SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 92.7% → 96.9%

Time: 12.3s

Alternatives: 9

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: 92.7% 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: 96.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. +-commutative 97.7%

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

   2. associate-*l* 99.5%

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

   3. fma-define 99.5%

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

3. Simplified 99.5%

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

   1. sub-neg 99.5%

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

   2. distribute-rgt-in 99.6%

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

6. Applied egg-rr 99.6%

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

7. Final simplification 99.6%

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

Alternative 2: 96.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. +-commutative 97.7%

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

   2. associate-*l* 99.5%

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

   3. fma-define 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 3: 92.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

3. Final simplification 97.7%

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

Alternative 4: 82.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{+89}:\\ \;\;\;\;x + y \cdot \left(\tanh \left(\frac{t}{y}\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 3.6e+89) (+ x (* y (* (tanh (/ t y)) z))) (+ x (* z (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.6e+89) {
		tmp = x + (y * (tanh((t / y)) * z));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y <= 3.6d+89) then
        tmp = x + (y * (tanh((t / y)) * z))
    else
        tmp = x + (z * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.6e+89) {
		tmp = x + (y * (Math.tanh((t / y)) * z));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 3.6e+89:
		tmp = x + (y * (math.tanh((t / y)) * z))
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 3.6e+89)
		tmp = Float64(x + Float64(y * Float64(tanh(Float64(t / y)) * z)));
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 3.6e+89)
		tmp = x + (y * (tanh((t / y)) * z));
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 3.6e+89], N[(x + N[(y * N[(N[Tanh[N[(t / y), $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 < 3.6e89

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0 28.1%

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

      1. associate-/r* 28.1%

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

      2. rec-exp 28.1%

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

      3. div-sub 28.1%

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

      4. rec-exp 28.1%

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

      5. tanh-def-a 86.0%

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

   5. Simplified 86.0%

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

   if 3.6e89 < y

   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 y around inf 86.8%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{+89}:\\ \;\;\;\;x + y \cdot \left(\tanh \left(\frac{t}{y}\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.4% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.8 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+99} \lor \neg \left(y \leq 5.5 \cdot 10^{+179}\right) \land y \leq 9.2 \cdot 10^{+225}:\\ \;\;\;\;x + t \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.8e+50)
   x
   (if (or (<= y 2.8e+99) (and (not (<= y 5.5e+179)) (<= y 9.2e+225)))
     (+ x (* t z))
     (* x (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.8e+50) {
		tmp = x;
	} else if ((y <= 2.8e+99) || (!(y <= 5.5e+179) && (y <= 9.2e+225))) {
		tmp = x + (t * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y <= 2.8d+50) then
        tmp = x
    else if ((y <= 2.8d+99) .or. (.not. (y <= 5.5d+179)) .and. (y <= 9.2d+225)) then
        tmp = x + (t * z)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.8e+50) {
		tmp = x;
	} else if ((y <= 2.8e+99) || (!(y <= 5.5e+179) && (y <= 9.2e+225))) {
		tmp = x + (t * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.8e+50:
		tmp = x
	elif (y <= 2.8e+99) or (not (y <= 5.5e+179) and (y <= 9.2e+225)):
		tmp = x + (t * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.8e+50)
		tmp = x;
	elseif ((y <= 2.8e+99) || (!(y <= 5.5e+179) && (y <= 9.2e+225)))
		tmp = Float64(x + Float64(t * z));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.8e+50)
		tmp = x;
	elseif ((y <= 2.8e+99) || (~((y <= 5.5e+179)) && (y <= 9.2e+225)))
		tmp = x + (t * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.8e+50], x, If[Or[LessEqual[y, 2.8e+99], And[N[Not[LessEqual[y, 5.5e+179]], $MachinePrecision], LessEqual[y, 9.2e+225]]], N[(x + N[(t * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.7999999999999998e50

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 70.5%

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

   if 2.7999999999999998e50 < y < 2.8e99 or 5.4999999999999998e179 < y < 9.1999999999999998e225

   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 34.2%

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

      1. associate-/r* 34.2%

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

      2. rec-exp 34.2%

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

      3. div-sub 34.2%

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

      4. rec-exp 34.2%

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

      5. tanh-def-a 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in y around inf 68.4%

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

      1. +-commutative 68.4%

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

   8. Simplified 68.4%

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

   if 2.8e99 < y < 5.4999999999999998e179 or 9.1999999999999998e225 < y

   1. Initial program 92.6%

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

   3. Taylor expanded in t around 0 35.0%

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

      1. sub-neg 35.0%

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

      2. +-commutative 35.0%

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

      3. neg-sub0 35.0%

         \[\leadsto x + y \cdot \left(z \cdot \left(\color{blue}{\left(0 - \frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}}\right)} + \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)\right) \]

      4. associate--r- 35.0%

         \[\leadsto x + y \cdot \left(z \cdot \color{blue}{\left(0 - \left(\frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}} - \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)\right)}\right) \]

   5. Simplified 75.6%

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

   6. Taylor expanded in x around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. unsub-neg 71.9%

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

   8. Simplified 71.9%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.8 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+99} \lor \neg \left(y \leq 5.5 \cdot 10^{+179}\right) \land y \leq 9.2 \cdot 10^{+225}:\\ \;\;\;\;x + t \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.5% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot z\\ \mathbf{if}\;y \leq 2.6 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+226}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* t z))))
   (if (<= y 2.6e+48)
     x
     (if (<= y 5e+101)
       t_1
       (if (<= y 3.6e+178)
         (* x (- 1.0 z))
         (if (<= y 1.85e+226) t_1 (- x (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (t * z);
	double tmp;
	if (y <= 2.6e+48) {
		tmp = x;
	} else if (y <= 5e+101) {
		tmp = t_1;
	} else if (y <= 3.6e+178) {
		tmp = x * (1.0 - z);
	} else if (y <= 1.85e+226) {
		tmp = t_1;
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * z)
    if (y <= 2.6d+48) then
        tmp = x
    else if (y <= 5d+101) then
        tmp = t_1
    else if (y <= 3.6d+178) then
        tmp = x * (1.0d0 - z)
    else if (y <= 1.85d+226) then
        tmp = t_1
    else
        tmp = x - (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (t * z);
	double tmp;
	if (y <= 2.6e+48) {
		tmp = x;
	} else if (y <= 5e+101) {
		tmp = t_1;
	} else if (y <= 3.6e+178) {
		tmp = x * (1.0 - z);
	} else if (y <= 1.85e+226) {
		tmp = t_1;
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (t * z)
	tmp = 0
	if y <= 2.6e+48:
		tmp = x
	elif y <= 5e+101:
		tmp = t_1
	elif y <= 3.6e+178:
		tmp = x * (1.0 - z)
	elif y <= 1.85e+226:
		tmp = t_1
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(t * z))
	tmp = 0.0
	if (y <= 2.6e+48)
		tmp = x;
	elseif (y <= 5e+101)
		tmp = t_1;
	elseif (y <= 3.6e+178)
		tmp = Float64(x * Float64(1.0 - z));
	elseif (y <= 1.85e+226)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (t * z);
	tmp = 0.0;
	if (y <= 2.6e+48)
		tmp = x;
	elseif (y <= 5e+101)
		tmp = t_1;
	elseif (y <= 3.6e+178)
		tmp = x * (1.0 - z);
	elseif (y <= 1.85e+226)
		tmp = t_1;
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 2.6e+48], x, If[LessEqual[y, 5e+101], t$95$1, If[LessEqual[y, 3.6e+178], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+226], t$95$1, N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < 2.59999999999999995e48

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 70.5%

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

   if 2.59999999999999995e48 < y < 4.99999999999999989e101 or 3.5999999999999998e178 < y < 1.84999999999999991e226

   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 34.2%

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

      1. associate-/r* 34.2%

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

      2. rec-exp 34.2%

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

      3. div-sub 34.2%

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

      4. rec-exp 34.2%

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

      5. tanh-def-a 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in y around inf 68.4%

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

      1. +-commutative 68.4%

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

   8. Simplified 68.4%

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

   if 4.99999999999999989e101 < y < 3.5999999999999998e178

   1. Initial program 94.6%

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

   3. Taylor expanded in t around 0 21.7%

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

      1. sub-neg 21.7%

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

      2. +-commutative 21.7%

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

      3. neg-sub0 21.7%

         \[\leadsto x + y \cdot \left(z \cdot \left(\color{blue}{\left(0 - \frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}}\right)} + \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)\right) \]

      4. associate--r- 21.7%

         \[\leadsto x + y \cdot \left(z \cdot \color{blue}{\left(0 - \left(\frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}} - \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)\right)}\right) \]

   5. Simplified 79.5%

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

   6. Taylor expanded in x around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. unsub-neg 71.2%

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

   8. Simplified 71.2%

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

   if 1.84999999999999991e226 < y

   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 t around 0 47.6%

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

      1. sub-neg 47.6%

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

      2. +-commutative 47.6%

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

      3. neg-sub0 47.6%

         \[\leadsto x + y \cdot \left(z \cdot \left(\color{blue}{\left(0 - \frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}}\right)} + \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)\right) \]

      4. associate--r- 47.6%

         \[\leadsto x + y \cdot \left(z \cdot \color{blue}{\left(0 - \left(\frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}} - \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)\right)}\right) \]

   5. Simplified 71.9%

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

      1. associate-*r* 67.4%

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

      2. distribute-rgt-neg-out 67.4%

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

      3. add-sqr-sqrt 22.4%

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

      4. sqrt-unprod 57.5%

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

      5. sqr-neg 57.5%

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

      6. sqrt-unprod 35.0%

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

      7. add-sqr-sqrt 51.7%

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

      8. cancel-sign-sub-inv 51.7%

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

      9. *-commutative 51.7%

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

      10. add-sqr-sqrt 35.0%

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

      11. sqrt-unprod 57.5%

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

      12. sqr-neg 57.5%

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

      13. sqrt-unprod 22.4%

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

      14. add-sqr-sqrt 67.4%

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

   7. Applied egg-rr 67.4%

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

   8. Taylor expanded in x around 0 72.6%

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

      1. *-commutative 72.6%

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

   10. Simplified 72.6%

       \[\leadsto x - \color{blue}{z \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+101}:\\ \;\;\;\;x + t \cdot z\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+226}:\\ \;\;\;\;x + t \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.7% accurate, 17.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.2e+50) x (+ x (* z (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.2e+50) {
		tmp = x;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y <= 2.2d+50) then
        tmp = x
    else
        tmp = x + (z * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.2e+50) {
		tmp = x;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.2e+50:
		tmp = x
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.2e+50)
		tmp = x;
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.2e+50)
		tmp = x;
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.2e+50], x, N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.20000000000000017e50

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 70.5%

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

   if 2.20000000000000017e50 < y

   1. Initial program 93.5%

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

   3. Taylor expanded in y around inf 81.8%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.2% accurate, 21.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.22 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 1.22e+63) x (* x (- 1.0 z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.22e+63) {
		tmp = x;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y <= 1.22d+63) then
        tmp = x
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.22e+63) {
		tmp = x;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.22e+63:
		tmp = x
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.22e+63)
		tmp = x;
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.22e+63)
		tmp = x;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.22e+63], x, N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.2199999999999999e63

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 69.2%

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

   if 1.2199999999999999e63 < y

   1. Initial program 93.1%

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

   3. Taylor expanded in t around 0 33.6%

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

      1. sub-neg 33.6%

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

      2. +-commutative 33.6%

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

      3. neg-sub0 33.6%

         \[\leadsto x + y \cdot \left(z \cdot \left(\color{blue}{\left(0 - \frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}}\right)} + \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)\right) \]

      4. associate--r- 33.6%

         \[\leadsto x + y \cdot \left(z \cdot \color{blue}{\left(0 - \left(\frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}} - \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)\right)}\right) \]

   5. Simplified 67.3%

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

   6. Taylor expanded in x around 0 64.8%

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

      1. mul-1-neg 64.8%

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

      2. unsub-neg 64.8%

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

   8. Simplified 64.8%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.22 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.6% accurate, 213.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

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

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
end function

Java

public static double code(double x, double y, double z, double t) {
	return x;
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 97.7%

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

3. Taylor expanded in x around inf 63.8%

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

4. Final simplification 63.8%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 96.9% 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 2024071 
(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))))))