SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.3% → 96.6%

Time: 10.9s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 5.2 \cdot 10^{+149}:\\ \;\;\;\;\mathsf{fma}\left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right), y\_m \cdot z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 5.2e+149)
   (fma (- (tanh (/ t y_m)) (tanh (/ x y_m))) (* y_m z) x)
   (fma z (- t x) x)))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 5.2e+149) {
		tmp = fma((tanh((t / y_m)) - tanh((x / y_m))), (y_m * z), x);
	} else {
		tmp = fma(z, (t - x), x);
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 5.2e+149)
		tmp = fma(Float64(tanh(Float64(t / y_m)) - tanh(Float64(x / y_m))), Float64(y_m * z), x);
	else
		tmp = fma(z, Float64(t - x), x);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 5.2e+149], N[(N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(y$95$m * z), $MachinePrecision] + x), $MachinePrecision], N[(z * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.19999999999999957e149

   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. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

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

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

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

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

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

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

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

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

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

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

      9. *-lowering-*.f64 95.4

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

   4. Applied egg-rr 95.4%

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

   if 5.19999999999999957e149 < y

   1. Initial program 71.1%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 90.0

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

   5. Simplified 90.0%

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

Alternative 2: 71.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_1 := z \cdot \left(t - x\right)\\ t_2 := x + \left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right) \cdot \left(y\_m \cdot z\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (let* ((t_1 (* z (- t x)))
        (t_2 (+ x (* (- (tanh (/ t y_m)) (tanh (/ x y_m))) (* y_m z)))))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 5e+297) x t_1))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double t_1 = z * (t - x);
	double t_2 = x + ((tanh((t / y_m)) - tanh((x / y_m))) * (y_m * z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 5e+297) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double t_1 = z * (t - x);
	double t_2 = x + ((Math.tanh((t / y_m)) - Math.tanh((x / y_m))) * (y_m * z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 5e+297) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	t_1 = z * (t - x)
	t_2 = x + ((math.tanh((t / y_m)) - math.tanh((x / y_m))) * (y_m * z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 5e+297:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	t_1 = Float64(z * Float64(t - x))
	t_2 = Float64(x + Float64(Float64(tanh(Float64(t / y_m)) - tanh(Float64(x / y_m))) * Float64(y_m * z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 5e+297)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	t_1 = z * (t - x);
	t_2 = x + ((tanh((t / y_m)) - tanh((x / y_m))) * (y_m * z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 5e+297)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := Block[{t$95$1 = N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(y$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 5e+297], x, 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 4.9999999999999998e297 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

   1. Initial program 58.9%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 97.5

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

   5. Simplified 97.5%

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

   6. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 97.5

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

   8. Simplified 97.5%

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

   if -inf.0 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < 4.9999999999999998e297

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 70.5%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right) \leq -\infty:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \mathbf{elif}\;x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right) \leq 5 \cdot 10^{+297}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_1 := x + \left(\tanh \left(\frac{t}{y\_m}\right) - \tanh \left(\frac{x}{y\_m}\right)\right) \cdot \left(y\_m \cdot z\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- (tanh (/ t y_m)) (tanh (/ x y_m))) (* y_m z)))))
   (if (<= t_1 (- INFINITY)) (* t z) (if (<= t_1 5e+297) x (* t z)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double t_1 = x + ((tanh((t / y_m)) - tanh((x / y_m))) * (y_m * z));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t * z;
	} else if (t_1 <= 5e+297) {
		tmp = x;
	} else {
		tmp = t * z;
	}
	return tmp;
}

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	double t_1 = x + ((Math.tanh((t / y_m)) - Math.tanh((x / y_m))) * (y_m * z));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t * z;
	} else if (t_1 <= 5e+297) {
		tmp = x;
	} else {
		tmp = t * z;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	t_1 = x + ((math.tanh((t / y_m)) - math.tanh((x / y_m))) * (y_m * z))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t * z
	elif t_1 <= 5e+297:
		tmp = x
	else:
		tmp = t * z
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	t_1 = Float64(x + Float64(Float64(tanh(Float64(t / y_m)) - tanh(Float64(x / y_m))) * Float64(y_m * z)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t * z);
	elseif (t_1 <= 5e+297)
		tmp = x;
	else
		tmp = Float64(t * z);
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z, t)
	t_1 = x + ((tanh((t / y_m)) - tanh((x / y_m))) * (y_m * z));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t * z;
	elseif (t_1 <= 5e+297)
		tmp = x;
	else
		tmp = t * z;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(y$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t * z), $MachinePrecision], If[LessEqual[t$95$1, 5e+297], x, N[(t * z), $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))))) < -inf.0 or 4.9999999999999998e297 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

   1. Initial program 58.9%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 97.5

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

   5. Simplified 97.5%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 53.6

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

   8. Simplified 53.6%

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

   if -inf.0 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < 4.9999999999999998e297

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 70.5%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right) \leq -\infty:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right) \leq 5 \cdot 10^{+297}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 7.2 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;y\_m \leq 7.5 \cdot 10^{+148}:\\ \;\;\;\;\mathsf{fma}\left(\tanh \left(\frac{t}{y\_m}\right) - \frac{x}{y\_m}, y\_m \cdot z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 7.2e-11)
   x
   (if (<= y_m 7.5e+148)
     (fma (- (tanh (/ t y_m)) (/ x y_m)) (* y_m z) x)
     (fma z (- t x) x))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 7.2e-11) {
		tmp = x;
	} else if (y_m <= 7.5e+148) {
		tmp = fma((tanh((t / y_m)) - (x / y_m)), (y_m * z), x);
	} else {
		tmp = fma(z, (t - x), x);
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 7.2e-11)
		tmp = x;
	elseif (y_m <= 7.5e+148)
		tmp = fma(Float64(tanh(Float64(t / y_m)) - Float64(x / y_m)), Float64(y_m * z), x);
	else
		tmp = fma(z, Float64(t - x), x);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 7.2e-11], x, If[LessEqual[y$95$m, 7.5e+148], N[(N[(N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] - N[(x / y$95$m), $MachinePrecision]), $MachinePrecision] * N[(y$95$m * z), $MachinePrecision] + x), $MachinePrecision], N[(z * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.19999999999999969e-11

   1. Initial program 95.5%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 65.5%

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

   if 7.19999999999999969e-11 < y < 7.50000000000000008e148

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 72.2

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

   5. Simplified 72.2%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 72.2

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

   7. Applied egg-rr 72.2%

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

   if 7.50000000000000008e148 < y

   1. Initial program 71.1%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 90.0

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

   5. Simplified 90.0%

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

Alternative 5: 82.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 7.8 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;y\_m \leq 1.3 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{fma}\left(z, -x, \mathsf{fma}\left(y\_m \cdot z, \tanh \left(\frac{t}{y\_m}\right), x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 7.8e-115)
   x
   (if (<= y_m 1.3e+147)
     (fma z (- x) (fma (* y_m z) (tanh (/ t y_m)) x))
     (fma z (- t x) x))))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 7.8e-115) {
		tmp = x;
	} else if (y_m <= 1.3e+147) {
		tmp = fma(z, -x, fma((y_m * z), tanh((t / y_m)), x));
	} else {
		tmp = fma(z, (t - x), x);
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 7.8e-115)
		tmp = x;
	elseif (y_m <= 1.3e+147)
		tmp = fma(z, Float64(-x), fma(Float64(y_m * z), tanh(Float64(t / y_m)), x));
	else
		tmp = fma(z, Float64(t - x), x);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 7.8e-115], x, If[LessEqual[y$95$m, 1.3e+147], N[(z * (-x) + N[(N[(y$95$m * z), $MachinePrecision] * N[Tanh[N[(t / y$95$m), $MachinePrecision]], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(z * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.7999999999999997e-115

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 64.4%

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

   if 7.7999999999999997e-115 < y < 1.2999999999999999e147

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 74.1

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

   5. Simplified 74.1%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. div-inv N/A

         \[\leadsto x + \left(y \cdot z\right) \cdot \left(\left(\mathsf{neg}\left(\color{blue}{x \cdot \frac{1}{y}}\right)\right) + \tanh \left(\frac{t}{y}\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto x + \left(y \cdot z\right) \cdot \left(\color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{y}} + \tanh \left(\frac{t}{y}\right)\right) \]

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

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

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

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

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

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

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

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

      9. /-lowering-/.f64 74.1

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

   7. Applied egg-rr 74.1%

      \[\leadsto x + \left(y \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-x, \frac{1}{y}, \tanh \left(\frac{t}{y}\right)\right)} \]
   8. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{y} + \tanh \left(\frac{t}{y}\right)\right) + x} \]

      2. distribute-lft-in N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{y}\right) + \left(y \cdot z\right) \cdot \tanh \left(\frac{t}{y}\right)\right)} + x \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{y}\right) + \left(\left(y \cdot z\right) \cdot \tanh \left(\frac{t}{y}\right) + x\right)} \]

      4. un-div-inv N/A

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

      5. associate-*r/ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*l/ N/A

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

      9. associate-*r* N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. div-inv N/A

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

      12. associate-*l* N/A

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

      13. inv-pow N/A

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

      14. pow-plus N/A

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

      15. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(z \cdot {y}^{\color{blue}{0}}, \mathsf{neg}\left(x\right), \left(y \cdot z\right) \cdot \tanh \left(\frac{t}{y}\right) + x\right) \]

      16. metadata-eval N/A

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

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

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

      18. neg-lowering-neg.f64 N/A

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

      19. accelerator-lowering-fma.f64 N/A

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

   9. Applied egg-rr 75.5%

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

   if 1.2999999999999999e147 < y

   1. Initial program 71.1%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 90.0

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

   5. Simplified 90.0%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.8 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{fma}\left(z, -x, \mathsf{fma}\left(y \cdot z, \tanh \left(\frac{t}{y}\right), x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.9% accurate, 14.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 1.1 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t)
 :precision binary64
 (if (<= y_m 1.1e+39) x (fma z (- t x) x)))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 1.1e+39) {
		tmp = x;
	} else {
		tmp = fma(z, (t - x), x);
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 1.1e+39)
		tmp = x;
	else
		tmp = fma(z, Float64(t - x), x);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 1.1e+39], x, N[(z * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.1000000000000001e39

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 64.8%

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

   if 1.1000000000000001e39 < y

   1. Initial program 80.6%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 77.5

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

   5. Simplified 77.5%

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

Alternative 7: 70.7% accurate, 18.4× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 6.2 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t, x\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t) :precision binary64 (if (<= y_m 6.2e+38) x (fma z t x)))

C

y_m = fabs(y);
double code(double x, double y_m, double z, double t) {
	double tmp;
	if (y_m <= 6.2e+38) {
		tmp = x;
	} else {
		tmp = fma(z, t, x);
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	tmp = 0.0
	if (y_m <= 6.2e+38)
		tmp = x;
	else
		tmp = fma(z, t, x);
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := If[LessEqual[y$95$m, 6.2e+38], x, N[(z * t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.20000000000000035e38

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 64.8%

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

   if 6.20000000000000035e38 < y

   1. Initial program 80.6%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 77.5

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

   5. Simplified 77.5%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 69.9%

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

Alternative 8: 59.9% accurate, 239.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z t) :precision binary64 x)

C

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

Fortran

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

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z, double t) {
	return x;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z, t):
	return x

Julia

y_m = abs(y)
function code(x, y_m, z, t)
	return x
end

MATLAB

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

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_, t_] := x

Derivation

1. Initial program 92.7%

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

3. Taylor expanded in x around inf

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

5. Simplified 60.6%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 97.1% 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 2024204 
(FPCore (x y z t)
  :name "SynthBasics:moogVCF from YampaSynth-0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (* y (* z (- (tanh (/ t y)) (tanh (/ x y)))))))

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