SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.3% → 97.5%

Time: 12.6s

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: 93.3% 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: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   11. lift-*.f64 N/A

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

   12. associate-*r* N/A

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

   13. lower-fma.f64 N/A

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

   14. lower-*.f64 97.2

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

4. Applied egg-rr 97.2%

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

5. Final simplification 97.2%

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

Alternative 2: 70.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{1}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right), z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 6.5e-89)
   (/ 1.0 (/ 1.0 x))
   (fma (* y (- (tanh (/ t y)) (/ x y))) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6.5e-89) {
		tmp = 1.0 / (1.0 / x);
	} else {
		tmp = fma((y * (tanh((t / y)) - (x / y))), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 6.5e-89)
		tmp = Float64(1.0 / Float64(1.0 / x));
	else
		tmp = fma(Float64(y * Float64(tanh(Float64(t / y)) - Float64(x / y))), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 6.5e-89], N[(1.0 / N[(1.0 / x), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.50000000000000034e-89

   1. Initial program 97.0%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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 52.1

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

   5. Simplified 52.1%

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

      1. lift--.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. difference-of-squares N/A

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

      9. lift-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower-*.f64 26.8

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

   7. Applied egg-rr 26.8%

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

   8. Taylor expanded in z around 0

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x}}} \]
   9. Step-by-step derivation

      1. lower-/.f64 67.3

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{x}}} \]

   10. Simplified 67.3%

       \[\leadsto \frac{1}{\color{blue}{\frac{1}{x}}} \]

   if 6.50000000000000034e-89 < y

   1. Initial program 85.5%

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

      1. lift-*.f64 N/A

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

      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. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 94.1

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

   4. Applied egg-rr 94.1%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 82.8

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

   7. Simplified 82.8%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{1}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right), z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.2% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-33}:\\ \;\;\;\;\mathsf{fma}\left(t, z, x\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-14}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(t, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t x))))
   (if (<= z -1.32e+122)
     t_1
     (if (<= z -1.08e-33)
       (fma t z x)
       (if (<= z 5.8e-14)
         (- x (* x z))
         (if (<= z 7.4e+65) (fma t z x) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (t - x);
	double tmp;
	if (z <= -1.32e+122) {
		tmp = t_1;
	} else if (z <= -1.08e-33) {
		tmp = fma(t, z, x);
	} else if (z <= 5.8e-14) {
		tmp = x - (x * z);
	} else if (z <= 7.4e+65) {
		tmp = fma(t, z, 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 <= -1.32e+122)
		tmp = t_1;
	elseif (z <= -1.08e-33)
		tmp = fma(t, z, x);
	elseif (z <= 5.8e-14)
		tmp = Float64(x - Float64(x * z));
	elseif (z <= 7.4e+65)
		tmp = fma(t, z, 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, -1.32e+122], t$95$1, If[LessEqual[z, -1.08e-33], N[(t * z + x), $MachinePrecision], If[LessEqual[z, 5.8e-14], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e+65], N[(t * z + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.31999999999999992e122 or 7.39999999999999989e65 < 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. lower-fma.f64 N/A

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

      3. lower--.f64 49.4

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

   5. Simplified 49.4%

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

   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 49.4

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

   8. Simplified 49.4%

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

   if -1.31999999999999992e122 < z < -1.08000000000000007e-33 or 5.8000000000000005e-14 < z < 7.39999999999999989e65

   1. Initial program 86.6%

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

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

      11. lift-*.f64 N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 92.4

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

   4. Applied egg-rr 92.4%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 53.4

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

   7. Simplified 53.4%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 54.0

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

   10. Simplified 54.0%

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

   if -1.08000000000000007e-33 < z < 5.8000000000000005e-14

   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. lower-fma.f64 N/A

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

      3. lower--.f64 72.3

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

   5. Simplified 72.3%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 88.3

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

   8. Simplified 88.3%

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

Alternative 4: 68.7% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 360:\\ \;\;\;\;\frac{1}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 360.0) (/ 1.0 (/ 1.0 x)) (fma z (- t x) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 360.0) {
		tmp = 1.0 / (1.0 / x);
	} else {
		tmp = fma(z, (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 360.0)
		tmp = Float64(1.0 / Float64(1.0 / x));
	else
		tmp = fma(z, Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 360.0], N[(1.0 / N[(1.0 / x), $MachinePrecision]), $MachinePrecision], N[(z * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 360

   1. Initial program 97.1%

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

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

      3. lower--.f64 51.9

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

   5. Simplified 51.9%

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

      1. lift--.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. difference-of-squares N/A

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

      9. lift-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower-*.f64 26.9

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

   7. Applied egg-rr 26.9%

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

   8. Taylor expanded in z around 0

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x}}} \]
   9. Step-by-step derivation

      1. lower-/.f64 67.3

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{x}}} \]

   10. Simplified 67.3%

       \[\leadsto \frac{1}{\color{blue}{\frac{1}{x}}} \]

   if 360 < y

   1. Initial program 82.3%

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

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

      3. lower--.f64 74.3

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

   5. Simplified 74.3%

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

Alternative 5: 63.6% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-33}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-14}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(t, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.08e-33)
   (fma z (- t x) x)
   (if (<= z 5.8e-14)
     (- x (* x z))
     (if (<= z 7.4e+65) (fma t z x) (* z (- t x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.08e-33) {
		tmp = fma(z, (t - x), x);
	} else if (z <= 5.8e-14) {
		tmp = x - (x * z);
	} else if (z <= 7.4e+65) {
		tmp = fma(t, z, x);
	} else {
		tmp = z * (t - x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.08e-33)
		tmp = fma(z, Float64(t - x), x);
	elseif (z <= 5.8e-14)
		tmp = Float64(x - Float64(x * z));
	elseif (z <= 7.4e+65)
		tmp = fma(t, z, x);
	else
		tmp = Float64(z * Float64(t - x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.08e-33], N[(z * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 5.8e-14], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e+65], N[(t * z + x), $MachinePrecision], N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.08000000000000007e-33

   1. Initial program 84.7%

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

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

      3. lower--.f64 42.4

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

   5. Simplified 42.4%

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

   if -1.08000000000000007e-33 < z < 5.8000000000000005e-14

   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. lower-fma.f64 N/A

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

      3. lower--.f64 72.3

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

   5. Simplified 72.3%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 88.3

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

   8. Simplified 88.3%

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

   if 5.8000000000000005e-14 < z < 7.39999999999999989e65

   1. Initial program 95.1%

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

      1. 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. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 95.1

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

   4. Applied egg-rr 95.1%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 61.9

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

   7. Simplified 61.9%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 63.1

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

   10. Simplified 63.1%

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

   if 7.39999999999999989e65 < z

   1. Initial program 91.9%

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
   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 52.3

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

   5. Simplified 52.3%

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

   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 52.3

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

   8. Simplified 52.3%

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

Alternative 6: 61.7% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(t, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t x))))
   (if (<= z -1.32e+122) t_1 (if (<= z 7.4e+65) (fma t z x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (t - x);
	double tmp;
	if (z <= -1.32e+122) {
		tmp = t_1;
	} else if (z <= 7.4e+65) {
		tmp = fma(t, z, 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 <= -1.32e+122)
		tmp = t_1;
	elseif (z <= 7.4e+65)
		tmp = fma(t, z, 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, -1.32e+122], t$95$1, If[LessEqual[z, 7.4e+65], N[(t * z + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.31999999999999992e122 or 7.39999999999999989e65 < 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. lower-fma.f64 N/A

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

      3. lower--.f64 49.4

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

   5. Simplified 49.4%

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

   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 49.4

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

   8. Simplified 49.4%

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

   if -1.31999999999999992e122 < z < 7.39999999999999989e65

   1. Initial program 96.0%

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

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

      11. lift-*.f64 N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 97.8

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

   4. Applied egg-rr 97.8%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 61.0

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

   7. Simplified 61.0%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 67.0

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

   10. Simplified 67.0%

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

Alternative 7: 57.8% accurate, 17.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e+155) (* x (- z)) (fma t z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+155) {
		tmp = x * -z;
	} else {
		tmp = fma(t, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e+155)
		tmp = Float64(x * Float64(-z));
	else
		tmp = fma(t, z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e+155], N[(x * (-z)), $MachinePrecision], N[(t * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000006e155

   1. Initial program 88.5%

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

   3. Taylor expanded in y around inf

      \[\leadsto x + \left(y \cdot z\right) \cdot \color{blue}{\frac{t - x}{y}} \]
   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 33.3

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

   5. Simplified 33.3%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 27.5

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

   8. Simplified 27.5%

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

   9. Taylor expanded in z around inf

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

       1. mul-1-neg N/A

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

       2. distribute-rgt-neg-in N/A

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

       3. mul-1-neg N/A

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

       4. lower-*.f64 N/A

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

       5. mul-1-neg N/A

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

       6. lower-neg.f64 36.3

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

   11. Simplified 36.3%

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

   if -1.60000000000000006e155 < z

   1. Initial program 94.8%

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

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

      11. lift-*.f64 N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 97.2

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

   4. Applied egg-rr 97.2%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 60.4

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

   7. Simplified 60.4%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 61.0

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

   10. Simplified 61.0%

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

Alternative 8: 58.2% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(t, z, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(t * z + x), $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. 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. *-commutative N/A

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

   11. lift-*.f64 N/A

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

   12. associate-*r* N/A

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

   13. lower-fma.f64 N/A

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

   14. lower-*.f64 97.2

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

4. Applied egg-rr 97.2%

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

5. Taylor expanded in t around 0

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

   1. lower-/.f64 59.3

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

7. Simplified 59.3%

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

8. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. lower-fma.f64 55.0

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

10. Simplified 55.0%

    \[\leadsto \color{blue}{\mathsf{fma}\left(t, z, x\right)} \]
11. Add Preprocessing

Alternative 9: 16.9% 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 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. lower-fma.f64 N/A

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

   3. lower--.f64 56.7

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

5. Simplified 56.7%

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

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 17.0

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

8. Simplified 17.0%

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

9. Final simplification 17.0%

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

Developer Target 1: 96.7% 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 2024212 
(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))))))