SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.4% → 98.8%

Time: 12.3s

Alternatives: 11

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 3.8 \cdot 10^{+217}:\\ \;\;\;\;\mathsf{fma}\left(z, y\_m \cdot \left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 3.8e+217)
   (fma z (* y_m (- (tanh (/ t y_m)) (tanh (/ x y_m)))) x)
   (+ x (* z (- t x)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 3.8e+217) {
		tmp = fma(z, (y_m * (tanh((t / y_m)) - tanh((x / y_m)))), x);
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 3.8e+217)
		tmp = fma(z, Float64(y_m * Float64(tanh(Float64(t / y_m)) - tanh(Float64(x / y_m)))), x);
	else
		tmp = Float64(x + Float64(z * Float64(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, 3.8e+217], N[(z * 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] + x), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.80000000000000002e217

   1. Initial program 95.6%

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

      1. +-commutative 95.6%

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

      2. *-commutative 95.6%

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

      3. associate-*l* 98.8%

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

      4. fma-def 98.8%

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

   3. Simplified 98.8%

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

   if 3.80000000000000002e217 < y

   1. Initial program 51.1%

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

   3. Taylor expanded in y around inf 100.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.8 \cdot 10^{+217}:\\ \;\;\;\;\mathsf{fma}\left(z, y \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_1 := x + \left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right) \cdot \left(y\_m \cdot z\right)\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+289}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

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 2e+289) t_1 (* z (- t x)))))

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 <= 2e+289) {
		tmp = t_1;
	} else {
		tmp = z * (t - x);
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((tanh((t / y_m)) - tanh((x / y_m))) * (y_m * z))
    if (t_1 <= 2d+289) then
        tmp = t_1
    else
        tmp = z * (t - x)
    end if
    code = tmp
end function

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 <= 2e+289) {
		tmp = t_1;
	} else {
		tmp = z * (t - x);
	}
	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 <= 2e+289:
		tmp = t_1
	else:
		tmp = z * (t - x)
	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 <= 2e+289)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(t - x));
	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 <= 2e+289)
		tmp = t_1;
	else
		tmp = z * (t - x);
	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, 2e+289], t$95$1, N[(z * N[(t - x), $MachinePrecision]), $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))))) < 2.0000000000000001e289

   1. Initial program 97.9%

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

   if 2.0000000000000001e289 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

   1. Initial program 36.7%

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

   3. Taylor expanded in y around inf 95.0%

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

   4. Taylor expanded in z around inf 95.0%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right) \leq 2 \cdot 10^{+289}:\\ \;\;\;\;x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_1 := x + y\_m \cdot \left(z \cdot \tanh \left(\frac{t}{y\_m}\right)\right)\\ \mathbf{if}\;t \leq -9.4 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-280}:\\ \;\;\;\;x + \left(y\_m \cdot z\right) \cdot \left(\frac{t}{y\_m} - \tanh \left(\frac{x}{y\_m}\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-33}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (let* ((t_1 (+ x (* y_m (* z (tanh (/ t y_m)))))))
   (if (<= t -9.4e-88)
     t_1
     (if (<= t -1.08e-280)
       (+ x (* (* y_m z) (- (/ t y_m) (tanh (/ x y_m)))))
       (if (<= t 1.15e-33) (+ x (* z (- t x))) t_1)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double t_1 = x + (y_m * (z * tanh((t / y_m))));
	double tmp;
	if (t <= -9.4e-88) {
		tmp = t_1;
	} else if (t <= -1.08e-280) {
		tmp = x + ((y_m * z) * ((t / y_m) - tanh((x / y_m))));
	} else if (t <= 1.15e-33) {
		tmp = x + (z * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y_m * (z * tanh((t / y_m))))
    if (t <= (-9.4d-88)) then
        tmp = t_1
    else if (t <= (-1.08d-280)) then
        tmp = x + ((y_m * z) * ((t / y_m) - tanh((x / y_m))))
    else if (t <= 1.15d-33) then
        tmp = x + (z * (t - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double t_1 = x + (y_m * (z * Math.tanh((t / y_m))));
	double tmp;
	if (t <= -9.4e-88) {
		tmp = t_1;
	} else if (t <= -1.08e-280) {
		tmp = x + ((y_m * z) * ((t / y_m) - Math.tanh((x / y_m))));
	} else if (t <= 1.15e-33) {
		tmp = x + (z * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	t_1 = x + (y_m * (z * math.tanh((t / y_m))))
	tmp = 0
	if t <= -9.4e-88:
		tmp = t_1
	elif t <= -1.08e-280:
		tmp = x + ((y_m * z) * ((t / y_m) - math.tanh((x / y_m))))
	elif t <= 1.15e-33:
		tmp = x + (z * (t - x))
	else:
		tmp = t_1
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	t_1 = Float64(x + Float64(y_m * Float64(z * tanh(Float64(t / y_m)))))
	tmp = 0.0
	if (t <= -9.4e-88)
		tmp = t_1;
	elseif (t <= -1.08e-280)
		tmp = Float64(x + Float64(Float64(y_m * z) * Float64(Float64(t / y_m) - tanh(Float64(x / y_m)))));
	elseif (t <= 1.15e-33)
		tmp = Float64(x + Float64(z * Float64(t - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	t_1 = x + (y_m * (z * tanh((t / y_m))));
	tmp = 0.0;
	if (t <= -9.4e-88)
		tmp = t_1;
	elseif (t <= -1.08e-280)
		tmp = x + ((y_m * z) * ((t / y_m) - tanh((x / y_m))));
	elseif (t <= 1.15e-33)
		tmp = x + (z * (t - x));
	else
		tmp = t_1;
	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[(y$95$m * N[(z * N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.4e-88], t$95$1, If[LessEqual[t, -1.08e-280], N[(x + N[(N[(y$95$m * z), $MachinePrecision] * N[(N[(t / y$95$m), $MachinePrecision] - N[Tanh[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-33], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.4e-88 or 1.14999999999999993e-33 < t

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 7.5%

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

      1. associate-/r* 7.5%

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

      2. div-sub 7.5%

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

      3. rec-exp 7.5%

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

      4. rec-exp 7.5%

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

      5. tanh-def-a 90.3%

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

   5. Simplified 90.3%

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

   if -9.4e-88 < t < -1.07999999999999996e-280

   1. Initial program 91.9%

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

   3. Taylor expanded in t around 0 89.1%

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

   if -1.07999999999999996e-280 < t < 1.14999999999999993e-33

   1. Initial program 82.3%

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

   3. Taylor expanded in y around inf 85.9%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{-88}:\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-280}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-33}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-88} \lor \neg \left(t \leq 7.2 \cdot 10^{-27}\right):\\ \;\;\;\;x + y\_m \cdot \left(z \cdot \tanh \left(\frac{t}{y\_m}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (or (<= t -9.5e-88) (not (<= t 7.2e-27)))
   (+ x (* y_m (* z (tanh (/ t y_m)))))
   (+ x (* z (- t x)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if ((t <= -9.5e-88) || !(t <= 7.2e-27)) {
		tmp = x + (y_m * (z * tanh((t / y_m))));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((t <= (-9.5d-88)) .or. (.not. (t <= 7.2d-27))) then
        tmp = x + (y_m * (z * tanh((t / y_m))))
    else
        tmp = x + (z * (t - x))
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double tmp;
	if ((t <= -9.5e-88) || !(t <= 7.2e-27)) {
		tmp = x + (y_m * (z * Math.tanh((t / y_m))));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if (t <= -9.5e-88) or not (t <= 7.2e-27):
		tmp = x + (y_m * (z * math.tanh((t / y_m))))
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if ((t <= -9.5e-88) || !(t <= 7.2e-27))
		tmp = Float64(x + Float64(y_m * Float64(z * tanh(Float64(t / y_m)))));
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	tmp = 0.0;
	if ((t <= -9.5e-88) || ~((t <= 7.2e-27)))
		tmp = x + (y_m * (z * tanh((t / y_m))));
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[Or[LessEqual[t, -9.5e-88], N[Not[LessEqual[t, 7.2e-27]], $MachinePrecision]], N[(x + N[(y$95$m * N[(z * N[Tanh[N[(t / y$95$m), $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 < -9.5e-88 or 7.1999999999999997e-27 < t

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 7.5%

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

      1. associate-/r* 7.5%

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

      2. div-sub 7.5%

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

      3. rec-exp 7.5%

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

      4. rec-exp 7.5%

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

      5. tanh-def-a 90.3%

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

   5. Simplified 90.3%

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

   if -9.5e-88 < t < 7.1999999999999997e-27

   1. Initial program 85.6%

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

   3. Taylor expanded in y around inf 81.8%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-88} \lor \neg \left(t \leq 7.2 \cdot 10^{-27}\right):\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 2.6 \cdot 10^{+75}:\\ \;\;\;\;x + y\_m \cdot \frac{z}{\frac{y\_m}{t} - \frac{t}{y\_m} \cdot -0.3333333333333333}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 2.6e+75)
   (+ x (* y_m (/ z (- (/ y_m t) (* (/ t y_m) -0.3333333333333333)))))
   (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 <= 2.6e+75) {
		tmp = x + (y_m * (z / ((y_m / t) - ((t / y_m) * -0.3333333333333333))));
	} 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 <= 2.6e+75)
		tmp = Float64(x + Float64(y_m * Float64(z / Float64(Float64(y_m / t) - Float64(Float64(t / y_m) * -0.3333333333333333)))));
	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, 2.6e+75], N[(x + N[(y$95$m * N[(z / N[(N[(y$95$m / t), $MachinePrecision] - N[(N[(t / y$95$m), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.59999999999999985e75

   1. Initial program 96.2%

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

   3. Taylor expanded in x around 0 17.7%

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

      1. associate-/r* 17.7%

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

      2. div-sub 17.7%

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

      3. rec-exp 17.7%

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

      4. rec-exp 17.7%

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

      5. tanh-def-a 80.3%

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

   5. Simplified 80.3%

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

      1. tanh-def-b 46.7%

         \[\leadsto x + y \cdot \left(z \cdot \color{blue}{\frac{e^{2 \cdot \frac{t}{y}} - 1}{e^{2 \cdot \frac{t}{y}} + 1}}\right) \]

      2. clear-num 46.7%

         \[\leadsto x + y \cdot \left(z \cdot \color{blue}{\frac{1}{\frac{e^{2 \cdot \frac{t}{y}} + 1}{e^{2 \cdot \frac{t}{y}} - 1}}}\right) \]

      3. +-commutative 46.7%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\frac{\color{blue}{1 + e^{2 \cdot \frac{t}{y}}}}{e^{2 \cdot \frac{t}{y}} - 1}}\right) \]

      4. exp-prod 46.7%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\frac{1 + \color{blue}{{\left(e^{2}\right)}^{\left(\frac{t}{y}\right)}}}{e^{2 \cdot \frac{t}{y}} - 1}}\right) \]

      5. expm1-def 51.1%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\frac{1 + {\left(e^{2}\right)}^{\left(\frac{t}{y}\right)}}{\color{blue}{\mathsf{expm1}\left(2 \cdot \frac{t}{y}\right)}}}\right) \]

      6. *-commutative 51.1%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\frac{1 + {\left(e^{2}\right)}^{\left(\frac{t}{y}\right)}}{\mathsf{expm1}\left(\color{blue}{\frac{t}{y} \cdot 2}\right)}}\right) \]

   7. Applied egg-rr 51.1%

      \[\leadsto x + y \cdot \left(z \cdot \color{blue}{\frac{1}{\frac{1 + {\left(e^{2}\right)}^{\left(\frac{t}{y}\right)}}{\mathsf{expm1}\left(\frac{t}{y} \cdot 2\right)}}}\right) \]

   8. Taylor expanded in y around -inf 69.8%

      \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\color{blue}{-1 \cdot \frac{-1 \cdot t - -0.6666666666666666 \cdot t}{y} + \frac{y}{t}}}\right) \]
   9. Step-by-step derivation

      1. +-commutative 69.8%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\color{blue}{\frac{y}{t} + -1 \cdot \frac{-1 \cdot t - -0.6666666666666666 \cdot t}{y}}}\right) \]

      2. mul-1-neg 69.8%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\frac{y}{t} + \color{blue}{\left(-\frac{-1 \cdot t - -0.6666666666666666 \cdot t}{y}\right)}}\right) \]

      3. unsub-neg 69.8%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\color{blue}{\frac{y}{t} - \frac{-1 \cdot t - -0.6666666666666666 \cdot t}{y}}}\right) \]

      4. distribute-rgt-out-- 69.8%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\frac{y}{t} - \frac{\color{blue}{t \cdot \left(-1 - -0.6666666666666666\right)}}{y}}\right) \]

      5. metadata-eval 69.8%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\frac{y}{t} - \frac{t \cdot \color{blue}{-0.3333333333333333}}{y}}\right) \]

   10. Simplified 69.8%

       \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\color{blue}{\frac{y}{t} - \frac{t \cdot -0.3333333333333333}{y}}}\right) \]

   11. Taylor expanded in z around 0 69.8%

       \[\leadsto x + y \cdot \color{blue}{\frac{z}{\frac{y}{t} - -0.3333333333333333 \cdot \frac{t}{y}}} \]

   if 2.59999999999999985e75 < y

   1. Initial program 80.2%

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

   3. Taylor expanded in y around inf 84.7%

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

      1. +-commutative 84.7%

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

      2. fma-def 84.8%

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

   5. Simplified 84.8%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{+75}:\\ \;\;\;\;x + y \cdot \frac{z}{\frac{y}{t} - \frac{t}{y} \cdot -0.3333333333333333}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.7% accurate, 10.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 1.15 \cdot 10^{+75}:\\ \;\;\;\;x + y\_m \cdot \frac{z}{\frac{y\_m}{t} - \frac{t}{y\_m} \cdot -0.3333333333333333}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 1.15e+75)
   (+ x (* y_m (/ z (- (/ y_m t) (* (/ t y_m) -0.3333333333333333)))))
   (+ x (* z (- t x)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 1.15e+75) {
		tmp = x + (y_m * (z / ((y_m / t) - ((t / y_m) * -0.3333333333333333))));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y_m <= 1.15d+75) then
        tmp = x + (y_m * (z / ((y_m / t) - ((t / y_m) * (-0.3333333333333333d0)))))
    else
        tmp = x + (z * (t - x))
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 1.15e+75) {
		tmp = x + (y_m * (z / ((y_m / t) - ((t / y_m) * -0.3333333333333333))));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if y_m <= 1.15e+75:
		tmp = x + (y_m * (z / ((y_m / t) - ((t / y_m) * -0.3333333333333333))))
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 1.15e+75)
		tmp = Float64(x + Float64(y_m * Float64(z / Float64(Float64(y_m / t) - Float64(Float64(t / y_m) * -0.3333333333333333)))));
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	tmp = 0.0;
	if (y_m <= 1.15e+75)
		tmp = x + (y_m * (z / ((y_m / t) - ((t / y_m) * -0.3333333333333333))));
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 1.15e+75], N[(x + N[(y$95$m * N[(z / N[(N[(y$95$m / t), $MachinePrecision] - N[(N[(t / y$95$m), $MachinePrecision] * -0.3333333333333333), $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 < 1.1499999999999999e75

   1. Initial program 96.2%

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

   3. Taylor expanded in x around 0 17.7%

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

      1. associate-/r* 17.7%

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

      2. div-sub 17.7%

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

      3. rec-exp 17.7%

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

      4. rec-exp 17.7%

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

      5. tanh-def-a 80.3%

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

   5. Simplified 80.3%

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

      1. tanh-def-b 46.7%

         \[\leadsto x + y \cdot \left(z \cdot \color{blue}{\frac{e^{2 \cdot \frac{t}{y}} - 1}{e^{2 \cdot \frac{t}{y}} + 1}}\right) \]

      2. clear-num 46.7%

         \[\leadsto x + y \cdot \left(z \cdot \color{blue}{\frac{1}{\frac{e^{2 \cdot \frac{t}{y}} + 1}{e^{2 \cdot \frac{t}{y}} - 1}}}\right) \]

      3. +-commutative 46.7%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\frac{\color{blue}{1 + e^{2 \cdot \frac{t}{y}}}}{e^{2 \cdot \frac{t}{y}} - 1}}\right) \]

      4. exp-prod 46.7%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\frac{1 + \color{blue}{{\left(e^{2}\right)}^{\left(\frac{t}{y}\right)}}}{e^{2 \cdot \frac{t}{y}} - 1}}\right) \]

      5. expm1-def 51.1%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\frac{1 + {\left(e^{2}\right)}^{\left(\frac{t}{y}\right)}}{\color{blue}{\mathsf{expm1}\left(2 \cdot \frac{t}{y}\right)}}}\right) \]

      6. *-commutative 51.1%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\frac{1 + {\left(e^{2}\right)}^{\left(\frac{t}{y}\right)}}{\mathsf{expm1}\left(\color{blue}{\frac{t}{y} \cdot 2}\right)}}\right) \]

   7. Applied egg-rr 51.1%

      \[\leadsto x + y \cdot \left(z \cdot \color{blue}{\frac{1}{\frac{1 + {\left(e^{2}\right)}^{\left(\frac{t}{y}\right)}}{\mathsf{expm1}\left(\frac{t}{y} \cdot 2\right)}}}\right) \]

   8. Taylor expanded in y around -inf 69.8%

      \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\color{blue}{-1 \cdot \frac{-1 \cdot t - -0.6666666666666666 \cdot t}{y} + \frac{y}{t}}}\right) \]
   9. Step-by-step derivation

      1. +-commutative 69.8%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\color{blue}{\frac{y}{t} + -1 \cdot \frac{-1 \cdot t - -0.6666666666666666 \cdot t}{y}}}\right) \]

      2. mul-1-neg 69.8%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\frac{y}{t} + \color{blue}{\left(-\frac{-1 \cdot t - -0.6666666666666666 \cdot t}{y}\right)}}\right) \]

      3. unsub-neg 69.8%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\color{blue}{\frac{y}{t} - \frac{-1 \cdot t - -0.6666666666666666 \cdot t}{y}}}\right) \]

      4. distribute-rgt-out-- 69.8%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\frac{y}{t} - \frac{\color{blue}{t \cdot \left(-1 - -0.6666666666666666\right)}}{y}}\right) \]

      5. metadata-eval 69.8%

         \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\frac{y}{t} - \frac{t \cdot \color{blue}{-0.3333333333333333}}{y}}\right) \]

   10. Simplified 69.8%

       \[\leadsto x + y \cdot \left(z \cdot \frac{1}{\color{blue}{\frac{y}{t} - \frac{t \cdot -0.3333333333333333}{y}}}\right) \]

   11. Taylor expanded in z around 0 69.8%

       \[\leadsto x + y \cdot \color{blue}{\frac{z}{\frac{y}{t} - -0.3333333333333333 \cdot \frac{t}{y}}} \]

   if 1.1499999999999999e75 < y

   1. Initial program 80.2%

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

   3. Taylor expanded in y around inf 84.7%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{+75}:\\ \;\;\;\;x + y \cdot \frac{z}{\frac{y}{t} - \frac{t}{y} \cdot -0.3333333333333333}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.6% accurate, 14.2× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 2.1 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y\_m \leq 2.35 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 2.1e+28) x (if (<= y_m 2.35e+198) (* x (- 1.0 z)) (* z (- t x)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 2.1e+28) {
		tmp = x;
	} else if (y_m <= 2.35e+198) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (t - x);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y_m <= 2.1d+28) then
        tmp = x
    else if (y_m <= 2.35d+198) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (t - x)
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 2.1e+28) {
		tmp = x;
	} else if (y_m <= 2.35e+198) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (t - x);
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if y_m <= 2.1e+28:
		tmp = x
	elif y_m <= 2.35e+198:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (t - x)
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 2.1e+28)
		tmp = x;
	elseif (y_m <= 2.35e+198)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(t - x));
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	tmp = 0.0;
	if (y_m <= 2.1e+28)
		tmp = x;
	elseif (y_m <= 2.35e+198)
		tmp = x * (1.0 - z);
	else
		tmp = z * (t - x);
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 2.1e+28], x, If[LessEqual[y$95$m, 2.35e+198], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.09999999999999989e28

   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. Taylor expanded in x around inf 67.1%

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

   if 2.09999999999999989e28 < y < 2.3500000000000001e198

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf 71.2%

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

   4. Taylor expanded in x around inf 55.5%

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

      1. mul-1-neg 55.5%

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

      2. unsub-neg 55.5%

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

   6. Simplified 55.5%

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

   if 2.3500000000000001e198 < y

   1. Initial program 56.6%

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

   3. Taylor expanded in y around inf 95.1%

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

   4. Taylor expanded in z around inf 73.6%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.1 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.3% accurate, 14.2× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 1.15 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;y\_m \leq 1.15 \cdot 10^{+199}:\\ \;\;\;\;x + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 1.15e+75) x (if (<= y_m 1.15e+199) (+ x (* z t)) (* z (- t x)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 1.15e+75) {
		tmp = x;
	} else if (y_m <= 1.15e+199) {
		tmp = x + (z * t);
	} else {
		tmp = z * (t - x);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y_m <= 1.15d+75) then
        tmp = x
    else if (y_m <= 1.15d+199) then
        tmp = x + (z * t)
    else
        tmp = z * (t - x)
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 1.15e+75) {
		tmp = x;
	} else if (y_m <= 1.15e+199) {
		tmp = x + (z * t);
	} else {
		tmp = z * (t - x);
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if y_m <= 1.15e+75:
		tmp = x
	elif y_m <= 1.15e+199:
		tmp = x + (z * t)
	else:
		tmp = z * (t - x)
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 1.15e+75)
		tmp = x;
	elseif (y_m <= 1.15e+199)
		tmp = Float64(x + Float64(z * t));
	else
		tmp = Float64(z * Float64(t - x));
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	tmp = 0.0;
	if (y_m <= 1.15e+75)
		tmp = x;
	elseif (y_m <= 1.15e+199)
		tmp = x + (z * t);
	else
		tmp = z * (t - x);
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 1.15e+75], x, If[LessEqual[y$95$m, 1.15e+199], N[(x + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.1499999999999999e75

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 65.6%

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

   if 1.1499999999999999e75 < y < 1.14999999999999997e199

   1. Initial program 93.9%

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

   3. Taylor expanded in x around 0 33.5%

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

      1. associate-/r* 33.5%

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

      2. div-sub 33.5%

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

      3. rec-exp 33.5%

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

      4. rec-exp 33.5%

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

      5. tanh-def-a 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in y around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. *-commutative 60.0%

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

   8. Simplified 60.0%

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

   if 1.14999999999999997e199 < y

   1. Initial program 56.6%

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

   3. Taylor expanded in y around inf 95.1%

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

   4. Taylor expanded in z around inf 73.6%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+199}:\\ \;\;\;\;x + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.4% accurate, 17.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 2.2 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 2.2e+75) x (+ x (* z (- t x)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 2.2e+75) {
		tmp = x;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y_m <= 2.2d+75) then
        tmp = x
    else
        tmp = x + (z * (t - x))
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 2.2e+75) {
		tmp = x;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if y_m <= 2.2e+75:
		tmp = x
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 2.2e+75)
		tmp = x;
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	tmp = 0.0;
	if (y_m <= 2.2e+75)
		tmp = x;
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 2.2e+75], x, N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.20000000000000012e75

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 65.6%

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

   if 2.20000000000000012e75 < y

   1. Initial program 80.2%

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

   3. Taylor expanded in y around inf 84.7%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.4% accurate, 21.3× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 2.1 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 2.1e+28) x (* x (- 1.0 z))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 2.1e+28) {
		tmp = x;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y_m <= 2.1d+28) then
        tmp = x
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 2.1e+28) {
		tmp = x;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if y_m <= 2.1e+28:
		tmp = x
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 2.1e+28)
		tmp = x;
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	tmp = 0.0;
	if (y_m <= 2.1e+28)
		tmp = x;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 2.1e+28], x, N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.09999999999999989e28

   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. Taylor expanded in x around inf 67.1%

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

   if 2.09999999999999989e28 < y

   1. Initial program 83.0%

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

   3. Taylor expanded in y around inf 78.7%

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

   4. Taylor expanded in x around inf 56.1%

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

      1. mul-1-neg 56.1%

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

      2. unsub-neg 56.1%

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

   6. Simplified 56.1%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.1 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.3% accurate, 213.0× 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 93.1%

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

3. Taylor expanded in x around inf 59.7%

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

4. Final simplification 59.7%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024040 
(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))))))