SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.1% → 97.5%

Time: 12.1s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 0.7× 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 94.4%

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. associate-*r* N/A

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

   4. fma-define N/A

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

   5. fma-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right), \color{blue}{z}, x\right) \]

   6. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), y\right), z, x\right) \]

   7. --lowering--.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\tanh \left(\frac{t}{y}\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z, x\right) \]

   8. tanh-lowering-tanh.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\left(\frac{t}{y}\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z, x\right) \]

   9. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z, x\right) \]

   10. tanh-lowering-tanh.f64 N/A

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\left(\frac{x}{y}\right)\right)\right), y\right), z, x\right) \]

   11. /-lowering-/.f64 98.0%

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right), y\right), z, x\right) \]

4. Applied egg-rr 98.0%

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

5. Final simplification 98.0%

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

Alternative 2: 96.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+303}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- (tanh (/ t y)) (tanh (/ x y))) (* y z)))))
   (if (<= t_1 5e+303) t_1 (* z (- t x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((tanh((t / y)) - tanh((x / y))) * (y * z));
	double tmp;
	if (t_1 <= 5e+303) {
		tmp = t_1;
	} else {
		tmp = z * (t - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((tanh((t / y)) - tanh((x / y))) * (y * z))
    if (t_1 <= 5d+303) then
        tmp = t_1
    else
        tmp = z * (t - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((Math.tanh((t / y)) - Math.tanh((x / y))) * (y * z));
	double tmp;
	if (t_1 <= 5e+303) {
		tmp = t_1;
	} else {
		tmp = z * (t - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((math.tanh((t / y)) - math.tanh((x / y))) * (y * z))
	tmp = 0
	if t_1 <= 5e+303:
		tmp = t_1
	else:
		tmp = z * (t - x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(tanh(Float64(t / y)) - tanh(Float64(x / y))) * Float64(y * z)))
	tmp = 0.0
	if (t_1 <= 5e+303)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(t - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((tanh((t / y)) - tanh((x / y))) * (y * z));
	tmp = 0.0;
	if (t_1 <= 5e+303)
		tmp = t_1;
	else
		tmp = z * (t - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+303], t$95$1, N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < 4.9999999999999997e303

   1. Initial program 97.7%

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

   if 4.9999999999999997e303 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

   1. Initial program 41.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \color{blue}{\left(\frac{t - x}{y}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{y}\right)\right)\right) \]

      2. --lowering--.f64 42.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), y\right)\right)\right) \]

   5. Simplified 42.4%

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

   6. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(t - x\right)}\right) \]

      2. --lowering--.f64 93.9%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right) \]

   8. Simplified 93.9%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right) \leq 5 \cdot 10^{+303}:\\ \;\;\;\;x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (* y z) (- (tanh (/ t y)) (/ x y))))))
   (if (<= t -8.5e+78)
     t_1
     (if (<= t 2.65e+67) (fma (* y (- (/ t y) (tanh (/ x y)))) z x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * z) * (tanh((t / y)) - (x / y)));
	double tmp;
	if (t <= -8.5e+78) {
		tmp = t_1;
	} else if (t <= 2.65e+67) {
		tmp = fma((y * ((t / y) - tanh((x / y)))), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y * z) * Float64(tanh(Float64(t / y)) - Float64(x / y))))
	tmp = 0.0
	if (t <= -8.5e+78)
		tmp = t_1;
	elseif (t <= 2.65e+67)
		tmp = fma(Float64(y * Float64(Float64(t / y) - tanh(Float64(x / y)))), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] * N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+78], t$95$1, If[LessEqual[t, 2.65e+67], N[(N[(y * N[(N[(t / y), $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.50000000000000079e78 or 2.65e67 < t

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \color{blue}{\left(\frac{x}{y}\right)}\right)\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 74.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right)\right) \]

   5. Simplified 74.3%

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

   if -8.50000000000000079e78 < t < 2.65e67

   1. Initial program 91.2%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. fma-define N/A

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

      5. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right), \color{blue}{z}, x\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), y\right), z, x\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\tanh \left(\frac{t}{y}\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z, x\right) \]

      8. tanh-lowering-tanh.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\left(\frac{t}{y}\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z, x\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z, x\right) \]

      10. tanh-lowering-tanh.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\left(\frac{x}{y}\right)\right)\right), y\right), z, x\right) \]

      11. /-lowering-/.f64 96.5%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right), y\right), z, x\right) \]

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(\frac{t}{y}\right)}, \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right), y\right), z, x\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 88.8%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right), y\right), z, x\right) \]

   7. Simplified 88.8%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+78}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.4%

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

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   2. associate-*r* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right), \color{blue}{z}\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\tanh \left(\frac{t}{y}\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

   6. tanh-lowering-tanh.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\left(\frac{t}{y}\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

   8. tanh-lowering-tanh.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\left(\frac{x}{y}\right)\right)\right), y\right), z\right)\right) \]

   9. /-lowering-/.f64 97.9%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right), y\right), z\right)\right) \]

4. Applied egg-rr 97.9%

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

5. Final simplification 97.9%

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

Alternative 5: 77.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+63}:\\ \;\;\;\;x + z \cdot \left(y \cdot \frac{t}{y} - y \cdot \tanh \left(\frac{x}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (* y z) (- (tanh (/ t y)) (/ x y))))))
   (if (<= t -2.25e+70)
     t_1
     (if (<= t 3.7e+63)
       (+ x (* z (- (* y (/ t y)) (* y (tanh (/ x y))))))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * z) * (tanh((t / y)) - (x / y)));
	double tmp;
	if (t <= -2.25e+70) {
		tmp = t_1;
	} else if (t <= 3.7e+63) {
		tmp = x + (z * ((y * (t / y)) - (y * tanh((x / y)))));
	} 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 = x + ((y * z) * (tanh((t / y)) - (x / y)))
    if (t <= (-2.25d+70)) then
        tmp = t_1
    else if (t <= 3.7d+63) then
        tmp = x + (z * ((y * (t / y)) - (y * tanh((x / y)))))
    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 = x + ((y * z) * (Math.tanh((t / y)) - (x / y)));
	double tmp;
	if (t <= -2.25e+70) {
		tmp = t_1;
	} else if (t <= 3.7e+63) {
		tmp = x + (z * ((y * (t / y)) - (y * Math.tanh((x / y)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y * z) * (math.tanh((t / y)) - (x / y)))
	tmp = 0
	if t <= -2.25e+70:
		tmp = t_1
	elif t <= 3.7e+63:
		tmp = x + (z * ((y * (t / y)) - (y * math.tanh((x / y)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y * z) * Float64(tanh(Float64(t / y)) - Float64(x / y))))
	tmp = 0.0
	if (t <= -2.25e+70)
		tmp = t_1;
	elseif (t <= 3.7e+63)
		tmp = Float64(x + Float64(z * Float64(Float64(y * Float64(t / y)) - Float64(y * tanh(Float64(x / y))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y * z) * (tanh((t / y)) - (x / y)));
	tmp = 0.0;
	if (t <= -2.25e+70)
		tmp = t_1;
	elseif (t <= 3.7e+63)
		tmp = x + (z * ((y * (t / y)) - (y * tanh((x / y)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] * N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.25e+70], t$95$1, If[LessEqual[t, 3.7e+63], N[(x + N[(z * N[(N[(y * N[(t / y), $MachinePrecision]), $MachinePrecision] - N[(y * N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.25e70 or 3.69999999999999968e63 < t

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \color{blue}{\left(\frac{x}{y}\right)}\right)\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 74.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right)\right) \]

   5. Simplified 74.3%

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

   if -2.25e70 < t < 3.69999999999999968e63

   1. Initial program 91.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right), \color{blue}{z}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\tanh \left(\frac{t}{y}\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

      6. tanh-lowering-tanh.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\left(\frac{t}{y}\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

      8. tanh-lowering-tanh.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\left(\frac{x}{y}\right)\right)\right), y\right), z\right)\right) \]

      9. /-lowering-/.f64 96.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right), y\right), z\right)\right) \]

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(\frac{t}{y}\right)}, \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right), y\right), z\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 88.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right), y\right), z\right)\right) \]

   7. Simplified 88.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y \cdot \left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right)\right), z\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y \cdot \left(\frac{t}{y} + \left(\mathsf{neg}\left(\tanh \left(\frac{x}{y}\right)\right)\right)\right)\right), z\right)\right) \]

      3. distribute-rgt-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{t}{y} \cdot y + \left(\mathsf{neg}\left(\tanh \left(\frac{x}{y}\right)\right)\right) \cdot y\right), z\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\frac{t}{y} \cdot y\right), \left(\left(\mathsf{neg}\left(\tanh \left(\frac{x}{y}\right)\right)\right) \cdot y\right)\right), z\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{t}{y}\right), y\right), \left(\left(\mathsf{neg}\left(\tanh \left(\frac{x}{y}\right)\right)\right) \cdot y\right)\right), z\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), y\right), \left(\left(\mathsf{neg}\left(\tanh \left(\frac{x}{y}\right)\right)\right) \cdot y\right)\right), z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), y\right), \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\tanh \left(\frac{x}{y}\right)\right)\right), y\right)\right), z\right)\right) \]

      8. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), y\right), \mathsf{*.f64}\left(\left(0 - \tanh \left(\frac{x}{y}\right)\right), y\right)\right), z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), y\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \tanh \left(\frac{x}{y}\right)\right), y\right)\right), z\right)\right) \]

      10. tanh-lowering-tanh.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), y\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{tanh.f64}\left(\left(\frac{x}{y}\right)\right)\right), y\right)\right), z\right)\right) \]

      11. /-lowering-/.f64 88.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), y\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right), y\right)\right), z\right)\right) \]

   9. Applied egg-rr 88.8%

      \[\leadsto x + \color{blue}{\left(\frac{t}{y} \cdot y + \left(0 - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right)} \cdot z \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+70}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+63}:\\ \;\;\;\;x + z \cdot \left(y \cdot \frac{t}{y} - y \cdot \tanh \left(\frac{x}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+64}:\\ \;\;\;\;x + z \cdot \left(y \cdot \left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (* y z) (- (tanh (/ t y)) (/ x y))))))
   (if (<= t -4.2e+70)
     t_1
     (if (<= t 5.2e+64) (+ x (* z (* y (- (/ t y) (tanh (/ x y)))))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * z) * (tanh((t / y)) - (x / y)));
	double tmp;
	if (t <= -4.2e+70) {
		tmp = t_1;
	} else if (t <= 5.2e+64) {
		tmp = x + (z * (y * ((t / y) - tanh((x / y)))));
	} 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 = x + ((y * z) * (tanh((t / y)) - (x / y)))
    if (t <= (-4.2d+70)) then
        tmp = t_1
    else if (t <= 5.2d+64) then
        tmp = x + (z * (y * ((t / y) - tanh((x / y)))))
    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 = x + ((y * z) * (Math.tanh((t / y)) - (x / y)));
	double tmp;
	if (t <= -4.2e+70) {
		tmp = t_1;
	} else if (t <= 5.2e+64) {
		tmp = x + (z * (y * ((t / y) - Math.tanh((x / y)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y * z) * (math.tanh((t / y)) - (x / y)))
	tmp = 0
	if t <= -4.2e+70:
		tmp = t_1
	elif t <= 5.2e+64:
		tmp = x + (z * (y * ((t / y) - math.tanh((x / y)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y * z) * Float64(tanh(Float64(t / y)) - Float64(x / y))))
	tmp = 0.0
	if (t <= -4.2e+70)
		tmp = t_1;
	elseif (t <= 5.2e+64)
		tmp = Float64(x + Float64(z * Float64(y * Float64(Float64(t / y) - tanh(Float64(x / y))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y * z) * (tanh((t / y)) - (x / y)));
	tmp = 0.0;
	if (t <= -4.2e+70)
		tmp = t_1;
	elseif (t <= 5.2e+64)
		tmp = x + (z * (y * ((t / y) - tanh((x / y)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] * N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+70], t$95$1, If[LessEqual[t, 5.2e+64], N[(x + N[(z * N[(y * N[(N[(t / y), $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.20000000000000015e70 or 5.19999999999999994e64 < t

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \color{blue}{\left(\frac{x}{y}\right)}\right)\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 74.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right)\right) \]

   5. Simplified 74.3%

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

   if -4.20000000000000015e70 < t < 5.19999999999999994e64

   1. Initial program 91.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right), \color{blue}{z}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\tanh \left(\frac{t}{y}\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

      6. tanh-lowering-tanh.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\left(\frac{t}{y}\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \tanh \left(\frac{x}{y}\right)\right), y\right), z\right)\right) \]

      8. tanh-lowering-tanh.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\left(\frac{x}{y}\right)\right)\right), y\right), z\right)\right) \]

      9. /-lowering-/.f64 96.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right), y\right), z\right)\right) \]

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(\frac{t}{y}\right)}, \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right), y\right), z\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 88.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{tanh.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right), y\right), z\right)\right) \]

   7. Simplified 88.8%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+70}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+64}:\\ \;\;\;\;x + z \cdot \left(y \cdot \left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9.5 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+167}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 9.5e-37)
   x
   (if (<= y 6.8e+167)
     (+ x (* (* y z) (- (tanh (/ t y)) (/ x y))))
     (+ x (* z (- t x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 9.5e-37) {
		tmp = x;
	} else if (y <= 6.8e+167) {
		tmp = x + ((y * z) * (tanh((t / y)) - (x / y)));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 9.5d-37) then
        tmp = x
    else if (y <= 6.8d+167) then
        tmp = x + ((y * z) * (tanh((t / y)) - (x / y)))
    else
        tmp = x + (z * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 9.5e-37) {
		tmp = x;
	} else if (y <= 6.8e+167) {
		tmp = x + ((y * z) * (Math.tanh((t / y)) - (x / y)));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 9.5e-37:
		tmp = x
	elif y <= 6.8e+167:
		tmp = x + ((y * z) * (math.tanh((t / y)) - (x / y)))
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 9.5e-37)
		tmp = x;
	elseif (y <= 6.8e+167)
		tmp = Float64(x + Float64(Float64(y * z) * Float64(tanh(Float64(t / y)) - Float64(x / y))));
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 9.5e-37)
		tmp = x;
	elseif (y <= 6.8e+167)
		tmp = x + ((y * z) * (tanh((t / y)) - (x / y)));
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 9.5e-37], x, If[LessEqual[y, 6.8e+167], N[(x + N[(N[(y * z), $MachinePrecision] * N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 9.49999999999999927e-37

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 66.7%

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

   if 9.49999999999999927e-37 < y < 6.8000000000000001e167

   1. Initial program 94.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \color{blue}{\left(\frac{x}{y}\right)}\right)\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 87.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{\_.f64}\left(\mathsf{tanh.f64}\left(\mathsf{/.f64}\left(t, y\right)\right), \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right)\right) \]

   5. Simplified 87.0%

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

   if 6.8000000000000001e167 < y

   1. Initial program 82.9%

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

   3. Taylor expanded in y around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 92.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 92.1%

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

Alternative 8: 64.4% accurate, 14.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+246}:\\ \;\;\;\;x + t \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 6.5e+42) x (if (<= y 1.25e+246) (+ x (* t z)) (* x (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6.5e+42) {
		tmp = x;
	} else if (y <= 1.25e+246) {
		tmp = x + (t * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 6.5d+42) then
        tmp = x
    else if (y <= 1.25d+246) then
        tmp = x + (t * z)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6.5e+42) {
		tmp = x;
	} else if (y <= 1.25e+246) {
		tmp = x + (t * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 6.5e+42:
		tmp = x
	elif y <= 1.25e+246:
		tmp = x + (t * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 6.5e+42)
		tmp = x;
	elseif (y <= 1.25e+246)
		tmp = Float64(x + Float64(t * z));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 6.5e+42)
		tmp = x;
	elseif (y <= 1.25e+246)
		tmp = x + (t * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 6.5e+42], x, If[LessEqual[y, 1.25e+246], N[(x + N[(t * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 6.50000000000000052e42

   1. Initial program 96.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 64.4%

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

   if 6.50000000000000052e42 < y < 1.24999999999999994e246

   1. Initial program 88.2%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \color{blue}{\left(\frac{t - x}{y}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{y}\right)\right)\right) \]

      2. --lowering--.f64 76.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), y\right)\right)\right) \]

   5. Simplified 76.7%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot z\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \color{blue}{t}\right)\right) \]

      2. *-lowering-*.f64 75.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right) \]

   8. Simplified 75.8%

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

   if 1.24999999999999994e246 < y

   1. Initial program 72.3%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \color{blue}{\left(\frac{t - x}{y}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{y}\right)\right)\right) \]

      2. --lowering--.f64 72.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), y\right)\right)\right) \]

   5. Simplified 72.3%

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

   6. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot z\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{z}\right)\right) \]

      4. --lowering--.f64 86.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]

   8. Simplified 86.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+246}:\\ \;\;\;\;x + t \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.4% accurate, 17.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.2e-36) x (+ x (* z (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.2e-36) {
		tmp = x;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 1.2d-36) then
        tmp = x
    else
        tmp = x + (z * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.2e-36) {
		tmp = x;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.2e-36:
		tmp = x
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.2e-36)
		tmp = x;
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.2e-36)
		tmp = x;
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.2e-36], x, N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.2e-36

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 66.7%

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

   if 1.2e-36 < y

   1. Initial program 89.2%

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 81.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 81.1%

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

Alternative 10: 63.0% accurate, 21.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 1.1e+94) x (* x (- 1.0 z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.1e+94) {
		tmp = x;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 1.1d+94) then
        tmp = x
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.1e+94) {
		tmp = x;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.1e+94:
		tmp = x
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.1e+94)
		tmp = x;
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.1e+94)
		tmp = x;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.1e+94], x, N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.10000000000000006e94

   1. Initial program 96.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 63.5%

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

   if 1.10000000000000006e94 < y

   1. Initial program 82.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \color{blue}{\left(\frac{t - x}{y}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{y}\right)\right)\right) \]

      2. --lowering--.f64 73.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), y\right)\right)\right) \]

   5. Simplified 73.4%

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

   6. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot z\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{z}\right)\right) \]

      4. --lowering--.f64 64.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]

   8. Simplified 64.1%

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

Alternative 11: 59.9% accurate, 213.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 94.4%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 60.5%

   \[\leadsto \color{blue}{x} \]
6. 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 2024150 
(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))))))