SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.4% → 98.5%

Time: 12.3s

Alternatives: 13

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: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 5 \cdot 10^{+216}:\\ \;\;\;\;\mathsf{fma}\left(y\_m, z \cdot \left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 5e+216)
   (fma y_m (* z (- (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 <= 5e+216) {
		tmp = fma(y_m, (z * (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 <= 5e+216)
		tmp = fma(y_m, Float64(z * 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, 5e+216], N[(y$95$m * N[(z * 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 < 4.9999999999999998e216

   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. associate-*l* 98.0%

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

      3. fma-define 98.0%

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

   3. Simplified 98.0%

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

   if 4.9999999999999998e216 < 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 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{+216}:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
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: 76.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 6.2 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y\_m \leq 0.00125:\\ \;\;\;\;z \cdot \left(y\_m \cdot \tanh \left(\frac{t}{y\_m}\right) - x\right)\\ \mathbf{elif}\;y\_m \leq 1.15 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 6.2e-36)
   x
   (if (<= y_m 0.00125)
     (* z (- (* y_m (tanh (/ t y_m))) x))
     (if (<= y_m 1.15e+75) x (fma z (- t x) x)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 6.2e-36) {
		tmp = x;
	} else if (y_m <= 0.00125) {
		tmp = z * ((y_m * tanh((t / y_m))) - x);
	} else if (y_m <= 1.15e+75) {
		tmp = x;
	} else {
		tmp = fma(z, (t - x), x);
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 6.2e-36)
		tmp = x;
	elseif (y_m <= 0.00125)
		tmp = Float64(z * Float64(Float64(y_m * tanh(Float64(t / y_m))) - x));
	elseif (y_m <= 1.15e+75)
		tmp = x;
	else
		tmp = fma(z, Float64(t - x), x);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 6.2e-36], x, If[LessEqual[y$95$m, 0.00125], N[(z * N[(N[(y$95$m * N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$95$m, 1.15e+75], x, N[(z * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 6.1999999999999997e-36 or 0.00125000000000000003 < y < 1.1499999999999999e75

   1. Initial program 96.1%

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

   3. Taylor expanded in x around inf 66.0%

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

   if 6.1999999999999997e-36 < y < 0.00125000000000000003

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 35.7%

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

      1. +-commutative 35.7%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in z around inf 25.0%

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

      1. associate-/l* 25.0%

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

      2. rec-exp 25.0%

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

      3. rec-exp 25.0%

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

      4. tanh-def-a 26.5%

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

   8. Simplified 26.5%

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

   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%

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

      1. +-commutative 84.7%

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

      2. fma-define 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 3 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.00125:\\ \;\;\;\;z \cdot \left(y \cdot \tanh \left(\frac{t}{y}\right) - x\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-90} \lor \neg \left(t \leq 3.8 \cdot 10^{-34}\right):\\ \;\;\;\;x + y\_m \cdot \left(z \cdot \tanh \left(\frac{t}{y\_m}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (or (<= t -1.75e-90) (not (<= t 3.8e-34)))
   (+ 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 <= -1.75e-90) || !(t <= 3.8e-34)) {
		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 <= (-1.75d-90)) .or. (.not. (t <= 3.8d-34))) 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 <= -1.75e-90) || !(t <= 3.8e-34)) {
		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 <= -1.75e-90) or not (t <= 3.8e-34):
		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 <= -1.75e-90) || !(t <= 3.8e-34))
		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 <= -1.75e-90) || ~((t <= 3.8e-34)))
		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, -1.75e-90], N[Not[LessEqual[t, 3.8e-34]], $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 < -1.7499999999999999e-90 or 3.8000000000000001e-34 < 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 -1.7499999999999999e-90 < t < 3.8000000000000001e-34

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-90} \lor \neg \left(t \leq 3.8 \cdot 10^{-34}\right):\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_1 := \tanh \left(\frac{t}{y\_m}\right)\\ \mathbf{if}\;y\_m \leq 1.75 \cdot 10^{-43}:\\ \;\;\;\;x + y\_m \cdot \left(z \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y\_m \cdot t\_1 - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (let* ((t_1 (tanh (/ t y_m))))
   (if (<= y_m 1.75e-43)
     (+ x (* y_m (* z t_1)))
     (+ x (* z (- (* y_m t_1) x))))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double t_1 = tanh((t / y_m));
	double tmp;
	if (y_m <= 1.75e-43) {
		tmp = x + (y_m * (z * t_1));
	} else {
		tmp = x + (z * ((y_m * t_1) - 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 = tanh((t / y_m))
    if (y_m <= 1.75d-43) then
        tmp = x + (y_m * (z * t_1))
    else
        tmp = x + (z * ((y_m * t_1) - 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 = Math.tanh((t / y_m));
	double tmp;
	if (y_m <= 1.75e-43) {
		tmp = x + (y_m * (z * t_1));
	} else {
		tmp = x + (z * ((y_m * t_1) - x));
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	t_1 = math.tanh((t / y_m))
	tmp = 0
	if y_m <= 1.75e-43:
		tmp = x + (y_m * (z * t_1))
	else:
		tmp = x + (z * ((y_m * t_1) - x))
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	t_1 = tanh(Float64(t / y_m))
	tmp = 0.0
	if (y_m <= 1.75e-43)
		tmp = Float64(x + Float64(y_m * Float64(z * t_1)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y_m * t_1) - x)));
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	t_1 = tanh((t / y_m));
	tmp = 0.0;
	if (y_m <= 1.75e-43)
		tmp = x + (y_m * (z * t_1));
	else
		tmp = x + (z * ((y_m * t_1) - 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[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y$95$m, 1.75e-43], N[(x + N[(y$95$m * N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y$95$m * t$95$1), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 1.74999999999999999e-43

   1. Initial program 95.8%

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

   3. Taylor expanded in x around 0 17.1%

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

      1. associate-/r* 17.1%

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

      2. div-sub 17.1%

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

      3. rec-exp 17.1%

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

      4. rec-exp 17.1%

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

      5. tanh-def-a 80.7%

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

   5. Simplified 80.7%

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

   if 1.74999999999999999e-43 < y

   1. Initial program 85.9%

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

   3. Taylor expanded in x around 0 47.9%

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

      1. +-commutative 47.9%

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

   5. Simplified 84.9%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{-43}:\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot \tanh \left(\frac{t}{y}\right) - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 1.2 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 1.2e+75) x (fma z (- t x) x)))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 1.2e+75) {
		tmp = x;
	} else {
		tmp = fma(z, (t - x), x);
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 1.2e+75)
		tmp = x;
	else
		tmp = fma(z, Float64(t - x), x);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 1.2e+75], x, N[(z * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.2e75

   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 1.2e75 < 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-define 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 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.6% accurate, 10.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 2.2 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y\_m \leq 8.8 \cdot 10^{+219} \lor \neg \left(y\_m \leq 7.6 \cdot 10^{+236}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 2.2e+28)
   x
   (if (or (<= y_m 8.8e+219) (not (<= y_m 7.6e+236)))
     (* x (- 1.0 z))
     (* z t))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 2.2e+28) {
		tmp = x;
	} else if ((y_m <= 8.8e+219) || !(y_m <= 7.6e+236)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * t;
	}
	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+28) then
        tmp = x
    else if ((y_m <= 8.8d+219) .or. (.not. (y_m <= 7.6d+236))) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * t
    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+28) {
		tmp = x;
	} else if ((y_m <= 8.8e+219) || !(y_m <= 7.6e+236)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if y_m <= 2.2e+28:
		tmp = x
	elif (y_m <= 8.8e+219) or not (y_m <= 7.6e+236):
		tmp = x * (1.0 - z)
	else:
		tmp = z * t
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 2.2e+28)
		tmp = x;
	elseif ((y_m <= 8.8e+219) || !(y_m <= 7.6e+236))
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * t);
	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+28)
		tmp = x;
	elseif ((y_m <= 8.8e+219) || ~((y_m <= 7.6e+236)))
		tmp = x * (1.0 - z);
	else
		tmp = z * t;
	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+28], x, If[Or[LessEqual[y$95$m, 8.8e+219], N[Not[LessEqual[y$95$m, 7.6e+236]], $MachinePrecision]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.19999999999999986e28

   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 2.19999999999999986e28 < y < 8.8000000000000006e219 or 7.59999999999999973e236 < y

   1. Initial program 82.1%

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

   3. Taylor expanded in x around 0 52.9%

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

      1. +-commutative 52.9%

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

   5. Simplified 85.9%

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

   6. Taylor expanded in x around inf 59.1%

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

      1. mul-1-neg 59.1%

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

      2. unsub-neg 59.1%

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

   8. Simplified 59.1%

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

   if 8.8000000000000006e219 < y < 7.59999999999999973e236

   1. Initial program 99.5%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around 0 100.0%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+219} \lor \neg \left(y \leq 7.6 \cdot 10^{+236}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.6% accurate, 14.2× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 2.6 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y\_m \leq 1.85 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 2.6e+28) x (if (<= y_m 1.85e+197) (* 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 <= 2.6e+28) {
		tmp = x;
	} else if (y_m <= 1.85e+197) {
		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 <= 2.6d+28) then
        tmp = x
    else if (y_m <= 1.85d+197) 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 <= 2.6e+28) {
		tmp = x;
	} else if (y_m <= 1.85e+197) {
		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 <= 2.6e+28:
		tmp = x
	elif y_m <= 1.85e+197:
		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 <= 2.6e+28)
		tmp = x;
	elseif (y_m <= 1.85e+197)
		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 <= 2.6e+28)
		tmp = x;
	elseif (y_m <= 1.85e+197)
		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, 2.6e+28], x, If[LessEqual[y$95$m, 1.85e+197], 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 < 2.6000000000000002e28

   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 2.6000000000000002e28 < y < 1.8500000000000002e197

   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 x around 0 47.0%

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

      1. +-commutative 47.0%

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

   5. Simplified 87.8%

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

   6. Taylor expanded in x around inf 55.5%

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

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

   8. Simplified 55.5%

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

   if 1.8500000000000002e197 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.3% accurate, 14.2× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 4 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;y\_m \leq 1.85 \cdot 10^{+198}:\\ \;\;\;\;x + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 4e+75) x (if (<= y_m 1.85e+198) (+ 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 <= 4e+75) {
		tmp = x;
	} else if (y_m <= 1.85e+198) {
		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 <= 4d+75) then
        tmp = x
    else if (y_m <= 1.85d+198) 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 <= 4e+75) {
		tmp = x;
	} else if (y_m <= 1.85e+198) {
		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 <= 4e+75:
		tmp = x
	elif y_m <= 1.85e+198:
		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 <= 4e+75)
		tmp = x;
	elseif (y_m <= 1.85e+198)
		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 <= 4e+75)
		tmp = x;
	elseif (y_m <= 1.85e+198)
		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, 4e+75], x, If[LessEqual[y$95$m, 1.85e+198], N[(x + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.99999999999999971e75

   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 3.99999999999999971e75 < y < 1.8499999999999999e198

   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%

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

      1. *-commutative 60.0%

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

   8. Simplified 60.0%

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

   if 1.8499999999999999e198 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+198}:\\ \;\;\;\;x + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.8% accurate, 15.2× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 5.2 \cdot 10^{+196}:\\ \;\;\;\;x\\ \mathbf{elif}\;y\_m \leq 2.1 \cdot 10^{+241}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;-z \cdot x\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 5.2e+196) x (if (<= y_m 2.1e+241) (* z t) (- (* z x)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 5.2e+196) {
		tmp = x;
	} else if (y_m <= 2.1e+241) {
		tmp = z * t;
	} else {
		tmp = -(z * 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 <= 5.2d+196) then
        tmp = x
    else if (y_m <= 2.1d+241) then
        tmp = z * t
    else
        tmp = -(z * 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 <= 5.2e+196) {
		tmp = x;
	} else if (y_m <= 2.1e+241) {
		tmp = z * t;
	} else {
		tmp = -(z * x);
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if y_m <= 5.2e+196:
		tmp = x
	elif y_m <= 2.1e+241:
		tmp = z * t
	else:
		tmp = -(z * x)
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 5.2e+196)
		tmp = x;
	elseif (y_m <= 2.1e+241)
		tmp = Float64(z * t);
	else
		tmp = Float64(-Float64(z * 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 <= 5.2e+196)
		tmp = x;
	elseif (y_m <= 2.1e+241)
		tmp = z * t;
	else
		tmp = -(z * 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, 5.2e+196], x, If[LessEqual[y$95$m, 2.1e+241], N[(z * t), $MachinePrecision], (-N[(z * x), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if y < 5.20000000000000024e196

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 62.3%

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

   if 5.20000000000000024e196 < y < 2.1e241

   1. Initial program 87.8%

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

   3. Taylor expanded in y around inf 88.9%

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

   4. Taylor expanded in x around 0 52.4%

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

   if 2.1e241 < y

   1. Initial program 31.7%

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

   3. Taylor expanded in x around 0 71.5%

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

      1. +-commutative 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in z around inf 52.5%

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

      1. associate-/l* 52.5%

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

      2. rec-exp 52.5%

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

      3. rec-exp 52.5%

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

      4. tanh-def-a 52.5%

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

   8. Simplified 52.5%

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

   9. Taylor expanded in y around 0 52.5%

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

       1. mul-1-neg 52.5%

          \[\leadsto \color{blue}{-x \cdot z} \]

       2. distribute-lft-neg-out 52.5%

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

       3. *-commutative 52.5%

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

   11. Simplified 52.5%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{+196}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+241}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;-z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.4% accurate, 17.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 1.2 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 1.2e+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 <= 1.2e+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 <= 1.2d+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 <= 1.2e+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 <= 1.2e+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 <= 1.2e+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 <= 1.2e+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, 1.2e+75], x, N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.2e75

   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 1.2e75 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.7% accurate, 26.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 9.5 \cdot 10^{+198}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t) :precision binary64 (if (<= y_m 9.5e+198) x (* z t)))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 9.5e+198) {
		tmp = x;
	} else {
		tmp = z * t;
	}
	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 <= 9.5d+198) then
        tmp = x
    else
        tmp = z * t
    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 <= 9.5e+198) {
		tmp = x;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if y_m <= 9.5e+198:
		tmp = x
	else:
		tmp = z * t
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 9.5e+198)
		tmp = x;
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	tmp = 0.0;
	if (y_m <= 9.5e+198)
		tmp = x;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 9.5e+198], x, N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9.5e198

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 62.3%

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

   if 9.5e198 < 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 x around 0 41.2%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 9.5 \cdot 10^{+198}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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))))))