SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.4% → 96.8%

Time: 13.5s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

   1. 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

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

   3. lift-tanh.f64 N/A

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

   4. lift-/.f64 N/A

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

   5. lift-tanh.f64 N/A

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

   6. lift--.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. +-commutative N/A

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

   9. lift-*.f64 N/A

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

   10. lift-*.f64 N/A

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

   11. associate-*l* N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. lower-*.f64 98.0

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

4. Applied rewrites 98.0%

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

   1. lift-/.f64 N/A

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

   2. lift-tanh.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lift-tanh.f64 N/A

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

   5. sub-neg N/A

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

   6. distribute-rgt-in N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-*.f64 N/A

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

   9. lower-neg.f64 98.1

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

6. Applied rewrites 98.1%

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

7. Final simplification 98.1%

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

Alternative 2: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

   1. 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

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

   3. lift-tanh.f64 N/A

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

   4. lift-/.f64 N/A

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

   5. lift-tanh.f64 N/A

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

   6. lift--.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. +-commutative N/A

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

   9. lift-*.f64 N/A

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

   10. lift-*.f64 N/A

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

   11. associate-*l* N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. lower-*.f64 98.0

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

4. Applied rewrites 98.0%

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

Alternative 3: 75.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z}{x \cdot x}\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+59}:\\ \;\;\;\;x + x \cdot \left(\mathsf{fma}\left(t, t\_1, -z\right) - \mathsf{fma}\left(t, t\_1, \frac{t \cdot \left(-z\right)}{x}\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ z (* x x)))))
   (if (<= x -7.8e+59)
     (+ x (* x (- (fma t t_1 (- z)) (fma t t_1 (/ (* t (- z)) x)))))
     (if (<= x 8.2e+113)
       (fma (* y (- (tanh (/ t y)) (/ x y))) z x)
       (+ x (* t z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (z / (x * x));
	double tmp;
	if (x <= -7.8e+59) {
		tmp = x + (x * (fma(t, t_1, -z) - fma(t, t_1, ((t * -z) / x))));
	} else if (x <= 8.2e+113) {
		tmp = fma((y * (tanh((t / y)) - (x / y))), z, x);
	} else {
		tmp = x + (t * z);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(z / Float64(x * x)))
	tmp = 0.0
	if (x <= -7.8e+59)
		tmp = Float64(x + Float64(x * Float64(fma(t, t_1, Float64(-z)) - fma(t, t_1, Float64(Float64(t * Float64(-z)) / x)))));
	elseif (x <= 8.2e+113)
		tmp = fma(Float64(y * Float64(tanh(Float64(t / y)) - Float64(x / y))), z, x);
	else
		tmp = Float64(x + Float64(t * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.8e+59], N[(x + N[(x * N[(N[(t * t$95$1 + (-z)), $MachinePrecision] - N[(t * t$95$1 + N[(N[(t * (-z)), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e+113], N[(N[(y * N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision], N[(x + N[(t * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.80000000000000043e59

   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

      \[\leadsto x + \left(y \cdot z\right) \cdot \color{blue}{\frac{t - x}{y}} \]
   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 51.6

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

   5. Applied rewrites 51.6%

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

      1. div-sub N/A

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

      2. lift-/.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. flip-- N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift-/.f64 N/A

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

      10. frac-times N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower-+.f64 17.8

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

   7. Applied rewrites 17.8%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. times-frac N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. difference-of-squares N/A

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

      7. lift-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. div-inv N/A

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

      12. lift-/.f64 N/A

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

      13. div-inv N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. lower-+.f64 N/A

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

      18. lift-/.f64 N/A

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

      19. lift-/.f64 N/A

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

      20. sub-div N/A

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

      21. lift--.f64 N/A

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

      22. lower-/.f64 32.5

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

   9. Applied rewrites 32.5%

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

   10. Taylor expanded in x around inf

       \[\leadsto x + \color{blue}{x \cdot \left(\left(-1 \cdot z + \left(\frac{z \cdot \left(t + -1 \cdot t\right)}{x} + \frac{{t}^{2} \cdot z}{{x}^{2}}\right)\right) - \left(-1 \cdot \frac{t \cdot z}{x} + \frac{t \cdot \left(z \cdot \left(t + -1 \cdot t\right) - -1 \cdot \left(t \cdot z\right)\right)}{{x}^{2}}\right)\right)} \]

   12. Applied rewrites 78.2%

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

   if -7.80000000000000043e59 < x < 8.19999999999999985e113

   1. Initial program 90.2%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 74.9

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

   5. Applied rewrites 74.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-tanh.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*r* N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 81.8

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

   7. Applied rewrites 81.8%

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

   if 8.19999999999999985e113 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto x + \left(y \cdot z\right) \cdot \color{blue}{\frac{t - x}{y}} \]
   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 43.1

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

   5. Applied rewrites 43.1%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 82.0

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

   8. Applied rewrites 82.0%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+59}:\\ \;\;\;\;x + x \cdot \left(\mathsf{fma}\left(t, t \cdot \frac{z}{x \cdot x}, -z\right) - \mathsf{fma}\left(t, t \cdot \frac{z}{x \cdot x}, \frac{t \cdot \left(-z\right)}{x}\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{-68}:\\ \;\;\;\;\mathsf{fma}\left(z, -x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right), y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 3.2e-68)
   (fma z (- x) x)
   (fma (* z (- (/ t y) (tanh (/ x y)))) y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.2e-68) {
		tmp = fma(z, -x, x);
	} else {
		tmp = fma((z * ((t / y) - tanh((x / y)))), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 3.2e-68)
		tmp = fma(z, Float64(-x), x);
	else
		tmp = fma(Float64(z * Float64(Float64(t / y) - tanh(Float64(x / y)))), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 3.2e-68], N[(z * (-x) + x), $MachinePrecision], N[(N[(z * N[(N[(t / y), $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.1999999999999999e-68

   1. Initial program 94.5%

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

   3. Taylor expanded in 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. lower-fma.f64 N/A

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

      3. lower--.f64 54.8

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 49.6

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

   8. Applied rewrites 49.6%

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

   if 3.1999999999999999e-68 < y

   1. Initial program 91.8%

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

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

      3. lift-tanh.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-tanh.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 96.3

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

   4. Applied rewrites 96.3%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 80.2

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

   7. Applied rewrites 80.2%

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

Alternative 5: 62.7% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6800:\\ \;\;\;\;\mathsf{fma}\left(z, -x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t x))))
   (if (<= z -4.2e-10) t_1 (if (<= z 6800.0) (fma z (- x) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (t - x);
	double tmp;
	if (z <= -4.2e-10) {
		tmp = t_1;
	} else if (z <= 6800.0) {
		tmp = fma(z, -x, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(t - x))
	tmp = 0.0
	if (z <= -4.2e-10)
		tmp = t_1;
	elseif (z <= 6800.0)
		tmp = fma(z, Float64(-x), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e-10], t$95$1, If[LessEqual[z, 6800.0], N[(z * (-x) + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2e-10 or 6800 < z

   1. Initial program 88.6%

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

   3. Taylor expanded in 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. lower-fma.f64 N/A

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

      3. lower--.f64 46.7

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

   5. Applied rewrites 46.7%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 46.4

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

   8. Applied rewrites 46.4%

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

   if -4.2e-10 < z < 6800

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 78.7

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

   5. Applied rewrites 78.7%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 86.1

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

   8. Applied rewrites 86.1%

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

Alternative 6: 61.2% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -2.65 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 360000:\\ \;\;\;\;x + t \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t x))))
   (if (<= z -2.65e+36) t_1 (if (<= z 360000.0) (+ x (* t z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (t - x);
	double tmp;
	if (z <= -2.65e+36) {
		tmp = t_1;
	} else if (z <= 360000.0) {
		tmp = x + (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (t - x)
    if (z <= (-2.65d+36)) then
        tmp = t_1
    else if (z <= 360000.0d0) then
        tmp = x + (t * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (t - x);
	double tmp;
	if (z <= -2.65e+36) {
		tmp = t_1;
	} else if (z <= 360000.0) {
		tmp = x + (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (t - x)
	tmp = 0
	if z <= -2.65e+36:
		tmp = t_1
	elif z <= 360000.0:
		tmp = x + (t * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(t - x))
	tmp = 0.0
	if (z <= -2.65e+36)
		tmp = t_1;
	elseif (z <= 360000.0)
		tmp = Float64(x + Float64(t * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (t - x);
	tmp = 0.0;
	if (z <= -2.65e+36)
		tmp = t_1;
	elseif (z <= 360000.0)
		tmp = x + (t * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.65e+36], t$95$1, If[LessEqual[z, 360000.0], N[(x + N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.65e36 or 3.6e5 < z

   1. Initial program 87.9%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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. lower-fma.f64 N/A

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

      3. lower--.f64 47.1

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

   5. Applied rewrites 47.1%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 47.1

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

   8. Applied rewrites 47.1%

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

   if -2.65e36 < z < 3.6e5

   1. Initial program 99.2%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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 60.0

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

   5. Applied rewrites 60.0%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 78.0

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

   8. Applied rewrites 78.0%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 360000:\\ \;\;\;\;x + t \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 20.6% accurate, 11.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-161}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-123}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6e-161) (* t z) (if (<= t 1.35e-123) (* z (- x)) (* t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6e-161) {
		tmp = t * z;
	} else if (t <= 1.35e-123) {
		tmp = z * -x;
	} else {
		tmp = t * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-6d-161)) then
        tmp = t * z
    else if (t <= 1.35d-123) then
        tmp = z * -x
    else
        tmp = t * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6e-161) {
		tmp = t * z;
	} else if (t <= 1.35e-123) {
		tmp = z * -x;
	} else {
		tmp = t * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6e-161:
		tmp = t * z
	elif t <= 1.35e-123:
		tmp = z * -x
	else:
		tmp = t * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6e-161)
		tmp = Float64(t * z);
	elseif (t <= 1.35e-123)
		tmp = Float64(z * Float64(-x));
	else
		tmp = Float64(t * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6e-161)
		tmp = t * z;
	elseif (t <= 1.35e-123)
		tmp = z * -x;
	else
		tmp = t * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6e-161], N[(t * z), $MachinePrecision], If[LessEqual[t, 1.35e-123], N[(z * (-x)), $MachinePrecision], N[(t * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.99999999999999977e-161 or 1.35e-123 < t

   1. Initial program 95.4%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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. lower-fma.f64 N/A

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

      3. lower--.f64 53.6

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

   5. Applied rewrites 53.6%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 23.8

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

   8. Applied rewrites 23.8%

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

   if -5.99999999999999977e-161 < t < 1.35e-123

   1. Initial program 89.0%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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. lower-fma.f64 N/A

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

      3. lower--.f64 84.1

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

   5. Applied rewrites 84.1%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 38.3

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

   8. Applied rewrites 38.3%

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

   9. Taylor expanded in t around 0

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

       1. mul-1-neg N/A

          \[\leadsto z \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \]

       2. lower-neg.f64 30.3

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

   11. Applied rewrites 30.3%

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

4. Final simplification 25.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-161}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-123}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.1% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-68}:\\ \;\;\;\;\mathsf{fma}\left(z, -x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 7.5e-68) (fma z (- x) x) (fma z (- t x) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7.5e-68) {
		tmp = fma(z, -x, x);
	} else {
		tmp = fma(z, (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 7.5e-68)
		tmp = fma(z, Float64(-x), x);
	else
		tmp = fma(z, Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 7.5e-68], N[(z * (-x) + x), $MachinePrecision], N[(z * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.50000000000000081e-68

   1. Initial program 94.5%

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

   3. Taylor expanded in 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. lower-fma.f64 N/A

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

      3. lower--.f64 54.8

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 49.6

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

   8. Applied rewrites 49.6%

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

   if 7.50000000000000081e-68 < y

   1. Initial program 91.8%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 77.0

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

   5. Applied rewrites 77.0%

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

Alternative 9: 26.4% accurate, 26.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

   \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
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. lower-fma.f64 N/A

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

   3. lower--.f64 62.0

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

5. Applied rewrites 62.0%

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

6. Taylor expanded in z around inf

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

   1. lower-*.f64 N/A

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

   2. lower--.f64 28.7

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

8. Applied rewrites 28.7%

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

Alternative 10: 17.1% accurate, 39.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

   \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
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. lower-fma.f64 N/A

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

   3. lower--.f64 62.0

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

5. Applied rewrites 62.0%

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

6. Taylor expanded in t around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 20.2

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

8. Applied rewrites 20.2%

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

9. Final simplification 20.2%

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

Developer Target 1: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024219 
(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))))))