SynthBasics:moogVCF from YampaSynth-0.2

Average Error: 4.5 → 1.6

Time: 14.9s

Precision: binary64

Cost: 41032

Math

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

↓

\[\begin{array}{l} t_1 := \tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\\ t_2 := x + \left(y \cdot z\right) \cdot t_1\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-58}:\\ \;\;\;\;x + y \cdot \left(z \cdot t_1\right)\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{+279}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (tanh (/ t y)) (tanh (/ x y)))) (t_2 (+ x (* (* y z) t_1))))
   (if (<= t_2 -2e-58)
     (+ x (* y (* z t_1)))
     (if (<= t_2 4e+279) t_2 (+ x (* z (- t x)))))))

C

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

↓

double code(double x, double y, double z, double t) {
	double t_1 = tanh((t / y)) - tanh((x / y));
	double t_2 = x + ((y * z) * t_1);
	double tmp;
	if (t_2 <= -2e-58) {
		tmp = x + (y * (z * t_1));
	} else if (t_2 <= 4e+279) {
		tmp = t_2;
	} 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
    code = x + ((y * z) * (tanh((t / y)) - tanh((x / y))))
end function

↓

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) :: t_2
    real(8) :: tmp
    t_1 = tanh((t / y)) - tanh((x / y))
    t_2 = x + ((y * z) * t_1)
    if (t_2 <= (-2d-58)) then
        tmp = x + (y * (z * t_1))
    else if (t_2 <= 4d+279) then
        tmp = t_2
    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) {
	return x + ((y * z) * (Math.tanh((t / y)) - Math.tanh((x / y))));
}

↓

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.tanh((t / y)) - Math.tanh((x / y));
	double t_2 = x + ((y * z) * t_1);
	double tmp;
	if (t_2 <= -2e-58) {
		tmp = x + (y * (z * t_1));
	} else if (t_2 <= 4e+279) {
		tmp = t_2;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = math.tanh((t / y)) - math.tanh((x / y))
	t_2 = x + ((y * z) * t_1)
	tmp = 0
	if t_2 <= -2e-58:
		tmp = x + (y * (z * t_1))
	elif t_2 <= 4e+279:
		tmp = t_2
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

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

↓

function code(x, y, z, t)
	t_1 = Float64(tanh(Float64(t / y)) - tanh(Float64(x / y)))
	t_2 = Float64(x + Float64(Float64(y * z) * t_1))
	tmp = 0.0
	if (t_2 <= -2e-58)
		tmp = Float64(x + Float64(y * Float64(z * t_1)));
	elseif (t_2 <= 4e+279)
		tmp = t_2;
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t)
	t_1 = tanh((t / y)) - tanh((x / y));
	t_2 = x + ((y * z) * t_1);
	tmp = 0.0;
	if (t_2 <= -2e-58)
		tmp = x + (y * (z * t_1));
	elseif (t_2 <= 4e+279)
		tmp = t_2;
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
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]

↓

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-58], N[(x + N[(y * N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+279], t$95$2, N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	4.5
Target	2.0
Herbie	1.6

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

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < -2.0000000000000001e-58

   1. Initial program 4.0

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

   2. Taylor expanded in y around 0 56.6

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

   3. Simplified 0.2

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

      [Start] 56.6	\[ x + y \cdot \left(\left(\left(\frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)} + \frac{e^{\frac{t}{y}}}{e^{\frac{t}{y}} + \frac{1}{e^{\frac{t}{y}}}}\right) - \left(\frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}} + \frac{1}{e^{\frac{t}{y}} \cdot \left(e^{\frac{t}{y}} + \frac{1}{e^{\frac{t}{y}}}\right)}\right)\right) \cdot z\right) \]
      *-commutative [=>] 56.6	\[ x + y \cdot \color{blue}{\left(z \cdot \left(\left(\frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)} + \frac{e^{\frac{t}{y}}}{e^{\frac{t}{y}} + \frac{1}{e^{\frac{t}{y}}}}\right) - \left(\frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}} + \frac{1}{e^{\frac{t}{y}} \cdot \left(e^{\frac{t}{y}} + \frac{1}{e^{\frac{t}{y}}}\right)}\right)\right)\right)} \]
      associate--l+ [=>] 56.6	\[ x + y \cdot \left(z \cdot \color{blue}{\left(\frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)} + \left(\frac{e^{\frac{t}{y}}}{e^{\frac{t}{y}} + \frac{1}{e^{\frac{t}{y}}}} - \left(\frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}} + \frac{1}{e^{\frac{t}{y}} \cdot \left(e^{\frac{t}{y}} + \frac{1}{e^{\frac{t}{y}}}\right)}\right)\right)\right)}\right) \]
      +-commutative [=>] 56.6	\[ x + y \cdot \left(z \cdot \color{blue}{\left(\left(\frac{e^{\frac{t}{y}}}{e^{\frac{t}{y}} + \frac{1}{e^{\frac{t}{y}}}} - \left(\frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}} + \frac{1}{e^{\frac{t}{y}} \cdot \left(e^{\frac{t}{y}} + \frac{1}{e^{\frac{t}{y}}}\right)}\right)\right) + \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)}\right) \]
      +-commutative [=>] 56.6	\[ x + y \cdot \left(z \cdot \left(\left(\frac{e^{\frac{t}{y}}}{e^{\frac{t}{y}} + \frac{1}{e^{\frac{t}{y}}}} - \color{blue}{\left(\frac{1}{e^{\frac{t}{y}} \cdot \left(e^{\frac{t}{y}} + \frac{1}{e^{\frac{t}{y}}}\right)} + \frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}}\right)}\right) + \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)\right) \]
      associate--r+ [=>] 56.6	\[ x + y \cdot \left(z \cdot \left(\color{blue}{\left(\left(\frac{e^{\frac{t}{y}}}{e^{\frac{t}{y}} + \frac{1}{e^{\frac{t}{y}}}} - \frac{1}{e^{\frac{t}{y}} \cdot \left(e^{\frac{t}{y}} + \frac{1}{e^{\frac{t}{y}}}\right)}\right) - \frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}}\right)} + \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)\right) \]
      associate-/r* [=>] 56.6	\[ x + y \cdot \left(z \cdot \left(\left(\left(\frac{e^{\frac{t}{y}}}{e^{\frac{t}{y}} + \frac{1}{e^{\frac{t}{y}}}} - \color{blue}{\frac{\frac{1}{e^{\frac{t}{y}}}}{e^{\frac{t}{y}} + \frac{1}{e^{\frac{t}{y}}}}}\right) - \frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}}\right) + \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)\right) \]
      div-sub [<=] 56.6	\[ x + y \cdot \left(z \cdot \left(\left(\color{blue}{\frac{e^{\frac{t}{y}} - \frac{1}{e^{\frac{t}{y}}}}{e^{\frac{t}{y}} + \frac{1}{e^{\frac{t}{y}}}}} - \frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}}\right) + \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)\right) \]
      rec-exp [=>] 56.5	\[ x + y \cdot \left(z \cdot \left(\left(\frac{e^{\frac{t}{y}} - \color{blue}{e^{-\frac{t}{y}}}}{e^{\frac{t}{y}} + \frac{1}{e^{\frac{t}{y}}}} - \frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}}\right) + \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)\right) \]
      rec-exp [=>] 56.5	\[ x + y \cdot \left(z \cdot \left(\left(\frac{e^{\frac{t}{y}} - e^{-\frac{t}{y}}}{e^{\frac{t}{y}} + \color{blue}{e^{-\frac{t}{y}}}} - \frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}}\right) + \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)\right) \]
      tanh-def-a [<=] 47.8	\[ x + y \cdot \left(z \cdot \left(\left(\color{blue}{\tanh \left(\frac{t}{y}\right)} - \frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}}\right) + \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)\right) \]
      associate--r- [<=] 41.7	\[ x + y \cdot \left(z \cdot \color{blue}{\left(\tanh \left(\frac{t}{y}\right) - \left(\frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}} - \frac{1}{e^{\frac{x}{y}} \cdot \left(e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}\right)}\right)\right)}\right) \]
      associate-/r* [=>] 41.7	\[ x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \left(\frac{e^{\frac{x}{y}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}} - \color{blue}{\frac{\frac{1}{e^{\frac{x}{y}}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}}}\right)\right)\right) \]
      div-sub [<=] 41.7	\[ x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \color{blue}{\frac{e^{\frac{x}{y}} - \frac{1}{e^{\frac{x}{y}}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}}}\right)\right) \]
      rec-exp [=>] 41.7	\[ x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{e^{\frac{x}{y}} - \color{blue}{e^{-\frac{x}{y}}}}{e^{\frac{x}{y}} + \frac{1}{e^{\frac{x}{y}}}}\right)\right) \]
      rec-exp [=>] 41.7	\[ x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{e^{\frac{x}{y}} - e^{-\frac{x}{y}}}{e^{\frac{x}{y}} + \color{blue}{e^{-\frac{x}{y}}}}\right)\right) \]
      tanh-def-a [<=] 0.2	\[ x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \color{blue}{\tanh \left(\frac{x}{y}\right)}\right)\right) \]

   if -2.0000000000000001e-58 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < 4.00000000000000023e279

   1. Initial program 1.0

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

   if 4.00000000000000023e279 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

   1. Initial program 36.8

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

   2. Simplified 13.8

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

      [Start] 36.8	\[ x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \]
      +-commutative [=>] 36.8	\[ \color{blue}{\left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) + x} \]
      *-commutative [=>] 36.8	\[ \color{blue}{\left(z \cdot y\right)} \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) + x \]
      associate-*l* [=>] 13.8	\[ \color{blue}{z \cdot \left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)} + x \]
      fma-def [=>] 13.8	\[ \color{blue}{\mathsf{fma}\left(z, y \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), x\right)} \]

   3. Taylor expanded in y around inf 15.0

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

4. Final simplification 1.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \leq -2 \cdot 10^{-58}:\\ \;\;\;\;x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\\ \mathbf{elif}\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \leq 4 \cdot 10^{+279}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	1.6
Cost	33604

\[\begin{array}{l} t_1 := \tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\\ \mathbf{if}\;x + \left(y \cdot z\right) \cdot t_1 \leq 4 \cdot 10^{+279}:\\ \;\;\;\;\mathsf{fma}\left(z, y \cdot t_1, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 2
Error	8.7
Cost	13904

\[\begin{array}{l} t_1 := \tanh \left(\frac{t}{y}\right)\\ t_2 := x + \left(y \cdot z\right) \cdot t_1\\ t_3 := \mathsf{fma}\left(z, y \cdot t_1 - x, x\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-223}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-207}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 3
Error	1.7
Cost	13764

\[\begin{array}{l} \mathbf{if}\;y \leq 1.35 \cdot 10^{+171}:\\ \;\;\;\;x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4
Error	9.8
Cost	7504

\[\begin{array}{l} t_1 := x + \left(y \cdot z\right) \cdot \tanh \left(\frac{t}{y}\right)\\ t_2 := x + z \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-207}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	23.2
Cost	717

\[\begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+277}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+205} \lor \neg \left(y \leq 1.42 \cdot 10^{+262}\right):\\ \;\;\;\;z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	15.5
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+43} \lor \neg \left(y \leq 0.185\right):\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	19.5
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-126} \lor \neg \left(y \leq 0.31\right):\\ \;\;\;\;x + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	23.0
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-225}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-283}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	23.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022364 
(FPCore (x y z t)
  :name "SynthBasics:moogVCF from YampaSynth-0.2"
  :precision binary64

  :herbie-target
  (+ x (* y (* z (- (tanh (/ t y)) (tanh (/ x y))))))

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