SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.6% → 97.9%

Time: 10.3s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.4%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lift-*.f64 N/A

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

   6. associate-*r* N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-*.f64 97.2

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

4. Applied rewrites 97.2%

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

Alternative 2: 64.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot z\\ t_2 := \left(z \cdot y\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) + x\\ t_3 := z \cdot t + x\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{-160}:\\ \;\;\;\;\mathsf{fma}\left(-x, z, x\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+307}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) z))
        (t_2 (+ (* (* z y) (- (tanh (/ t y)) (tanh (/ x y)))) x))
        (t_3 (+ (* z t) x)))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e+17)
       t_3
       (if (<= t_2 4e-160) (fma (- x) z x) (if (<= t_2 1e+307) t_3 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * z;
	double t_2 = ((z * y) * (tanh((t / y)) - tanh((x / y)))) + x;
	double t_3 = (z * t) + x;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e+17) {
		tmp = t_3;
	} else if (t_2 <= 4e-160) {
		tmp = fma(-x, z, x);
	} else if (t_2 <= 1e+307) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - x) * z)
	t_2 = Float64(Float64(Float64(z * y) * Float64(tanh(Float64(t / y)) - tanh(Float64(x / y)))) + x)
	t_3 = Float64(Float64(z * t) + x)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e+17)
		tmp = t_3;
	elseif (t_2 <= 4e-160)
		tmp = fma(Float64(-x), z, x);
	elseif (t_2 <= 1e+307)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z * y), $MachinePrecision] * N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e+17], t$95$3, If[LessEqual[t$95$2, 4e-160], N[((-x) * z + x), $MachinePrecision], If[LessEqual[t$95$2, 1e+307], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < -inf.0 or 9.99999999999999986e306 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

   1. Initial program 59.5%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 100.0%

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

   if -inf.0 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < -5e17 or 4e-160 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < 9.99999999999999986e306

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 54.4

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

   5. Applied rewrites 54.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 64.3%

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

   if -5e17 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < 4e-160

   1. Initial program 94.0%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 48.5

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

   5. Applied rewrites 48.5%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(-1 \cdot x, z, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 53.0%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot y\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) + x \leq -\infty:\\ \;\;\;\;\left(t - x\right) \cdot z\\ \mathbf{elif}\;\left(z \cdot y\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) + x \leq -5 \cdot 10^{+17}:\\ \;\;\;\;z \cdot t + x\\ \mathbf{elif}\;\left(z \cdot y\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) + x \leq 4 \cdot 10^{-160}:\\ \;\;\;\;\mathsf{fma}\left(-x, z, x\right)\\ \mathbf{elif}\;\left(z \cdot y\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) + x \leq 10^{+307}:\\ \;\;\;\;z \cdot t + x\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{-57}:\\ \;\;\;\;{\left(\frac{\frac{\mathsf{fma}\left(y, x, \frac{x \cdot y}{t} \cdot x\right)}{t} + y}{t}\right)}^{-1} \cdot \left(z \cdot y\right) + x\\ \mathbf{elif}\;y \leq 3.85 \cdot 10^{+14}:\\ \;\;\;\;{\left(\frac{\mathsf{fma}\left(\frac{x \cdot x}{t}, \frac{y}{t}, \mathsf{fma}\left(y, \frac{x}{t}, y\right)\right)}{t}\right)}^{-1} \cdot \left(z \cdot y\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t, \left(-x\right) \cdot z\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.8e-57)
   (+ (* (pow (/ (+ (/ (fma y x (* (/ (* x y) t) x)) t) y) t) -1.0) (* z y)) x)
   (if (<= y 3.85e+14)
     (+
      (*
       (pow (/ (fma (/ (* x x) t) (/ y t) (fma y (/ x t) y)) t) -1.0)
       (* z y))
      x)
     (+ (fma z t (* (- x) z)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.8e-57) {
		tmp = (pow((((fma(y, x, (((x * y) / t) * x)) / t) + y) / t), -1.0) * (z * y)) + x;
	} else if (y <= 3.85e+14) {
		tmp = (pow((fma(((x * x) / t), (y / t), fma(y, (x / t), y)) / t), -1.0) * (z * y)) + x;
	} else {
		tmp = fma(z, t, (-x * z)) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.8e-57)
		tmp = Float64(Float64((Float64(Float64(Float64(fma(y, x, Float64(Float64(Float64(x * y) / t) * x)) / t) + y) / t) ^ -1.0) * Float64(z * y)) + x);
	elseif (y <= 3.85e+14)
		tmp = Float64(Float64((Float64(fma(Float64(Float64(x * x) / t), Float64(y / t), fma(y, Float64(x / t), y)) / t) ^ -1.0) * Float64(z * y)) + x);
	else
		tmp = Float64(fma(z, t, Float64(Float64(-x) * z)) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.8e-57], N[(N[(N[Power[N[(N[(N[(N[(y * x + N[(N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision] / t), $MachinePrecision], -1.0], $MachinePrecision] * N[(z * y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[y, 3.85e+14], N[(N[(N[Power[N[(N[(N[(N[(x * x), $MachinePrecision] / t), $MachinePrecision] * N[(y / t), $MachinePrecision] + N[(y * N[(x / t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], -1.0], $MachinePrecision] * N[(z * y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(z * t + N[((-x) * z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.8000000000000001e-57

   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 y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 40.8

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

   5. Applied rewrites 40.8%

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

   7. Applied rewrites 40.7%

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

   8. Taylor expanded in t around -inf

      \[\leadsto x + \left(y \cdot z\right) \cdot \frac{1}{-1 \cdot \color{blue}{\frac{-1 \cdot y + -1 \cdot \frac{x \cdot y + \frac{{x}^{2} \cdot y}{t}}{t}}{t}}} \]
   9. Step-by-step derivation

   10. Applied rewrites 56.3%

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

   if 1.8000000000000001e-57 < y < 3.85e14

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 39.2

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

   5. Applied rewrites 39.2%

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

   7. Applied rewrites 39.3%

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

   8. Taylor expanded in t around inf

      \[\leadsto x + \left(y \cdot z\right) \cdot \frac{1}{\frac{\left(y + \frac{{x}^{2} \cdot y}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot y}{t}}{\color{blue}{t}}} \]
   9. Step-by-step derivation

   10. Applied rewrites 57.7%

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

   if 3.85e14 < y

   1. Initial program 85.2%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.8

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

   5. Applied rewrites 83.8%

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

   7. Applied rewrites 83.8%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{-57}:\\ \;\;\;\;{\left(\frac{\frac{\mathsf{fma}\left(y, x, \frac{x \cdot y}{t} \cdot x\right)}{t} + y}{t}\right)}^{-1} \cdot \left(z \cdot y\right) + x\\ \mathbf{elif}\;y \leq 3.85 \cdot 10^{+14}:\\ \;\;\;\;{\left(\frac{\mathsf{fma}\left(\frac{x \cdot x}{t}, \frac{y}{t}, \mathsf{fma}\left(y, \frac{x}{t}, y\right)\right)}{t}\right)}^{-1} \cdot \left(z \cdot y\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t, \left(-x\right) \cdot z\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.18 \cdot 10^{-63}:\\ \;\;\;\;{\left(\frac{\frac{\mathsf{fma}\left(y, x, \frac{x \cdot y}{t} \cdot x\right)}{t} + y}{t}\right)}^{-1} \cdot \left(z \cdot y\right) + x\\ \mathbf{elif}\;y \leq 10^{+177}:\\ \;\;\;\;\mathsf{fma}\left(\left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right) \cdot y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t, \left(-x\right) \cdot z\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.18e-63)
   (+ (* (pow (/ (+ (/ (fma y x (* (/ (* x y) t) x)) t) y) t) -1.0) (* z y)) x)
   (if (<= y 1e+177)
     (fma (* (- (/ t y) (tanh (/ x y))) y) z x)
     (+ (fma z t (* (- x) z)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.18e-63) {
		tmp = (pow((((fma(y, x, (((x * y) / t) * x)) / t) + y) / t), -1.0) * (z * y)) + x;
	} else if (y <= 1e+177) {
		tmp = fma((((t / y) - tanh((x / y))) * y), z, x);
	} else {
		tmp = fma(z, t, (-x * z)) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.18e-63)
		tmp = Float64(Float64((Float64(Float64(Float64(fma(y, x, Float64(Float64(Float64(x * y) / t) * x)) / t) + y) / t) ^ -1.0) * Float64(z * y)) + x);
	elseif (y <= 1e+177)
		tmp = fma(Float64(Float64(Float64(t / y) - tanh(Float64(x / y))) * y), z, x);
	else
		tmp = Float64(fma(z, t, Float64(Float64(-x) * z)) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.18e-63], N[(N[(N[Power[N[(N[(N[(N[(y * x + N[(N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision] / t), $MachinePrecision], -1.0], $MachinePrecision] * N[(z * y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[y, 1e+177], N[(N[(N[(N[(t / y), $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(z * t + N[((-x) * z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.17999999999999999e-63

   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. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 40.3

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

   5. Applied rewrites 40.3%

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

   7. Applied rewrites 40.3%

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

   8. Taylor expanded in t around -inf

      \[\leadsto x + \left(y \cdot z\right) \cdot \frac{1}{-1 \cdot \color{blue}{\frac{-1 \cdot y + -1 \cdot \frac{x \cdot y + \frac{{x}^{2} \cdot y}{t}}{t}}{t}}} \]
   9. Step-by-step derivation

   10. Applied rewrites 56.1%

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

   if 1.17999999999999999e-63 < y < 1e177

   1. Initial program 92.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 98.1

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

   4. Applied rewrites 98.1%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 70.2

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

   7. Applied rewrites 70.2%

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

   if 1e177 < y

   1. Initial program 81.4%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 96.6

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

   5. Applied rewrites 96.6%

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

   7. Applied rewrites 96.6%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.18 \cdot 10^{-63}:\\ \;\;\;\;{\left(\frac{\frac{\mathsf{fma}\left(y, x, \frac{x \cdot y}{t} \cdot x\right)}{t} + y}{t}\right)}^{-1} \cdot \left(z \cdot y\right) + x\\ \mathbf{elif}\;y \leq 10^{+177}:\\ \;\;\;\;\mathsf{fma}\left(\left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right) \cdot y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t, \left(-x\right) \cdot z\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.6 \cdot 10^{+30}:\\ \;\;\;\;{\left(\frac{\frac{\mathsf{fma}\left(y, x, \frac{x \cdot y}{t} \cdot x\right)}{t} + y}{t}\right)}^{-1} \cdot \left(z \cdot y\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t, \left(-x\right) \cdot z\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 6.6e+30)
   (+ (* (pow (/ (+ (/ (fma y x (* (/ (* x y) t) x)) t) y) t) -1.0) (* z y)) x)
   (+ (fma z t (* (- x) z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6.6e+30) {
		tmp = (pow((((fma(y, x, (((x * y) / t) * x)) / t) + y) / t), -1.0) * (z * y)) + x;
	} else {
		tmp = fma(z, t, (-x * z)) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 6.6e+30)
		tmp = Float64(Float64((Float64(Float64(Float64(fma(y, x, Float64(Float64(Float64(x * y) / t) * x)) / t) + y) / t) ^ -1.0) * Float64(z * y)) + x);
	else
		tmp = Float64(fma(z, t, Float64(Float64(-x) * z)) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 6.6e+30], N[(N[(N[Power[N[(N[(N[(N[(y * x + N[(N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision] / t), $MachinePrecision], -1.0], $MachinePrecision] * N[(z * y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(z * t + N[((-x) * z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.60000000000000053e30

   1. Initial program 95.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 40.7

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

   5. Applied rewrites 40.7%

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

   7. Applied rewrites 40.6%

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

   8. Taylor expanded in t around -inf

      \[\leadsto x + \left(y \cdot z\right) \cdot \frac{1}{-1 \cdot \color{blue}{\frac{-1 \cdot y + -1 \cdot \frac{x \cdot y + \frac{{x}^{2} \cdot y}{t}}{t}}{t}}} \]
   9. Step-by-step derivation

   10. Applied rewrites 55.2%

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

   if 6.60000000000000053e30 < y

   1. Initial program 84.4%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 86.2

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

   5. Applied rewrites 86.2%

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

   7. Applied rewrites 86.2%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.6 \cdot 10^{+30}:\\ \;\;\;\;{\left(\frac{\frac{\mathsf{fma}\left(y, x, \frac{x \cdot y}{t} \cdot x\right)}{t} + y}{t}\right)}^{-1} \cdot \left(z \cdot y\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t, \left(-x\right) \cdot z\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(\left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right) \cdot y, z, x\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+173}:\\ \;\;\;\;\mathsf{fma}\left(\left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right) \cdot y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.6e+48)
   (fma (* (- (/ t y) (tanh (/ x y))) y) z x)
   (if (<= x 5.4e+173)
     (fma (* (- (tanh (/ t y)) (/ x y)) y) z x)
     (+ (* z t) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.6e+48) {
		tmp = fma((((t / y) - tanh((x / y))) * y), z, x);
	} else if (x <= 5.4e+173) {
		tmp = fma(((tanh((t / y)) - (x / y)) * y), z, x);
	} else {
		tmp = (z * t) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.6e+48)
		tmp = fma(Float64(Float64(Float64(t / y) - tanh(Float64(x / y))) * y), z, x);
	elseif (x <= 5.4e+173)
		tmp = fma(Float64(Float64(tanh(Float64(t / y)) - Float64(x / y)) * y), z, x);
	else
		tmp = Float64(Float64(z * t) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.6e+48], N[(N[(N[(N[(t / y), $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[x, 5.4e+173], N[(N[(N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(z * t), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.60000000000000001e48

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 73.7

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

   7. Applied rewrites 73.7%

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

   if -7.60000000000000001e48 < x < 5.4000000000000002e173

   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. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 96.1

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

   4. Applied rewrites 96.1%

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

   5. Taylor expanded in y around inf

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

      1. lower-/.f64 80.4

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

   7. Applied rewrites 80.4%

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

   if 5.4000000000000002e173 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 61.0

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

   5. Applied rewrites 61.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 91.7%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(\left(\frac{t}{y} - \tanh \left(\frac{x}{y}\right)\right) \cdot y, z, x\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+173}:\\ \;\;\;\;\mathsf{fma}\left(\left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right) \cdot y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.5% accurate, 10.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.55 \cdot 10^{-80}:\\ \;\;\;\;z \cdot t + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t, \left(-x\right) \cdot z\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.55e-80) (+ (* z t) x) (+ (fma z t (* (- x) z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.55e-80) {
		tmp = (z * t) + x;
	} else {
		tmp = fma(z, t, (-x * z)) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.55e-80)
		tmp = Float64(Float64(z * t) + x);
	else
		tmp = Float64(fma(z, t, Float64(Float64(-x) * z)) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.55e-80], N[(N[(z * t), $MachinePrecision] + x), $MachinePrecision], N[(N[(z * t + N[((-x) * z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.55000000000000004e-80

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.6

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

   5. Applied rewrites 52.6%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 59.0%

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

   if 2.55000000000000004e-80 < 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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.8

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

   5. Applied rewrites 72.8%

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

   7. Applied rewrites 72.8%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.55 \cdot 10^{-80}:\\ \;\;\;\;z \cdot t + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t, \left(-x\right) \cdot z\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.1% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.014 \lor \neg \left(z \leq 0.029\right):\\ \;\;\;\;\left(t - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.014) (not (<= z 0.029))) (* (- t x) z) (fma (- x) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.014) || !(z <= 0.029)) {
		tmp = (t - x) * z;
	} else {
		tmp = fma(-x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.014) || !(z <= 0.029))
		tmp = Float64(Float64(t - x) * z);
	else
		tmp = fma(Float64(-x), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.014], N[Not[LessEqual[z, 0.029]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * z), $MachinePrecision], N[((-x) * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0140000000000000003 or 0.0290000000000000015 < z

   1. Initial program 88.4%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 46.0

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

   5. Applied rewrites 46.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 45.5%

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

   if -0.0140000000000000003 < z < 0.0290000000000000015

   1. Initial program 99.5%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 74.7

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

   5. Applied rewrites 74.7%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(-1 \cdot x, z, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 79.1%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.014 \lor \neg \left(z \leq 0.029\right):\\ \;\;\;\;\left(t - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 20.8% accurate, 11.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-86} \lor \neg \left(x \leq 5 \cdot 10^{-64}\right):\\ \;\;\;\;\left(-x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.1e-86) (not (<= x 5e-64))) (* (- x) z) (* z t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.1e-86) || !(x <= 5e-64)) {
		tmp = -x * z;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.1d-86)) .or. (.not. (x <= 5d-64))) then
        tmp = -x * z
    else
        tmp = z * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.1e-86) || !(x <= 5e-64)) {
		tmp = -x * z;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.1e-86) or not (x <= 5e-64):
		tmp = -x * z
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.1e-86) || !(x <= 5e-64))
		tmp = Float64(Float64(-x) * z);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.1e-86) || ~((x <= 5e-64)))
		tmp = -x * z;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.1e-86], N[Not[LessEqual[x, 5e-64]], $MachinePrecision]], N[((-x) * z), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.09999999999999989e-86 or 5.00000000000000033e-64 < x

   1. Initial program 95.7%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 58.9

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

   5. Applied rewrites 58.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 21.2%

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

   9. Taylor expanded in t around 0

      \[\leadsto \left(-1 \cdot x\right) \cdot z \]
   10. Step-by-step derivation

   11. Applied rewrites 17.1%

       \[\leadsto \left(-x\right) \cdot z \]

   if -3.09999999999999989e-86 < x < 5.00000000000000033e-64

   1. Initial program 90.0%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 59.2

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

   5. Applied rewrites 59.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 38.4%

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

4. Final simplification 25.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-86} \lor \neg \left(x \leq 5 \cdot 10^{-64}\right):\\ \;\;\;\;\left(-x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.6% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.55 \cdot 10^{-80}:\\ \;\;\;\;z \cdot t + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.55e-80) (+ (* z t) x) (fma (- t x) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.55e-80) {
		tmp = (z * t) + x;
	} else {
		tmp = fma((t - x), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.55e-80)
		tmp = Float64(Float64(z * t) + x);
	else
		tmp = fma(Float64(t - x), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.55e-80], N[(N[(z * t), $MachinePrecision] + x), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.55000000000000004e-80

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.6

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

   5. Applied rewrites 52.6%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 59.0%

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

   if 2.55000000000000004e-80 < 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. 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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 72.8

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

   5. Applied rewrites 72.8%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.55 \cdot 10^{-80}:\\ \;\;\;\;z \cdot t + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 26.8% accurate, 26.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.4%

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

3. Taylor expanded in 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. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lower--.f64 59.0

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

5. Applied rewrites 59.0%

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

6. Taylor expanded in z around inf

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

8. Applied rewrites 30.2%

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

Alternative 12: 16.9% accurate, 39.8× speedup

Math

\[\begin{array}{l} \\ z \cdot t \end{array} \]

FPCore

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

C

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

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 = z * t
end function

Java

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

Python

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

Julia

function code(x, y, z, t)
	return Float64(z * t)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(z * t), $MachinePrecision]

Derivation

1. Initial program 93.4%

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

3. Taylor expanded in 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. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lower--.f64 59.0

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

5. Applied rewrites 59.0%

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

6. Taylor expanded in t around inf

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

8. Applied rewrites 20.4%

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

9. Final simplification 20.4%

   \[\leadsto z \cdot t \]
10. 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 2024271 
(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))))))