SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.3% → 98.3%

Time: 7.6s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.3% 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: 98.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{+187}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.65e+187)
   (fma (* y (- (tanh (/ t y)) (tanh (/ x y)))) z x)
   (+ x (* z (- t x)))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.65e+187) {
		tmp = fma((y * (tanh((t / y)) - tanh((x / y)))), z, x);
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.65e+187)
		tmp = fma(Float64(y * Float64(tanh(Float64(t / y)) - tanh(Float64(x / y)))), z, x);
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[y, 1.65e+187], N[(N[(y * N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.6500000000000001e187

   1. Initial program 94.8%

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

      1. +-commutative 94.8%

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

      2. *-commutative 94.8%

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

      3. associate-*r* 98.1%

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

      4. fma-def 98.2%

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

   3. Applied egg-rr 98.2%

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

   if 1.6500000000000001e187 < y

   1. Initial program 60.7%

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

   2. Taylor expanded in 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 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{+187}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 2: 96.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{+178}:\\ \;\;\;\;x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (<= y 3.1e+178)
   (+ x (* (- (tanh (/ t y)) (tanh (/ x y))) (* y z)))
   (+ x (* z (- t x)))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.1e+178) {
		tmp = x + ((tanh((t / y)) - tanh((x / y))) * (y * z));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 3.1d+178) then
        tmp = x + ((tanh((t / y)) - tanh((x / y))) * (y * z))
    else
        tmp = x + (z * (t - x))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.1e+178) {
		tmp = x + ((Math.tanh((t / y)) - Math.tanh((x / y))) * (y * z));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	tmp = 0
	if y <= 3.1e+178:
		tmp = x + ((math.tanh((t / y)) - math.tanh((x / y))) * (y * z))
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 3.1e+178)
		tmp = Float64(x + Float64(Float64(tanh(Float64(t / y)) - tanh(Float64(x / y))) * Float64(y * z)));
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 3.1e+178)
		tmp = x + ((tanh((t / y)) - tanh((x / y))) * (y * z));
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[y, 3.1e+178], N[(x + N[(N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.09999999999999991e178

   1. Initial program 94.8%

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

   if 3.09999999999999991e178 < y

   1. Initial program 64.0%

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

   2. Taylor expanded in y around inf 96.2%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{+178}:\\ \;\;\;\;x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 3: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} t_1 := \tanh \left(\frac{t}{y}\right)\\ \mathbf{if}\;y \leq 3.4 \cdot 10^{+44}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot t_1, z, x\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+75}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+113}:\\ \;\;\;\;x + t_1 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (tanh (/ t y))))
   (if (<= y 3.4e+44)
     (fma (* y t_1) z x)
     (if (<= y 5.1e+75)
       (+ x (* (* y z) (- (/ t y) (tanh (/ x y)))))
       (if (<= y 1.55e+113) (+ x (* t_1 (* y z))) (+ x (* z (- t x))))))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double t_1 = tanh((t / y));
	double tmp;
	if (y <= 3.4e+44) {
		tmp = fma((y * t_1), z, x);
	} else if (y <= 5.1e+75) {
		tmp = x + ((y * z) * ((t / y) - tanh((x / y))));
	} else if (y <= 1.55e+113) {
		tmp = x + (t_1 * (y * z));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Julia

y = abs(y)
function code(x, y, z, t)
	t_1 = tanh(Float64(t / y))
	tmp = 0.0
	if (y <= 3.4e+44)
		tmp = fma(Float64(y * t_1), z, x);
	elseif (y <= 5.1e+75)
		tmp = Float64(x + Float64(Float64(y * z) * Float64(Float64(t / y) - tanh(Float64(x / y)))));
	elseif (y <= 1.55e+113)
		tmp = Float64(x + Float64(t_1 * Float64(y * z)));
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, 3.4e+44], N[(N[(y * t$95$1), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[y, 5.1e+75], N[(x + N[(N[(y * z), $MachinePrecision] * N[(N[(t / y), $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+113], N[(x + N[(t$95$1 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < 3.4e44

   1. Initial program 95.0%

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

      1. +-commutative 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*r* 98.4%

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

      4. fma-def 98.4%

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

   3. Applied egg-rr 98.4%

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

   4. Taylor expanded in x around 0 25.6%

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

      1. associate-/r* 25.6%

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

      2. div-sub 25.6%

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

      3. rec-exp 25.7%

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

      4. rec-exp 25.7%

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

      5. tanh-def-a 81.8%

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

   6. Simplified 81.8%

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

   if 3.4e44 < y < 5.10000000000000037e75

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 83.9%

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

   if 5.10000000000000037e75 < y < 1.54999999999999996e113

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 34.3%

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

      1. *-commutative 34.3%

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

      2. associate-/r* 34.3%

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

      3. div-sub 34.3%

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

      4. rec-exp 34.3%

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

      5. rec-exp 34.3%

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

      6. tanh-def-a 88.9%

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

   4. Simplified 88.9%

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

   if 1.54999999999999996e113 < y

   1. Initial program 70.7%

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

   2. Taylor expanded in y around inf 87.2%

      \[\leadsto x + \color{blue}{z \cdot \left(t - x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.4 \cdot 10^{+44}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \tanh \left(\frac{t}{y}\right), z, x\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+75}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+113}:\\ \;\;\;\;x + \tanh \left(\frac{t}{y}\right) \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4: 85.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} t_1 := x + \tanh \left(\frac{t}{y}\right) \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq 2.9 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+76}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (tanh (/ t y)) (* y z)))))
   (if (<= y 2.9e+44)
     t_1
     (if (<= y 1.36e+76)
       (+ x (* (* y z) (- (/ t y) (tanh (/ x y)))))
       (if (<= y 4.1e+113) t_1 (+ x (* z (- t x))))))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double t_1 = x + (tanh((t / y)) * (y * z));
	double tmp;
	if (y <= 2.9e+44) {
		tmp = t_1;
	} else if (y <= 1.36e+76) {
		tmp = x + ((y * z) * ((t / y) - tanh((x / y))));
	} else if (y <= 4.1e+113) {
		tmp = t_1;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (tanh((t / y)) * (y * z))
    if (y <= 2.9d+44) then
        tmp = t_1
    else if (y <= 1.36d+76) then
        tmp = x + ((y * z) * ((t / y) - tanh((x / y))))
    else if (y <= 4.1d+113) then
        tmp = t_1
    else
        tmp = x + (z * (t - x))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double t_1 = x + (Math.tanh((t / y)) * (y * z));
	double tmp;
	if (y <= 2.9e+44) {
		tmp = t_1;
	} else if (y <= 1.36e+76) {
		tmp = x + ((y * z) * ((t / y) - Math.tanh((x / y))));
	} else if (y <= 4.1e+113) {
		tmp = t_1;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	t_1 = x + (math.tanh((t / y)) * (y * z))
	tmp = 0
	if y <= 2.9e+44:
		tmp = t_1
	elif y <= 1.36e+76:
		tmp = x + ((y * z) * ((t / y) - math.tanh((x / y))))
	elif y <= 4.1e+113:
		tmp = t_1
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	t_1 = Float64(x + Float64(tanh(Float64(t / y)) * Float64(y * z)))
	tmp = 0.0
	if (y <= 2.9e+44)
		tmp = t_1;
	elseif (y <= 1.36e+76)
		tmp = Float64(x + Float64(Float64(y * z) * Float64(Float64(t / y) - tanh(Float64(x / y)))));
	elseif (y <= 4.1e+113)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	t_1 = x + (tanh((t / y)) * (y * z));
	tmp = 0.0;
	if (y <= 2.9e+44)
		tmp = t_1;
	elseif (y <= 1.36e+76)
		tmp = x + ((y * z) * ((t / y) - tanh((x / y))));
	elseif (y <= 4.1e+113)
		tmp = t_1;
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 2.9e+44], t$95$1, If[LessEqual[y, 1.36e+76], N[(x + N[(N[(y * z), $MachinePrecision] * N[(N[(t / y), $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+113], t$95$1, N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.9000000000000002e44 or 1.36000000000000004e76 < y < 4.09999999999999993e113

   1. Initial program 95.3%

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

   2. Taylor expanded in x around 0 26.0%

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

      1. *-commutative 26.0%

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

      2. associate-/r* 26.0%

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

      3. div-sub 26.0%

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

      4. rec-exp 26.0%

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

      5. rec-exp 26.0%

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

      6. tanh-def-a 81.9%

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

   4. Simplified 81.6%

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

   if 2.9000000000000002e44 < y < 1.36000000000000004e76

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 83.9%

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

   if 4.09999999999999993e113 < y

   1. Initial program 70.7%

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

   2. Taylor expanded in y around inf 87.2%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{+44}:\\ \;\;\;\;x + \tanh \left(\frac{t}{y}\right) \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+76}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+113}:\\ \;\;\;\;x + \tanh \left(\frac{t}{y}\right) \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 5: 85.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.14 \cdot 10^{+114}:\\ \;\;\;\;x + \tanh \left(\frac{t}{y}\right) \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.14e+114) (+ x (* (tanh (/ t y)) (* y z))) (+ x (* z (- t x)))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.14e+114) {
		tmp = x + (tanh((t / y)) * (y * z));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 1.14d+114) then
        tmp = x + (tanh((t / y)) * (y * z))
    else
        tmp = x + (z * (t - x))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.14e+114) {
		tmp = x + (Math.tanh((t / y)) * (y * z));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	tmp = 0
	if y <= 1.14e+114:
		tmp = x + (math.tanh((t / y)) * (y * z))
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.14e+114)
		tmp = Float64(x + Float64(tanh(Float64(t / y)) * Float64(y * z)));
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.14e+114)
		tmp = x + (tanh((t / y)) * (y * z));
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[y, 1.14e+114], N[(x + N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.14e114

   1. Initial program 95.4%

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

   2. Taylor expanded in x around 0 25.3%

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

      1. *-commutative 25.3%

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

      2. associate-/r* 25.3%

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

      3. div-sub 25.3%

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

      4. rec-exp 25.4%

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

      5. rec-exp 25.4%

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

      6. tanh-def-a 80.6%

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

   4. Simplified 80.8%

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

   if 1.14e114 < y

   1. Initial program 70.7%

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

   2. Taylor expanded in y around inf 87.2%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.14 \cdot 10^{+114}:\\ \;\;\;\;x + \tanh \left(\frac{t}{y}\right) \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 6: 67.0% accurate, 19.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.95 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+187} \lor \neg \left(y \leq 2.7 \cdot 10^{+259}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.95e+59)
   x
   (if (or (<= y 6.3e+187) (not (<= y 2.7e+259)))
     (* x (- 1.0 z))
     (* z (- t x)))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.95e+59) {
		tmp = x;
	} else if ((y <= 6.3e+187) || !(y <= 2.7e+259)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (t - x);
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 1.95d+59) then
        tmp = x
    else if ((y <= 6.3d+187) .or. (.not. (y <= 2.7d+259))) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (t - x)
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.95e+59) {
		tmp = x;
	} else if ((y <= 6.3e+187) || !(y <= 2.7e+259)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (t - x);
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	tmp = 0
	if y <= 1.95e+59:
		tmp = x
	elif (y <= 6.3e+187) or not (y <= 2.7e+259):
		tmp = x * (1.0 - z)
	else:
		tmp = z * (t - x)
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.95e+59)
		tmp = x;
	elseif ((y <= 6.3e+187) || !(y <= 2.7e+259))
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(t - x));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.95e+59)
		tmp = x;
	elseif ((y <= 6.3e+187) || ~((y <= 2.7e+259)))
		tmp = x * (1.0 - z);
	else
		tmp = z * (t - x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[y, 1.95e+59], x, If[Or[LessEqual[y, 6.3e+187], N[Not[LessEqual[y, 2.7e+259]], $MachinePrecision]], 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 < 1.95000000000000011e59

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf 65.3%

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

   if 1.95000000000000011e59 < y < 6.30000000000000005e187 or 2.69999999999999988e259 < y

   1. Initial program 86.0%

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

   2. Taylor expanded in y around inf 75.5%

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

   3. Taylor expanded in x around inf 60.7%

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

   4. Taylor expanded in z around 0 60.7%

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

      1. associate-*r* 60.7%

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

      2. distribute-lft1-in 60.7%

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

      3. *-commutative 60.7%

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

      4. +-commutative 60.7%

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

      5. mul-1-neg 60.7%

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

      6. unsub-neg 60.7%

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

   6. Simplified 60.7%

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

   if 6.30000000000000005e187 < y < 2.69999999999999988e259

   1. Initial program 52.4%

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

   2. Taylor expanded in y around inf 100.0%

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

   3. Taylor expanded in z around inf 82.8%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.95 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+187} \lor \neg \left(y \leq 2.7 \cdot 10^{+259}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 7: 59.6% accurate, 20.9× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{+187}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+257}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+294}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (<= y 8.5e+187)
   x
   (if (<= y 1.9e+257) (* t z) (if (<= y 6.1e+294) x (* x (- z))))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 8.5e+187) {
		tmp = x;
	} else if (y <= 1.9e+257) {
		tmp = t * z;
	} else if (y <= 6.1e+294) {
		tmp = x;
	} else {
		tmp = x * -z;
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 8.5d+187) then
        tmp = x
    else if (y <= 1.9d+257) then
        tmp = t * z
    else if (y <= 6.1d+294) then
        tmp = x
    else
        tmp = x * -z
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 8.5e+187) {
		tmp = x;
	} else if (y <= 1.9e+257) {
		tmp = t * z;
	} else if (y <= 6.1e+294) {
		tmp = x;
	} else {
		tmp = x * -z;
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	tmp = 0
	if y <= 8.5e+187:
		tmp = x
	elif y <= 1.9e+257:
		tmp = t * z
	elif y <= 6.1e+294:
		tmp = x
	else:
		tmp = x * -z
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 8.5e+187)
		tmp = x;
	elseif (y <= 1.9e+257)
		tmp = Float64(t * z);
	elseif (y <= 6.1e+294)
		tmp = x;
	else
		tmp = Float64(x * Float64(-z));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 8.5e+187)
		tmp = x;
	elseif (y <= 1.9e+257)
		tmp = t * z;
	elseif (y <= 6.1e+294)
		tmp = x;
	else
		tmp = x * -z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[y, 8.5e+187], x, If[LessEqual[y, 1.9e+257], N[(t * z), $MachinePrecision], If[LessEqual[y, 6.1e+294], x, N[(x * (-z)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 8.49999999999999989e187 or 1.89999999999999999e257 < y < 6.1000000000000002e294

   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. Taylor expanded in x around inf 61.5%

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

   if 8.49999999999999989e187 < y < 1.89999999999999999e257

   1. Initial program 52.4%

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

   2. Taylor expanded in y around inf 100.0%

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

   3. Taylor expanded in x around 0 38.5%

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

   if 6.1000000000000002e294 < y

   1. Initial program 37.4%

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

   2. Taylor expanded in y around inf 100.0%

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

   3. Taylor expanded in x around inf 37.4%

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

   4. Taylor expanded in z around inf 7.4%

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

      1. associate-*r* 7.4%

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

      2. mul-1-neg 7.4%

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

   6. Simplified 7.4%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{+187}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+257}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+294}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 8: 59.5% accurate, 23.2× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 4.4 \cdot 10^{+188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+252}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+275}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (<= y 4.4e+188)
   x
   (if (<= y 2.8e+252) (* t z) (if (<= y 1.65e+275) x (* t z)))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.4e+188) {
		tmp = x;
	} else if (y <= 2.8e+252) {
		tmp = t * z;
	} else if (y <= 1.65e+275) {
		tmp = x;
	} else {
		tmp = t * z;
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 4.4d+188) then
        tmp = x
    else if (y <= 2.8d+252) then
        tmp = t * z
    else if (y <= 1.65d+275) then
        tmp = x
    else
        tmp = t * z
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.4e+188) {
		tmp = x;
	} else if (y <= 2.8e+252) {
		tmp = t * z;
	} else if (y <= 1.65e+275) {
		tmp = x;
	} else {
		tmp = t * z;
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	tmp = 0
	if y <= 4.4e+188:
		tmp = x
	elif y <= 2.8e+252:
		tmp = t * z
	elif y <= 1.65e+275:
		tmp = x
	else:
		tmp = t * z
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 4.4e+188)
		tmp = x;
	elseif (y <= 2.8e+252)
		tmp = Float64(t * z);
	elseif (y <= 1.65e+275)
		tmp = x;
	else
		tmp = Float64(t * z);
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 4.4e+188)
		tmp = x;
	elseif (y <= 2.8e+252)
		tmp = t * z;
	elseif (y <= 1.65e+275)
		tmp = x;
	else
		tmp = t * z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[y, 4.4e+188], x, If[LessEqual[y, 2.8e+252], N[(t * z), $MachinePrecision], If[LessEqual[y, 1.65e+275], x, N[(t * z), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if y < 4.39999999999999998e188 or 2.80000000000000003e252 < y < 1.65000000000000011e275

   1. Initial program 94.9%

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

   2. Taylor expanded in x around inf 62.2%

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

   if 4.39999999999999998e188 < y < 2.80000000000000003e252 or 1.65000000000000011e275 < y

   1. Initial program 52.0%

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

   2. Taylor expanded in y around inf 100.0%

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

   3. Taylor expanded in x around 0 41.0%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.4 \cdot 10^{+188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+252}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+275}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \]

Alternative 9: 78.0% accurate, 23.5× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 4.3 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (<= y 4.3e+61) x (+ x (* z (- t x)))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.3e+61) {
		tmp = x;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 4.3d+61) then
        tmp = x
    else
        tmp = x + (z * (t - x))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.3e+61) {
		tmp = x;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	tmp = 0
	if y <= 4.3e+61:
		tmp = x
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 4.3e+61)
		tmp = x;
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 4.3e+61)
		tmp = x;
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[y, 4.3e+61], x, N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.3000000000000001e61

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf 65.3%

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

   if 4.3000000000000001e61 < y

   1. Initial program 78.5%

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

   2. Taylor expanded in y around inf 81.0%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.3 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 10: 67.8% accurate, 30.2× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z t) :precision binary64 (if (<= y 2e+61) x (* x (- 1.0 z))))

C

y = abs(y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2e+61) {
		tmp = x;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 2d+61) then
        tmp = x
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2e+61) {
		tmp = x;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z, t):
	tmp = 0
	if y <= 2e+61:
		tmp = x
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

y = abs(y)
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2e+61)
		tmp = x;
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2e+61)
		tmp = x;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[y, 2e+61], x, N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.9999999999999999e61

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf 65.3%

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

   if 1.9999999999999999e61 < y

   1. Initial program 78.5%

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

   2. Taylor expanded in y around inf 81.0%

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

   3. Taylor expanded in x around inf 60.7%

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

   4. Taylor expanded in z around 0 60.7%

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

      1. associate-*r* 60.7%

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

      2. distribute-lft1-in 60.7%

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

      3. *-commutative 60.7%

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

      4. +-commutative 60.7%

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

      5. mul-1-neg 60.7%

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

      6. unsub-neg 60.7%

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

   6. Simplified 60.7%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 11: 60.6% accurate, 213.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: y should be positive before calling this function
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.9%

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

2. Taylor expanded in x around inf 59.5%

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

3. Final simplification 59.5%

   \[\leadsto x \]

Developer target: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023268 
(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))))))