SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.6% → 98.3%

Time: 13.1s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\\ \mathbf{if}\;x + \left(y \cdot z\right) \cdot t_1 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;x + z \cdot \left(y \cdot t_1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right) + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (tanh (/ t y)) (tanh (/ x y)))))
   (if (<= (+ x (* (* y z) t_1)) 2e+300)
     (+ x (* z (* y t_1)))
     (+ (* x (- 1.0 z)) (* z t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = tanh((t / y)) - tanh((x / y));
	double tmp;
	if ((x + ((y * z) * t_1)) <= 2e+300) {
		tmp = x + (z * (y * t_1));
	} else {
		tmp = (x * (1.0 - z)) + (z * t);
	}
	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 = tanh((t / y)) - tanh((x / y))
    if ((x + ((y * z) * t_1)) <= 2d+300) then
        tmp = x + (z * (y * t_1))
    else
        tmp = (x * (1.0d0 - z)) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.tanh((t / y)) - Math.tanh((x / y));
	double tmp;
	if ((x + ((y * z) * t_1)) <= 2e+300) {
		tmp = x + (z * (y * t_1));
	} else {
		tmp = (x * (1.0 - z)) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.tanh((t / y)) - math.tanh((x / y))
	tmp = 0
	if (x + ((y * z) * t_1)) <= 2e+300:
		tmp = x + (z * (y * t_1))
	else:
		tmp = (x * (1.0 - z)) + (z * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(tanh(Float64(t / y)) - tanh(Float64(x / y)))
	tmp = 0.0
	if (Float64(x + Float64(Float64(y * z) * t_1)) <= 2e+300)
		tmp = Float64(x + Float64(z * Float64(y * t_1)));
	else
		tmp = Float64(Float64(x * Float64(1.0 - z)) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = tanh((t / y)) - tanh((x / y));
	tmp = 0.0;
	if ((x + ((y * z) * t_1)) <= 2e+300)
		tmp = x + (z * (y * t_1));
	else
		tmp = (x * (1.0 - z)) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

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]}, If[LessEqual[N[(x + N[(N[(y * z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], 2e+300], N[(x + N[(z * N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(z * t), $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))))) < 2.0000000000000001e300

   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. Step-by-step derivation

      1. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

      1. associate-*r* 96.6%

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

      2. sub-neg 96.6%

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

      3. distribute-lft-in 94.7%

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

   5. Applied egg-rr 94.7%

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

      1. distribute-lft-out 96.6%

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

      2. *-commutative 96.6%

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

      3. sub-neg 96.6%

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

      4. associate-*r* 99.2%

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

   7. Simplified 99.2%

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

   if 2.0000000000000001e300 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

   1. Initial program 45.0%

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

      1. associate-*l* 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in y around inf 99.9%

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

   5. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \leq 2 \cdot 10^{+300}:\\ \;\;\;\;x + z \cdot \left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right) + z \cdot t\\ \end{array} \]

Alternative 2: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{+137}:\\ \;\;\;\;x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right) + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.55e+137)
   (+ x (* y (* z (- (tanh (/ t y)) (tanh (/ x y))))))
   (+ (* x (- 1.0 z)) (* z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.55e+137) {
		tmp = x + (y * (z * (tanh((t / y)) - tanh((x / y)))));
	} else {
		tmp = (x * (1.0 - z)) + (z * t);
	}
	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 <= 1.55d+137) then
        tmp = x + (y * (z * (tanh((t / y)) - tanh((x / y)))))
    else
        tmp = (x * (1.0d0 - z)) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.55e+137) {
		tmp = x + (y * (z * (Math.tanh((t / y)) - Math.tanh((x / y)))));
	} else {
		tmp = (x * (1.0 - z)) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.55e+137:
		tmp = x + (y * (z * (math.tanh((t / y)) - math.tanh((x / y)))))
	else:
		tmp = (x * (1.0 - z)) + (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.55e+137)
		tmp = Float64(x + Float64(y * Float64(z * Float64(tanh(Float64(t / y)) - tanh(Float64(x / y))))));
	else
		tmp = Float64(Float64(x * Float64(1.0 - z)) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.55e+137)
		tmp = x + (y * (z * (tanh((t / y)) - tanh((x / y)))));
	else
		tmp = (x * (1.0 - z)) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.55e+137], 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], N[(N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.55e137

   1. Initial program 95.9%

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

      1. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

   if 1.55e137 < y

   1. Initial program 65.0%

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

      1. associate-*l* 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in y around inf 99.8%

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

   5. Taylor expanded in x around 0 99.9%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{+137}:\\ \;\;\;\;x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right) + z \cdot t\\ \end{array} \]

Alternative 3: 84.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+191}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+130}:\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right) + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e+191)
   (+ x (* z (- t x)))
   (if (<= y 2.8e+130)
     (+ x (* y (* z (tanh (/ t y)))))
     (+ (* x (- 1.0 z)) (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e+191) {
		tmp = x + (z * (t - x));
	} else if (y <= 2.8e+130) {
		tmp = x + (y * (z * tanh((t / y))));
	} else {
		tmp = (x * (1.0 - z)) + (z * t);
	}
	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 <= (-1.05d+191)) then
        tmp = x + (z * (t - x))
    else if (y <= 2.8d+130) then
        tmp = x + (y * (z * tanh((t / y))))
    else
        tmp = (x * (1.0d0 - z)) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e+191) {
		tmp = x + (z * (t - x));
	} else if (y <= 2.8e+130) {
		tmp = x + (y * (z * Math.tanh((t / y))));
	} else {
		tmp = (x * (1.0 - z)) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e+191:
		tmp = x + (z * (t - x))
	elif y <= 2.8e+130:
		tmp = x + (y * (z * math.tanh((t / y))))
	else:
		tmp = (x * (1.0 - z)) + (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e+191)
		tmp = Float64(x + Float64(z * Float64(t - x)));
	elseif (y <= 2.8e+130)
		tmp = Float64(x + Float64(y * Float64(z * tanh(Float64(t / y)))));
	else
		tmp = Float64(Float64(x * Float64(1.0 - z)) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.05e+191)
		tmp = x + (z * (t - x));
	elseif (y <= 2.8e+130)
		tmp = x + (y * (z * tanh((t / y))));
	else
		tmp = (x * (1.0 - z)) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e+191], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+130], N[(x + N[(y * N[(z * N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e191

   1. Initial program 71.3%

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

      1. associate-*l* 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in y around inf 93.7%

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

   if -1.05e191 < y < 2.7999999999999999e130

   1. Initial program 99.4%

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

      1. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around 0 29.9%

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

      1. associate-/r* 30.0%

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

      2. div-sub 29.9%

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

      3. rec-exp 29.9%

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

      4. rec-exp 29.9%

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

      5. tanh-def-a 85.7%

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

   6. Simplified 85.7%

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

   if 2.7999999999999999e130 < y

   1. Initial program 66.6%

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

      1. associate-*l* 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around inf 97.8%

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

   5. Taylor expanded in x around 0 97.8%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+191}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+130}:\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right) + z \cdot t\\ \end{array} \]

Alternative 4: 85.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \tanh \left(\frac{t}{y}\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{-64}:\\ \;\;\;\;x + z \cdot \left(y \cdot t_1 - x\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+131}:\\ \;\;\;\;x + y \cdot \left(z \cdot t_1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right) + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (tanh (/ t y))))
   (if (<= y -3.2e-64)
     (+ x (* z (- (* y t_1) x)))
     (if (<= y 1.55e+131) (+ x (* y (* z t_1))) (+ (* x (- 1.0 z)) (* z t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = tanh((t / y));
	double tmp;
	if (y <= -3.2e-64) {
		tmp = x + (z * ((y * t_1) - x));
	} else if (y <= 1.55e+131) {
		tmp = x + (y * (z * t_1));
	} else {
		tmp = (x * (1.0 - z)) + (z * t);
	}
	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 = tanh((t / y))
    if (y <= (-3.2d-64)) then
        tmp = x + (z * ((y * t_1) - x))
    else if (y <= 1.55d+131) then
        tmp = x + (y * (z * t_1))
    else
        tmp = (x * (1.0d0 - z)) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.tanh((t / y));
	double tmp;
	if (y <= -3.2e-64) {
		tmp = x + (z * ((y * t_1) - x));
	} else if (y <= 1.55e+131) {
		tmp = x + (y * (z * t_1));
	} else {
		tmp = (x * (1.0 - z)) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.tanh((t / y))
	tmp = 0
	if y <= -3.2e-64:
		tmp = x + (z * ((y * t_1) - x))
	elif y <= 1.55e+131:
		tmp = x + (y * (z * t_1))
	else:
		tmp = (x * (1.0 - z)) + (z * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = tanh(Float64(t / y))
	tmp = 0.0
	if (y <= -3.2e-64)
		tmp = Float64(x + Float64(z * Float64(Float64(y * t_1) - x)));
	elseif (y <= 1.55e+131)
		tmp = Float64(x + Float64(y * Float64(z * t_1)));
	else
		tmp = Float64(Float64(x * Float64(1.0 - z)) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = tanh((t / y));
	tmp = 0.0;
	if (y <= -3.2e-64)
		tmp = x + (z * ((y * t_1) - x));
	elseif (y <= 1.55e+131)
		tmp = x + (y * (z * t_1));
	else
		tmp = (x * (1.0 - z)) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, -3.2e-64], N[(x + N[(z * N[(N[(y * t$95$1), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+131], N[(x + N[(y * N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.19999999999999975e-64

   1. Initial program 90.3%

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

      1. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

      1. associate-*r* 90.3%

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

      2. sub-neg 90.3%

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

      3. distribute-lft-in 87.6%

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

   5. Applied egg-rr 87.6%

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

      1. distribute-lft-out 90.3%

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

      2. *-commutative 90.3%

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

      3. sub-neg 90.3%

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

      4. associate-*r* 95.5%

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

   7. Simplified 95.5%

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

   8. Taylor expanded in x around 0 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

   10. Simplified 91.3%

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

   if -3.19999999999999975e-64 < y < 1.55000000000000008e131

   1. Initial program 99.2%

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

      1. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 21.4%

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

      1. associate-/r* 21.4%

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

      2. div-sub 21.4%

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

      3. rec-exp 21.4%

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

      4. rec-exp 21.4%

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

      5. tanh-def-a 86.3%

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

   6. Simplified 86.3%

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

   if 1.55000000000000008e131 < y

   1. Initial program 66.6%

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

      1. associate-*l* 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around inf 97.8%

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

   5. Taylor expanded in x around 0 97.8%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-64}:\\ \;\;\;\;x + z \cdot \left(y \cdot \tanh \left(\frac{t}{y}\right) - x\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+131}:\\ \;\;\;\;x + y \cdot \left(z \cdot \tanh \left(\frac{t}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right) + z \cdot t\\ \end{array} \]

Alternative 5: 75.8% accurate, 16.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-68}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right) + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.6e-68)
   (+ x (* z (- t x)))
   (if (<= y 4.7e+32) x (+ (* x (- 1.0 z)) (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.6e-68) {
		tmp = x + (z * (t - x));
	} else if (y <= 4.7e+32) {
		tmp = x;
	} else {
		tmp = (x * (1.0 - z)) + (z * t);
	}
	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 <= (-3.6d-68)) then
        tmp = x + (z * (t - x))
    else if (y <= 4.7d+32) then
        tmp = x
    else
        tmp = (x * (1.0d0 - z)) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.6e-68) {
		tmp = x + (z * (t - x));
	} else if (y <= 4.7e+32) {
		tmp = x;
	} else {
		tmp = (x * (1.0 - z)) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.6e-68:
		tmp = x + (z * (t - x))
	elif y <= 4.7e+32:
		tmp = x
	else:
		tmp = (x * (1.0 - z)) + (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.6e-68)
		tmp = Float64(x + Float64(z * Float64(t - x)));
	elseif (y <= 4.7e+32)
		tmp = x;
	else
		tmp = Float64(Float64(x * Float64(1.0 - z)) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.6e-68)
		tmp = x + (z * (t - x));
	elseif (y <= 4.7e+32)
		tmp = x;
	else
		tmp = (x * (1.0 - z)) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.6e-68], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e+32], x, N[(N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.60000000000000007e-68

   1. Initial program 90.4%

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

      1. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around inf 80.1%

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

   if -3.60000000000000007e-68 < y < 4.70000000000000023e32

   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. Step-by-step derivation

      1. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 38.5%

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

   5. Taylor expanded in z around 0 73.9%

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

   if 4.70000000000000023e32 < y

   1. Initial program 77.8%

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

      1. associate-*l* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in y around inf 83.7%

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

   5. Taylor expanded in x around 0 83.7%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-68}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right) + z \cdot t\\ \end{array} \]

Alternative 6: 67.8% accurate, 19.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+248}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-83} \lor \neg \left(y \leq 2.55 \cdot 10^{-34}\right):\\ \;\;\;\;x + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.6e+248)
   (* z (- t x))
   (if (or (<= y -7.8e-83) (not (<= y 2.55e-34))) (+ x (* z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e+248) {
		tmp = z * (t - x);
	} else if ((y <= -7.8e-83) || !(y <= 2.55e-34)) {
		tmp = x + (z * t);
	} else {
		tmp = 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 <= (-1.6d+248)) then
        tmp = z * (t - x)
    else if ((y <= (-7.8d-83)) .or. (.not. (y <= 2.55d-34))) then
        tmp = x + (z * t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e+248) {
		tmp = z * (t - x);
	} else if ((y <= -7.8e-83) || !(y <= 2.55e-34)) {
		tmp = x + (z * t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.6e+248:
		tmp = z * (t - x)
	elif (y <= -7.8e-83) or not (y <= 2.55e-34):
		tmp = x + (z * t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.6e+248)
		tmp = Float64(z * Float64(t - x));
	elseif ((y <= -7.8e-83) || !(y <= 2.55e-34))
		tmp = Float64(x + Float64(z * t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.6e+248)
		tmp = z * (t - x);
	elseif ((y <= -7.8e-83) || ~((y <= 2.55e-34)))
		tmp = x + (z * t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.6e+248], N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -7.8e-83], N[Not[LessEqual[y, 2.55e-34]], $MachinePrecision]], N[(x + N[(z * t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if y < -1.59999999999999992e248

   1. Initial program 73.3%

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

      1. associate-*l* 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in z around inf 97.5%

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

   if -1.59999999999999992e248 < y < -7.800000000000001e-83 or 2.55e-34 < y

   1. Initial program 86.9%

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

      1. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in x around 0 39.8%

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

      1. associate-/r* 39.8%

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

      2. div-sub 39.8%

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

      3. rec-exp 39.8%

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

      4. rec-exp 39.8%

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

      5. tanh-def-a 79.1%

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

   6. Simplified 79.1%

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

   7. Taylor expanded in y around inf 68.1%

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

   if -7.800000000000001e-83 < y < 2.55e-34

   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. Step-by-step derivation

      1. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 35.5%

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

   5. Taylor expanded in z around 0 75.6%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+248}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-83} \lor \neg \left(y \leq 2.55 \cdot 10^{-34}\right):\\ \;\;\;\;x + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 76.0% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-68} \lor \neg \left(y \leq 1.1 \cdot 10^{+32}\right):\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.6e-68) (not (<= y 1.1e+32))) (+ x (* z (- t x))) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.6e-68) || !(y <= 1.1e+32)) {
		tmp = x + (z * (t - x));
	} else {
		tmp = 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 <= (-3.6d-68)) .or. (.not. (y <= 1.1d+32))) then
        tmp = x + (z * (t - x))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.6e-68) || !(y <= 1.1e+32)) {
		tmp = x + (z * (t - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.6e-68) or not (y <= 1.1e+32):
		tmp = x + (z * (t - x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.6e-68) || !(y <= 1.1e+32))
		tmp = Float64(x + Float64(z * Float64(t - x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.6e-68) || ~((y <= 1.1e+32)))
		tmp = x + (z * (t - x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.6e-68], N[Not[LessEqual[y, 1.1e+32]], $MachinePrecision]], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.60000000000000007e-68 or 1.1e32 < y

   1. Initial program 84.6%

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

      1. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in y around inf 81.7%

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

   if -3.60000000000000007e-68 < y < 1.1e32

   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. Step-by-step derivation

      1. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 38.5%

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

   5. Taylor expanded in z around 0 73.9%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-68} \lor \neg \left(y \leq 1.1 \cdot 10^{+32}\right):\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 63.2% accurate, 23.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+191} \lor \neg \left(y \leq 5.2 \cdot 10^{+72}\right):\\ \;\;\;\;z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.02e+191) (not (<= y 5.2e+72))) (* z (- t x)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e+191) || !(y <= 5.2e+72)) {
		tmp = z * (t - x);
	} else {
		tmp = 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 <= (-1.02d+191)) .or. (.not. (y <= 5.2d+72))) then
        tmp = z * (t - x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e+191) || !(y <= 5.2e+72)) {
		tmp = z * (t - x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.02e+191) or not (y <= 5.2e+72):
		tmp = z * (t - x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.02e+191) || !(y <= 5.2e+72))
		tmp = Float64(z * Float64(t - x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.02e+191) || ~((y <= 5.2e+72)))
		tmp = z * (t - x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.02e+191], N[Not[LessEqual[y, 5.2e+72]], $MachinePrecision]], N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.02000000000000006e191 or 5.19999999999999963e72 < y

   1. Initial program 72.6%

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

      1. associate-*l* 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in y around inf 88.0%

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

   5. Taylor expanded in z around inf 64.1%

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

   if -1.02000000000000006e191 < y < 5.19999999999999963e72

   1. Initial program 99.9%

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

      1. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 52.0%

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

   5. Taylor expanded in z around 0 68.8%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+191} \lor \neg \left(y \leq 5.2 \cdot 10^{+72}\right):\\ \;\;\;\;z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 57.7% accurate, 42.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= z 7e+64) x (* z t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 7e+64) {
		tmp = x;
	} else {
		tmp = z * t;
	}
	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 (z <= 7d+64) then
        tmp = x
    else
        tmp = z * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 7e+64) {
		tmp = x;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 7e+64:
		tmp = x
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 7e+64)
		tmp = x;
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 7e+64)
		tmp = x;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 7e+64], x, N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6.9999999999999997e64

   1. Initial program 93.7%

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

      1. associate-*l* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in y around inf 67.5%

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

   5. Taylor expanded in z around 0 66.0%

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

   if 6.9999999999999997e64 < z

   1. Initial program 81.4%

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

      1. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around inf 51.1%

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

   5. Taylor expanded in x around 0 40.8%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 10: 59.1% 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 91.0%

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

   1. associate-*l* 95.9%

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

3. Simplified 95.9%

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

4. Taylor expanded in y around inf 63.8%

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

5. Taylor expanded in z around 0 55.5%

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

6. Final simplification 55.5%

   \[\leadsto x \]

Developer target: 97.2% 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 2023182 
(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))))))