SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 94.1% → 98.3%

Time: 9.9s

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: 94.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 3.9 \cdot 10^{+248}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right), y\_m, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 3.9e+248)
   (fma (* z (- (tanh (/ t y_m)) (tanh (/ x y_m)))) y_m x)
   (fma (- t x) z x)))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 3.9e+248) {
		tmp = fma((z * (tanh((t / y_m)) - tanh((x / y_m)))), y_m, x);
	} else {
		tmp = fma((t - x), z, x);
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 3.9e+248)
		tmp = fma(Float64(z * Float64(tanh(Float64(t / y_m)) - tanh(Float64(x / y_m)))), y_m, x);
	else
		tmp = fma(Float64(t - x), z, x);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 3.9e+248], N[(N[(z * N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y$95$m + x), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.8999999999999999e248

   1. Initial program 94.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 96.1

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

   4. Applied rewrites 96.1%

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

   if 3.8999999999999999e248 < y

   1. Initial program 83.3%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.9 \cdot 10^{+248}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot z\\ t_2 := \left(z \cdot y\_m\right) \cdot \left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right) + x\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (let* ((t_1 (* (- t x) z))
        (t_2 (+ (* (* z y_m) (- (tanh (/ t y_m)) (tanh (/ x y_m)))) x)))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 2e+306) (* 1.0 x) t_1))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double t_1 = (t - x) * z;
	double t_2 = ((z * y_m) * (tanh((t / y_m)) - tanh((x / y_m)))) + x;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 2e+306) {
		tmp = 1.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double t_1 = (t - x) * z;
	double t_2 = ((z * y_m) * (Math.tanh((t / y_m)) - Math.tanh((x / y_m)))) + x;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 2e+306) {
		tmp = 1.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	t_1 = (t - x) * z
	t_2 = ((z * y_m) * (math.tanh((t / y_m)) - math.tanh((x / y_m)))) + x
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 2e+306:
		tmp = 1.0 * x
	else:
		tmp = t_1
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	t_1 = Float64(Float64(t - x) * z)
	t_2 = Float64(Float64(Float64(z * y_m) * Float64(tanh(Float64(t / y_m)) - tanh(Float64(x / y_m)))) + x)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 2e+306)
		tmp = Float64(1.0 * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	t_1 = (t - x) * z;
	t_2 = ((z * y_m) * (tanh((t / y_m)) - tanh((x / y_m)))) + x;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 2e+306)
		tmp = 1.0 * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z * y$95$m), $MachinePrecision] * N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 2e+306], N[(1.0 * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < -inf.0 or 2.00000000000000003e306 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

   1. Initial program 61.9%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 97.0

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

   5. Applied rewrites 97.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 97.0%

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

   if -inf.0 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < 2.00000000000000003e306

   1. Initial program 98.3%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 55.8

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

   5. Applied rewrites 55.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, z, x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 37.2%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 50.8%

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

   11. Taylor expanded in z around 0

       \[\leadsto 1 \cdot x \]
   12. Step-by-step derivation

   13. Applied rewrites 68.2%

       \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot y\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) + x \leq -\infty:\\ \;\;\;\;\left(t - x\right) \cdot z\\ \mathbf{elif}\;\left(z \cdot y\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) + x \leq 2 \cdot 10^{+306}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_1 := \left(-z\right) \cdot x\\ t_2 := \left(z \cdot y\_m\right) \cdot \left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right) + x\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (let* ((t_1 (* (- z) x))
        (t_2 (+ (* (* z y_m) (- (tanh (/ t y_m)) (tanh (/ x y_m)))) x)))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 2e+306) (* 1.0 x) t_1))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double t_1 = -z * x;
	double t_2 = ((z * y_m) * (tanh((t / y_m)) - tanh((x / y_m)))) + x;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 2e+306) {
		tmp = 1.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double t_1 = -z * x;
	double t_2 = ((z * y_m) * (Math.tanh((t / y_m)) - Math.tanh((x / y_m)))) + x;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 2e+306) {
		tmp = 1.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	t_1 = -z * x
	t_2 = ((z * y_m) * (math.tanh((t / y_m)) - math.tanh((x / y_m)))) + x
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 2e+306:
		tmp = 1.0 * x
	else:
		tmp = t_1
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	t_1 = Float64(Float64(-z) * x)
	t_2 = Float64(Float64(Float64(z * y_m) * Float64(tanh(Float64(t / y_m)) - tanh(Float64(x / y_m)))) + x)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 2e+306)
		tmp = Float64(1.0 * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	t_1 = -z * x;
	t_2 = ((z * y_m) * (tanh((t / y_m)) - tanh((x / y_m)))) + x;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 2e+306)
		tmp = 1.0 * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := Block[{t$95$1 = N[((-z) * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z * y$95$m), $MachinePrecision] * N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 2e+306], N[(1.0 * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < -inf.0 or 2.00000000000000003e306 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

   1. Initial program 61.9%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 97.0

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

   5. Applied rewrites 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, z, x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 87.3%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 61.4%

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

   11. Taylor expanded in z around inf

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

   13. Applied rewrites 61.4%

       \[\leadsto \left(-z\right) \cdot x \]

   if -inf.0 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < 2.00000000000000003e306

   1. Initial program 98.3%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 55.8

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

   5. Applied rewrites 55.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, z, x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 37.2%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 50.8%

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

   11. Taylor expanded in z around 0

       \[\leadsto 1 \cdot x \]
   12. Step-by-step derivation

   13. Applied rewrites 68.2%

       \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot y\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) + x \leq -\infty:\\ \;\;\;\;\left(-z\right) \cdot x\\ \mathbf{elif}\;\left(z \cdot y\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) + x \leq 2 \cdot 10^{+306}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_1 := \left(z \cdot y\_m\right) \cdot \left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right) + x\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (let* ((t_1 (+ (* (* z y_m) (- (tanh (/ t y_m)) (tanh (/ x y_m)))) x)))
   (if (<= t_1 (- INFINITY)) (* z t) (if (<= t_1 2e+306) (* 1.0 x) (* z t)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double t_1 = ((z * y_m) * (tanh((t / y_m)) - tanh((x / y_m)))) + x;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z * t;
	} else if (t_1 <= 2e+306) {
		tmp = 1.0 * x;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double t_1 = ((z * y_m) * (Math.tanh((t / y_m)) - Math.tanh((x / y_m)))) + x;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z * t;
	} else if (t_1 <= 2e+306) {
		tmp = 1.0 * x;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	t_1 = ((z * y_m) * (math.tanh((t / y_m)) - math.tanh((x / y_m)))) + x
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z * t
	elif t_1 <= 2e+306:
		tmp = 1.0 * x
	else:
		tmp = z * t
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	t_1 = Float64(Float64(Float64(z * y_m) * Float64(tanh(Float64(t / y_m)) - tanh(Float64(x / y_m)))) + x)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z * t);
	elseif (t_1 <= 2e+306)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	t_1 = ((z * y_m) * (tanh((t / y_m)) - tanh((x / y_m)))) + x;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z * t;
	elseif (t_1 <= 2e+306)
		tmp = 1.0 * x;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := Block[{t$95$1 = N[(N[(N[(z * y$95$m), $MachinePrecision] * N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z * t), $MachinePrecision], If[LessEqual[t$95$1, 2e+306], N[(1.0 * x), $MachinePrecision], N[(z * t), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < -inf.0 or 2.00000000000000003e306 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

   1. Initial program 61.9%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 97.0

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

   5. Applied rewrites 97.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 41.4%

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

   if -inf.0 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < 2.00000000000000003e306

   1. Initial program 98.3%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 55.8

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

   5. Applied rewrites 55.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, z, x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 37.2%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 50.8%

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

   11. Taylor expanded in z around 0

       \[\leadsto 1 \cdot x \]
   12. Step-by-step derivation

   13. Applied rewrites 68.2%

       \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot y\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) + x \leq -\infty:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;\left(z \cdot y\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) + x \leq 2 \cdot 10^{+306}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 4.8 \cdot 10^{-72}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;y\_m \leq 1.3 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(\tanh \left(\frac{t}{y\_m}\right), z \cdot y\_m, x\right) - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 4.8e-72)
   (* 1.0 x)
   (if (<= y_m 1.3e+67)
     (- (fma (tanh (/ t y_m)) (* z y_m) x) (* z x))
     (fma (- t x) z x))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 4.8e-72) {
		tmp = 1.0 * x;
	} else if (y_m <= 1.3e+67) {
		tmp = fma(tanh((t / y_m)), (z * y_m), x) - (z * x);
	} else {
		tmp = fma((t - x), z, x);
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 4.8e-72)
		tmp = Float64(1.0 * x);
	elseif (y_m <= 1.3e+67)
		tmp = Float64(fma(tanh(Float64(t / y_m)), Float64(z * y_m), x) - Float64(z * x));
	else
		tmp = fma(Float64(t - x), z, x);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 4.8e-72], N[(1.0 * x), $MachinePrecision], If[LessEqual[y$95$m, 1.3e+67], N[(N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] * N[(z * y$95$m), $MachinePrecision] + x), $MachinePrecision] - N[(z * x), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * z + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 4.8e-72

   1. Initial program 94.7%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 54.9

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

   5. Applied rewrites 54.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, z, x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 39.5%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 50.1%

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

   11. Taylor expanded in z around 0

       \[\leadsto 1 \cdot x \]
   12. Step-by-step derivation

   13. Applied rewrites 68.2%

       \[\leadsto 1 \cdot x \]

   if 4.8e-72 < y < 1.3e67

   1. Initial program 97.8%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. distribute-lft-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. distribute-rgt-neg-out N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 97.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 97.5

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

   4. Applied rewrites 97.5%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 81.6

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

   7. Applied rewrites 81.6%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate-+r+ N/A

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

      4. lift-neg.f64 N/A

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

      5. unsub-neg N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 81.6

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 81.6

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

   9. Applied rewrites 81.6%

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

   if 1.3e67 < y

   1. Initial program 88.9%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 79.7

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

   5. Applied rewrites 79.7%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{-72}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(\tanh \left(\frac{t}{y}\right), z \cdot y, x\right) - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 4.8 \cdot 10^{-72}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \tanh \left(\frac{t}{y\_m}\right), y\_m, -z \cdot x\right) + x\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 4.8e-72)
   (* 1.0 x)
   (+ (fma (* z (tanh (/ t y_m))) y_m (- (* z x))) x)))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 4.8e-72) {
		tmp = 1.0 * x;
	} else {
		tmp = fma((z * tanh((t / y_m))), y_m, -(z * x)) + x;
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 4.8e-72)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(fma(Float64(z * tanh(Float64(t / y_m))), y_m, Float64(-Float64(z * x))) + x);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 4.8e-72], N[(1.0 * x), $MachinePrecision], N[(N[(N[(z * N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * y$95$m + (-N[(z * x), $MachinePrecision])), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.8e-72

   1. Initial program 94.7%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 54.9

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

   5. Applied rewrites 54.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, z, x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 39.5%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 50.1%

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

   11. Taylor expanded in z around 0

       \[\leadsto 1 \cdot x \]
   12. Step-by-step derivation

   13. Applied rewrites 68.2%

       \[\leadsto 1 \cdot x \]

   if 4.8e-72 < y

   1. Initial program 92.8%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. distribute-lft-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. distribute-rgt-neg-out N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 83.6

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 83.6

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

   4. Applied rewrites 83.6%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 77.9

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

   7. Applied rewrites 77.9%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 86.6

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

   9. Applied rewrites 86.6%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{-72}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \tanh \left(\frac{t}{y}\right), y, -z \cdot x\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.0% accurate, 14.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 9 \cdot 10^{-30}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 9e-30) (* 1.0 x) (fma (- t x) z x)))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 9e-30) {
		tmp = 1.0 * x;
	} else {
		tmp = fma((t - x), z, x);
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 9e-30)
		tmp = Float64(1.0 * x);
	else
		tmp = fma(Float64(t - x), z, x);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 9e-30], N[(1.0 * x), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.99999999999999935e-30

   1. Initial program 95.0%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 54.8

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

   5. Applied rewrites 54.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, z, x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 38.7%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 50.3%

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

   11. Taylor expanded in z around 0

       \[\leadsto 1 \cdot x \]
   12. Step-by-step derivation

   13. Applied rewrites 68.3%

       \[\leadsto 1 \cdot x \]

   if 8.99999999999999935e-30 < y

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 73.5

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

   5. Applied rewrites 73.5%

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

Alternative 8: 66.8% accurate, 15.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 7.9:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 7.9) (* 1.0 x) (* (- 1.0 z) x)))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 7.9) {
		tmp = 1.0 * x;
	} else {
		tmp = (1.0 - z) * x;
	}
	return tmp;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y_m <= 7.9d0) then
        tmp = 1.0d0 * x
    else
        tmp = (1.0d0 - z) * x
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 7.9) {
		tmp = 1.0 * x;
	} else {
		tmp = (1.0 - z) * x;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	tmp = 0
	if y_m <= 7.9:
		tmp = 1.0 * x
	else:
		tmp = (1.0 - z) * x
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 7.9)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(Float64(1.0 - z) * x);
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	tmp = 0.0;
	if (y_m <= 7.9)
		tmp = 1.0 * x;
	else
		tmp = (1.0 - z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 7.9], N[(1.0 * x), $MachinePrecision], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.9000000000000004

   1. Initial program 95.3%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 55.6

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

   5. Applied rewrites 55.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, z, x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 38.1%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 50.1%

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

   11. Taylor expanded in z around 0

       \[\leadsto 1 \cdot x \]
   12. Step-by-step derivation

   13. Applied rewrites 67.7%

       \[\leadsto 1 \cdot x \]

   if 7.9000000000000004 < y

   1. Initial program 90.9%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 73.8

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

   5. Applied rewrites 73.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 57.0%

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

Alternative 9: 16.7% accurate, 39.8× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ z \cdot t \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t) :precision binary64 (* z t))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	return z * t;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = z * t
end function

Java

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

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	return z * t

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	return Float64(z * t)
end

MATLAB

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

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := N[(z * t), $MachinePrecision]

Derivation

1. Initial program 94.1%

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

3. Taylor expanded in y around inf

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lower--.f64 60.7

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

5. Applied rewrites 60.7%

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

6. Taylor expanded in t around inf

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

8. Applied rewrites 16.2%

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

9. Final simplification 16.2%

   \[\leadsto z \cdot t \]
10. Add Preprocessing

Developer Target 1: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024277 
(FPCore (x y z t)
  :name "SynthBasics:moogVCF from YampaSynth-0.2"
  :precision binary64

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

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