SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.7% → 98.4%

Time: 12.9s

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: 93.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 3 \cdot 10^{+217}:\\ \;\;\;\;\mathsf{fma}\left(y\_m, z \cdot \left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 3e+217)
   (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 <= 3e+217) {
		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 <= 3e+217)
		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, 3e+217], 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 < 2.99999999999999976e217

   1. Initial program 97.2%

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

      1. +-commutative 97.2%

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

      2. associate-*l* 98.3%

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

      3. fma-define 98.3%

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

   3. Simplified 98.3%

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

   if 2.99999999999999976e217 < y

   1. Initial program 60.1%

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

   3. Taylor expanded in y around inf 94.6%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{+217}:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_1 := \tanh \left(\frac{t}{y\_m}\right)\\ \mathbf{if}\;y\_m \leq 6.4 \cdot 10^{+40}:\\ \;\;\;\;x + t\_1 \cdot \left(y\_m \cdot z\right)\\ \mathbf{elif}\;y\_m \leq 2 \cdot 10^{+178}:\\ \;\;\;\;\mathsf{fma}\left(y\_m, z \cdot \left(t\_1 - \frac{x}{y\_m}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (let* ((t_1 (tanh (/ t y_m))))
   (if (<= y_m 6.4e+40)
     (+ x (* t_1 (* y_m z)))
     (if (<= y_m 2e+178)
       (fma y_m (* z (- t_1 (/ 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 t_1 = tanh((t / y_m));
	double tmp;
	if (y_m <= 6.4e+40) {
		tmp = x + (t_1 * (y_m * z));
	} else if (y_m <= 2e+178) {
		tmp = fma(y_m, (z * (t_1 - (x / y_m))), x);
	} else {
		tmp = x + (z * (t - 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 <= 6.4e+40)
		tmp = Float64(x + Float64(t_1 * Float64(y_m * z)));
	elseif (y_m <= 2e+178)
		tmp = fma(y_m, Float64(z * Float64(t_1 - 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_] := Block[{t$95$1 = N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y$95$m, 6.4e+40], N[(x + N[(t$95$1 * N[(y$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$95$m, 2e+178], N[(y$95$m * N[(z * N[(t$95$1 - N[(x / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 6.39999999999999961e40

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 23.2%

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

      1. associate-/r* 23.2%

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

      2. rec-exp 23.2%

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

      3. div-sub 23.2%

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

      4. rec-exp 23.2%

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

      5. tanh-def-a 84.3%

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

   5. Simplified 84.3%

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

   if 6.39999999999999961e40 < y < 2.0000000000000001e178

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 94.7%

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

   if 2.0000000000000001e178 < y

   1. Initial program 64.3%

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

   3. Taylor expanded in y around inf 89.9%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.4 \cdot 10^{+40}:\\ \;\;\;\;x + \tanh \left(\frac{t}{y}\right) \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+178}:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 1.4 \cdot 10^{+215}:\\ \;\;\;\;x + \left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right) \cdot \left(y\_m \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 1.4e+215)
   (+ x (* (- (tanh (/ t y_m)) (tanh (/ x y_m))) (* y_m z)))
   (+ 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 <= 1.4e+215) {
		tmp = x + ((tanh((t / y_m)) - tanh((x / y_m))) * (y_m * z));
	} 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 <= 1.4d+215) then
        tmp = x + ((tanh((t / y_m)) - tanh((x / y_m))) * (y_m * z))
    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 <= 1.4e+215) {
		tmp = x + ((Math.tanh((t / y_m)) - Math.tanh((x / y_m))) * (y_m * z));
	} 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 <= 1.4e+215:
		tmp = x + ((math.tanh((t / y_m)) - math.tanh((x / y_m))) * (y_m * z))
	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 <= 1.4e+215)
		tmp = Float64(x + Float64(Float64(tanh(Float64(t / y_m)) - tanh(Float64(x / y_m))) * Float64(y_m * z)));
	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 <= 1.4e+215)
		tmp = x + ((tanh((t / y_m)) - tanh((x / y_m))) * (y_m * z));
	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, 1.4e+215], 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], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.4e215

   1. Initial program 97.2%

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

   if 1.4e215 < y

   1. Initial program 60.1%

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

   3. Taylor expanded in y around inf 94.6%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{+215}:\\ \;\;\;\;x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 1.32 \cdot 10^{+54} \lor \neg \left(y\_m \leq 2.6 \cdot 10^{+138}\right) \land y\_m \leq 10^{+171}:\\ \;\;\;\;x + \tanh \left(\frac{t}{y\_m}\right) \cdot \left(y\_m \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (or (<= y_m 1.32e+54) (and (not (<= y_m 2.6e+138)) (<= y_m 1e+171)))
   (+ x (* (tanh (/ t y_m)) (* y_m z)))
   (+ 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 <= 1.32e+54) || (!(y_m <= 2.6e+138) && (y_m <= 1e+171))) {
		tmp = x + (tanh((t / y_m)) * (y_m * z));
	} 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 <= 1.32d+54) .or. (.not. (y_m <= 2.6d+138)) .and. (y_m <= 1d+171)) then
        tmp = x + (tanh((t / y_m)) * (y_m * z))
    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 <= 1.32e+54) || (!(y_m <= 2.6e+138) && (y_m <= 1e+171))) {
		tmp = x + (Math.tanh((t / y_m)) * (y_m * z));
	} 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 <= 1.32e+54) or (not (y_m <= 2.6e+138) and (y_m <= 1e+171)):
		tmp = x + (math.tanh((t / y_m)) * (y_m * z))
	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 <= 1.32e+54) || (!(y_m <= 2.6e+138) && (y_m <= 1e+171)))
		tmp = Float64(x + Float64(tanh(Float64(t / y_m)) * Float64(y_m * z)));
	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 <= 1.32e+54) || (~((y_m <= 2.6e+138)) && (y_m <= 1e+171)))
		tmp = x + (tanh((t / y_m)) * (y_m * z));
	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[y$95$m, 1.32e+54], And[N[Not[LessEqual[y$95$m, 2.6e+138]], $MachinePrecision], LessEqual[y$95$m, 1e+171]]], N[(x + N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] * N[(y$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.3200000000000001e54 or 2.6000000000000001e138 < y < 9.99999999999999954e170

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0 24.7%

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

      1. associate-/r* 24.7%

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

      2. rec-exp 24.7%

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

      3. div-sub 24.7%

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

      4. rec-exp 24.7%

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

      5. tanh-def-a 85.3%

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

   5. Simplified 85.3%

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

   if 1.3200000000000001e54 < y < 2.6000000000000001e138 or 9.99999999999999954e170 < y

   1. Initial program 83.4%

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

   3. Taylor expanded in y around inf 88.5%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.32 \cdot 10^{+54} \lor \neg \left(y \leq 2.6 \cdot 10^{+138}\right) \land y \leq 10^{+171}:\\ \;\;\;\;x + \tanh \left(\frac{t}{y}\right) \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_1 := \tanh \left(\frac{t}{y\_m}\right)\\ \mathbf{if}\;y\_m \leq 8 \cdot 10^{+40}:\\ \;\;\;\;x + t\_1 \cdot \left(y\_m \cdot z\right)\\ \mathbf{elif}\;y\_m \leq 1.46 \cdot 10^{+178}:\\ \;\;\;\;x + \left(y\_m \cdot z\right) \cdot \left(t\_1 - \frac{x}{y\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (let* ((t_1 (tanh (/ t y_m))))
   (if (<= y_m 8e+40)
     (+ x (* t_1 (* y_m z)))
     (if (<= y_m 1.46e+178)
       (+ x (* (* y_m z) (- t_1 (/ x y_m))))
       (+ x (* z (- t 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 <= 8e+40) {
		tmp = x + (t_1 * (y_m * z));
	} else if (y_m <= 1.46e+178) {
		tmp = x + ((y_m * z) * (t_1 - (x / 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) :: t_1
    real(8) :: tmp
    t_1 = tanh((t / y_m))
    if (y_m <= 8d+40) then
        tmp = x + (t_1 * (y_m * z))
    else if (y_m <= 1.46d+178) then
        tmp = x + ((y_m * z) * (t_1 - (x / 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 t_1 = Math.tanh((t / y_m));
	double tmp;
	if (y_m <= 8e+40) {
		tmp = x + (t_1 * (y_m * z));
	} else if (y_m <= 1.46e+178) {
		tmp = x + ((y_m * z) * (t_1 - (x / y_m)));
	} else {
		tmp = x + (z * (t - 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 <= 8e+40:
		tmp = x + (t_1 * (y_m * z))
	elif y_m <= 1.46e+178:
		tmp = x + ((y_m * z) * (t_1 - (x / y_m)))
	else:
		tmp = x + (z * (t - 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 <= 8e+40)
		tmp = Float64(x + Float64(t_1 * Float64(y_m * z)));
	elseif (y_m <= 1.46e+178)
		tmp = Float64(x + Float64(Float64(y_m * z) * Float64(t_1 - Float64(x / 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)
	t_1 = tanh((t / y_m));
	tmp = 0.0;
	if (y_m <= 8e+40)
		tmp = x + (t_1 * (y_m * z));
	elseif (y_m <= 1.46e+178)
		tmp = x + ((y_m * z) * (t_1 - (x / 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_] := Block[{t$95$1 = N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y$95$m, 8e+40], N[(x + N[(t$95$1 * N[(y$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$95$m, 1.46e+178], N[(x + N[(N[(y$95$m * z), $MachinePrecision] * N[(t$95$1 - N[(x / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 8.00000000000000024e40

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 23.2%

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

      1. associate-/r* 23.2%

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

      2. rec-exp 23.2%

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

      3. div-sub 23.2%

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

      4. rec-exp 23.2%

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

      5. tanh-def-a 84.3%

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

   5. Simplified 84.3%

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

   if 8.00000000000000024e40 < y < 1.46000000000000003e178

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 94.7%

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

   if 1.46000000000000003e178 < y

   1. Initial program 64.3%

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

   3. Taylor expanded in y around inf 89.9%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{+40}:\\ \;\;\;\;x + \tanh \left(\frac{t}{y}\right) \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{+178}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.3% accurate, 10.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 1.38 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;y\_m \leq 9 \cdot 10^{+198} \lor \neg \left(y\_m \leq 8.5 \cdot 10^{+236}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 1.38e+54)
   x
   (if (or (<= y_m 9e+198) (not (<= y_m 8.5e+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 <= 1.38e+54) {
		tmp = x;
	} else if ((y_m <= 9e+198) || !(y_m <= 8.5e+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 <= 1.38d+54) then
        tmp = x
    else if ((y_m <= 9d+198) .or. (.not. (y_m <= 8.5d+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 <= 1.38e+54) {
		tmp = x;
	} else if ((y_m <= 9e+198) || !(y_m <= 8.5e+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 <= 1.38e+54:
		tmp = x
	elif (y_m <= 9e+198) or not (y_m <= 8.5e+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 <= 1.38e+54)
		tmp = x;
	elseif ((y_m <= 9e+198) || !(y_m <= 8.5e+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 <= 1.38e+54)
		tmp = x;
	elseif ((y_m <= 9e+198) || ~((y_m <= 8.5e+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, 1.38e+54], x, If[Or[LessEqual[y$95$m, 9e+198], N[Not[LessEqual[y$95$m, 8.5e+236]], $MachinePrecision]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.38e54

   1. Initial program 96.8%

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

      1. +-commutative 96.8%

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

      2. associate-*l* 98.1%

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

      3. fma-define 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in y around 0 66.9%

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

   if 1.38e54 < y < 9.00000000000000003e198 or 8.5000000000000008e236 < y

   1. Initial program 84.6%

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

   3. Taylor expanded in y around inf 69.9%

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

   4. Taylor expanded in t around 0 60.5%

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

      1. mul-1-neg 60.5%

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

      2. distribute-frac-neg 60.5%

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

   6. Simplified 60.5%

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

   7. Taylor expanded in x around 0 63.1%

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

      1. neg-mul-1 63.1%

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

      2. unsub-neg 63.1%

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

   9. Simplified 63.1%

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

   if 9.00000000000000003e198 < y < 8.5000000000000008e236

   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 41.9%

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

      1. associate-/r* 41.9%

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

      2. rec-exp 41.9%

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

      3. div-sub 41.9%

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

      4. rec-exp 41.9%

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

      5. tanh-def-a 66.2%

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

   5. Simplified 66.2%

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

   6. Taylor expanded in y around inf 66.7%

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

      1. +-commutative 66.7%

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

      2. *-commutative 66.7%

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

   8. Simplified 66.7%

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

   9. Taylor expanded in z around inf 34.5%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.38 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+198} \lor \neg \left(y \leq 8.5 \cdot 10^{+236}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.0% accurate, 10.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 2.9 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y\_m \leq 3.5 \cdot 10^{+146} \lor \neg \left(y\_m \leq 7.8 \cdot 10^{+195}\right):\\ \;\;\;\;x + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 2.9e+36)
   x
   (if (or (<= y_m 3.5e+146) (not (<= y_m 7.8e+195)))
     (+ x (* z t))
     (* x (- 1.0 z)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 2.9e+36) {
		tmp = x;
	} else if ((y_m <= 3.5e+146) || !(y_m <= 7.8e+195)) {
		tmp = x + (z * t);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y_m <= 2.9d+36) then
        tmp = x
    else if ((y_m <= 3.5d+146) .or. (.not. (y_m <= 7.8d+195))) then
        tmp = x + (z * t)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 2.9e+36) {
		tmp = x;
	} else if ((y_m <= 3.5e+146) || !(y_m <= 7.8e+195)) {
		tmp = x + (z * t);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if y_m <= 2.9e+36:
		tmp = x
	elif (y_m <= 3.5e+146) or not (y_m <= 7.8e+195):
		tmp = x + (z * t)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 2.9e+36)
		tmp = x;
	elseif ((y_m <= 3.5e+146) || !(y_m <= 7.8e+195))
		tmp = Float64(x + Float64(z * t));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	tmp = 0.0;
	if (y_m <= 2.9e+36)
		tmp = x;
	elseif ((y_m <= 3.5e+146) || ~((y_m <= 7.8e+195)))
		tmp = x + (z * t);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 2.9e+36], x, If[Or[LessEqual[y$95$m, 3.5e+146], N[Not[LessEqual[y$95$m, 7.8e+195]], $MachinePrecision]], N[(x + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.9e36

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      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

   5. Taylor expanded in y around 0 67.4%

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

   if 2.9e36 < y < 3.5000000000000001e146 or 7.7999999999999995e195 < y

   1. Initial program 85.2%

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

   3. Taylor expanded in x around 0 30.3%

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

      1. associate-/r* 30.3%

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

      2. rec-exp 30.3%

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

      3. div-sub 30.3%

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

      4. rec-exp 30.3%

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

      5. tanh-def-a 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in y around inf 62.3%

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

      1. +-commutative 62.3%

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

      2. *-commutative 62.3%

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

   8. Simplified 62.3%

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

   if 3.5000000000000001e146 < y < 7.7999999999999995e195

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 62.5%

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

   4. Taylor expanded in t around 0 61.8%

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

      1. mul-1-neg 61.8%

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

      2. distribute-frac-neg 61.8%

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

   6. Simplified 61.8%

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

   7. Taylor expanded in x around 0 61.8%

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

      1. neg-mul-1 61.8%

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

      2. unsub-neg 61.8%

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

   9. Simplified 61.8%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+146} \lor \neg \left(y \leq 7.8 \cdot 10^{+195}\right):\\ \;\;\;\;x + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.1% accurate, 17.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 6.4 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 6.4e+40) 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 <= 6.4e+40) {
		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 <= 6.4d+40) 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 <= 6.4e+40) {
		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 <= 6.4e+40:
		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 <= 6.4e+40)
		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 <= 6.4e+40)
		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, 6.4e+40], x, N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.39999999999999961e40

   1. Initial program 96.7%

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

      1. +-commutative 96.7%

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

      2. associate-*l* 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

   5. Taylor expanded in y around 0 67.7%

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

   if 6.39999999999999961e40 < y

   1. Initial program 87.4%

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

   3. Taylor expanded in 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 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.4 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.8% accurate, 23.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;z \leq 6.8 \cdot 10^{+222}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t) :precision binary64 (if (<= z 6.8e+222) x (* z (- x))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (z <= 6.8e+222) {
		tmp = x;
	} 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 (z <= 6.8d+222) then
        tmp = x
    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 (z <= 6.8e+222) {
		tmp = x;
	} else {
		tmp = z * -x;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if z <= 6.8e+222:
		tmp = x
	else:
		tmp = z * -x
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (z <= 6.8e+222)
		tmp = x;
	else
		tmp = Float64(z * Float64(-x));
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	tmp = 0.0;
	if (z <= 6.8e+222)
		tmp = x;
	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[z, 6.8e+222], x, N[(z * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6.80000000000000032e222

   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. Step-by-step derivation

      1. +-commutative 95.4%

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

      2. associate-*l* 96.7%

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

      3. fma-define 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in y around 0 67.0%

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

   if 6.80000000000000032e222 < z

   1. Initial program 87.0%

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

   3. Taylor expanded in y around inf 41.5%

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

   4. Taylor expanded in t around 0 40.8%

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

      1. mul-1-neg 40.8%

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

      2. distribute-frac-neg 40.8%

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

   6. Simplified 40.8%

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

      1. distribute-frac-neg 40.8%

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

      2. distribute-rgt-neg-out 40.8%

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

      3. add-sqr-sqrt 16.0%

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

      4. sqrt-unprod 16.0%

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

      5. sqr-neg 16.0%

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

      6. sqrt-unprod 0.1%

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

      7. add-sqr-sqrt 1.2%

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

      8. sub-neg 1.2%

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

      9. associate-*l* 1.4%

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

      10. add-sqr-sqrt 0.1%

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

      11. sqrt-unprod 15.9%

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

      12. sqr-neg 15.9%

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

      13. sqrt-unprod 15.7%

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

      14. add-sqr-sqrt 40.8%

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

   8. Applied egg-rr 40.8%

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

      1. associate-*r* 40.8%

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

      2. *-commutative 40.8%

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

   10. Simplified 40.8%

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

   11. Taylor expanded in z around inf 40.8%

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

       1. associate-*r* 40.8%

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

       2. neg-mul-1 40.8%

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

   13. Simplified 40.8%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6.8 \cdot 10^{+222}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.9% accurate, 26.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 8 \cdot 10^{+196}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t) :precision binary64 (if (<= y_m 8e+196) x (* z t)))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 8e+196) {
		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 <= 8d+196) 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 <= 8e+196) {
		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 <= 8e+196:
		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 <= 8e+196)
		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 <= 8e+196)
		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, 8e+196], x, N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.9999999999999996e196

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. associate-*l* 98.3%

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

      3. fma-define 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in y around 0 63.6%

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

   if 7.9999999999999996e196 < y

   1. Initial program 62.4%

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

   3. Taylor expanded in x around 0 29.9%

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

      1. associate-/r* 29.9%

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

      2. rec-exp 29.9%

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

      3. div-sub 29.9%

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

      4. rec-exp 29.9%

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

      5. tanh-def-a 40.1%

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

   5. Simplified 40.1%

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

   6. Taylor expanded in y around inf 56.7%

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

      1. +-commutative 56.7%

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

      2. *-commutative 56.7%

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

   8. Simplified 56.7%

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

   9. Taylor expanded in z around inf 30.1%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{+196}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.2% 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 94.7%

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

   1. +-commutative 94.7%

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

   2. associate-*l* 96.9%

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

   3. fma-define 96.9%

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

3. Simplified 96.9%

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

5. Taylor expanded in y around 0 62.0%

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

6. Final simplification 62.0%

   \[\leadsto x \]
7. 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 2024050 
(FPCore (x y z t)
  :name "SynthBasics:moogVCF from YampaSynth-0.2"
  :precision binary64

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

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