SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.8% → 97.2%

Time: 14.4s

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: 93.8% 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: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.1%

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

   1. sub-neg 92.1%

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

   2. distribute-lft-in 86.8%

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

4. Applied egg-rr 86.8%

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

   1. distribute-rgt-neg-out 86.8%

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

   2. distribute-lft-neg-in 86.8%

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

   3. add-sqr-sqrt 40.0%

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

   4. sqrt-unprod 75.2%

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

   5. sqr-neg 75.2%

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

   6. sqrt-unprod 42.0%

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

   7. add-sqr-sqrt 70.4%

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

   8. cancel-sign-sub-inv 70.4%

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

   9. associate-*l* 70.4%

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

   10. associate-*l* 74.7%

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

   11. distribute-lft-out-- 74.7%

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

   12. add-sqr-sqrt 45.2%

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

   13. sqrt-unprod 82.5%

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

6. Applied egg-rr 97.0%

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

7. Final simplification 97.0%

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

Alternative 2: 97.2% 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]

Derivation

1. Initial program 92.1%

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

   1. sub-neg 92.1%

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

   2. distribute-lft-in 86.8%

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

4. Applied egg-rr 86.8%

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

   1. distribute-lft-out 92.1%

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

   2. sub-neg 92.1%

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

   3. associate-*l* 97.0%

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

6. Simplified 97.0%

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

7. Final simplification 97.0%

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

Alternative 3: 82.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{+59} \lor \neg \left(y \leq 1.35 \cdot 10^{+100}\right) \land y \leq 9 \cdot 10^{+134}:\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y 1.8e+59) (and (not (<= y 1.35e+100)) (<= y 9e+134)))
   (+ x (* y (* z (tanh (/ t y)))))
   (+ x (* z (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= 1.8e+59) || (!(y <= 1.35e+100) && (y <= 9e+134))) {
		tmp = x + (y * (z * tanh((t / y))));
	} 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 <= 1.8d+59) .or. (.not. (y <= 1.35d+100)) .and. (y <= 9d+134)) then
        tmp = x + (y * (z * tanh((t / y))))
    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 <= 1.8e+59) || (!(y <= 1.35e+100) && (y <= 9e+134))) {
		tmp = x + (y * (z * Math.tanh((t / y))));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= 1.8e+59) or (not (y <= 1.35e+100) and (y <= 9e+134)):
		tmp = x + (y * (z * math.tanh((t / y))))
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= 1.8e+59) || (!(y <= 1.35e+100) && (y <= 9e+134)))
		tmp = Float64(x + Float64(y * Float64(z * tanh(Float64(t / y)))));
	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 <= 1.8e+59) || (~((y <= 1.35e+100)) && (y <= 9e+134)))
		tmp = x + (y * (z * tanh((t / y))));
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, 1.8e+59], And[N[Not[LessEqual[y, 1.35e+100]], $MachinePrecision], LessEqual[y, 9e+134]]], N[(x + N[(y * N[(z * N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.7999999999999999e59 or 1.34999999999999999e100 < y < 8.9999999999999995e134

   1. Initial program 94.2%

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

   3. Taylor expanded in x around 0 24.8%

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

      1. associate-/r* 24.8%

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

      2. rec-exp 24.8%

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

      3. div-sub 24.8%

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

      4. rec-exp 24.8%

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

      5. tanh-def-a 80.1%

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

   5. Simplified 80.1%

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

   if 1.7999999999999999e59 < y < 1.34999999999999999e100 or 8.9999999999999995e134 < y

   1. Initial program 84.3%

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

   3. Taylor expanded in y around inf 89.3%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{+59} \lor \neg \left(y \leq 1.35 \cdot 10^{+100}\right) \land y \leq 9 \cdot 10^{+134}:\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \tanh \left(\frac{t}{y}\right)\\ \mathbf{if}\;y \leq 1.45 \cdot 10^{+59}:\\ \;\;\;\;x + y \cdot \left(z \cdot t\_1\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+100} \lor \neg \left(y \leq 1.7 \cdot 10^{+131}\right):\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (tanh (/ t y))))
   (if (<= y 1.45e+59)
     (+ x (* y (* z t_1)))
     (if (or (<= y 3.6e+100) (not (<= y 1.7e+131)))
       (+ x (* z (- t x)))
       (+ x (* t_1 (* y z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = tanh((t / y));
	double tmp;
	if (y <= 1.45e+59) {
		tmp = x + (y * (z * t_1));
	} else if ((y <= 3.6e+100) || !(y <= 1.7e+131)) {
		tmp = x + (z * (t - x));
	} else {
		tmp = x + (t_1 * (y * 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) :: t_1
    real(8) :: tmp
    t_1 = tanh((t / y))
    if (y <= 1.45d+59) then
        tmp = x + (y * (z * t_1))
    else if ((y <= 3.6d+100) .or. (.not. (y <= 1.7d+131))) then
        tmp = x + (z * (t - x))
    else
        tmp = x + (t_1 * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.tanh((t / y));
	double tmp;
	if (y <= 1.45e+59) {
		tmp = x + (y * (z * t_1));
	} else if ((y <= 3.6e+100) || !(y <= 1.7e+131)) {
		tmp = x + (z * (t - x));
	} else {
		tmp = x + (t_1 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.tanh((t / y))
	tmp = 0
	if y <= 1.45e+59:
		tmp = x + (y * (z * t_1))
	elif (y <= 3.6e+100) or not (y <= 1.7e+131):
		tmp = x + (z * (t - x))
	else:
		tmp = x + (t_1 * (y * z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = tanh(Float64(t / y))
	tmp = 0.0
	if (y <= 1.45e+59)
		tmp = Float64(x + Float64(y * Float64(z * t_1)));
	elseif ((y <= 3.6e+100) || !(y <= 1.7e+131))
		tmp = Float64(x + Float64(z * Float64(t - x)));
	else
		tmp = Float64(x + Float64(t_1 * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = tanh((t / y));
	tmp = 0.0;
	if (y <= 1.45e+59)
		tmp = x + (y * (z * t_1));
	elseif ((y <= 3.6e+100) || ~((y <= 1.7e+131)))
		tmp = x + (z * (t - x));
	else
		tmp = x + (t_1 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, 1.45e+59], N[(x + N[(y * N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.6e+100], N[Not[LessEqual[y, 1.7e+131]], $MachinePrecision]], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.44999999999999995e59

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0 24.6%

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

      1. associate-/r* 24.6%

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

      2. rec-exp 24.6%

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

      3. div-sub 24.6%

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

      4. rec-exp 24.6%

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

      5. tanh-def-a 80.2%

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

   5. Simplified 80.2%

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

   if 1.44999999999999995e59 < y < 3.6e100 or 1.69999999999999993e131 < y

   1. Initial program 84.3%

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

   3. Taylor expanded in y around inf 89.3%

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

   if 3.6e100 < y < 1.69999999999999993e131

   1. Initial program 88.6%

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

   3. Taylor expanded in x around 0 27.3%

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

      1. associate-/r* 27.3%

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

      2. rec-exp 27.3%

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

      3. div-sub 27.3%

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

      4. rec-exp 27.3%

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

      5. tanh-def-a 78.3%

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

   5. Simplified 78.3%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{+59}:\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+100} \lor \neg \left(y \leq 1.7 \cdot 10^{+131}\right):\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \tanh \left(\frac{t}{y}\right) \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-7} \lor \neg \left(x \leq 0.000135\right):\\ \;\;\;\;x - y \cdot \left(z \cdot \tanh \left(\frac{x}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.1e-7) (not (<= x 0.000135)))
   (- x (* y (* z (tanh (/ x y)))))
   (+ x (* (* y z) (- (tanh (/ t y)) (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.1e-7) || !(x <= 0.000135)) {
		tmp = x - (y * (z * tanh((x / y))));
	} else {
		tmp = x + ((y * z) * (tanh((t / y)) - (x / y)));
	}
	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 ((x <= (-2.1d-7)) .or. (.not. (x <= 0.000135d0))) then
        tmp = x - (y * (z * tanh((x / y))))
    else
        tmp = x + ((y * z) * (tanh((t / y)) - (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.1e-7) || !(x <= 0.000135)) {
		tmp = x - (y * (z * Math.tanh((x / y))));
	} else {
		tmp = x + ((y * z) * (Math.tanh((t / y)) - (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.1e-7) or not (x <= 0.000135):
		tmp = x - (y * (z * math.tanh((x / y))))
	else:
		tmp = x + ((y * z) * (math.tanh((t / y)) - (x / y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.1e-7) || !(x <= 0.000135))
		tmp = Float64(x - Float64(y * Float64(z * tanh(Float64(x / y)))));
	else
		tmp = Float64(x + Float64(Float64(y * z) * Float64(tanh(Float64(t / y)) - Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.1e-7) || ~((x <= 0.000135)))
		tmp = x - (y * (z * tanh((x / y))));
	else
		tmp = x + ((y * z) * (tanh((t / y)) - (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.1e-7], N[Not[LessEqual[x, 0.000135]], $MachinePrecision]], N[(x - N[(y * N[(z * N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] * N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1e-7 or 1.35000000000000002e-4 < x

   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. Step-by-step derivation

      1. sub-neg 92.6%

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

      2. distribute-lft-in 86.9%

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

   4. Applied egg-rr 86.9%

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

      1. distribute-rgt-neg-out 86.9%

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

      2. distribute-lft-neg-in 86.9%

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

      3. add-sqr-sqrt 39.2%

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

      4. sqrt-unprod 76.4%

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

      5. sqr-neg 76.4%

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

      6. sqrt-unprod 37.9%

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

      7. add-sqr-sqrt 69.8%

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

      8. cancel-sign-sub-inv 69.8%

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

      9. associate-*l* 69.8%

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

      10. associate-*l* 70.6%

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

      11. distribute-lft-out-- 70.6%

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

      12. add-sqr-sqrt 37.9%

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

      13. sqrt-unprod 81.3%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 12.6%

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

      1. mul-1-neg 12.6%

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

      2. associate-/l* 12.6%

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

      3. associate-/l* 12.6%

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

      4. rec-exp 12.6%

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

      5. rec-exp 12.6%

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

      6. tanh-def-a 89.7%

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

      7. distribute-rgt-neg-in 89.7%

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

   9. Simplified 89.7%

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

   if -2.1e-7 < x < 1.35000000000000002e-4

   1. Initial program 91.6%

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

   3. Taylor expanded in x around 0 80.3%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-7} \lor \neg \left(x \leq 0.000135\right):\\ \;\;\;\;x - y \cdot \left(z \cdot \tanh \left(\frac{x}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-10} \lor \neg \left(t \leq 1.45 \cdot 10^{-48}\right):\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot t - y \cdot \left(z \cdot \tanh \left(\frac{x}{y}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.25e-10) (not (<= t 1.45e-48)))
   (+ x (* y (* z (tanh (/ t y)))))
   (+ x (- (* z t) (* y (* z (tanh (/ x y))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.25e-10) || !(t <= 1.45e-48)) {
		tmp = x + (y * (z * tanh((t / y))));
	} else {
		tmp = x + ((z * t) - (y * (z * tanh((x / y)))));
	}
	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 ((t <= (-1.25d-10)) .or. (.not. (t <= 1.45d-48))) then
        tmp = x + (y * (z * tanh((t / y))))
    else
        tmp = x + ((z * t) - (y * (z * tanh((x / y)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.25e-10) || !(t <= 1.45e-48)) {
		tmp = x + (y * (z * Math.tanh((t / y))));
	} else {
		tmp = x + ((z * t) - (y * (z * Math.tanh((x / y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.25e-10) or not (t <= 1.45e-48):
		tmp = x + (y * (z * math.tanh((t / y))))
	else:
		tmp = x + ((z * t) - (y * (z * math.tanh((x / y)))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.25e-10) || !(t <= 1.45e-48))
		tmp = Float64(x + Float64(y * Float64(z * tanh(Float64(t / y)))));
	else
		tmp = Float64(x + Float64(Float64(z * t) - Float64(y * Float64(z * tanh(Float64(x / y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.25e-10) || ~((t <= 1.45e-48)))
		tmp = x + (y * (z * tanh((t / y))));
	else
		tmp = x + ((z * t) - (y * (z * tanh((x / y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.25e-10], N[Not[LessEqual[t, 1.45e-48]], $MachinePrecision]], N[(x + N[(y * N[(z * N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * t), $MachinePrecision] - N[(y * N[(z * N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.25000000000000008e-10 or 1.4500000000000001e-48 < t

   1. Initial program 94.4%

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

   3. Taylor expanded in x around 0 11.0%

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

      1. associate-/r* 11.0%

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

      2. rec-exp 11.1%

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

      3. div-sub 11.1%

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

      4. rec-exp 11.1%

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

      5. tanh-def-a 84.3%

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

   5. Simplified 84.3%

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

   if -1.25000000000000008e-10 < t < 1.4500000000000001e-48

   1. Initial program 89.4%

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

      1. sub-neg 89.4%

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

      2. distribute-lft-in 83.1%

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

   4. Applied egg-rr 83.1%

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

   5. Taylor expanded in t around 0 28.8%

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

      1. +-commutative 28.8%

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

      2. mul-1-neg 28.8%

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

      3. unsub-neg 28.8%

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

      4. *-commutative 28.8%

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

      5. associate-/l* 28.8%

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

      6. associate-/l* 28.8%

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

      7. rec-exp 28.8%

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

   7. Simplified 89.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-10} \lor \neg \left(t \leq 1.45 \cdot 10^{-48}\right):\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot t - y \cdot \left(z \cdot \tanh \left(\frac{x}{y}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-6} \lor \neg \left(x \leq 0.000205\right):\\ \;\;\;\;x - y \cdot \left(z \cdot \tanh \left(\frac{x}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.8e-6) (not (<= x 0.000205)))
   (- x (* y (* z (tanh (/ x y)))))
   (+ x (* y (* z (tanh (/ t y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.8e-6) || !(x <= 0.000205)) {
		tmp = x - (y * (z * tanh((x / y))));
	} else {
		tmp = x + (y * (z * tanh((t / y))));
	}
	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 ((x <= (-5.8d-6)) .or. (.not. (x <= 0.000205d0))) then
        tmp = x - (y * (z * tanh((x / y))))
    else
        tmp = x + (y * (z * tanh((t / y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.8e-6) || !(x <= 0.000205)) {
		tmp = x - (y * (z * Math.tanh((x / y))));
	} else {
		tmp = x + (y * (z * Math.tanh((t / y))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.8e-6) or not (x <= 0.000205):
		tmp = x - (y * (z * math.tanh((x / y))))
	else:
		tmp = x + (y * (z * math.tanh((t / y))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.8e-6) || !(x <= 0.000205))
		tmp = Float64(x - Float64(y * Float64(z * tanh(Float64(x / y)))));
	else
		tmp = Float64(x + Float64(y * Float64(z * tanh(Float64(t / y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.8e-6) || ~((x <= 0.000205)))
		tmp = x - (y * (z * tanh((x / y))));
	else
		tmp = x + (y * (z * tanh((t / y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.8e-6], N[Not[LessEqual[x, 0.000205]], $MachinePrecision]], N[(x - N[(y * N[(z * N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z * N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.8000000000000004e-6 or 2.05e-4 < x

   1. Initial program 92.5%

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

      1. sub-neg 92.5%

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

      2. distribute-lft-in 86.8%

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

   4. Applied egg-rr 86.8%

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

      1. distribute-rgt-neg-out 86.8%

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

      2. distribute-lft-neg-in 86.8%

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

      3. add-sqr-sqrt 39.5%

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

      4. sqrt-unprod 76.2%

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

      5. sqr-neg 76.2%

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

      6. sqrt-unprod 37.4%

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

      7. add-sqr-sqrt 69.6%

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

      8. cancel-sign-sub-inv 69.6%

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

      9. associate-*l* 69.6%

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

      10. associate-*l* 70.3%

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

      11. distribute-lft-out-- 70.4%

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

      12. add-sqr-sqrt 37.4%

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

      13. sqrt-unprod 81.2%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 12.7%

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

      1. mul-1-neg 12.7%

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

      2. associate-/l* 12.7%

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

      3. associate-/l* 12.7%

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

      4. rec-exp 12.7%

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

      5. rec-exp 12.7%

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

      6. tanh-def-a 89.7%

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

      7. distribute-rgt-neg-in 89.7%

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

   9. Simplified 89.7%

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

   if -5.8000000000000004e-6 < x < 2.05e-4

   1. Initial program 91.7%

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

   3. Taylor expanded in x around 0 20.9%

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

      1. associate-/r* 20.9%

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

      2. rec-exp 20.9%

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

      3. div-sub 20.9%

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

      4. rec-exp 20.9%

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

      5. tanh-def-a 80.0%

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

   5. Simplified 80.0%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-6} \lor \neg \left(x \leq 0.000205\right):\\ \;\;\;\;x - y \cdot \left(z \cdot \tanh \left(\frac{x}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.6% accurate, 14.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+210}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.6e+59) x (if (<= y 1.9e+210) (* x (- 1.0 z)) (+ x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.6e+59) {
		tmp = x;
	} else if (y <= 1.9e+210) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x + (z * t);
	}
	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 <= 1.6d+59) then
        tmp = x
    else if (y <= 1.9d+210) then
        tmp = x * (1.0d0 - z)
    else
        tmp = x + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.6e+59) {
		tmp = x;
	} else if (y <= 1.9e+210) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.6e+59:
		tmp = x
	elif y <= 1.9e+210:
		tmp = x * (1.0 - z)
	else:
		tmp = x + (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.6e+59)
		tmp = x;
	elseif (y <= 1.9e+210)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(x + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.6e+59)
		tmp = x;
	elseif (y <= 1.9e+210)
		tmp = x * (1.0 - z);
	else
		tmp = x + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.6e+59], x, If[LessEqual[y, 1.9e+210], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.59999999999999991e59

   1. Initial program 94.5%

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

      1. +-commutative 94.5%

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

      2. associate-*l* 98.5%

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

      3. fma-define 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around 0 60.6%

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

   if 1.59999999999999991e59 < y < 1.90000000000000014e210

   1. Initial program 83.8%

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

   3. Taylor expanded in x around 0 67.4%

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

   4. Taylor expanded in x around inf 59.8%

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

      1. mul-1-neg 59.8%

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

      2. unsub-neg 59.8%

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

   6. Simplified 59.8%

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

   if 1.90000000000000014e210 < y

   1. Initial program 86.1%

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

   3. Taylor expanded in y around inf 82.5%

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

   4. Taylor expanded in t around inf 85.9%

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

      1. *-commutative 85.9%

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

   6. Simplified 85.9%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+210}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.0% accurate, 17.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.75 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.75e+57) x (+ x (* z (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.75e+57) {
		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 <= 2.75d+57) 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 <= 2.75e+57) {
		tmp = x;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.75e+57:
		tmp = x
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.75e+57)
		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 <= 2.75e+57)
		tmp = x;
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.75e+57], x, N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.7500000000000001e57

   1. Initial program 94.5%

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

      1. +-commutative 94.5%

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

      2. associate-*l* 98.5%

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

      3. fma-define 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around 0 60.6%

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

   if 2.7500000000000001e57 < y

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf 83.1%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.75 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.5% accurate, 21.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 7e+58) x (* x (- 1.0 z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7e+58) {
		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 <= 7d+58) 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 <= 7e+58) {
		tmp = x;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 7e+58:
		tmp = x
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 7e+58)
		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 <= 7e+58)
		tmp = x;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 7e+58], x, N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.9999999999999995e58

   1. Initial program 94.5%

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

      1. +-commutative 94.5%

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

      2. associate-*l* 98.5%

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

      3. fma-define 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around 0 60.6%

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

   if 6.9999999999999995e58 < y

   1. Initial program 84.8%

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

   3. Taylor expanded in x around 0 75.8%

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

   4. Taylor expanded in x around inf 59.2%

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

      1. mul-1-neg 59.2%

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

      2. unsub-neg 59.2%

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

   6. Simplified 59.2%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.4% 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 92.1%

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

   1. +-commutative 92.1%

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

   2. associate-*l* 97.0%

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

   3. fma-define 97.0%

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

3. Simplified 97.0%

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

5. Taylor expanded in y around 0 55.4%

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

6. Final simplification 55.4%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.2% 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 2024060 
(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))))))