SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.4% → 98.6%

Time: 11.9s

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: 93.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 5.8 \cdot 10^{+229}:\\ \;\;\;\;\mathsf{fma}\left(y\_m \cdot \left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 5.8e+229)
   (fma (* y_m (- (tanh (/ t y_m)) (tanh (/ x y_m)))) z 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 <= 5.8e+229) {
		tmp = fma((y_m * (tanh((t / y_m)) - tanh((x / y_m)))), z, 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 <= 5.8e+229)
		tmp = fma(Float64(y_m * Float64(tanh(Float64(t / y_m)) - tanh(Float64(x / y_m)))), z, 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, 5.8e+229], N[(N[(y$95$m * N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.79999999999999963e229

   1. Initial program 92.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. fma-define N/A

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

      5. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right), \color{blue}{z}, x\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), y\right), z, x\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\tanh \left(\frac{t}{y}\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z, x\right) \]

      8. tanh-lowering-tanh.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\left(\frac{t}{y}\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z, x\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z, x\right) \]

      10. tanh-lowering-tanh.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\left(\frac{x}{y}\right)\right)\right), y\right), z, x\right) \]

      11. /-lowering-/.f64 96.3%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right), y\right), z, x\right) \]

   4. Applied egg-rr 96.3%

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

   if 5.79999999999999963e229 < y

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 100.0%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.8 \cdot 10^{+229}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 4.7 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;y\_m \leq 5 \cdot 10^{+229}:\\ \;\;\;\;\mathsf{fma}\left(y\_m \cdot \left(\tanh \left(\frac{t}{y\_m}\right) - \frac{x}{y\_m}\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 4.7e-64)
   x
   (if (<= y_m 5e+229)
     (fma (* y_m (- (tanh (/ t y_m)) (/ x y_m))) z 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 <= 4.7e-64) {
		tmp = x;
	} else if (y_m <= 5e+229) {
		tmp = fma((y_m * (tanh((t / y_m)) - (x / y_m))), z, 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 <= 4.7e-64)
		tmp = x;
	elseif (y_m <= 5e+229)
		tmp = fma(Float64(y_m * Float64(tanh(Float64(t / y_m)) - Float64(x / y_m))), z, 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, 4.7e-64], x, If[LessEqual[y$95$m, 5e+229], N[(N[(y$95$m * N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - N[(x / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 4.6999999999999998e-64

   1. Initial program 91.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 69.7%

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

   if 4.6999999999999998e-64 < y < 5.0000000000000005e229

   1. Initial program 93.8%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. fma-define N/A

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

      5. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right), \color{blue}{z}, x\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), y\right), z, x\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\tanh \left(\frac{t}{y}\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z, x\right) \]

      8. tanh-lowering-tanh.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\left(\frac{t}{y}\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z, x\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z, x\right) \]

      10. tanh-lowering-tanh.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\left(\frac{x}{y}\right)\right)\right), y\right), z, x\right) \]

      11. /-lowering-/.f64 98.5%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right), y\right), z, x\right) \]

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \color{blue}{\left(\frac{x}{y}\right)}\right), y\right), z, x\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 83.6%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{/.f64}\left(x, y\right)\right), y\right), z, x\right) \]

   7. Simplified 83.6%

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

   if 5.0000000000000005e229 < y

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 100.0%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.7 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+229}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 1.2 \cdot 10^{+231}:\\ \;\;\;\;x + \left(y\_m \cdot \left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right)\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 1.2e+231)
   (+ x (* (* y_m (- (tanh (/ t y_m)) (tanh (/ x 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 <= 1.2e+231) {
		tmp = x + ((y_m * (tanh((t / y_m)) - tanh((x / 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 <= 1.2d+231) then
        tmp = x + ((y_m * (tanh((t / y_m)) - tanh((x / 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 <= 1.2e+231) {
		tmp = x + ((y_m * (Math.tanh((t / y_m)) - Math.tanh((x / 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 <= 1.2e+231:
		tmp = x + ((y_m * (math.tanh((t / y_m)) - math.tanh((x / 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 <= 1.2e+231)
		tmp = Float64(x + Float64(Float64(y_m * Float64(tanh(Float64(t / y_m)) - tanh(Float64(x / 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 <= 1.2e+231)
		tmp = x + ((y_m * (tanh((t / y_m)) - tanh((x / 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, 1.2e+231], N[(x + N[(N[(y$95$m * N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.20000000000000003e231

   1. Initial program 92.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right), \color{blue}{z}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\tanh \left(\frac{t}{y}\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

      6. tanh-lowering-tanh.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\left(\frac{t}{y}\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

      8. tanh-lowering-tanh.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\left(\frac{x}{y}\right)\right)\right), y\right), z\right)\right) \]

      9. /-lowering-/.f64 96.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right), y\right), z\right)\right) \]

   4. Applied egg-rr 96.2%

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

   if 1.20000000000000003e231 < y

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 100.0%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{+231}:\\ \;\;\;\;x + \left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 1.75 \cdot 10^{+229}:\\ \;\;\;\;x + y\_m \cdot \left(\left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 1.75e+229)
   (+ x (* y_m (* (- (tanh (/ t y_m)) (tanh (/ x 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 <= 1.75e+229) {
		tmp = x + (y_m * ((tanh((t / y_m)) - tanh((x / 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 <= 1.75d+229) then
        tmp = x + (y_m * ((tanh((t / y_m)) - tanh((x / 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 <= 1.75e+229) {
		tmp = x + (y_m * ((Math.tanh((t / y_m)) - Math.tanh((x / 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 <= 1.75e+229:
		tmp = x + (y_m * ((math.tanh((t / y_m)) - math.tanh((x / 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 <= 1.75e+229)
		tmp = Float64(x + Float64(y_m * Float64(Float64(tanh(Float64(t / y_m)) - tanh(Float64(x / 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 <= 1.75e+229)
		tmp = x + (y_m * ((tanh((t / y_m)) - tanh((x / 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, 1.75e+229], N[(x + N[(y$95$m * N[(N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.7500000000000001e229

   1. Initial program 92.0%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right) \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right), \color{blue}{y}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right), y\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\tanh \left(\frac{t}{y}\right), \tanh \left(\frac{x}{y}\right)\right)\right), y\right)\right) \]

      6. tanh-lowering-tanh.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\left(\frac{t}{y}\right)\right), \tanh \left(\frac{x}{y}\right)\right)\right), y\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \tanh \left(\frac{x}{y}\right)\right)\right), y\right)\right) \]

      8. tanh-lowering-tanh.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\left(\frac{x}{y}\right)\right)\right)\right), y\right)\right) \]

      9. /-lowering-/.f64 95.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right)\right), y\right)\right) \]

   4. Applied egg-rr 95.4%

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

   if 1.7500000000000001e229 < y

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 100.0%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{+229}:\\ \;\;\;\;x + y \cdot \left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 1.26 \cdot 10^{+157}:\\ \;\;\;\;x + \left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right) \cdot \left(y\_m \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 1.26e+157)
   (+ 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 <= 1.26e+157) {
		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 <= 1.26d+157) 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 <= 1.26e+157) {
		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 <= 1.26e+157:
		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 <= 1.26e+157)
		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 <= 1.26e+157)
		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, 1.26e+157], 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 < 1.25999999999999996e157

   1. Initial program 92.3%

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

   if 1.25999999999999996e157 < y

   1. Initial program 80.9%

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

   3. Taylor expanded in y around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 94.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 94.2%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.26 \cdot 10^{+157}:\\ \;\;\;\;x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 1.5 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;y\_m \leq 1.5 \cdot 10^{+231}:\\ \;\;\;\;x + z \cdot \left(y\_m \cdot \left(\tanh \left(\frac{t}{y\_m}\right) - \frac{x}{y\_m}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 1.5e-63)
   x
   (if (<= y_m 1.5e+231)
     (+ x (* z (* y_m (- (tanh (/ t y_m)) (/ x y_m)))))
     (+ x (* z (- t x))))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 1.5e-63) {
		tmp = x;
	} else if (y_m <= 1.5e+231) {
		tmp = x + (z * (y_m * (tanh((t / y_m)) - (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) :: tmp
    if (y_m <= 1.5d-63) then
        tmp = x
    else if (y_m <= 1.5d+231) then
        tmp = x + (z * (y_m * (tanh((t / y_m)) - (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 tmp;
	if (y_m <= 1.5e-63) {
		tmp = x;
	} else if (y_m <= 1.5e+231) {
		tmp = x + (z * (y_m * (Math.tanh((t / y_m)) - (x / y_m))));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if y_m <= 1.5e-63:
		tmp = x
	elif y_m <= 1.5e+231:
		tmp = x + (z * (y_m * (math.tanh((t / y_m)) - (x / y_m))))
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 1.5e-63)
		tmp = x;
	elseif (y_m <= 1.5e+231)
		tmp = Float64(x + Float64(z * Float64(y_m * Float64(tanh(Float64(t / y_m)) - 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)
	tmp = 0.0;
	if (y_m <= 1.5e-63)
		tmp = x;
	elseif (y_m <= 1.5e+231)
		tmp = x + (z * (y_m * (tanh((t / y_m)) - (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_] := If[LessEqual[y$95$m, 1.5e-63], x, If[LessEqual[y$95$m, 1.5e+231], N[(x + N[(z * N[(y$95$m * N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - N[(x / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.4999999999999999e-63

   1. Initial program 91.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 69.7%

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

   if 1.4999999999999999e-63 < y < 1.5000000000000001e231

   1. Initial program 93.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right), \color{blue}{z}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\tanh \left(\frac{t}{y}\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

      6. tanh-lowering-tanh.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\left(\frac{t}{y}\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

      8. tanh-lowering-tanh.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\left(\frac{x}{y}\right)\right)\right), y\right), z\right)\right) \]

      9. /-lowering-/.f64 98.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right), y\right), z\right)\right) \]

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \color{blue}{\left(\frac{x}{y}\right)}\right), y\right), z\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 83.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{/.f64}\left(x, y\right)\right), y\right), z\right)\right) \]

   7. Simplified 83.6%

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

   if 1.5000000000000001e231 < y

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 100.0%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+231}:\\ \;\;\;\;x + z \cdot \left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 5.8 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;y\_m \leq 2.5 \cdot 10^{+131}:\\ \;\;\;\;x + \left(y\_m \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y\_m}\right) - \frac{x}{y\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 5.8e-64)
   x
   (if (<= y_m 2.5e+131)
     (+ x (* (* y_m z) (- (tanh (/ t y_m)) (/ x y_m))))
     (+ x (* z (- t x))))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 5.8e-64) {
		tmp = x;
	} else if (y_m <= 2.5e+131) {
		tmp = x + ((y_m * z) * (tanh((t / y_m)) - (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) :: tmp
    if (y_m <= 5.8d-64) then
        tmp = x
    else if (y_m <= 2.5d+131) then
        tmp = x + ((y_m * z) * (tanh((t / y_m)) - (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 tmp;
	if (y_m <= 5.8e-64) {
		tmp = x;
	} else if (y_m <= 2.5e+131) {
		tmp = x + ((y_m * z) * (Math.tanh((t / y_m)) - (x / y_m)));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if y_m <= 5.8e-64:
		tmp = x
	elif y_m <= 2.5e+131:
		tmp = x + ((y_m * z) * (math.tanh((t / y_m)) - (x / y_m)))
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 5.8e-64)
		tmp = x;
	elseif (y_m <= 2.5e+131)
		tmp = Float64(x + Float64(Float64(y_m * z) * Float64(tanh(Float64(t / y_m)) - 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)
	tmp = 0.0;
	if (y_m <= 5.8e-64)
		tmp = x;
	elseif (y_m <= 2.5e+131)
		tmp = x + ((y_m * z) * (tanh((t / y_m)) - (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_] := If[LessEqual[y$95$m, 5.8e-64], x, If[LessEqual[y$95$m, 2.5e+131], N[(x + N[(N[(y$95$m * z), $MachinePrecision] * N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - 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 < 5.7999999999999998e-64

   1. Initial program 91.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 69.7%

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

   if 5.7999999999999998e-64 < y < 2.49999999999999998e131

   1. Initial program 95.2%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \color{blue}{\left(\frac{x}{y}\right)}\right)\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 79.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right)\right) \]

   5. Simplified 79.3%

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

   if 2.49999999999999998e131 < y

   1. Initial program 84.1%

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

   3. Taylor expanded in y around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 90.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 90.8%

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

Alternative 8: 77.8% accurate, 17.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 1.35 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 1.35e+33) x (+ x (* z (- t x)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 1.35e+33) {
		tmp = x;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y_m <= 1.35d+33) then
        tmp = x
    else
        tmp = x + (z * (t - x))
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 1.35e+33) {
		tmp = x;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if y_m <= 1.35e+33:
		tmp = x
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 1.35e+33)
		tmp = x;
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	tmp = 0.0;
	if (y_m <= 1.35e+33)
		tmp = x;
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 1.35e+33], x, N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.34999999999999996e33

   1. Initial program 92.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 68.1%

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

   if 1.34999999999999996e33 < y

   1. Initial program 87.3%

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

   3. Taylor expanded in y around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 81.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 81.9%

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

Alternative 9: 70.7% accurate, 21.3× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 2.05 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot z\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t) :precision binary64 (if (<= y_m 2.05e+18) x (+ x (* t z))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 2.05e+18) {
		tmp = x;
	} else {
		tmp = x + (t * 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 <= 2.05d+18) then
        tmp = x
    else
        tmp = x + (t * 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 <= 2.05e+18) {
		tmp = x;
	} else {
		tmp = x + (t * z);
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if y_m <= 2.05e+18:
		tmp = x
	else:
		tmp = x + (t * z)
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 2.05e+18)
		tmp = x;
	else
		tmp = Float64(x + Float64(t * 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 <= 2.05e+18)
		tmp = x;
	else
		tmp = x + (t * 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, 2.05e+18], x, N[(x + N[(t * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.05e18

   1. Initial program 91.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 69.1%

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

   if 2.05e18 < y

   1. Initial program 87.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \color{blue}{\left(\frac{t - x}{y}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{y}\right)\right)\right) \]

      2. --lowering--.f64 67.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), y\right)\right)\right) \]

   5. Simplified 67.9%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot z\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \color{blue}{t}\right)\right) \]

      2. *-lowering-*.f64 70.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right) \]

   8. Simplified 70.2%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.05 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.5% accurate, 21.3× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 7.8 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 7.8e+115) x (* x (- 1.0 z))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 7.8e+115) {
		tmp = x;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y_m <= 7.8d+115) then
        tmp = x
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 7.8e+115) {
		tmp = x;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if y_m <= 7.8e+115:
		tmp = x
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 7.8e+115)
		tmp = x;
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	tmp = 0.0;
	if (y_m <= 7.8e+115)
		tmp = x;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 7.8e+115], x, N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.80000000000000012e115

   1. Initial program 92.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 67.9%

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

   if 7.80000000000000012e115 < y

   1. Initial program 82.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \color{blue}{\left(\frac{t - x}{y}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{y}\right)\right)\right) \]

      2. --lowering--.f64 72.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), y\right)\right)\right) \]

   5. Simplified 72.0%

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

   6. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot z\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{z}\right)\right) \]

      4. --lowering--.f64 53.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]

   8. Simplified 53.0%

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

Alternative 11: 60.1% 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 90.7%

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

3. Taylor expanded in x around inf

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

5. Simplified 62.4%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 96.8% 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 2024145 
(FPCore (x y z t)
  :name "SynthBasics:moogVCF from YampaSynth-0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (* y (* z (- (tanh (/ t y)) (tanh (/ x y)))))))

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