

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

      3. fma-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around 0 85.1%

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

   5. Taylor expanded in t around inf 55.6%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.8 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+134} \lor \neg \left(y \leq 1.4 \cdot 10^{+200}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 8: 77.7% accurate, 19.3× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot t - x \cdot \left(z + -1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.2e+47) x (- (* z t) (* x (+ z -1.0)))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.2e+47) {
		tmp = x;
	} else {
		tmp = (z * t) - (x * (z + -1.0));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= 1.2d+47) then
        tmp = x
    else
        tmp = (z * t) - (x * (z + (-1.0d0)))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.2e+47) {
		tmp = x;
	} else {
		tmp = (z * t) - (x * (z + -1.0));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	tmp = 0
	if y <= 1.2e+47:
		tmp = x
	else:
		tmp = (z * t) - (x * (z + -1.0))
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.2e+47)
		tmp = x;
	else
		tmp = Float64(Float64(z * t) - Float64(x * Float64(z + -1.0)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.2e+47)
		tmp = x;
	else
		tmp = (z * t) - (x * (z + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[y, 1.2e+47], x, N[(N[(z * t), $MachinePrecision] - N[(x * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.20000000000000009e47

   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. Taylor expanded in x around inf 65.3%

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

   if 1.20000000000000009e47 < y

   1. Initial program 86.5%

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

      1. associate-*l* 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in y around inf 78.1%

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

      1. expm1-log1p-u 46.8%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \frac{z \cdot \left(t - x\right)}{y}\right)\right)} \]

      2. expm1-udef 41.4%

         \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(y \cdot \frac{z \cdot \left(t - x\right)}{y}\right)} - 1\right)} \]

      3. associate-/l* 41.5%

         \[\leadsto x + \left(e^{\mathsf{log1p}\left(y \cdot \color{blue}{\frac{z}{\frac{y}{t - x}}}\right)} - 1\right) \]

   6. Applied egg-rr 41.5%

      \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(y \cdot \frac{z}{\frac{y}{t - x}}\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 45.2%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \frac{z}{\frac{y}{t - x}}\right)\right)} \]

      2. expm1-log1p 72.6%

         \[\leadsto x + \color{blue}{y \cdot \frac{z}{\frac{y}{t - x}}} \]

      3. associate-*r/ 67.0%

         \[\leadsto x + \color{blue}{\frac{y \cdot z}{\frac{y}{t - x}}} \]

   8. Simplified 67.0%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{\frac{y}{t - x}}} \]

   9. Taylor expanded in x around -inf 80.5%

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

       1. +-commutative 80.5%

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

       2. mul-1-neg 80.5%

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

       3. unsub-neg 80.5%

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

       4. sub-neg 80.5%

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

       5. metadata-eval 80.5%

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

   11. Simplified 80.5%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot t - x \cdot \left(z + -1\right)\\ \end{array} \]

Alternative 9: 58.9% accurate, 23.1× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 3.3 \cdot 10^{+132} \lor \neg \left(y \leq 5.8 \cdot 10^{+289}\right) \land y \leq 7.2 \cdot 10^{+300}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y 3.3e+132) (and (not (<= y 5.8e+289)) (<= y 7.2e+300)))
   x
   (* z t)))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= 3.3e+132) || (!(y <= 5.8e+289) && (y <= 7.2e+300))) {
		tmp = x;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= 3.3d+132) .or. (.not. (y <= 5.8d+289)) .and. (y <= 7.2d+300)) then
        tmp = x
    else
        tmp = z * t
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= 3.3e+132) || (!(y <= 5.8e+289) && (y <= 7.2e+300))) {
		tmp = x;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	tmp = 0
	if (y <= 3.3e+132) or (not (y <= 5.8e+289) and (y <= 7.2e+300)):
		tmp = x
	else:
		tmp = z * t
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= 3.3e+132) || (!(y <= 5.8e+289) && (y <= 7.2e+300)))
		tmp = x;
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= 3.3e+132) || (~((y <= 5.8e+289)) && (y <= 7.2e+300)))
		tmp = x;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[Or[LessEqual[y, 3.3e+132], And[N[Not[LessEqual[y, 5.8e+289]], $MachinePrecision], LessEqual[y, 7.2e+300]]], x, N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.3000000000000003e132 or 5.79999999999999967e289 < y < 7.2000000000000004e300

   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. Taylor expanded in x around inf 61.7%

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

   if 3.3000000000000003e132 < y < 5.79999999999999967e289 or 7.2000000000000004e300 < y

   1. Initial program 81.7%

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

      1. +-commutative 81.7%

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

      2. associate-*l* 90.3%

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

      3. fma-def 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in t around 0 82.1%

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

   5. Taylor expanded in t around inf 52.0%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.3 \cdot 10^{+132} \lor \neg \left(y \leq 5.8 \cdot 10^{+289}\right) \land y \leq 7.2 \cdot 10^{+300}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 10: 78.3% accurate, 23.5× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.05 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.05e+47) x (+ x (* z (- t x)))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.05e+47) {
		tmp = x;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= 1.05d+47) then
        tmp = x
    else
        tmp = x + (z * (t - x))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.05e+47) {
		tmp = x;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	tmp = 0
	if y <= 1.05e+47:
		tmp = x
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.05e+47)
		tmp = x;
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.05e+47)
		tmp = x;
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[y, 1.05e+47], x, N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.05e47

   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. Taylor expanded in x around inf 65.3%

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

   if 1.05e47 < y

   1. Initial program 86.5%

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

      1. associate-*l* 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in y around inf 80.5%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.05 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 11: 71.1% accurate, 30.2× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t) :precision binary64 (if (<= y 1.45e+47) x (+ x (* z t))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.45e+47) {
		tmp = x;
	} else {
		tmp = x + (z * t);
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= 1.45d+47) then
        tmp = x
    else
        tmp = x + (z * t)
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.45e+47) {
		tmp = x;
	} else {
		tmp = x + (z * t);
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	tmp = 0
	if y <= 1.45e+47:
		tmp = x
	else:
		tmp = x + (z * t)
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.45e+47)
		tmp = x;
	else
		tmp = Float64(x + Float64(z * t));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.45e+47)
		tmp = x;
	else
		tmp = x + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[y, 1.45e+47], x, N[(x + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.4499999999999999e47

   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. Taylor expanded in x around inf 65.3%

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

   if 1.4499999999999999e47 < y

   1. Initial program 86.5%

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

   2. Taylor expanded in t around 0 70.6%

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

   3. Taylor expanded in y around 0 56.3%

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

      1. +-commutative 56.3%

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

      2. *-commutative 56.3%

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

   5. Simplified 56.3%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot t\\ \end{array} \]

Alternative 12: 60.1% accurate, 213.0× speedup

Math

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

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t) :precision binary64 x)

C

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

Fortran

NOTE: y should be positive before calling this function
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
end function

Java

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

Python

y = abs(y)
def code(x, y, z, t):
	return x

Julia

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

MATLAB

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

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := x

Derivation

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. Taylor expanded in x around inf 55.9%

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

3. Final simplification 55.9%

   \[\leadsto x \]

Developer target: 97.0% 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 2023311 
(FPCore (x y z t)
  :name "SynthBasics:moogVCF from YampaSynth-0.2"
  :precision binary64

  :herbie-target
  (+ x (* y (* z (- (tanh (/ t y)) (tanh (/ x y))))))

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