SynthBasics:moogVCF from YampaSynth-0.2

Percentage Accurate: 93.6% → 98.0%

Time: 3.8s

Alternatives: 8

Speedup: 0.5×

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\\ \mathbf{if}\;x + \left(y \cdot z\right) \cdot t\_1 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(t\_1 \cdot z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (tanh (/ t y)) (tanh (/ x y)))))
   (if (<= (+ x (* (* y z) t_1)) INFINITY) (fma (* t_1 z) y x) (* (- t x) z))))

C

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

Julia

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

Wolfram

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

   1. Initial program 93.6%

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

      1. 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. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-tanh.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. lift-tanh.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   3. Applied rewrites 93.7%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-tanh.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-tanh.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-tanh.f64 N/A

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

      12. lift-/.f64 N/A

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

      13. lift-tanh.f64 N/A

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

      14. lift-/.f64 N/A

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

      15. lift--.f64 97.0

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

   5. Applied rewrites 97.0%

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

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

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 60.0

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

   4. Applied rewrites 60.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 57.8%

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

   8. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 26.1

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

   10. Applied rewrites 26.1%

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

Alternative 2: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \tanh \left(\frac{t}{y}\right)\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-41}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, t\_1, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t\_1 - \frac{x}{y}\right) \cdot z, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (tanh (/ t y))))
   (if (<= y -2.9e+137)
     (fma (- t x) z x)
     (if (<= y 8.2e-41) (fma (* z y) t_1 x) (fma (* (- t_1 (/ x y)) z) y x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = tanh((t / y));
	double tmp;
	if (y <= -2.9e+137) {
		tmp = fma((t - x), z, x);
	} else if (y <= 8.2e-41) {
		tmp = fma((z * y), t_1, x);
	} else {
		tmp = fma(((t_1 - (x / y)) * z), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = tanh(Float64(t / y))
	tmp = 0.0
	if (y <= -2.9e+137)
		tmp = fma(Float64(t - x), z, x);
	elseif (y <= 8.2e-41)
		tmp = fma(Float64(z * y), t_1, x);
	else
		tmp = fma(Float64(Float64(t_1 - Float64(x / y)) * z), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, -2.9e+137], N[(N[(t - x), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[y, 8.2e-41], N[(N[(z * y), $MachinePrecision] * t$95$1 + x), $MachinePrecision], N[(N[(N[(t$95$1 - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.89999999999999985e137

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 60.0

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

   4. Applied rewrites 60.0%

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

   if -2.89999999999999985e137 < y < 8.20000000000000028e-41

   1. Initial program 93.6%

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

   2. Taylor expanded in x around 0

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

      1. associate-/r* N/A

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

      2. div-sub N/A

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

      3. rec-exp N/A

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

      4. rec-exp N/A

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

      5. tanh-def-a N/A

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

      6. lift-tanh.f64 N/A

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

      7. lift-/.f64 79.2

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

   4. Applied rewrites 79.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 79.2

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 79.2

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

   6. Applied rewrites 79.2%

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

   if 8.20000000000000028e-41 < y

   1. Initial program 93.6%

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

      1. 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. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-tanh.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. lift-tanh.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   3. Applied rewrites 93.7%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-tanh.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-tanh.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-tanh.f64 N/A

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

      12. lift-/.f64 N/A

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

      13. lift-tanh.f64 N/A

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

      14. lift-/.f64 N/A

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

      15. lift--.f64 97.0

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

   5. Applied rewrites 97.0%

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

   6. Taylor expanded in x around 0

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

      1. lift-/.f64 67.7

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

   8. Applied rewrites 67.7%

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

Alternative 3: 83.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \tanh \left(\frac{t}{y}\right)\\ t_2 := x + \left(y \cdot z\right) \cdot \left(t\_1 - \tanh \left(\frac{x}{y}\right)\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+303}:\\ \;\;\;\;\mathsf{fma}\left(t - x, z, x\right)\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, t\_1, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (tanh (/ t y))) (t_2 (+ x (* (* y z) (- t_1 (tanh (/ x y)))))))
   (if (<= t_2 -2e+303)
     (fma (- t x) z x)
     (if (<= t_2 INFINITY) (fma (* z y) t_1 x) (* (- t x) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = tanh((t / y));
	double t_2 = x + ((y * z) * (t_1 - tanh((x / y))));
	double tmp;
	if (t_2 <= -2e+303) {
		tmp = fma((t - x), z, x);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = fma((z * y), t_1, x);
	} else {
		tmp = (t - x) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = tanh(Float64(t / y))
	t_2 = Float64(x + Float64(Float64(y * z) * Float64(t_1 - tanh(Float64(x / y)))))
	tmp = 0.0
	if (t_2 <= -2e+303)
		tmp = fma(Float64(t - x), z, x);
	elseif (t_2 <= Inf)
		tmp = fma(Float64(z * y), t_1, x);
	else
		tmp = Float64(Float64(t - x) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] * N[(t$95$1 - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+303], N[(N[(t - x), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(z * y), $MachinePrecision] * t$95$1 + x), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * z), $MachinePrecision]]]]]

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))))) < -2e303

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 60.0

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

   4. Applied rewrites 60.0%

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

   if -2e303 < (+.f64 x (*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) < +inf.0

   1. Initial program 93.6%

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

   2. Taylor expanded in x around 0

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

      1. associate-/r* N/A

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

      2. div-sub N/A

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

      3. rec-exp N/A

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

      4. rec-exp N/A

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

      5. tanh-def-a N/A

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

      6. lift-tanh.f64 N/A

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

      7. lift-/.f64 79.2

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

   4. Applied rewrites 79.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 79.2

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 79.2

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

   6. Applied rewrites 79.2%

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

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

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 60.0

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

   4. Applied rewrites 60.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 57.8%

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

   8. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 26.1

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

   10. Applied rewrites 26.1%

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

Alternative 4: 69.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, z, x\right)\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -30000000:\\ \;\;\;\;\left(z \cdot y\right) \cdot \tanh \left(\frac{t}{y}\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{t} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (- t x) z x)))
   (if (<= y -4.9e+30)
     t_1
     (if (<= y -30000000.0)
       (* (* z y) (tanh (/ t y)))
       (if (<= y 2.5e-43) (* (/ x t) t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((t - x), z, x);
	double tmp;
	if (y <= -4.9e+30) {
		tmp = t_1;
	} else if (y <= -30000000.0) {
		tmp = (z * y) * tanh((t / y));
	} else if (y <= 2.5e-43) {
		tmp = (x / t) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(t - x), z, x)
	tmp = 0.0
	if (y <= -4.9e+30)
		tmp = t_1;
	elseif (y <= -30000000.0)
		tmp = Float64(Float64(z * y) * tanh(Float64(t / y)));
	elseif (y <= 2.5e-43)
		tmp = Float64(Float64(x / t) * t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[y, -4.9e+30], t$95$1, If[LessEqual[y, -30000000.0], N[(N[(z * y), $MachinePrecision] * N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-43], N[(N[(x / t), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.89999999999999984e30 or 2.50000000000000009e-43 < y

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 60.0

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

   4. Applied rewrites 60.0%

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

   if -4.89999999999999984e30 < y < -3e7

   1. Initial program 93.6%

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

   2. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. associate-/r* N/A

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

      3. div-sub N/A

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

      4. rec-exp N/A

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

      5. rec-exp N/A

         \[\leadsto \left(y \cdot z\right) \cdot \frac{e^{\frac{t}{y}} - e^{\mathsf{neg}\left(\frac{t}{y}\right)}}{e^{\frac{t}{y}} + e^{\mathsf{neg}\left(\frac{t}{y}\right)}} \]

      6. tanh-def-a N/A

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

   4. Applied rewrites 24.0%

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

   if -3e7 < y < 2.50000000000000009e-43

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 60.0

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

   4. Applied rewrites 60.0%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lower-neg.f64 51.1

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

   7. Applied rewrites 51.1%

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

   8. Taylor expanded in z around 0

      \[\leadsto \frac{x}{t} \cdot t \]
   9. Step-by-step derivation

      1. lower-/.f64 49.0

         \[\leadsto \frac{x}{t} \cdot t \]

   10. Applied rewrites 49.0%

       \[\leadsto \frac{x}{t} \cdot t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 68.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, z, x\right)\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{t} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (- t x) z x)))
   (if (<= y -2.8e-30) t_1 (if (<= y 2.5e-43) (* (/ x t) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((t - x), z, x);
	double tmp;
	if (y <= -2.8e-30) {
		tmp = t_1;
	} else if (y <= 2.5e-43) {
		tmp = (x / t) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(t - x), z, x)
	tmp = 0.0
	if (y <= -2.8e-30)
		tmp = t_1;
	elseif (y <= 2.5e-43)
		tmp = Float64(Float64(x / t) * t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[y, -2.8e-30], t$95$1, If[LessEqual[y, 2.5e-43], N[(N[(x / t), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.79999999999999988e-30 or 2.50000000000000009e-43 < y

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 60.0

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

   4. Applied rewrites 60.0%

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

   if -2.79999999999999988e-30 < y < 2.50000000000000009e-43

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 60.0

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

   4. Applied rewrites 60.0%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lower-neg.f64 51.1

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

   7. Applied rewrites 51.1%

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

   8. Taylor expanded in z around 0

      \[\leadsto \frac{x}{t} \cdot t \]
   9. Step-by-step derivation

      1. lower-/.f64 49.0

         \[\leadsto \frac{x}{t} \cdot t \]

   10. Applied rewrites 49.0%

       \[\leadsto \frac{x}{t} \cdot t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 61.0% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) z))
        (t_2 (+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 INFINITY) (fma t z x) t_1))))

C

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

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - x) * z)
	t_2 = Float64(x + Float64(Float64(y * z) * Float64(tanh(Float64(t / y)) - tanh(Float64(x / y)))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= Inf)
		tmp = fma(t, z, x);
	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[(x + N[(N[(y * z), $MachinePrecision] * N[(N[Tanh[N[(t / y), $MachinePrecision]], $MachinePrecision] - N[Tanh[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, Infinity], N[(t * z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 60.0

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

   4. Applied rewrites 60.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 57.8%

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

   8. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 26.1

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

   10. Applied rewrites 26.1%

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

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

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 60.0

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

   4. Applied rewrites 60.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 57.8%

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

Alternative 7: 57.8% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(t, z, x\right) \end{array} \]

FPCore

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

C

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

Julia

function code(x, y, z, t)
	return fma(t, z, x)
end

Wolfram

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

Derivation

1. Initial program 93.6%

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

2. Taylor expanded in y around inf

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lower--.f64 60.0

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

4. Applied rewrites 60.0%

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

5. Taylor expanded in x around 0

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

7. Applied rewrites 57.8%

   \[\leadsto \mathsf{fma}\left(t, z, x\right) \]
8. Add Preprocessing

Alternative 8: 16.0% accurate, 8.8× 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 93.6%

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

2. Taylor expanded in y around inf

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lower--.f64 60.0

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

4. Applied rewrites 60.0%

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

5. Taylor expanded in x around 0

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

   1. *-commutative N/A

      \[\leadsto z \cdot t \]

   2. lower-*.f64 16.0

      \[\leadsto z \cdot t \]

7. Applied rewrites 16.0%

   \[\leadsto z \cdot \color{blue}{t} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025139 
(FPCore (x y z t)
  :name "SynthBasics:moogVCF from YampaSynth-0.2"
  :precision binary64
  (+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))))