Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B

Percentage Accurate: 99.8% → 99.9%

Time: 3.2s

Alternatives: 13

Speedup: 1.2×

• 73.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

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) + z) + y) + t)) + (y * 5.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

Python

def code(x, y, z, t):
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(Float64(Float64(Float64(y + z) + z) + y) + t)) + Float64(y * 5.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(N[(N[(N[(y + z), $MachinePrecision] + z), $MachinePrecision] + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

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) + z) + y) + t)) + (y * 5.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

Python

def code(x, y, z, t):
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(Float64(Float64(Float64(y + z) + z) + y) + t)) + Float64(y * 5.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(N[(N[(N[(y + z), $MachinePrecision] + z), $MachinePrecision] + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.2× speedup

Math

\[\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, z + y, t\right) \cdot x\right) \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (fma y 5.0 (* (fma 2.0 (+ z y) t) x)))

C

double code(double x, double y, double z, double t) {
	return fma(y, 5.0, (fma(2.0, (z + y), t) * x));
}

Julia

function code(x, y, z, t)
	return fma(y, 5.0, Float64(fma(2.0, Float64(z + y), t) * x))
end

Wolfram

code[x_, y_, z_, t_] := N[(y * 5.0 + N[(N[(2.0 * N[(z + y), $MachinePrecision] + t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
2. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{y \cdot 5} + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \]

   4. lower-fma.f64 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

   5. lift-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

   7. lower-*.f64 99.9%

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

   8. lift-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \cdot x\right) \]

   9. lift-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t\right) \cdot x\right) \]

   10. lift-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t\right) \cdot x\right) \]

   11. associate-+l+ N/A

       \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) \cdot x\right) \]

   12. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

   13. lift-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

   14. count-2 N/A

       \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{2 \cdot \left(y + z\right)} + t\right) \cdot x\right) \]

   15. lower-fma.f64 99.9%

       \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y + z, t\right)} \cdot x\right) \]

   16. lift-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{y + z}, t\right) \cdot x\right) \]

   17. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

   18. lower-+.f64 99.9%

       \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

3. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, z + y, t\right) \cdot x\right)} \]
4. Add Preprocessing

Alternative 2: 91.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-51}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + z\right) + z, x, 5 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (fma 5.0 y (* x (+ t (* 2.0 y))))))
  (if (<= y -5.8e+46)
    t_1
    (if (<= y 2.6e-51) (fma (+ (+ t z) z) x (* 5.0 y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(5.0, y, (x * (t + (2.0 * y))));
	double tmp;
	if (y <= -5.8e+46) {
		tmp = t_1;
	} else if (y <= 2.6e-51) {
		tmp = fma(((t + z) + z), x, (5.0 * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(5.0, y, Float64(x * Float64(t + Float64(2.0 * y))))
	tmp = 0.0
	if (y <= -5.8e+46)
		tmp = t_1;
	elseif (y <= 2.6e-51)
		tmp = fma(Float64(Float64(t + z) + z), x, Float64(5.0 * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(5.0 * y + N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+46], t$95$1, If[LessEqual[y, 2.6e-51], N[(N[(N[(t + z), $MachinePrecision] + z), $MachinePrecision] * x + N[(5.0 * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8000000000000004e46 or 2.6e-51 < y

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{5 \cdot y + x \cdot \left(t + 2 \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(5, \color{blue}{y}, x \cdot \left(t + 2 \cdot y\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right) \]

      4. lower-*.f64 74.9%

         \[\leadsto \mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right) \]

   4. Applied rewrites 74.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right)} \]

   if -5.8000000000000004e46 < y < 2.6e-51

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x} + y \cdot 5 \]

      4. lower-fma.f64 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t, x, y \cdot 5\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right) + t}, x, y \cdot 5\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t, x, y \cdot 5\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t, x, y \cdot 5\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, x, y \cdot 5\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(y + z\right)} + t, x, y \cdot 5\right) \]

      12. lower-fma.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y + z, t\right)}, x, y \cdot 5\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{y + z}, t\right), x, y \cdot 5\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      15. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{y \cdot 5}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

      18. lower-*.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, 5 \cdot y\right)} \]

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z}, t\right), x, 5 \cdot y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 84.3%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z}, t\right), x, 5 \cdot y\right) \]
   7. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot z + t}, x, 5 \cdot y\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{t + 2 \cdot z}, x, 5 \cdot y\right) \]

      3. count-2-rev N/A

         \[\leadsto \mathsf{fma}\left(t + \color{blue}{\left(z + z\right)}, x, 5 \cdot y\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + z\right) + z}, x, 5 \cdot y\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + z\right) + z}, x, 5 \cdot y\right) \]

      6. lower-+.f64 84.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + z\right)} + z, x, 5 \cdot y\right) \]

   8. Applied rewrites 84.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + z\right) + z}, x, 5 \cdot y\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 90.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, 5\right), x \cdot t\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-51}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + z\right) + z, x, 5 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (fma y (fma x 2.0 5.0) (* x t))))
  (if (<= y -5.8e+46)
    t_1
    (if (<= y 2.6e-51) (fma (+ (+ t z) z) x (* 5.0 y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(y, fma(x, 2.0, 5.0), (x * t));
	double tmp;
	if (y <= -5.8e+46) {
		tmp = t_1;
	} else if (y <= 2.6e-51) {
		tmp = fma(((t + z) + z), x, (5.0 * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(y, fma(x, 2.0, 5.0), Float64(x * t))
	tmp = 0.0
	if (y <= -5.8e+46)
		tmp = t_1;
	elseif (y <= 2.6e-51)
		tmp = fma(Float64(Float64(t + z) + z), x, Float64(5.0 * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * 2.0 + 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+46], t$95$1, If[LessEqual[y, 2.6e-51], N[(N[(N[(t + z), $MachinePrecision] + z), $MachinePrecision] * x + N[(5.0 * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8000000000000004e46 or 2.6e-51 < y

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{5 \cdot y + x \cdot \left(t + 2 \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(5, \color{blue}{y}, x \cdot \left(t + 2 \cdot y\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right) \]

      4. lower-*.f64 74.9%

         \[\leadsto \mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right) \]

   4. Applied rewrites 74.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto 5 \cdot y + \color{blue}{x \cdot \left(t + 2 \cdot y\right)} \]

      2. *-commutative N/A

         \[\leadsto y \cdot 5 + \color{blue}{x} \cdot \left(t + 2 \cdot y\right) \]

      3. lift-*.f64 N/A

         \[\leadsto y \cdot 5 + \color{blue}{x} \cdot \left(t + 2 \cdot y\right) \]

      4. lift-*.f64 N/A

         \[\leadsto y \cdot 5 + x \cdot \color{blue}{\left(t + 2 \cdot y\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto y \cdot 5 + x \cdot \left(t + \color{blue}{2 \cdot y}\right) \]

      6. +-commutative N/A

         \[\leadsto y \cdot 5 + x \cdot \left(2 \cdot y + \color{blue}{t}\right) \]

      7. distribute-lft-in N/A

         \[\leadsto y \cdot 5 + \left(x \cdot \left(2 \cdot y\right) + \color{blue}{x \cdot t}\right) \]

      8. *-commutative N/A

         \[\leadsto y \cdot 5 + \left(x \cdot \left(2 \cdot y\right) + t \cdot \color{blue}{x}\right) \]

      9. lift-*.f64 N/A

         \[\leadsto y \cdot 5 + \left(x \cdot \left(2 \cdot y\right) + t \cdot \color{blue}{x}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \left(y \cdot 5 + x \cdot \left(2 \cdot y\right)\right) + \color{blue}{t \cdot x} \]

      11. +-commutative N/A

          \[\leadsto \left(x \cdot \left(2 \cdot y\right) + y \cdot 5\right) + \color{blue}{t} \cdot x \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(2 \cdot y\right) + y \cdot 5\right) + t \cdot x \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(2 \cdot y\right) + 5 \cdot y\right) + t \cdot x \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(2 \cdot y\right) + 5 \cdot y\right) + t \cdot x \]

      15. associate-*r* N/A

          \[\leadsto \left(\left(x \cdot 2\right) \cdot y + 5 \cdot y\right) + t \cdot x \]

      16. distribute-rgt-out N/A

          \[\leadsto y \cdot \left(x \cdot 2 + 5\right) + \color{blue}{t} \cdot x \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{x \cdot 2 + 5}, t \cdot x\right) \]

      18. lower-fma.f64 73.9%

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(x, \color{blue}{2}, 5\right), t \cdot x\right) \]

      19. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, \color{blue}{5}\right), t \cdot x\right) \]

      20. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, \color{blue}{5}\right), x \cdot t\right) \]

      21. lower-*.f64 73.9%

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, \color{blue}{5}\right), x \cdot t\right) \]

   6. Applied rewrites 73.9%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, 2, 5\right)}, x \cdot t\right) \]

   if -5.8000000000000004e46 < y < 2.6e-51

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x} + y \cdot 5 \]

      4. lower-fma.f64 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t, x, y \cdot 5\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right) + t}, x, y \cdot 5\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t, x, y \cdot 5\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t, x, y \cdot 5\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, x, y \cdot 5\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(y + z\right)} + t, x, y \cdot 5\right) \]

      12. lower-fma.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y + z, t\right)}, x, y \cdot 5\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{y + z}, t\right), x, y \cdot 5\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      15. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{y \cdot 5}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

      18. lower-*.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, 5 \cdot y\right)} \]

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z}, t\right), x, 5 \cdot y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 84.3%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z}, t\right), x, 5 \cdot y\right) \]
   7. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot z + t}, x, 5 \cdot y\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{t + 2 \cdot z}, x, 5 \cdot y\right) \]

      3. count-2-rev N/A

         \[\leadsto \mathsf{fma}\left(t + \color{blue}{\left(z + z\right)}, x, 5 \cdot y\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + z\right) + z}, x, 5 \cdot y\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + z\right) + z}, x, 5 \cdot y\right) \]

      6. lower-+.f64 84.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + z\right)} + z, x, 5 \cdot y\right) \]

   8. Applied rewrites 84.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + z\right) + z}, x, 5 \cdot y\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 90.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, 5\right), x \cdot t\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-51}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(2, z, t\right), x, 5 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (fma y (fma x 2.0 5.0) (* x t))))
  (if (<= y -5.8e+46)
    t_1
    (if (<= y 2.6e-51) (fma (fma 2.0 z t) x (* 5.0 y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(y, fma(x, 2.0, 5.0), (x * t));
	double tmp;
	if (y <= -5.8e+46) {
		tmp = t_1;
	} else if (y <= 2.6e-51) {
		tmp = fma(fma(2.0, z, t), x, (5.0 * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(y, fma(x, 2.0, 5.0), Float64(x * t))
	tmp = 0.0
	if (y <= -5.8e+46)
		tmp = t_1;
	elseif (y <= 2.6e-51)
		tmp = fma(fma(2.0, z, t), x, Float64(5.0 * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * 2.0 + 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+46], t$95$1, If[LessEqual[y, 2.6e-51], N[(N[(2.0 * z + t), $MachinePrecision] * x + N[(5.0 * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8000000000000004e46 or 2.6e-51 < y

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{5 \cdot y + x \cdot \left(t + 2 \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(5, \color{blue}{y}, x \cdot \left(t + 2 \cdot y\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right) \]

      4. lower-*.f64 74.9%

         \[\leadsto \mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right) \]

   4. Applied rewrites 74.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto 5 \cdot y + \color{blue}{x \cdot \left(t + 2 \cdot y\right)} \]

      2. *-commutative N/A

         \[\leadsto y \cdot 5 + \color{blue}{x} \cdot \left(t + 2 \cdot y\right) \]

      3. lift-*.f64 N/A

         \[\leadsto y \cdot 5 + \color{blue}{x} \cdot \left(t + 2 \cdot y\right) \]

      4. lift-*.f64 N/A

         \[\leadsto y \cdot 5 + x \cdot \color{blue}{\left(t + 2 \cdot y\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto y \cdot 5 + x \cdot \left(t + \color{blue}{2 \cdot y}\right) \]

      6. +-commutative N/A

         \[\leadsto y \cdot 5 + x \cdot \left(2 \cdot y + \color{blue}{t}\right) \]

      7. distribute-lft-in N/A

         \[\leadsto y \cdot 5 + \left(x \cdot \left(2 \cdot y\right) + \color{blue}{x \cdot t}\right) \]

      8. *-commutative N/A

         \[\leadsto y \cdot 5 + \left(x \cdot \left(2 \cdot y\right) + t \cdot \color{blue}{x}\right) \]

      9. lift-*.f64 N/A

         \[\leadsto y \cdot 5 + \left(x \cdot \left(2 \cdot y\right) + t \cdot \color{blue}{x}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \left(y \cdot 5 + x \cdot \left(2 \cdot y\right)\right) + \color{blue}{t \cdot x} \]

      11. +-commutative N/A

          \[\leadsto \left(x \cdot \left(2 \cdot y\right) + y \cdot 5\right) + \color{blue}{t} \cdot x \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(2 \cdot y\right) + y \cdot 5\right) + t \cdot x \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(2 \cdot y\right) + 5 \cdot y\right) + t \cdot x \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(2 \cdot y\right) + 5 \cdot y\right) + t \cdot x \]

      15. associate-*r* N/A

          \[\leadsto \left(\left(x \cdot 2\right) \cdot y + 5 \cdot y\right) + t \cdot x \]

      16. distribute-rgt-out N/A

          \[\leadsto y \cdot \left(x \cdot 2 + 5\right) + \color{blue}{t} \cdot x \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{x \cdot 2 + 5}, t \cdot x\right) \]

      18. lower-fma.f64 73.9%

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(x, \color{blue}{2}, 5\right), t \cdot x\right) \]

      19. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, \color{blue}{5}\right), t \cdot x\right) \]

      20. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, \color{blue}{5}\right), x \cdot t\right) \]

      21. lower-*.f64 73.9%

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, \color{blue}{5}\right), x \cdot t\right) \]

   6. Applied rewrites 73.9%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, 2, 5\right)}, x \cdot t\right) \]

   if -5.8000000000000004e46 < y < 2.6e-51

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x} + y \cdot 5 \]

      4. lower-fma.f64 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t, x, y \cdot 5\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right) + t}, x, y \cdot 5\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t, x, y \cdot 5\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t, x, y \cdot 5\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, x, y \cdot 5\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(y + z\right)} + t, x, y \cdot 5\right) \]

      12. lower-fma.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y + z, t\right)}, x, y \cdot 5\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{y + z}, t\right), x, y \cdot 5\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      15. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{y \cdot 5}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

      18. lower-*.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, 5 \cdot y\right)} \]

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z}, t\right), x, 5 \cdot y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 84.3%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z}, t\right), x, 5 \cdot y\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 83.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, 5\right), x \cdot t\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (fma y (fma x 2.0 5.0) (* x t))))
  (if (<= y -5.5e-28)
    t_1
    (if (<= y 5e-114) (* x (+ t (* 2.0 z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(y, fma(x, 2.0, 5.0), (x * t));
	double tmp;
	if (y <= -5.5e-28) {
		tmp = t_1;
	} else if (y <= 5e-114) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(y, fma(x, 2.0, 5.0), Float64(x * t))
	tmp = 0.0
	if (y <= -5.5e-28)
		tmp = t_1;
	elseif (y <= 5e-114)
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * 2.0 + 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e-28], t$95$1, If[LessEqual[y, 5e-114], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4999999999999997e-28 or 4.9999999999999999e-114 < y

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{5 \cdot y + x \cdot \left(t + 2 \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(5, \color{blue}{y}, x \cdot \left(t + 2 \cdot y\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right) \]

      4. lower-*.f64 74.9%

         \[\leadsto \mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right) \]

   4. Applied rewrites 74.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto 5 \cdot y + \color{blue}{x \cdot \left(t + 2 \cdot y\right)} \]

      2. *-commutative N/A

         \[\leadsto y \cdot 5 + \color{blue}{x} \cdot \left(t + 2 \cdot y\right) \]

      3. lift-*.f64 N/A

         \[\leadsto y \cdot 5 + \color{blue}{x} \cdot \left(t + 2 \cdot y\right) \]

      4. lift-*.f64 N/A

         \[\leadsto y \cdot 5 + x \cdot \color{blue}{\left(t + 2 \cdot y\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto y \cdot 5 + x \cdot \left(t + \color{blue}{2 \cdot y}\right) \]

      6. +-commutative N/A

         \[\leadsto y \cdot 5 + x \cdot \left(2 \cdot y + \color{blue}{t}\right) \]

      7. distribute-lft-in N/A

         \[\leadsto y \cdot 5 + \left(x \cdot \left(2 \cdot y\right) + \color{blue}{x \cdot t}\right) \]

      8. *-commutative N/A

         \[\leadsto y \cdot 5 + \left(x \cdot \left(2 \cdot y\right) + t \cdot \color{blue}{x}\right) \]

      9. lift-*.f64 N/A

         \[\leadsto y \cdot 5 + \left(x \cdot \left(2 \cdot y\right) + t \cdot \color{blue}{x}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \left(y \cdot 5 + x \cdot \left(2 \cdot y\right)\right) + \color{blue}{t \cdot x} \]

      11. +-commutative N/A

          \[\leadsto \left(x \cdot \left(2 \cdot y\right) + y \cdot 5\right) + \color{blue}{t} \cdot x \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(2 \cdot y\right) + y \cdot 5\right) + t \cdot x \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(2 \cdot y\right) + 5 \cdot y\right) + t \cdot x \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(2 \cdot y\right) + 5 \cdot y\right) + t \cdot x \]

      15. associate-*r* N/A

          \[\leadsto \left(\left(x \cdot 2\right) \cdot y + 5 \cdot y\right) + t \cdot x \]

      16. distribute-rgt-out N/A

          \[\leadsto y \cdot \left(x \cdot 2 + 5\right) + \color{blue}{t} \cdot x \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{x \cdot 2 + 5}, t \cdot x\right) \]

      18. lower-fma.f64 73.9%

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(x, \color{blue}{2}, 5\right), t \cdot x\right) \]

      19. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, \color{blue}{5}\right), t \cdot x\right) \]

      20. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, \color{blue}{5}\right), x \cdot t\right) \]

      21. lower-*.f64 73.9%

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, \color{blue}{5}\right), x \cdot t\right) \]

   6. Applied rewrites 73.9%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, 2, 5\right)}, x \cdot t\right) \]

   if -5.4999999999999997e-28 < y < 4.9999999999999999e-114

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x} + y \cdot 5 \]

      4. lower-fma.f64 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t, x, y \cdot 5\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right) + t}, x, y \cdot 5\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t, x, y \cdot 5\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t, x, y \cdot 5\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, x, y \cdot 5\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(y + z\right)} + t, x, y \cdot 5\right) \]

      12. lower-fma.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y + z, t\right)}, x, y \cdot 5\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{y + z}, t\right), x, y \cdot 5\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      15. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{y \cdot 5}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

      18. lower-*.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, 5 \cdot y\right)} \]
   4. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(z + y\right) + t}, x, 5 \cdot y\right) \]

      2. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(z + y\right)} + t, x, 5 \cdot y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(y + z\right)} + t, x, 5 \cdot y\right) \]

      4. count-2-rev N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(y + z\right)\right)} + t, x, 5 \cdot y\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + y\right) + z\right)} + t, x, 5 \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + \left(y + z\right)\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      9. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + y\right) + z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      10. count-2-rev N/A

          \[\leadsto \mathsf{fma}\left(\left(\color{blue}{2 \cdot y} + z\right) + \left(z + t\right), x, 5 \cdot y\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      12. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, y, z\right) + \color{blue}{\left(z + t\right)}, x, 5 \cdot y\right) \]

   5. Applied rewrites 99.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

   6. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(t + 2 \cdot z\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(t + \color{blue}{2 \cdot z}\right) \]

      3. lower-*.f64 55.7%

         \[\leadsto x \cdot \left(t + 2 \cdot \color{blue}{z}\right) \]

   8. Applied rewrites 55.7%

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

Alternative 6: 79.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, 5, \left(y + y\right) \cdot x\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.58 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (fma y 5.0 (* (+ y y) x))))
  (if (<= y -8.2e+30)
    t_1
    (if (<= y 1.58e+32) (* x (+ t (* 2.0 z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(y, 5.0, ((y + y) * x));
	double tmp;
	if (y <= -8.2e+30) {
		tmp = t_1;
	} else if (y <= 1.58e+32) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(y, 5.0, Float64(Float64(y + y) * x))
	tmp = 0.0
	if (y <= -8.2e+30)
		tmp = t_1;
	elseif (y <= 1.58e+32)
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * 5.0 + N[(N[(y + y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+30], t$95$1, If[LessEqual[y, 1.58e+32], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2000000000000001e30 or 1.5800000000000001e32 < y

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot 5} + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \]

      4. lower-fma.f64 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

      7. lower-*.f64 99.9%

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

      8. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \cdot x\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t\right) \cdot x\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t\right) \cdot x\right) \]

      11. associate-+l+ N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) \cdot x\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

      14. count-2 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{2 \cdot \left(y + z\right)} + t\right) \cdot x\right) \]

      15. lower-fma.f64 99.9%

          \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y + z, t\right)} \cdot x\right) \]

      16. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{y + z}, t\right) \cdot x\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

      18. lower-+.f64 99.9%

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

   3. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, z + y, t\right) \cdot x\right)} \]

   4. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{2 \cdot \left(x \cdot y\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, 2 \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

      2. lower-*.f64 49.2%

         \[\leadsto \mathsf{fma}\left(y, 5, 2 \cdot \left(x \cdot \color{blue}{y}\right)\right) \]

   6. Applied rewrites 49.2%

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{2 \cdot \left(x \cdot y\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, 2 \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, 2 \cdot \left(x \cdot \color{blue}{y}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, 5, 2 \cdot \left(y \cdot \color{blue}{x}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \left(2 \cdot y\right) \cdot \color{blue}{x}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \left(2 \cdot y\right) \cdot \color{blue}{x}\right) \]

      6. count-2-rev N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \left(y + y\right) \cdot x\right) \]

      7. lower-+.f64 49.2%

         \[\leadsto \mathsf{fma}\left(y, 5, \left(y + y\right) \cdot x\right) \]

   8. Applied rewrites 49.2%

      \[\leadsto \mathsf{fma}\left(y, 5, \left(y + y\right) \cdot \color{blue}{x}\right) \]

   if -8.2000000000000001e30 < y < 1.5800000000000001e32

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x} + y \cdot 5 \]

      4. lower-fma.f64 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t, x, y \cdot 5\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right) + t}, x, y \cdot 5\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t, x, y \cdot 5\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t, x, y \cdot 5\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, x, y \cdot 5\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(y + z\right)} + t, x, y \cdot 5\right) \]

      12. lower-fma.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y + z, t\right)}, x, y \cdot 5\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{y + z}, t\right), x, y \cdot 5\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      15. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{y \cdot 5}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

      18. lower-*.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, 5 \cdot y\right)} \]
   4. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(z + y\right) + t}, x, 5 \cdot y\right) \]

      2. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(z + y\right)} + t, x, 5 \cdot y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(y + z\right)} + t, x, 5 \cdot y\right) \]

      4. count-2-rev N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(y + z\right)\right)} + t, x, 5 \cdot y\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + y\right) + z\right)} + t, x, 5 \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + \left(y + z\right)\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      9. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + y\right) + z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      10. count-2-rev N/A

          \[\leadsto \mathsf{fma}\left(\left(\color{blue}{2 \cdot y} + z\right) + \left(z + t\right), x, 5 \cdot y\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      12. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, y, z\right) + \color{blue}{\left(z + t\right)}, x, 5 \cdot y\right) \]

   5. Applied rewrites 99.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

   6. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(t + 2 \cdot z\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(t + \color{blue}{2 \cdot z}\right) \]

      3. lower-*.f64 55.7%

         \[\leadsto x \cdot \left(t + 2 \cdot \color{blue}{z}\right) \]

   8. Applied rewrites 55.7%

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

Alternative 7: 79.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.58 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (* (fma 2.0 x 5.0) y)))
  (if (<= y -8.2e+30)
    t_1
    (if (<= y 1.58e+32) (* x (+ t (* 2.0 z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(2.0, x, 5.0) * y;
	double tmp;
	if (y <= -8.2e+30) {
		tmp = t_1;
	} else if (y <= 1.58e+32) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(2.0, x, 5.0) * y)
	tmp = 0.0
	if (y <= -8.2e+30)
		tmp = t_1;
	elseif (y <= 1.58e+32)
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 * x + 5.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -8.2e+30], t$95$1, If[LessEqual[y, 1.58e+32], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2000000000000001e30 or 1.5800000000000001e32 < y

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x} + y \cdot 5 \]

      4. lower-fma.f64 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t, x, y \cdot 5\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right) + t}, x, y \cdot 5\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t, x, y \cdot 5\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t, x, y \cdot 5\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, x, y \cdot 5\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(y + z\right)} + t, x, y \cdot 5\right) \]

      12. lower-fma.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y + z, t\right)}, x, y \cdot 5\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{y + z}, t\right), x, y \cdot 5\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      15. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{y \cdot 5}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

      18. lower-*.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, 5 \cdot y\right)} \]
   4. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(z + y\right) + t}, x, 5 \cdot y\right) \]

      2. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(z + y\right)} + t, x, 5 \cdot y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(y + z\right)} + t, x, 5 \cdot y\right) \]

      4. count-2-rev N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(y + z\right)\right)} + t, x, 5 \cdot y\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + y\right) + z\right)} + t, x, 5 \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + \left(y + z\right)\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      9. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + y\right) + z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      10. count-2-rev N/A

          \[\leadsto \mathsf{fma}\left(\left(\color{blue}{2 \cdot y} + z\right) + \left(z + t\right), x, 5 \cdot y\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      12. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, y, z\right) + \color{blue}{\left(z + t\right)}, x, 5 \cdot y\right) \]

   5. Applied rewrites 99.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(5 + 2 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y \cdot \left(5 + \color{blue}{2 \cdot x}\right) \]

      3. lower-*.f64 49.2%

         \[\leadsto y \cdot \left(5 + 2 \cdot \color{blue}{x}\right) \]

   8. Applied rewrites 49.2%

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(5 + 2 \cdot x\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(5 + 2 \cdot x\right) \cdot \color{blue}{y} \]

      3. lower-*.f64 49.2%

         \[\leadsto \left(5 + 2 \cdot x\right) \cdot \color{blue}{y} \]

      4. lift-+.f64 N/A

         \[\leadsto \left(5 + 2 \cdot x\right) \cdot y \]

      5. +-commutative N/A

         \[\leadsto \left(2 \cdot x + 5\right) \cdot y \]

      6. lift-*.f64 N/A

         \[\leadsto \left(2 \cdot x + 5\right) \cdot y \]

      7. lower-fma.f64 49.2%

         \[\leadsto \mathsf{fma}\left(2, x, 5\right) \cdot y \]

   10. Applied rewrites 49.2%

       \[\leadsto \mathsf{fma}\left(2, x, 5\right) \cdot \color{blue}{y} \]

   if -8.2000000000000001e30 < y < 1.5800000000000001e32

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x} + y \cdot 5 \]

      4. lower-fma.f64 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t, x, y \cdot 5\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right) + t}, x, y \cdot 5\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t, x, y \cdot 5\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t, x, y \cdot 5\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, x, y \cdot 5\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(y + z\right)} + t, x, y \cdot 5\right) \]

      12. lower-fma.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y + z, t\right)}, x, y \cdot 5\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{y + z}, t\right), x, y \cdot 5\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      15. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{y \cdot 5}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

      18. lower-*.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, 5 \cdot y\right)} \]
   4. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(z + y\right) + t}, x, 5 \cdot y\right) \]

      2. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(z + y\right)} + t, x, 5 \cdot y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(y + z\right)} + t, x, 5 \cdot y\right) \]

      4. count-2-rev N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(y + z\right)\right)} + t, x, 5 \cdot y\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + y\right) + z\right)} + t, x, 5 \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + \left(y + z\right)\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      9. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + y\right) + z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      10. count-2-rev N/A

          \[\leadsto \mathsf{fma}\left(\left(\color{blue}{2 \cdot y} + z\right) + \left(z + t\right), x, 5 \cdot y\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      12. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, y, z\right) + \color{blue}{\left(z + t\right)}, x, 5 \cdot y\right) \]

   5. Applied rewrites 99.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

   6. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(t + 2 \cdot z\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(t + \color{blue}{2 \cdot z}\right) \]

      3. lower-*.f64 55.7%

         \[\leadsto x \cdot \left(t + 2 \cdot \color{blue}{z}\right) \]

   8. Applied rewrites 55.7%

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

Alternative 8: 74.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{if}\;x \leq -2100000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 12.5:\\ \;\;\;\;\mathsf{fma}\left(y, 5, x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (* x (+ t (* 2.0 y)))))
  (if (<= x -2100000000.0)
    t_1
    (if (<= x 12.5) (fma y 5.0 (* x t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -2100000000.0) {
		tmp = t_1;
	} else if (x <= 12.5) {
		tmp = fma(y, 5.0, (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * y)))
	tmp = 0.0
	if (x <= -2100000000.0)
		tmp = t_1;
	elseif (x <= 12.5)
		tmp = fma(y, 5.0, Float64(x * t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2100000000.0], t$95$1, If[LessEqual[x, 12.5], N[(y * 5.0 + N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1e9 or 12.5 < x

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{5 \cdot y + x \cdot \left(t + 2 \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(5, \color{blue}{y}, x \cdot \left(t + 2 \cdot y\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right) \]

      4. lower-*.f64 74.9%

         \[\leadsto \mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right) \]

   4. Applied rewrites 74.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(5, y, x \cdot \left(t + 2 \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto 5 \cdot y + \color{blue}{x \cdot \left(t + 2 \cdot y\right)} \]

      2. *-commutative N/A

         \[\leadsto y \cdot 5 + \color{blue}{x} \cdot \left(t + 2 \cdot y\right) \]

      3. lift-*.f64 N/A

         \[\leadsto y \cdot 5 + \color{blue}{x} \cdot \left(t + 2 \cdot y\right) \]

      4. lift-*.f64 N/A

         \[\leadsto y \cdot 5 + x \cdot \color{blue}{\left(t + 2 \cdot y\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto y \cdot 5 + x \cdot \left(t + \color{blue}{2 \cdot y}\right) \]

      6. +-commutative N/A

         \[\leadsto y \cdot 5 + x \cdot \left(2 \cdot y + \color{blue}{t}\right) \]

      7. distribute-lft-in N/A

         \[\leadsto y \cdot 5 + \left(x \cdot \left(2 \cdot y\right) + \color{blue}{x \cdot t}\right) \]

      8. *-commutative N/A

         \[\leadsto y \cdot 5 + \left(x \cdot \left(2 \cdot y\right) + t \cdot \color{blue}{x}\right) \]

      9. lift-*.f64 N/A

         \[\leadsto y \cdot 5 + \left(x \cdot \left(2 \cdot y\right) + t \cdot \color{blue}{x}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \left(y \cdot 5 + x \cdot \left(2 \cdot y\right)\right) + \color{blue}{t \cdot x} \]

      11. +-commutative N/A

          \[\leadsto \left(x \cdot \left(2 \cdot y\right) + y \cdot 5\right) + \color{blue}{t} \cdot x \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(2 \cdot y\right) + y \cdot 5\right) + t \cdot x \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(2 \cdot y\right) + 5 \cdot y\right) + t \cdot x \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(2 \cdot y\right) + 5 \cdot y\right) + t \cdot x \]

      15. associate-*r* N/A

          \[\leadsto \left(\left(x \cdot 2\right) \cdot y + 5 \cdot y\right) + t \cdot x \]

      16. distribute-rgt-out N/A

          \[\leadsto y \cdot \left(x \cdot 2 + 5\right) + \color{blue}{t} \cdot x \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{x \cdot 2 + 5}, t \cdot x\right) \]

      18. lower-fma.f64 73.9%

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(x, \color{blue}{2}, 5\right), t \cdot x\right) \]

      19. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, \color{blue}{5}\right), t \cdot x\right) \]

      20. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, \color{blue}{5}\right), x \cdot t\right) \]

      21. lower-*.f64 73.9%

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, \color{blue}{5}\right), x \cdot t\right) \]

   6. Applied rewrites 73.9%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, 2, 5\right)}, x \cdot t\right) \]

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(t + \color{blue}{2 \cdot y}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(t + 2 \cdot \color{blue}{y}\right) \]

      3. lower-*.f64 46.3%

         \[\leadsto x \cdot \left(t + 2 \cdot y\right) \]

   9. Applied rewrites 46.3%

      \[\leadsto x \cdot \color{blue}{\left(t + 2 \cdot y\right)} \]

   if -2.1e9 < x < 12.5

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot x} + y \cdot 5 \]
   3. Step-by-step derivation

      1. lower-*.f64 58.5%

         \[\leadsto t \cdot \color{blue}{x} + y \cdot 5 \]

   4. Applied rewrites 58.5%

      \[\leadsto \color{blue}{t \cdot x} + y \cdot 5 \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{t \cdot x + y \cdot 5} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot 5 + t \cdot x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot 5} + t \cdot x \]

      4. lower-fma.f64 58.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, t \cdot x\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, t \cdot \color{blue}{x}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{t}\right) \]

      7. lower-*.f64 58.5%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{t}\right) \]

   6. Applied rewrites 58.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot t\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 66.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, 5, x \cdot t\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{-102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4200000:\\ \;\;\;\;\mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (fma y 5.0 (* x t))))
  (if (<= t -2.5e-102)
    t_1
    (if (<= t 4200000.0) (* (fma 2.0 x 5.0) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(y, 5.0, (x * t));
	double tmp;
	if (t <= -2.5e-102) {
		tmp = t_1;
	} else if (t <= 4200000.0) {
		tmp = fma(2.0, x, 5.0) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(y, 5.0, Float64(x * t))
	tmp = 0.0
	if (t <= -2.5e-102)
		tmp = t_1;
	elseif (t <= 4200000.0)
		tmp = Float64(fma(2.0, x, 5.0) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * 5.0 + N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e-102], t$95$1, If[LessEqual[t, 4200000.0], N[(N[(2.0 * x + 5.0), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5000000000000001e-102 or 4.2e6 < t

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot x} + y \cdot 5 \]
   3. Step-by-step derivation

      1. lower-*.f64 58.5%

         \[\leadsto t \cdot \color{blue}{x} + y \cdot 5 \]

   4. Applied rewrites 58.5%

      \[\leadsto \color{blue}{t \cdot x} + y \cdot 5 \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{t \cdot x + y \cdot 5} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot 5 + t \cdot x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot 5} + t \cdot x \]

      4. lower-fma.f64 58.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, t \cdot x\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, t \cdot \color{blue}{x}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{t}\right) \]

      7. lower-*.f64 58.5%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{t}\right) \]

   6. Applied rewrites 58.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot t\right)} \]

   if -2.5000000000000001e-102 < t < 4.2e6

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x} + y \cdot 5 \]

      4. lower-fma.f64 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t, x, y \cdot 5\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right) + t}, x, y \cdot 5\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t, x, y \cdot 5\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t, x, y \cdot 5\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, x, y \cdot 5\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(y + z\right)} + t, x, y \cdot 5\right) \]

      12. lower-fma.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y + z, t\right)}, x, y \cdot 5\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{y + z}, t\right), x, y \cdot 5\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      15. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{y \cdot 5}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

      18. lower-*.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, 5 \cdot y\right)} \]
   4. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(z + y\right) + t}, x, 5 \cdot y\right) \]

      2. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(z + y\right)} + t, x, 5 \cdot y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(y + z\right)} + t, x, 5 \cdot y\right) \]

      4. count-2-rev N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(y + z\right)\right)} + t, x, 5 \cdot y\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + y\right) + z\right)} + t, x, 5 \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + \left(y + z\right)\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      9. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + y\right) + z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      10. count-2-rev N/A

          \[\leadsto \mathsf{fma}\left(\left(\color{blue}{2 \cdot y} + z\right) + \left(z + t\right), x, 5 \cdot y\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      12. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, y, z\right) + \color{blue}{\left(z + t\right)}, x, 5 \cdot y\right) \]

   5. Applied rewrites 99.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(5 + 2 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y \cdot \left(5 + \color{blue}{2 \cdot x}\right) \]

      3. lower-*.f64 49.2%

         \[\leadsto y \cdot \left(5 + 2 \cdot \color{blue}{x}\right) \]

   8. Applied rewrites 49.2%

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(5 + 2 \cdot x\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(5 + 2 \cdot x\right) \cdot \color{blue}{y} \]

      3. lower-*.f64 49.2%

         \[\leadsto \left(5 + 2 \cdot x\right) \cdot \color{blue}{y} \]

      4. lift-+.f64 N/A

         \[\leadsto \left(5 + 2 \cdot x\right) \cdot y \]

      5. +-commutative N/A

         \[\leadsto \left(2 \cdot x + 5\right) \cdot y \]

      6. lift-*.f64 N/A

         \[\leadsto \left(2 \cdot x + 5\right) \cdot y \]

      7. lower-fma.f64 49.2%

         \[\leadsto \mathsf{fma}\left(2, x, 5\right) \cdot y \]

   10. Applied rewrites 49.2%

       \[\leadsto \mathsf{fma}\left(2, x, 5\right) \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 59.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-114}:\\ \;\;\;\;\left(z + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (* (fma 2.0 x 5.0) y)))
  (if (<= y -5.5e-28) t_1 (if (<= y 5e-114) (* (+ z z) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(2.0, x, 5.0) * y;
	double tmp;
	if (y <= -5.5e-28) {
		tmp = t_1;
	} else if (y <= 5e-114) {
		tmp = (z + z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(2.0, x, 5.0) * y)
	tmp = 0.0
	if (y <= -5.5e-28)
		tmp = t_1;
	elseif (y <= 5e-114)
		tmp = Float64(Float64(z + z) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 * x + 5.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -5.5e-28], t$95$1, If[LessEqual[y, 5e-114], N[(N[(z + z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4999999999999997e-28 or 4.9999999999999999e-114 < y

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x} + y \cdot 5 \]

      4. lower-fma.f64 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t, x, y \cdot 5\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right) + t}, x, y \cdot 5\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t, x, y \cdot 5\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t, x, y \cdot 5\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, x, y \cdot 5\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(y + z\right)} + t, x, y \cdot 5\right) \]

      12. lower-fma.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y + z, t\right)}, x, y \cdot 5\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{y + z}, t\right), x, y \cdot 5\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      15. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{y \cdot 5}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

      18. lower-*.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, 5 \cdot y\right)} \]
   4. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(z + y\right) + t}, x, 5 \cdot y\right) \]

      2. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(z + y\right)} + t, x, 5 \cdot y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(y + z\right)} + t, x, 5 \cdot y\right) \]

      4. count-2-rev N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(y + z\right)\right)} + t, x, 5 \cdot y\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + y\right) + z\right)} + t, x, 5 \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + \left(y + z\right)\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      9. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + y\right) + z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      10. count-2-rev N/A

          \[\leadsto \mathsf{fma}\left(\left(\color{blue}{2 \cdot y} + z\right) + \left(z + t\right), x, 5 \cdot y\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      12. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, y, z\right) + \color{blue}{\left(z + t\right)}, x, 5 \cdot y\right) \]

   5. Applied rewrites 99.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(5 + 2 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y \cdot \left(5 + \color{blue}{2 \cdot x}\right) \]

      3. lower-*.f64 49.2%

         \[\leadsto y \cdot \left(5 + 2 \cdot \color{blue}{x}\right) \]

   8. Applied rewrites 49.2%

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(5 + 2 \cdot x\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(5 + 2 \cdot x\right) \cdot \color{blue}{y} \]

      3. lower-*.f64 49.2%

         \[\leadsto \left(5 + 2 \cdot x\right) \cdot \color{blue}{y} \]

      4. lift-+.f64 N/A

         \[\leadsto \left(5 + 2 \cdot x\right) \cdot y \]

      5. +-commutative N/A

         \[\leadsto \left(2 \cdot x + 5\right) \cdot y \]

      6. lift-*.f64 N/A

         \[\leadsto \left(2 \cdot x + 5\right) \cdot y \]

      7. lower-fma.f64 49.2%

         \[\leadsto \mathsf{fma}\left(2, x, 5\right) \cdot y \]

   10. Applied rewrites 49.2%

       \[\leadsto \mathsf{fma}\left(2, x, 5\right) \cdot \color{blue}{y} \]

   if -5.4999999999999997e-28 < y < 4.9999999999999999e-114

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x} + y \cdot 5 \]

      4. lower-fma.f64 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t, x, y \cdot 5\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right) + t}, x, y \cdot 5\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t, x, y \cdot 5\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t, x, y \cdot 5\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, x, y \cdot 5\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(y + z\right)} + t, x, y \cdot 5\right) \]

      12. lower-fma.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y + z, t\right)}, x, y \cdot 5\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{y + z}, t\right), x, y \cdot 5\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      15. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{y \cdot 5}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

      18. lower-*.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, 5 \cdot y\right)} \]
   4. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(z + y\right) + t}, x, 5 \cdot y\right) \]

      2. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(z + y\right)} + t, x, 5 \cdot y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(y + z\right)} + t, x, 5 \cdot y\right) \]

      4. count-2-rev N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(y + z\right)\right)} + t, x, 5 \cdot y\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + y\right) + z\right)} + t, x, 5 \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + \left(y + z\right)\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      9. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + y\right) + z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      10. count-2-rev N/A

          \[\leadsto \mathsf{fma}\left(\left(\color{blue}{2 \cdot y} + z\right) + \left(z + t\right), x, 5 \cdot y\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      12. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, y, z\right) + \color{blue}{\left(z + t\right)}, x, 5 \cdot y\right) \]

   5. Applied rewrites 99.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot z\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot z\right)} \]

      2. lower-*.f64 30.0%

         \[\leadsto 2 \cdot \left(x \cdot \color{blue}{z}\right) \]

   8. Applied rewrites 30.0%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot z\right)} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot z\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto 2 \cdot \left(x \cdot \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto 2 \cdot \left(z \cdot \color{blue}{x}\right) \]

      4. associate-*r* N/A

         \[\leadsto \left(2 \cdot z\right) \cdot \color{blue}{x} \]

      5. count-2 N/A

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

      6. lift-+.f64 N/A

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

      7. lower-*.f64 29.9%

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

   10. Applied rewrites 29.9%

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

Alternative 11: 47.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-23}:\\ \;\;\;\;\left(z + z\right) \cdot x\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+26}:\\ \;\;\;\;5 \cdot y\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<= x -1.8e-23)
  (* (+ z z) x)
  (if (<= x 4.6e+26) (* 5.0 y) (* 2.0 (* x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.8e-23) {
		tmp = (z + z) * x;
	} else if (x <= 4.6e+26) {
		tmp = 5.0 * y;
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (x <= (-1.8d-23)) then
        tmp = (z + z) * x
    else if (x <= 4.6d+26) then
        tmp = 5.0d0 * y
    else
        tmp = 2.0d0 * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.8e-23) {
		tmp = (z + z) * x;
	} else if (x <= 4.6e+26) {
		tmp = 5.0 * y;
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.8e-23:
		tmp = (z + z) * x
	elif x <= 4.6e+26:
		tmp = 5.0 * y
	else:
		tmp = 2.0 * (x * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.8e-23)
		tmp = Float64(Float64(z + z) * x);
	elseif (x <= 4.6e+26)
		tmp = Float64(5.0 * y);
	else
		tmp = Float64(2.0 * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.8e-23)
		tmp = (z + z) * x;
	elseif (x <= 4.6e+26)
		tmp = 5.0 * y;
	else
		tmp = 2.0 * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.8e-23], N[(N[(z + z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 4.6e+26], N[(5.0 * y), $MachinePrecision], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7999999999999999e-23

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x} + y \cdot 5 \]

      4. lower-fma.f64 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t, x, y \cdot 5\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right) + t}, x, y \cdot 5\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t, x, y \cdot 5\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t, x, y \cdot 5\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, x, y \cdot 5\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(y + z\right)} + t, x, y \cdot 5\right) \]

      12. lower-fma.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y + z, t\right)}, x, y \cdot 5\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{y + z}, t\right), x, y \cdot 5\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      15. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{y \cdot 5}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

      18. lower-*.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, 5 \cdot y\right)} \]
   4. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(z + y\right) + t}, x, 5 \cdot y\right) \]

      2. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(z + y\right)} + t, x, 5 \cdot y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(y + z\right)} + t, x, 5 \cdot y\right) \]

      4. count-2-rev N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(y + z\right)\right)} + t, x, 5 \cdot y\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + y\right) + z\right)} + t, x, 5 \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + \left(y + z\right)\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      9. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + y\right) + z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      10. count-2-rev N/A

          \[\leadsto \mathsf{fma}\left(\left(\color{blue}{2 \cdot y} + z\right) + \left(z + t\right), x, 5 \cdot y\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      12. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, y, z\right) + \color{blue}{\left(z + t\right)}, x, 5 \cdot y\right) \]

   5. Applied rewrites 99.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot z\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot z\right)} \]

      2. lower-*.f64 30.0%

         \[\leadsto 2 \cdot \left(x \cdot \color{blue}{z}\right) \]

   8. Applied rewrites 30.0%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot z\right)} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot z\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto 2 \cdot \left(x \cdot \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto 2 \cdot \left(z \cdot \color{blue}{x}\right) \]

      4. associate-*r* N/A

         \[\leadsto \left(2 \cdot z\right) \cdot \color{blue}{x} \]

      5. count-2 N/A

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

      6. lift-+.f64 N/A

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

      7. lower-*.f64 29.9%

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

   10. Applied rewrites 29.9%

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

   if -1.7999999999999999e-23 < x < 4.6000000000000001e26

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 30.7%

         \[\leadsto 5 \cdot \color{blue}{y} \]

   4. Applied rewrites 30.7%

      \[\leadsto \color{blue}{5 \cdot y} \]

   if 4.6000000000000001e26 < x

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x} + y \cdot 5 \]

      4. lower-fma.f64 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t, x, y \cdot 5\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right) + t}, x, y \cdot 5\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t, x, y \cdot 5\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t, x, y \cdot 5\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, x, y \cdot 5\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(y + z\right)} + t, x, y \cdot 5\right) \]

      12. lower-fma.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y + z, t\right)}, x, y \cdot 5\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{y + z}, t\right), x, y \cdot 5\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      15. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{y \cdot 5}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

      18. lower-*.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, 5 \cdot y\right)} \]
   4. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(z + y\right) + t}, x, 5 \cdot y\right) \]

      2. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(z + y\right)} + t, x, 5 \cdot y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(y + z\right)} + t, x, 5 \cdot y\right) \]

      4. count-2-rev N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(y + z\right)\right)} + t, x, 5 \cdot y\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + y\right) + z\right)} + t, x, 5 \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + \left(y + z\right)\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      9. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + y\right) + z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      10. count-2-rev N/A

          \[\leadsto \mathsf{fma}\left(\left(\color{blue}{2 \cdot y} + z\right) + \left(z + t\right), x, 5 \cdot y\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      12. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, y, z\right) + \color{blue}{\left(z + t\right)}, x, 5 \cdot y\right) \]

   5. Applied rewrites 99.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(5 + 2 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y \cdot \left(5 + \color{blue}{2 \cdot x}\right) \]

      3. lower-*.f64 49.2%

         \[\leadsto y \cdot \left(5 + 2 \cdot \color{blue}{x}\right) \]

   8. Applied rewrites 49.2%

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto 2 \cdot \left(x \cdot \color{blue}{y}\right) \]

       2. lower-*.f64 20.9%

          \[\leadsto 2 \cdot \left(x \cdot y\right) \]

   11. Applied rewrites 20.9%

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

Alternative 12: 47.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_1 := \left(z + z\right) \cdot x\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+22}:\\ \;\;\;\;5 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (* (+ z z) x)))
  (if (<= x -1.8e-23) t_1 (if (<= x 1.7e+22) (* 5.0 y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z + z) * x;
	double tmp;
	if (x <= -1.8e-23) {
		tmp = t_1;
	} else if (x <= 1.7e+22) {
		tmp = 5.0 * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + z) * x
    if (x <= (-1.8d-23)) then
        tmp = t_1
    else if (x <= 1.7d+22) then
        tmp = 5.0d0 * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z + z) * x;
	double tmp;
	if (x <= -1.8e-23) {
		tmp = t_1;
	} else if (x <= 1.7e+22) {
		tmp = 5.0 * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z + z) * x
	tmp = 0
	if x <= -1.8e-23:
		tmp = t_1
	elif x <= 1.7e+22:
		tmp = 5.0 * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z + z) * x)
	tmp = 0.0
	if (x <= -1.8e-23)
		tmp = t_1;
	elseif (x <= 1.7e+22)
		tmp = Float64(5.0 * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z + z) * x;
	tmp = 0.0;
	if (x <= -1.8e-23)
		tmp = t_1;
	elseif (x <= 1.7e+22)
		tmp = 5.0 * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z + z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.8e-23], t$95$1, If[LessEqual[x, 1.7e+22], N[(5.0 * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7999999999999999e-23 or 1.7e22 < x

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x} + y \cdot 5 \]

      4. lower-fma.f64 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t, x, y \cdot 5\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right) + t}, x, y \cdot 5\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t, x, y \cdot 5\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t, x, y \cdot 5\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, x, y \cdot 5\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, x, y \cdot 5\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(y + z\right)} + t, x, y \cdot 5\right) \]

      12. lower-fma.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y + z, t\right)}, x, y \cdot 5\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{y + z}, t\right), x, y \cdot 5\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      15. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, \color{blue}{z + y}, t\right), x, y \cdot 5\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{y \cdot 5}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

      18. lower-*.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, \color{blue}{5 \cdot y}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, z + y, t\right), x, 5 \cdot y\right)} \]
   4. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \left(z + y\right) + t}, x, 5 \cdot y\right) \]

      2. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(z + y\right)} + t, x, 5 \cdot y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\left(y + z\right)} + t, x, 5 \cdot y\right) \]

      4. count-2-rev N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + \left(y + z\right)\right)} + t, x, 5 \cdot y\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(\left(y + z\right) + y\right) + z\right)} + t, x, 5 \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + z\right) + y\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + \left(y + z\right)\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      9. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y + y\right) + z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      10. count-2-rev N/A

          \[\leadsto \mathsf{fma}\left(\left(\color{blue}{2 \cdot y} + z\right) + \left(z + t\right), x, 5 \cdot y\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right)} + \left(z + t\right), x, 5 \cdot y\right) \]

      12. lower-+.f64 99.8%

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, y, z\right) + \color{blue}{\left(z + t\right)}, x, 5 \cdot y\right) \]

   5. Applied rewrites 99.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, z\right) + \left(z + t\right)}, x, 5 \cdot y\right) \]

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot z\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot z\right)} \]

      2. lower-*.f64 30.0%

         \[\leadsto 2 \cdot \left(x \cdot \color{blue}{z}\right) \]

   8. Applied rewrites 30.0%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot z\right)} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot z\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto 2 \cdot \left(x \cdot \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto 2 \cdot \left(z \cdot \color{blue}{x}\right) \]

      4. associate-*r* N/A

         \[\leadsto \left(2 \cdot z\right) \cdot \color{blue}{x} \]

      5. count-2 N/A

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

      6. lift-+.f64 N/A

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

      7. lower-*.f64 29.9%

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

   10. Applied rewrites 29.9%

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

   if -1.7999999999999999e-23 < x < 1.7e22

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 30.7%

         \[\leadsto 5 \cdot \color{blue}{y} \]

   4. Applied rewrites 30.7%

      \[\leadsto \color{blue}{5 \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 30.7% accurate, 5.0× speedup

Math

\[5 \cdot y \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 5.0 * 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 = 5.0d0 * y
end function

Java

public static double code(double x, double y, double z, double t) {
	return 5.0 * y;
}

Python

def code(x, y, z, t):
	return 5.0 * y

Julia

function code(x, y, z, t)
	return Float64(5.0 * y)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 5.0 * y;
end

Wolfram

code[x_, y_, z_, t_] := N[(5.0 * y), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

2. Taylor expanded in x around 0

   \[\leadsto \color{blue}{5 \cdot y} \]
3. Step-by-step derivation

   1. lower-*.f64 30.7%

      \[\leadsto 5 \cdot \color{blue}{y} \]

4. Applied rewrites 30.7%

   \[\leadsto \color{blue}{5 \cdot y} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025212 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))