SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.6% → 97.6%

Time: 8.8s

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: 93.6% 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: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot z, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5e+194)
   (fma (- t x) z x)
   (fma (* (- (tanh (/ t y)) (tanh (/ x y))) z) y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e+194) {
		tmp = fma((t - x), z, x);
	} else {
		tmp = fma(((tanh((t / y)) - tanh((x / y))) * z), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5e+194)
		tmp = fma(Float64(t - x), z, x);
	else
		tmp = fma(Float64(Float64(tanh(Float64(t / y)) - tanh(Float64(x / y))) * z), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5e+194], N[(N[(t - x), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999989e194

   1. Initial program 77.1%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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 99.9

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

   5. Applied rewrites 99.9%

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

   if -4.99999999999999989e194 < y

   1. Initial program 95.5%

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

      1. 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 97.3

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

   4. Applied rewrites 97.3%

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

Alternative 2: 74.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \tanh \left(\frac{t}{y}\right) - \frac{x}{y}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+200}:\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-21}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot t\_1\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-71}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right), z \cdot y, x\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-192}:\\ \;\;\;\;\frac{x}{t} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1 \cdot z, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (tanh (/ t y)) (/ x y))))
   (if (<= y -1.5e+200)
     (fma (- t x) z x)
     (if (<= y -6.2e-21)
       (+ x (* (* y z) t_1))
       (if (<= y -4.3e-71)
         (fma (- (/ t y) (tanh (/ x y))) (* z y) x)
         (if (<= y 1.3e-192) (* (/ x t) t) (fma (* t_1 z) y x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = tanh((t / y)) - (x / y);
	double tmp;
	if (y <= -1.5e+200) {
		tmp = fma((t - x), z, x);
	} else if (y <= -6.2e-21) {
		tmp = x + ((y * z) * t_1);
	} else if (y <= -4.3e-71) {
		tmp = fma(((t / y) - tanh((x / y))), (z * y), x);
	} else if (y <= 1.3e-192) {
		tmp = (x / t) * t;
	} else {
		tmp = fma((t_1 * z), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(tanh(Float64(t / y)) - Float64(x / y))
	tmp = 0.0
	if (y <= -1.5e+200)
		tmp = fma(Float64(t - x), z, x);
	elseif (y <= -6.2e-21)
		tmp = Float64(x + Float64(Float64(y * z) * t_1));
	elseif (y <= -4.3e-71)
		tmp = fma(Float64(Float64(t / y) - tanh(Float64(x / y))), Float64(z * y), x);
	elseif (y <= 1.3e-192)
		tmp = Float64(Float64(x / t) * t);
	else
		tmp = fma(Float64(t_1 * z), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+200], N[(N[(t - x), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[y, -6.2e-21], N[(x + N[(N[(y * z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.3e-71], N[(N[(N[(t / y), $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(z * y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[y, 1.3e-192], N[(N[(x / t), $MachinePrecision] * t), $MachinePrecision], N[(N[(t$95$1 * z), $MachinePrecision] * y + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.49999999999999995e200

   1. Initial program 74.6%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x + z \cdot \left(t - x\right)} \]
   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 99.9

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

   5. Applied rewrites 99.9%

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

   if -1.49999999999999995e200 < y < -6.1999999999999997e-21

   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. Taylor expanded in x around 0

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

      1. lower-/.f64 86.8

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

   5. Applied rewrites 86.8%

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

   if -6.1999999999999997e-21 < y < -4.2999999999999997e-71

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 89.2

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

   5. Applied rewrites 89.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 89.2

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 89.2

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

   7. Applied rewrites 89.2%

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

   if -4.2999999999999997e-71 < y < 1.3000000000000001e-192

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x + z \cdot \left(t - x\right)} \]
   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 39.8

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

   5. Applied rewrites 39.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 33.6%

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

   9. Taylor expanded in z around 0

      \[\leadsto \frac{x}{t} \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 74.3%

       \[\leadsto \frac{x}{t} \cdot t \]

   if 1.3000000000000001e-192 < y

   1. Initial program 91.4%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 75.8

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

   5. Applied rewrites 75.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 78.7

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

   7. Applied rewrites 78.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right) \cdot z, y, x\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 3: 75.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right) \cdot z, y, x\right)\\ \mathbf{if}\;y \leq -1.28 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-71}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right), z \cdot y, x\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-192}:\\ \;\;\;\;\frac{x}{t} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (* (- (tanh (/ t y)) (/ x y)) z) y x)))
   (if (<= y -1.28e+194)
     (fma (- t x) z x)
     (if (<= y -6.2e-21)
       t_1
       (if (<= y -4.3e-71)
         (fma (- (/ t y) (tanh (/ x y))) (* z y) x)
         (if (<= y 1.3e-192) (* (/ x t) t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(((tanh((t / y)) - (x / y)) * z), y, x);
	double tmp;
	if (y <= -1.28e+194) {
		tmp = fma((t - x), z, x);
	} else if (y <= -6.2e-21) {
		tmp = t_1;
	} else if (y <= -4.3e-71) {
		tmp = fma(((t / y) - tanh((x / y))), (z * y), x);
	} else if (y <= 1.3e-192) {
		tmp = (x / t) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(Float64(tanh(Float64(t / y)) - Float64(x / y)) * z), y, x)
	tmp = 0.0
	if (y <= -1.28e+194)
		tmp = fma(Float64(t - x), z, x);
	elseif (y <= -6.2e-21)
		tmp = t_1;
	elseif (y <= -4.3e-71)
		tmp = fma(Float64(Float64(t / y) - tanh(Float64(x / y))), Float64(z * y), x);
	elseif (y <= 1.3e-192)
		tmp = Float64(Float64(x / t) * t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[y, -1.28e+194], N[(N[(t - x), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[y, -6.2e-21], t$95$1, If[LessEqual[y, -4.3e-71], N[(N[(N[(t / y), $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(z * y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[y, 1.3e-192], N[(N[(x / t), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.28000000000000005e194

   1. Initial program 77.1%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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 99.9

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

   5. Applied rewrites 99.9%

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

   if -1.28000000000000005e194 < y < -6.1999999999999997e-21 or 1.3000000000000001e-192 < y

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 78.5

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

   5. Applied rewrites 78.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 80.6

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

   7. Applied rewrites 80.6%

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

   if -6.1999999999999997e-21 < y < -4.2999999999999997e-71

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 89.2

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

   5. Applied rewrites 89.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 89.2

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 89.2

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

   7. Applied rewrites 89.2%

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

   if -4.2999999999999997e-71 < y < 1.3000000000000001e-192

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x + z \cdot \left(t - x\right)} \]
   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 39.8

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

   5. Applied rewrites 39.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 33.6%

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

   9. Taylor expanded in z around 0

      \[\leadsto \frac{x}{t} \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 74.3%

       \[\leadsto \frac{x}{t} \cdot t \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 75.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-71} \lor \neg \left(y \leq 1.3 \cdot 10^{-192}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right) \cdot z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.28e+194)
   (fma (- t x) z x)
   (if (or (<= y -1.7e-71) (not (<= y 1.3e-192)))
     (fma (* (- (tanh (/ t y)) (/ x y)) z) y x)
     (* (/ x t) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.28e+194) {
		tmp = fma((t - x), z, x);
	} else if ((y <= -1.7e-71) || !(y <= 1.3e-192)) {
		tmp = fma(((tanh((t / y)) - (x / y)) * z), y, x);
	} else {
		tmp = (x / t) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.28e+194)
		tmp = fma(Float64(t - x), z, x);
	elseif ((y <= -1.7e-71) || !(y <= 1.3e-192))
		tmp = fma(Float64(Float64(tanh(Float64(t / y)) - Float64(x / y)) * z), y, x);
	else
		tmp = Float64(Float64(x / t) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.28e+194], N[(N[(t - x), $MachinePrecision] * z + x), $MachinePrecision], If[Or[LessEqual[y, -1.7e-71], N[Not[LessEqual[y, 1.3e-192]], $MachinePrecision]], N[(N[(N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(x / t), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.28000000000000005e194

   1. Initial program 77.1%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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 99.9

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

   5. Applied rewrites 99.9%

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

   if -1.28000000000000005e194 < y < -1.70000000000000002e-71 or 1.3000000000000001e-192 < y

   1. Initial program 93.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 75.7

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

   5. Applied rewrites 75.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 77.6

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

   7. Applied rewrites 77.6%

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

   if -1.70000000000000002e-71 < y < 1.3000000000000001e-192

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x + z \cdot \left(t - x\right)} \]
   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 39.8

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

   5. Applied rewrites 39.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 33.6%

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

   9. Taylor expanded in z around 0

      \[\leadsto \frac{x}{t} \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 74.3%

       \[\leadsto \frac{x}{t} \cdot t \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-71} \lor \neg \left(y \leq 1.3 \cdot 10^{-192}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right) \cdot z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.0% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, z, x\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.76 \cdot 10^{-71}:\\ \;\;\;\;\mathsf{fma}\left(-x, z, x\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{t} \cdot t\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+141}:\\ \;\;\;\;\mathsf{fma}\left(\left(\left(t - x\right) \cdot \frac{x + t}{\left(x + t\right) \cdot y}\right) \cdot y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (- t x) z x)))
   (if (<= y -8.5e+148)
     t_1
     (if (<= y -1.76e-71)
       (fma (- x) z x)
       (if (<= y 9.8e-48)
         (* (/ x t) t)
         (if (<= y 1.16e+141)
           (fma (* (* (- t x) (/ (+ x t) (* (+ x t) y))) y) z x)
           t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((t - x), z, x);
	double tmp;
	if (y <= -8.5e+148) {
		tmp = t_1;
	} else if (y <= -1.76e-71) {
		tmp = fma(-x, z, x);
	} else if (y <= 9.8e-48) {
		tmp = (x / t) * t;
	} else if (y <= 1.16e+141) {
		tmp = fma((((t - x) * ((x + t) / ((x + t) * y))) * y), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(t - x), z, x)
	tmp = 0.0
	if (y <= -8.5e+148)
		tmp = t_1;
	elseif (y <= -1.76e-71)
		tmp = fma(Float64(-x), z, x);
	elseif (y <= 9.8e-48)
		tmp = Float64(Float64(x / t) * t);
	elseif (y <= 1.16e+141)
		tmp = fma(Float64(Float64(Float64(t - x) * Float64(Float64(x + t) / Float64(Float64(x + t) * y))) * y), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[y, -8.5e+148], t$95$1, If[LessEqual[y, -1.76e-71], N[((-x) * z + x), $MachinePrecision], If[LessEqual[y, 9.8e-48], N[(N[(x / t), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 1.16e+141], N[(N[(N[(N[(t - x), $MachinePrecision] * N[(N[(x + t), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.4999999999999996e148 or 1.16e141 < y

   1. Initial program 82.9%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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 93.0

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

   5. Applied rewrites 93.0%

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

   if -8.4999999999999996e148 < y < -1.76000000000000002e-71

   1. Initial program 98.1%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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 54.2

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

   5. Applied rewrites 54.2%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot x, z, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 64.4%

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

   if -1.76000000000000002e-71 < y < 9.8000000000000005e-48

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x + z \cdot \left(t - x\right)} \]
   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 39.2

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

   5. Applied rewrites 39.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 34.0%

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

   9. Taylor expanded in z around 0

      \[\leadsto \frac{x}{t} \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 67.3%

       \[\leadsto \frac{x}{t} \cdot t \]

   if 9.8000000000000005e-48 < y < 1.16e141

   1. Initial program 97.2%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 50.4

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

   5. Applied rewrites 50.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 53.1

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

   7. Applied rewrites 53.1%

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

   9. Applied rewrites 66.1%

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

Alternative 6: 68.9% accurate, 6.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, z, x\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.76 \cdot 10^{-71}:\\ \;\;\;\;\mathsf{fma}\left(-x, z, x\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{t} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (- t x) z x)))
   (if (<= y -8.5e+148)
     t_1
     (if (<= y -1.76e-71)
       (fma (- x) z x)
       (if (<= y 9.5e-65) (* (/ x t) t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((t - x), z, x);
	double tmp;
	if (y <= -8.5e+148) {
		tmp = t_1;
	} else if (y <= -1.76e-71) {
		tmp = fma(-x, z, x);
	} else if (y <= 9.5e-65) {
		tmp = (x / t) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(t - x), z, x)
	tmp = 0.0
	if (y <= -8.5e+148)
		tmp = t_1;
	elseif (y <= -1.76e-71)
		tmp = fma(Float64(-x), z, x);
	elseif (y <= 9.5e-65)
		tmp = Float64(Float64(x / t) * t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[y, -8.5e+148], t$95$1, If[LessEqual[y, -1.76e-71], N[((-x) * z + x), $MachinePrecision], If[LessEqual[y, 9.5e-65], N[(N[(x / t), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.4999999999999996e148 or 9.5000000000000004e-65 < y

   1. Initial program 87.5%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x + z \cdot \left(t - x\right)} \]
   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 80.6

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

   5. Applied rewrites 80.6%

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

   if -8.4999999999999996e148 < y < -1.76000000000000002e-71

   1. Initial program 98.1%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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 54.2

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

   5. Applied rewrites 54.2%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot x, z, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 64.4%

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

   if -1.76000000000000002e-71 < y < 9.5000000000000004e-65

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x + z \cdot \left(t - x\right)} \]
   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 38.5

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

   5. Applied rewrites 38.5%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 33.2%

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

   9. Taylor expanded in z around 0

      \[\leadsto \frac{x}{t} \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 67.0%

       \[\leadsto \frac{x}{t} \cdot t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 64.1% accurate, 10.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+148} \lor \neg \left(y \leq 2.9 \cdot 10^{-69}\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.5e+148) (not (<= y 2.9e-69)))
   (fma (- t x) z x)
   (fma (- x) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.5e+148) || !(y <= 2.9e-69)) {
		tmp = fma((t - x), z, x);
	} else {
		tmp = fma(-x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8.5e+148) || !(y <= 2.9e-69))
		tmp = fma(Float64(t - x), z, x);
	else
		tmp = fma(Float64(-x), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8.5e+148], N[Not[LessEqual[y, 2.9e-69]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * z + x), $MachinePrecision], N[((-x) * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4999999999999996e148 or 2.8999999999999998e-69 < y

   1. Initial program 87.7%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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 79.2

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

   5. Applied rewrites 79.2%

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

   if -8.4999999999999996e148 < y < 2.8999999999999998e-69

   1. Initial program 99.3%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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 44.6

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

   5. Applied rewrites 44.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot x, z, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 53.0%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+148} \lor \neg \left(y \leq 2.9 \cdot 10^{-69}\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.8% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+179} \lor \neg \left(z \leq 5.2 \cdot 10^{-32}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6e+179) (not (<= z 5.2e-32))) (* z t) (fma (- x) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e+179) || !(z <= 5.2e-32)) {
		tmp = z * t;
	} else {
		tmp = fma(-x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6e+179) || !(z <= 5.2e-32))
		tmp = Float64(z * t);
	else
		tmp = fma(Float64(-x), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6e+179], N[Not[LessEqual[z, 5.2e-32]], $MachinePrecision]], N[(z * t), $MachinePrecision], N[((-x) * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.9999999999999996e179 or 5.1999999999999995e-32 < z

   1. Initial program 90.0%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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 42.3

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

   5. Applied rewrites 42.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 27.7%

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

   if -5.9999999999999996e179 < z < 5.1999999999999995e-32

   1. Initial program 96.4%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x + z \cdot \left(t - x\right)} \]
   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 71.3

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

   5. Applied rewrites 71.3%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot x, z, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 71.6%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+179} \lor \neg \left(z \leq 5.2 \cdot 10^{-32}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 16.7% accurate, 39.8× speedup

Math

\[\begin{array}{l} \\ z \cdot t \end{array} \]

FPCore

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

C

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

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 = z * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(z * t), $MachinePrecision]

Derivation

1. Initial program 94.0%

   \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
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 60.4

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

5. Applied rewrites 60.4%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 17.3%

   \[\leadsto z \cdot \color{blue}{t} \]
9. Add Preprocessing

Developer Target 1: 97.0% 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 2024339 
(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))))))