SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.4% → 99.1%

Time: 13.7s

Alternatives: 10

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+306}\right):\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- (tanh (/ t y)) (tanh (/ x y))) (* y z)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+306)))
     (+ x (* z (- t x)))
     t_1)))

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 <= -((double) INFINITY)) || !(t_1 <= 5e+306)) {
		tmp = x + (z * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+306)) {
		tmp = x + (z * (t - x));
	} else {
		tmp = t_1;
	}
	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 <= -math.inf) or not (t_1 <= 5e+306):
		tmp = x + (z * (t - x))
	else:
		tmp = t_1
	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 <= Float64(-Inf)) || !(t_1 <= 5e+306))
		tmp = Float64(x + Float64(z * Float64(t - x)));
	else
		tmp = t_1;
	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 <= -Inf) || ~((t_1 <= 5e+306)))
		tmp = x + (z * (t - x));
	else
		tmp = t_1;
	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[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+306]], $MachinePrecision]], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

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))))) < -inf.0 or 4.99999999999999993e306 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

   1. Initial program 47.0%

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

   2. Taylor expanded in y around inf 100.0%

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

   if -inf.0 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < 4.99999999999999993e306

   1. Initial program 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right) \leq -\infty \lor \neg \left(x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right) \leq 5 \cdot 10^{+306}\right):\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 2: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.3e+194)
   (fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
   (+ x (* z (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.3e+194) {
		tmp = fma(y, (z * (tanh((t / y)) - tanh((x / y)))), x);
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.3e+194)
		tmp = fma(y, Float64(z * Float64(tanh(Float64(t / y)) - tanh(Float64(x / y)))), x);
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.3e+194], N[(y * N[(z * N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.2999999999999999e194

   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. Step-by-step derivation

      1. +-commutative 94.7%

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

      2. associate-*l* 98.7%

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

      3. fma-def 98.7%

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

   3. Simplified 98.7%

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

   if 1.2999999999999999e194 < y

   1. Initial program 90.8%

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

   2. Taylor expanded in y around inf 95.9%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 3: 82.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \tanh \left(\frac{t}{y}\right)\\ \mathbf{if}\;y \leq 3.4 \cdot 10^{+34}:\\ \;\;\;\;x + t_1 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+193}:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot \left(t_1 - \frac{x}{y}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (tanh (/ t y))))
   (if (<= y 3.4e+34)
     (+ x (* t_1 (* y z)))
     (if (<= y 7e+193) (fma y (* z (- t_1 (/ x y))) x) (+ x (* z (- t x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = tanh((t / y));
	double tmp;
	if (y <= 3.4e+34) {
		tmp = x + (t_1 * (y * z));
	} else if (y <= 7e+193) {
		tmp = fma(y, (z * (t_1 - (x / y))), x);
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = tanh(Float64(t / y))
	tmp = 0.0
	if (y <= 3.4e+34)
		tmp = Float64(x + Float64(t_1 * Float64(y * z)));
	elseif (y <= 7e+193)
		tmp = fma(y, Float64(z * Float64(t_1 - Float64(x / y))), x);
	else
		tmp = Float64(x + Float64(z * Float64(t - x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, 3.4e+34], N[(x + N[(t$95$1 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+193], N[(y * N[(z * N[(t$95$1 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.3999999999999999e34

   1. Initial program 95.3%

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

   2. Taylor expanded in x around 0 27.3%

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

      1. associate-*r* 27.1%

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

      2. associate-/r* 27.1%

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

      3. div-sub 27.1%

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

      4. rec-exp 27.1%

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

      5. rec-exp 27.1%

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

      6. tanh-def-a 83.2%

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

   4. Simplified 83.2%

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

   if 3.3999999999999999e34 < y < 7.00000000000000026e193

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 91.9%

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

   if 7.00000000000000026e193 < y

   1. Initial program 90.8%

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

   2. Taylor expanded in y around inf 95.9%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.4 \cdot 10^{+34}:\\ \;\;\;\;x + \tanh \left(\frac{t}{y}\right) \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+193}:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4: 81.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{+44} \lor \neg \left(y \leq 3.7 \cdot 10^{+77}\right) \land y \leq 1.25 \cdot 10^{+132}:\\ \;\;\;\;x + \tanh \left(\frac{t}{y}\right) \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y 1.75e+44) (and (not (<= y 3.7e+77)) (<= y 1.25e+132)))
   (+ x (* (tanh (/ t y)) (* y z)))
   (+ x (* z (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= 1.75e+44) || (!(y <= 3.7e+77) && (y <= 1.25e+132))) {
		tmp = x + (tanh((t / y)) * (y * z));
	} 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 <= 1.75d+44) .or. (.not. (y <= 3.7d+77)) .and. (y <= 1.25d+132)) then
        tmp = x + (tanh((t / y)) * (y * z))
    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 <= 1.75e+44) || (!(y <= 3.7e+77) && (y <= 1.25e+132))) {
		tmp = x + (Math.tanh((t / y)) * (y * z));
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= 1.75e+44) or (not (y <= 3.7e+77) and (y <= 1.25e+132)):
		tmp = x + (math.tanh((t / y)) * (y * z))
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= 1.75e+44) || (!(y <= 3.7e+77) && (y <= 1.25e+132)))
		tmp = Float64(x + Float64(tanh(Float64(t / y)) * Float64(y * z)));
	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 <= 1.75e+44) || (~((y <= 3.7e+77)) && (y <= 1.25e+132)))
		tmp = x + (tanh((t / y)) * (y * z));
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, 1.75e+44], And[N[Not[LessEqual[y, 3.7e+77]], $MachinePrecision], LessEqual[y, 1.25e+132]]], N[(x + N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.75e44 or 3.69999999999999995e77 < y < 1.25e132

   1. Initial program 95.0%

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

   2. Taylor expanded in x around 0 27.6%

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

      1. associate-*r* 27.4%

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

      2. associate-/r* 27.4%

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

      3. div-sub 27.4%

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

      4. rec-exp 27.4%

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

      5. rec-exp 27.4%

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

      6. tanh-def-a 83.0%

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

   4. Simplified 83.0%

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

   if 1.75e44 < y < 3.69999999999999995e77 or 1.25e132 < y

   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. Taylor expanded in y around inf 86.1%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{+44} \lor \neg \left(y \leq 3.7 \cdot 10^{+77}\right) \land y \leq 1.25 \cdot 10^{+132}:\\ \;\;\;\;x + \tanh \left(\frac{t}{y}\right) \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 5: 65.2% accurate, 19.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+78}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.75e+38)
   x
   (if (<= y 1e+78) (* x (- 1.0 z)) (if (<= y 3.6e+98) x (+ x (* z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.75e+38) {
		tmp = x;
	} else if (y <= 1e+78) {
		tmp = x * (1.0 - z);
	} else if (y <= 3.6e+98) {
		tmp = x;
	} else {
		tmp = x + (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 <= 1.75d+38) then
        tmp = x
    else if (y <= 1d+78) then
        tmp = x * (1.0d0 - z)
    else if (y <= 3.6d+98) then
        tmp = x
    else
        tmp = x + (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 <= 1.75e+38) {
		tmp = x;
	} else if (y <= 1e+78) {
		tmp = x * (1.0 - z);
	} else if (y <= 3.6e+98) {
		tmp = x;
	} else {
		tmp = x + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.75e+38:
		tmp = x
	elif y <= 1e+78:
		tmp = x * (1.0 - z)
	elif y <= 3.6e+98:
		tmp = x
	else:
		tmp = x + (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.75e+38)
		tmp = x;
	elseif (y <= 1e+78)
		tmp = Float64(x * Float64(1.0 - z));
	elseif (y <= 3.6e+98)
		tmp = x;
	else
		tmp = Float64(x + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.75e+38)
		tmp = x;
	elseif (y <= 1e+78)
		tmp = x * (1.0 - z);
	elseif (y <= 3.6e+98)
		tmp = x;
	else
		tmp = x + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.75e+38], x, If[LessEqual[y, 1e+78], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+98], x, N[(x + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.75000000000000001e38 or 1.00000000000000001e78 < y < 3.59999999999999981e98

   1. Initial program 95.4%

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

      1. +-commutative 95.4%

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

      2. associate-*l* 98.6%

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

      3. fma-def 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in y around 0 70.1%

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

   if 1.75000000000000001e38 < y < 1.00000000000000001e78

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 86.4%

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

   5. Taylor expanded in x around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. neg-sub0 63.2%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0 - z\right)}\right) \]

      3. metadata-eval 63.2%

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

      4. associate-+r- 63.2%

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

      5. metadata-eval 63.2%

         \[\leadsto x \cdot \left(\left(1 + \color{blue}{0}\right) - z\right) \]

      6. metadata-eval 63.2%

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

   7. Simplified 63.2%

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

   if 3.59999999999999981e98 < y

   1. Initial program 89.3%

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

   2. Taylor expanded in x around 0 39.7%

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

      1. associate-*r* 39.4%

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

      2. associate-/r* 39.4%

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

      3. div-sub 39.4%

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

      4. rec-exp 39.4%

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

      5. rec-exp 39.4%

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

      6. tanh-def-a 77.7%

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

   4. Simplified 77.7%

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

   5. Taylor expanded in y around inf 67.3%

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

      1. +-commutative 67.3%

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

      2. *-commutative 67.3%

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

   7. Simplified 67.3%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+78}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot t\\ \end{array} \]

Alternative 6: 65.2% accurate, 19.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.46 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+79}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.46e+37)
   x
   (if (<= y 1.22e+79) (- x (* z x)) (if (<= y 1.1e+99) x (+ x (* z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.46e+37) {
		tmp = x;
	} else if (y <= 1.22e+79) {
		tmp = x - (z * x);
	} else if (y <= 1.1e+99) {
		tmp = x;
	} else {
		tmp = x + (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 <= 1.46d+37) then
        tmp = x
    else if (y <= 1.22d+79) then
        tmp = x - (z * x)
    else if (y <= 1.1d+99) then
        tmp = x
    else
        tmp = x + (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 <= 1.46e+37) {
		tmp = x;
	} else if (y <= 1.22e+79) {
		tmp = x - (z * x);
	} else if (y <= 1.1e+99) {
		tmp = x;
	} else {
		tmp = x + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.46e+37:
		tmp = x
	elif y <= 1.22e+79:
		tmp = x - (z * x)
	elif y <= 1.1e+99:
		tmp = x
	else:
		tmp = x + (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.46e+37)
		tmp = x;
	elseif (y <= 1.22e+79)
		tmp = Float64(x - Float64(z * x));
	elseif (y <= 1.1e+99)
		tmp = x;
	else
		tmp = Float64(x + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.46e+37)
		tmp = x;
	elseif (y <= 1.22e+79)
		tmp = x - (z * x);
	elseif (y <= 1.1e+99)
		tmp = x;
	else
		tmp = x + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.46e+37], x, If[LessEqual[y, 1.22e+79], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+99], x, N[(x + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.4599999999999999e37 or 1.22000000000000002e79 < y < 1.09999999999999989e99

   1. Initial program 95.4%

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

      1. +-commutative 95.4%

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

      2. associate-*l* 98.6%

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

      3. fma-def 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in y around 0 70.1%

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

   if 1.4599999999999999e37 < y < 1.22000000000000002e79

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 86.0%

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

   3. Taylor expanded in t around 0 62.8%

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

      1. mul-1-neg 62.8%

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

      2. distribute-frac-neg 62.8%

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

   5. Simplified 62.8%

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

      1. clear-num 62.8%

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

      2. un-div-inv 63.2%

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

      3. add-sqr-sqrt 61.4%

         \[\leadsto x + \frac{y \cdot z}{\frac{y}{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      4. sqrt-unprod 40.3%

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

      5. sqr-neg 40.3%

         \[\leadsto x + \frac{y \cdot z}{\frac{y}{\sqrt{\color{blue}{x \cdot x}}}} \]

      6. sqrt-unprod 1.7%

         \[\leadsto x + \frac{y \cdot z}{\frac{y}{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      7. add-sqr-sqrt 27.6%

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

   7. Applied egg-rr 27.6%

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

      1. frac-2neg 27.6%

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

      2. distribute-frac-neg 27.6%

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

      3. add-sqr-sqrt 26.7%

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

      4. sqrt-unprod 63.2%

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

      5. sqr-neg 63.2%

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

      6. sqrt-unprod 36.0%

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

      7. add-sqr-sqrt 63.2%

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

      8. distribute-rgt-neg-in 63.2%

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

      9. frac-2neg 63.2%

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

      10. sub-neg 63.2%

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

      11. associate-/r/ 63.2%

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

      12. *-commutative 63.2%

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

      13. div-inv 63.2%

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

      14. add-sqr-sqrt 26.7%

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

      15. sqrt-unprod 27.6%

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

      16. sqr-neg 27.6%

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

      17. sqrt-unprod 0.9%

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

      18. add-sqr-sqrt 27.6%

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

      19. associate-*l* 27.6%

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

      20. associate-*l* 27.6%

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

   9. Applied egg-rr 63.2%

      \[\leadsto \color{blue}{x - z \cdot \frac{y \cdot x}{y}} \]
   10. Step-by-step derivation

       1. *-commutative 63.2%

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

       2. *-commutative 63.2%

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

       3. associate-/l* 63.2%

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

       4. *-inverses 63.2%

          \[\leadsto x - \frac{x}{\color{blue}{1}} \cdot z \]

       5. /-rgt-identity 63.2%

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

   11. Simplified 63.2%

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

   if 1.09999999999999989e99 < y

   1. Initial program 89.3%

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

   2. Taylor expanded in x around 0 39.7%

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

      1. associate-*r* 39.4%

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

      2. associate-/r* 39.4%

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

      3. div-sub 39.4%

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

      4. rec-exp 39.4%

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

      5. rec-exp 39.4%

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

      6. tanh-def-a 77.7%

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

   4. Simplified 77.7%

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

   5. Taylor expanded in y around inf 67.3%

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

      1. +-commutative 67.3%

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

      2. *-commutative 67.3%

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

   7. Simplified 67.3%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.46 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+79}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot t\\ \end{array} \]

Alternative 7: 69.0% accurate, 23.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.5e+39) x (+ x (* z (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.5e+39) {
		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 <= 1.5d+39) 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 <= 1.5e+39) {
		tmp = x;
	} else {
		tmp = x + (z * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.5e+39:
		tmp = x
	else:
		tmp = x + (z * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.5e+39)
		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 <= 1.5e+39)
		tmp = x;
	else
		tmp = x + (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.5e+39], x, N[(x + N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.5e39

   1. Initial program 95.3%

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

      1. +-commutative 95.3%

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

      2. associate-*l* 98.5%

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

      3. fma-def 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around 0 69.9%

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

   if 1.5e39 < y

   1. Initial program 90.9%

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

   2. Taylor expanded in y around inf 84.7%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 8: 59.6% accurate, 29.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-257}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.7e-160) x (if (<= x -7.5e-257) (* z t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.7e-160) {
		tmp = x;
	} else if (x <= -7.5e-257) {
		tmp = 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 (x <= (-3.7d-160)) then
        tmp = x
    else if (x <= (-7.5d-257)) then
        tmp = 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 (x <= -3.7e-160) {
		tmp = x;
	} else if (x <= -7.5e-257) {
		tmp = z * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.7e-160:
		tmp = x
	elif x <= -7.5e-257:
		tmp = z * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.7e-160)
		tmp = x;
	elseif (x <= -7.5e-257)
		tmp = Float64(z * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.7e-160)
		tmp = x;
	elseif (x <= -7.5e-257)
		tmp = z * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.7e-160], x, If[LessEqual[x, -7.5e-257], N[(z * t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.69999999999999977e-160 or -7.4999999999999995e-257 < x

   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. Step-by-step derivation

      1. +-commutative 96.3%

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

      2. associate-*l* 99.1%

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

      3. fma-def 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 70.8%

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

   if -3.69999999999999977e-160 < x < -7.4999999999999995e-257

   1. Initial program 74.5%

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

   2. Taylor expanded in x around 0 2.9%

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

      1. associate-*r* 2.3%

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

      2. associate-/r* 2.3%

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

      3. div-sub 2.3%

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

      4. rec-exp 2.4%

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

      5. rec-exp 2.4%

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

      6. tanh-def-a 66.0%

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

   4. Simplified 66.0%

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

   5. Taylor expanded in y around inf 45.5%

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

      1. +-commutative 45.5%

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

      2. *-commutative 45.5%

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

   7. Simplified 45.5%

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

   8. Taylor expanded in z around inf 45.3%

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

      1. *-commutative 45.3%

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

   10. Simplified 45.3%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-257}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 63.8% accurate, 30.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.6 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 8.6e+37) x (* x (- 1.0 z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 8.6e+37) {
		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 <= 8.6d+37) 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 <= 8.6e+37) {
		tmp = x;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 8.6e+37:
		tmp = x
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 8.6e+37)
		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 <= 8.6e+37)
		tmp = x;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 8.6e+37], x, N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.5999999999999994e37

   1. Initial program 95.3%

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

      1. +-commutative 95.3%

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

      2. associate-*l* 98.5%

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

      3. fma-def 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around 0 69.9%

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

   if 8.5999999999999994e37 < y

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-*l* 92.5%

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

      3. fma-def 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in x around 0 87.9%

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

   5. Taylor expanded in x around inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. neg-sub0 62.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0 - z\right)}\right) \]

      3. metadata-eval 62.6%

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

      4. associate-+r- 62.6%

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

      5. metadata-eval 62.6%

         \[\leadsto x \cdot \left(\left(1 + \color{blue}{0}\right) - z\right) \]

      6. metadata-eval 62.6%

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

   7. Simplified 62.6%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.6 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 10: 60.2% 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. Step-by-step derivation

   1. +-commutative 94.4%

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

   2. associate-*l* 97.3%

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

   3. fma-def 97.3%

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

3. Simplified 97.3%

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

4. Taylor expanded in y around 0 65.1%

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

5. Final simplification 65.1%

   \[\leadsto x \]

Developer target: 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 2023336 
(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))))))