Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, C

Percentage Accurate: 97.8% → 98.8%

Time: 11.5s

Alternatives: 14

Speedup: 0.5×

• 32.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Initial Program: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Alternative 1: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (fma x y (fma (/ z 16.0) t (fma (/ a -4.0) b c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return fma(x, y, fma((z / 16.0), t, fma((a / -4.0), b, c)));
}

Julia

function code(x, y, z, t, a, b, c)
	return fma(x, y, fma(Float64(z / 16.0), t, fma(Float64(a / -4.0), b, c)))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x * y + N[(N[(z / 16.0), $MachinePrecision] * t + N[(N[(a / -4.0), $MachinePrecision] * b + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.2%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Step-by-step derivation

   1. associate-+l- 97.2%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

   2. associate--l+ 97.2%

      \[\leadsto \color{blue}{x \cdot y + \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

   3. fma-def 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

   4. associate-*l/ 99.2%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

   5. fma-neg 99.2%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

   6. sub-neg 99.2%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, -\color{blue}{\left(\frac{a \cdot b}{4} + \left(-c\right)\right)}\right)\right) \]

   7. distribute-neg-in 99.2%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(-\frac{a \cdot b}{4}\right) + \left(-\left(-c\right)\right)}\right)\right) \]

   8. remove-double-neg 99.2%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\frac{a \cdot b}{4}\right) + \color{blue}{c}\right)\right) \]

   9. associate-/l* 99.2%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

   10. distribute-frac-neg 99.2%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{\frac{4}{b}}} + c\right)\right) \]

   11. associate-/r/ 99.2%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{4} \cdot b} + c\right)\right) \]

   12. fma-def 99.2%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\mathsf{fma}\left(\frac{-a}{4}, b, c\right)}\right)\right) \]

   13. neg-mul-1 99.2%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

   14. *-commutative 99.2%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

   15. associate-/l* 99.2%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

   16. metadata-eval 99.2%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{\color{blue}{-4}}, b, c\right)\right)\right) \]

3. Simplified 99.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
4. Add Preprocessing

5. Final simplification 99.2%

   \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right) \]
6. Add Preprocessing

Alternative 2: 98.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;\left(x \cdot y + \mathsf{fma}\left(a, b \cdot -0.25, c\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* z 0.0625))))
   (if (<= (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) INFINITY)
     (+ (+ (* x y) (fma a (* b -0.25) c)) t_1)
     (+ t_1 (* a (* b -0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (z * 0.0625);
	double tmp;
	if ((((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) <= ((double) INFINITY)) {
		tmp = ((x * y) + fma(a, (b * -0.25), c)) + t_1;
	} else {
		tmp = t_1 + (a * (b * -0.25));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(z * 0.0625))
	tmp = 0.0
	if (Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) <= Inf)
		tmp = Float64(Float64(Float64(x * y) + fma(a, Float64(b * -0.25), c)) + t_1);
	else
		tmp = Float64(t_1 + Float64(a * Float64(b * -0.25)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(x * y), $MachinePrecision] + N[(a * N[(b * -0.25), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. associate--l+ 100.0%

         \[\leadsto \color{blue}{x \cdot y + \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      4. associate-*l/ 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

      5. fma-neg 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

      6. sub-neg 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, -\color{blue}{\left(\frac{a \cdot b}{4} + \left(-c\right)\right)}\right)\right) \]

      7. distribute-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(-\frac{a \cdot b}{4}\right) + \left(-\left(-c\right)\right)}\right)\right) \]

      8. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\frac{a \cdot b}{4}\right) + \color{blue}{c}\right)\right) \]

      9. associate-/l* 99.9%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      10. distribute-frac-neg 99.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{\frac{4}{b}}} + c\right)\right) \]

      11. associate-/r/ 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{4} \cdot b} + c\right)\right) \]

      12. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\mathsf{fma}\left(\frac{-a}{4}, b, c\right)}\right)\right) \]

      13. neg-mul-1 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

      14. *-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

      15. associate-/l* 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

      16. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{\color{blue}{-4}}, b, c\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 100.0%

         \[\leadsto \color{blue}{x \cdot y + \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      2. fma-udef 100.0%

         \[\leadsto x \cdot y + \color{blue}{\left(\frac{z}{16} \cdot t + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      3. associate-*l/ 100.0%

         \[\leadsto x \cdot y + \left(\color{blue}{\frac{z \cdot t}{16}} + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right) \]

      4. fma-udef 100.0%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \color{blue}{\left(\frac{a}{-4} \cdot b + c\right)}\right) \]

      5. associate-/r/ 99.9%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \left(\color{blue}{\frac{a}{\frac{-4}{b}}} + c\right)\right) \]

      6. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]

      7. associate-*l/ 99.9%

         \[\leadsto \left(x \cdot y + \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      8. fma-udef 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      9. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(\frac{a}{\frac{-4}{b}} + c\right) + \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} \]

      10. fma-udef 99.9%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} \]

      11. associate-*l/ 99.9%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) \]

      12. associate-+r+ 99.9%

          \[\leadsto \color{blue}{\left(\left(\frac{a}{\frac{-4}{b}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16}} \]

      13. div-inv 100.0%

          \[\leadsto \left(\left(\color{blue}{a \cdot \frac{1}{\frac{-4}{b}}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      14. fma-def 100.0%

          \[\leadsto \left(\color{blue}{\mathsf{fma}\left(a, \frac{1}{\frac{-4}{b}}, c\right)} + x \cdot y\right) + \frac{z \cdot t}{16} \]

      15. clear-num 100.0%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{\frac{b}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      16. div-inv 100.0%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{b \cdot \frac{1}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      17. metadata-eval 100.0%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot \color{blue}{-0.25}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      18. associate-*l/ 100.0%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\frac{z}{16} \cdot t} \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + t \cdot \left(z \cdot 0.0625\right)} \]

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4))

   1. Initial program 0.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. associate--l+ 0.0%

         \[\leadsto \color{blue}{x \cdot y + \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. fma-def 71.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      4. associate-*l/ 71.4%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

      5. fma-neg 71.4%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

      6. sub-neg 71.4%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, -\color{blue}{\left(\frac{a \cdot b}{4} + \left(-c\right)\right)}\right)\right) \]

      7. distribute-neg-in 71.4%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(-\frac{a \cdot b}{4}\right) + \left(-\left(-c\right)\right)}\right)\right) \]

      8. remove-double-neg 71.4%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\frac{a \cdot b}{4}\right) + \color{blue}{c}\right)\right) \]

      9. associate-/l* 71.4%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      10. distribute-frac-neg 71.4%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{\frac{4}{b}}} + c\right)\right) \]

      11. associate-/r/ 71.4%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{4} \cdot b} + c\right)\right) \]

      12. fma-def 71.4%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\mathsf{fma}\left(\frac{-a}{4}, b, c\right)}\right)\right) \]

      13. neg-mul-1 71.4%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

      14. *-commutative 71.4%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

      15. associate-/l* 71.4%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

      16. metadata-eval 71.4%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{\color{blue}{-4}}, b, c\right)\right)\right) \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 0.0%

         \[\leadsto \color{blue}{x \cdot y + \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      2. fma-udef 0.0%

         \[\leadsto x \cdot y + \color{blue}{\left(\frac{z}{16} \cdot t + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      3. associate-*l/ 0.0%

         \[\leadsto x \cdot y + \left(\color{blue}{\frac{z \cdot t}{16}} + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right) \]

      4. fma-udef 0.0%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \color{blue}{\left(\frac{a}{-4} \cdot b + c\right)}\right) \]

      5. associate-/r/ 0.0%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \left(\color{blue}{\frac{a}{\frac{-4}{b}}} + c\right)\right) \]

      6. associate-+r+ 0.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]

      7. associate-*l/ 0.0%

         \[\leadsto \left(x \cdot y + \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      8. fma-udef 28.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      9. +-commutative 28.6%

         \[\leadsto \color{blue}{\left(\frac{a}{\frac{-4}{b}} + c\right) + \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} \]

      10. fma-udef 0.0%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} \]

      11. associate-*l/ 0.0%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) \]

      12. associate-+r+ 0.0%

          \[\leadsto \color{blue}{\left(\left(\frac{a}{\frac{-4}{b}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16}} \]

      13. div-inv 0.0%

          \[\leadsto \left(\left(\color{blue}{a \cdot \frac{1}{\frac{-4}{b}}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      14. fma-def 0.0%

          \[\leadsto \left(\color{blue}{\mathsf{fma}\left(a, \frac{1}{\frac{-4}{b}}, c\right)} + x \cdot y\right) + \frac{z \cdot t}{16} \]

      15. clear-num 0.0%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{\frac{b}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      16. div-inv 0.0%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{b \cdot \frac{1}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      17. metadata-eval 0.0%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot \color{blue}{-0.25}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      18. associate-*l/ 0.0%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\frac{z}{16} \cdot t} \]

   6. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + t \cdot \left(z \cdot 0.0625\right)} \]

   7. Taylor expanded in a around inf 71.4%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + t \cdot \left(z \cdot 0.0625\right) \]
   8. Step-by-step derivation

      1. *-commutative 71.4%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + t \cdot \left(z \cdot 0.0625\right) \]

      2. associate-*r* 71.4%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + t \cdot \left(z \cdot 0.0625\right) \]

      3. *-commutative 71.4%

         \[\leadsto a \cdot \color{blue}{\left(-0.25 \cdot b\right)} + t \cdot \left(z \cdot 0.0625\right) \]

   9. Simplified 71.4%

      \[\leadsto \color{blue}{a \cdot \left(-0.25 \cdot b\right)} + t \cdot \left(z \cdot 0.0625\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;\left(x \cdot y + \mathsf{fma}\left(a, b \cdot -0.25, c\right)\right) + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right) + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(c + \frac{a}{\frac{-4}{b}}\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (fma x y (* (/ z 16.0) t)) (+ c (/ a (/ -4.0 b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return fma(x, y, ((z / 16.0) * t)) + (c + (a / (-4.0 / b)));
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(fma(x, y, Float64(Float64(z / 16.0) * t)) + Float64(c + Float64(a / Float64(-4.0 / b))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(x * y + N[(N[(z / 16.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(c + N[(a / N[(-4.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.2%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Step-by-step derivation

   1. sub-neg 97.2%

      \[\leadsto \color{blue}{\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\frac{a \cdot b}{4}\right)\right)} + c \]

   2. associate-+l+ 97.2%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right)} \]

   3. fma-def 98.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16}\right)} + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

   4. associate-*l/ 98.0%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\left(-\frac{a \cdot b}{4}\right) + c\right) \]

   5. distribute-frac-neg 98.0%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{-a \cdot b}{4}} + c\right) \]

   6. distribute-rgt-neg-out 98.0%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{\color{blue}{a \cdot \left(-b\right)}}{4} + c\right) \]

   7. associate-/l* 98.0%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{a}{\frac{4}{-b}}} + c\right) \]

   8. neg-mul-1 98.0%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{4}{\color{blue}{-1 \cdot b}}} + c\right) \]

   9. associate-/r* 98.0%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\color{blue}{\frac{\frac{4}{-1}}{b}}} + c\right) \]

   10. metadata-eval 98.0%

       \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{\color{blue}{-4}}{b}} + c\right) \]

3. Simplified 98.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]
4. Add Preprocessing

5. Final simplification 98.0%

   \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(c + \frac{a}{\frac{-4}{b}}\right) \]
6. Add Preprocessing

Alternative 4: 98.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;c + t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right) + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
   (if (<= t_1 INFINITY) (+ c t_1) (+ (* t (* z 0.0625)) (* a (* b -0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = c + t_1;
	} else {
		tmp = (t * (z * 0.0625)) + (a * (b * -0.25));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = c + t_1;
	} else {
		tmp = (t * (z * 0.0625)) + (a * (b * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)
	tmp = 0
	if t_1 <= math.inf:
		tmp = c + t_1
	else:
		tmp = (t * (z * 0.0625)) + (a * (b * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(c + t_1);
	else
		tmp = Float64(Float64(t * Float64(z * 0.0625)) + Float64(a * Float64(b * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = c + t_1;
	else
		tmp = (t * (z * 0.0625)) + (a * (b * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(c + t$95$1), $MachinePrecision], N[(N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4))

   1. Initial program 0.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. associate--l+ 0.0%

         \[\leadsto \color{blue}{x \cdot y + \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. fma-def 71.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      4. associate-*l/ 71.4%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

      5. fma-neg 71.4%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

      6. sub-neg 71.4%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, -\color{blue}{\left(\frac{a \cdot b}{4} + \left(-c\right)\right)}\right)\right) \]

      7. distribute-neg-in 71.4%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(-\frac{a \cdot b}{4}\right) + \left(-\left(-c\right)\right)}\right)\right) \]

      8. remove-double-neg 71.4%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\frac{a \cdot b}{4}\right) + \color{blue}{c}\right)\right) \]

      9. associate-/l* 71.4%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      10. distribute-frac-neg 71.4%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{\frac{4}{b}}} + c\right)\right) \]

      11. associate-/r/ 71.4%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{4} \cdot b} + c\right)\right) \]

      12. fma-def 71.4%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\mathsf{fma}\left(\frac{-a}{4}, b, c\right)}\right)\right) \]

      13. neg-mul-1 71.4%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

      14. *-commutative 71.4%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

      15. associate-/l* 71.4%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

      16. metadata-eval 71.4%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{\color{blue}{-4}}, b, c\right)\right)\right) \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 0.0%

         \[\leadsto \color{blue}{x \cdot y + \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      2. fma-udef 0.0%

         \[\leadsto x \cdot y + \color{blue}{\left(\frac{z}{16} \cdot t + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      3. associate-*l/ 0.0%

         \[\leadsto x \cdot y + \left(\color{blue}{\frac{z \cdot t}{16}} + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right) \]

      4. fma-udef 0.0%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \color{blue}{\left(\frac{a}{-4} \cdot b + c\right)}\right) \]

      5. associate-/r/ 0.0%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \left(\color{blue}{\frac{a}{\frac{-4}{b}}} + c\right)\right) \]

      6. associate-+r+ 0.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]

      7. associate-*l/ 0.0%

         \[\leadsto \left(x \cdot y + \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      8. fma-udef 28.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      9. +-commutative 28.6%

         \[\leadsto \color{blue}{\left(\frac{a}{\frac{-4}{b}} + c\right) + \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} \]

      10. fma-udef 0.0%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} \]

      11. associate-*l/ 0.0%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) \]

      12. associate-+r+ 0.0%

          \[\leadsto \color{blue}{\left(\left(\frac{a}{\frac{-4}{b}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16}} \]

      13. div-inv 0.0%

          \[\leadsto \left(\left(\color{blue}{a \cdot \frac{1}{\frac{-4}{b}}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      14. fma-def 0.0%

          \[\leadsto \left(\color{blue}{\mathsf{fma}\left(a, \frac{1}{\frac{-4}{b}}, c\right)} + x \cdot y\right) + \frac{z \cdot t}{16} \]

      15. clear-num 0.0%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{\frac{b}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      16. div-inv 0.0%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{b \cdot \frac{1}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      17. metadata-eval 0.0%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot \color{blue}{-0.25}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      18. associate-*l/ 0.0%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\frac{z}{16} \cdot t} \]

   6. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + t \cdot \left(z \cdot 0.0625\right)} \]

   7. Taylor expanded in a around inf 71.4%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + t \cdot \left(z \cdot 0.0625\right) \]
   8. Step-by-step derivation

      1. *-commutative 71.4%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + t \cdot \left(z \cdot 0.0625\right) \]

      2. associate-*r* 71.4%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + t \cdot \left(z \cdot 0.0625\right) \]

      3. *-commutative 71.4%

         \[\leadsto a \cdot \color{blue}{\left(-0.25 \cdot b\right)} + t \cdot \left(z \cdot 0.0625\right) \]

   9. Simplified 71.4%

      \[\leadsto \color{blue}{a \cdot \left(-0.25 \cdot b\right)} + t \cdot \left(z \cdot 0.0625\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right) + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ t_2 := t \cdot \left(z \cdot 0.0625\right)\\ t_3 := x \cdot y + t_2\\ \mathbf{if}\;x \cdot y \leq -6.2 \cdot 10^{+91}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -2.35 \cdot 10^{-265}:\\ \;\;\;\;c + t_1\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{-65}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))) (t_2 (* t (* z 0.0625))) (t_3 (+ (* x y) t_2)))
   (if (<= (* x y) -6.2e+91)
     t_3
     (if (<= (* x y) -2.35e-265)
       (+ c t_1)
       (if (<= (* x y) 2.2e-65) (+ t_2 t_1) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double t_2 = t * (z * 0.0625);
	double t_3 = (x * y) + t_2;
	double tmp;
	if ((x * y) <= -6.2e+91) {
		tmp = t_3;
	} else if ((x * y) <= -2.35e-265) {
		tmp = c + t_1;
	} else if ((x * y) <= 2.2e-65) {
		tmp = t_2 + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (b * (-0.25d0))
    t_2 = t * (z * 0.0625d0)
    t_3 = (x * y) + t_2
    if ((x * y) <= (-6.2d+91)) then
        tmp = t_3
    else if ((x * y) <= (-2.35d-265)) then
        tmp = c + t_1
    else if ((x * y) <= 2.2d-65) then
        tmp = t_2 + t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double t_2 = t * (z * 0.0625);
	double t_3 = (x * y) + t_2;
	double tmp;
	if ((x * y) <= -6.2e+91) {
		tmp = t_3;
	} else if ((x * y) <= -2.35e-265) {
		tmp = c + t_1;
	} else if ((x * y) <= 2.2e-65) {
		tmp = t_2 + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	t_2 = t * (z * 0.0625)
	t_3 = (x * y) + t_2
	tmp = 0
	if (x * y) <= -6.2e+91:
		tmp = t_3
	elif (x * y) <= -2.35e-265:
		tmp = c + t_1
	elif (x * y) <= 2.2e-65:
		tmp = t_2 + t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	t_2 = Float64(t * Float64(z * 0.0625))
	t_3 = Float64(Float64(x * y) + t_2)
	tmp = 0.0
	if (Float64(x * y) <= -6.2e+91)
		tmp = t_3;
	elseif (Float64(x * y) <= -2.35e-265)
		tmp = Float64(c + t_1);
	elseif (Float64(x * y) <= 2.2e-65)
		tmp = Float64(t_2 + t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b * -0.25);
	t_2 = t * (z * 0.0625);
	t_3 = (x * y) + t_2;
	tmp = 0.0;
	if ((x * y) <= -6.2e+91)
		tmp = t_3;
	elseif ((x * y) <= -2.35e-265)
		tmp = c + t_1;
	elseif ((x * y) <= 2.2e-65)
		tmp = t_2 + t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -6.2e+91], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -2.35e-265], N[(c + t$95$1), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.2e-65], N[(t$95$2 + t$95$1), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -6.19999999999999995e91 or 2.20000000000000021e-65 < (*.f64 x y)

   1. Initial program 94.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 94.9%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. associate--l+ 94.9%

         \[\leadsto \color{blue}{x \cdot y + \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. fma-def 99.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      4. associate-*l/ 99.2%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

      5. fma-neg 99.2%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

      6. sub-neg 99.2%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, -\color{blue}{\left(\frac{a \cdot b}{4} + \left(-c\right)\right)}\right)\right) \]

      7. distribute-neg-in 99.2%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(-\frac{a \cdot b}{4}\right) + \left(-\left(-c\right)\right)}\right)\right) \]

      8. remove-double-neg 99.2%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\frac{a \cdot b}{4}\right) + \color{blue}{c}\right)\right) \]

      9. associate-/l* 99.2%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      10. distribute-frac-neg 99.2%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{\frac{4}{b}}} + c\right)\right) \]

      11. associate-/r/ 99.2%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{4} \cdot b} + c\right)\right) \]

      12. fma-def 99.2%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\mathsf{fma}\left(\frac{-a}{4}, b, c\right)}\right)\right) \]

      13. neg-mul-1 99.2%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

      14. *-commutative 99.2%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

      15. associate-/l* 99.2%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

      16. metadata-eval 99.2%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{\color{blue}{-4}}, b, c\right)\right)\right) \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 94.9%

         \[\leadsto \color{blue}{x \cdot y + \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      2. fma-udef 94.9%

         \[\leadsto x \cdot y + \color{blue}{\left(\frac{z}{16} \cdot t + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      3. associate-*l/ 94.9%

         \[\leadsto x \cdot y + \left(\color{blue}{\frac{z \cdot t}{16}} + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right) \]

      4. fma-udef 94.9%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \color{blue}{\left(\frac{a}{-4} \cdot b + c\right)}\right) \]

      5. associate-/r/ 94.9%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \left(\color{blue}{\frac{a}{\frac{-4}{b}}} + c\right)\right) \]

      6. associate-+r+ 94.9%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]

      7. associate-*l/ 94.9%

         \[\leadsto \left(x \cdot y + \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      8. fma-udef 96.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      9. +-commutative 96.6%

         \[\leadsto \color{blue}{\left(\frac{a}{\frac{-4}{b}} + c\right) + \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} \]

      10. fma-udef 94.9%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} \]

      11. associate-*l/ 94.9%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) \]

      12. associate-+r+ 94.9%

          \[\leadsto \color{blue}{\left(\left(\frac{a}{\frac{-4}{b}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16}} \]

      13. div-inv 94.9%

          \[\leadsto \left(\left(\color{blue}{a \cdot \frac{1}{\frac{-4}{b}}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      14. fma-def 94.9%

          \[\leadsto \left(\color{blue}{\mathsf{fma}\left(a, \frac{1}{\frac{-4}{b}}, c\right)} + x \cdot y\right) + \frac{z \cdot t}{16} \]

      15. clear-num 94.9%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{\frac{b}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      16. div-inv 94.9%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{b \cdot \frac{1}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      17. metadata-eval 94.9%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot \color{blue}{-0.25}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      18. associate-*l/ 94.9%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\frac{z}{16} \cdot t} \]

   6. Applied egg-rr 94.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + t \cdot \left(z \cdot 0.0625\right)} \]

   7. Taylor expanded in x around inf 82.0%

      \[\leadsto \color{blue}{x \cdot y} + t \cdot \left(z \cdot 0.0625\right) \]

   if -6.19999999999999995e91 < (*.f64 x y) < -2.34999999999999993e-265

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 77.8%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 77.8%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

      2. associate-*r* 77.8%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   5. Simplified 77.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   if -2.34999999999999993e-265 < (*.f64 x y) < 2.20000000000000021e-65

   1. Initial program 98.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 98.7%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. associate--l+ 98.7%

         \[\leadsto \color{blue}{x \cdot y + \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. fma-def 98.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      4. associate-*l/ 98.7%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

      5. fma-neg 98.7%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

      6. sub-neg 98.7%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, -\color{blue}{\left(\frac{a \cdot b}{4} + \left(-c\right)\right)}\right)\right) \]

      7. distribute-neg-in 98.7%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(-\frac{a \cdot b}{4}\right) + \left(-\left(-c\right)\right)}\right)\right) \]

      8. remove-double-neg 98.7%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\frac{a \cdot b}{4}\right) + \color{blue}{c}\right)\right) \]

      9. associate-/l* 98.6%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      10. distribute-frac-neg 98.6%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{\frac{4}{b}}} + c\right)\right) \]

      11. associate-/r/ 98.7%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{4} \cdot b} + c\right)\right) \]

      12. fma-def 98.7%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\mathsf{fma}\left(\frac{-a}{4}, b, c\right)}\right)\right) \]

      13. neg-mul-1 98.7%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

      14. *-commutative 98.7%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

      15. associate-/l* 98.7%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

      16. metadata-eval 98.7%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{\color{blue}{-4}}, b, c\right)\right)\right) \]

   3. Simplified 98.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 98.7%

         \[\leadsto \color{blue}{x \cdot y + \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      2. fma-udef 98.7%

         \[\leadsto x \cdot y + \color{blue}{\left(\frac{z}{16} \cdot t + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      3. associate-*l/ 98.7%

         \[\leadsto x \cdot y + \left(\color{blue}{\frac{z \cdot t}{16}} + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right) \]

      4. fma-udef 98.7%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \color{blue}{\left(\frac{a}{-4} \cdot b + c\right)}\right) \]

      5. associate-/r/ 98.6%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \left(\color{blue}{\frac{a}{\frac{-4}{b}}} + c\right)\right) \]

      6. associate-+r+ 98.6%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]

      7. associate-*l/ 98.6%

         \[\leadsto \left(x \cdot y + \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      8. fma-udef 98.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      9. +-commutative 98.6%

         \[\leadsto \color{blue}{\left(\frac{a}{\frac{-4}{b}} + c\right) + \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} \]

      10. fma-udef 98.6%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} \]

      11. associate-*l/ 98.6%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) \]

      12. associate-+r+ 98.6%

          \[\leadsto \color{blue}{\left(\left(\frac{a}{\frac{-4}{b}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16}} \]

      13. div-inv 98.6%

          \[\leadsto \left(\left(\color{blue}{a \cdot \frac{1}{\frac{-4}{b}}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      14. fma-def 98.7%

          \[\leadsto \left(\color{blue}{\mathsf{fma}\left(a, \frac{1}{\frac{-4}{b}}, c\right)} + x \cdot y\right) + \frac{z \cdot t}{16} \]

      15. clear-num 98.7%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{\frac{b}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      16. div-inv 98.7%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{b \cdot \frac{1}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      17. metadata-eval 98.7%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot \color{blue}{-0.25}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      18. associate-*l/ 98.7%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\frac{z}{16} \cdot t} \]

   6. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + t \cdot \left(z \cdot 0.0625\right)} \]

   7. Taylor expanded in a around inf 78.0%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + t \cdot \left(z \cdot 0.0625\right) \]
   8. Step-by-step derivation

      1. *-commutative 78.0%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + t \cdot \left(z \cdot 0.0625\right) \]

      2. associate-*r* 78.0%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + t \cdot \left(z \cdot 0.0625\right) \]

      3. *-commutative 78.0%

         \[\leadsto a \cdot \color{blue}{\left(-0.25 \cdot b\right)} + t \cdot \left(z \cdot 0.0625\right) \]

   9. Simplified 78.0%

      \[\leadsto \color{blue}{a \cdot \left(-0.25 \cdot b\right)} + t \cdot \left(z \cdot 0.0625\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.2 \cdot 10^{+91}:\\ \;\;\;\;x \cdot y + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -2.35 \cdot 10^{-265}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right) + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{if}\;x \cdot y \leq -1.6 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-320}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 6.5 \cdot 10^{+43}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* t (* z 0.0625)))))
   (if (<= (* x y) -1.6e+85)
     t_1
     (if (<= (* x y) -1e-320)
       (+ c (* a (* b -0.25)))
       (if (<= (* x y) 6.5e+43) (+ c (* 0.0625 (* z t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + (t * (z * 0.0625));
	double tmp;
	if ((x * y) <= -1.6e+85) {
		tmp = t_1;
	} else if ((x * y) <= -1e-320) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 6.5e+43) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (t * (z * 0.0625d0))
    if ((x * y) <= (-1.6d+85)) then
        tmp = t_1
    else if ((x * y) <= (-1d-320)) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 6.5d+43) then
        tmp = c + (0.0625d0 * (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + (t * (z * 0.0625));
	double tmp;
	if ((x * y) <= -1.6e+85) {
		tmp = t_1;
	} else if ((x * y) <= -1e-320) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 6.5e+43) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + (t * (z * 0.0625))
	tmp = 0
	if (x * y) <= -1.6e+85:
		tmp = t_1
	elif (x * y) <= -1e-320:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 6.5e+43:
		tmp = c + (0.0625 * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + Float64(t * Float64(z * 0.0625)))
	tmp = 0.0
	if (Float64(x * y) <= -1.6e+85)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e-320)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 6.5e+43)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + (t * (z * 0.0625));
	tmp = 0.0;
	if ((x * y) <= -1.6e+85)
		tmp = t_1;
	elseif ((x * y) <= -1e-320)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 6.5e+43)
		tmp = c + (0.0625 * (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.6e+85], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e-320], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.5e+43], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.60000000000000009e85 or 6.4999999999999998e43 < (*.f64 x y)

   1. Initial program 94.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 94.1%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. associate--l+ 94.1%

         \[\leadsto \color{blue}{x \cdot y + \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. fma-def 99.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      4. associate-*l/ 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

      5. fma-neg 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

      6. sub-neg 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, -\color{blue}{\left(\frac{a \cdot b}{4} + \left(-c\right)\right)}\right)\right) \]

      7. distribute-neg-in 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(-\frac{a \cdot b}{4}\right) + \left(-\left(-c\right)\right)}\right)\right) \]

      8. remove-double-neg 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\frac{a \cdot b}{4}\right) + \color{blue}{c}\right)\right) \]

      9. associate-/l* 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      10. distribute-frac-neg 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{\frac{4}{b}}} + c\right)\right) \]

      11. associate-/r/ 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{4} \cdot b} + c\right)\right) \]

      12. fma-def 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\mathsf{fma}\left(\frac{-a}{4}, b, c\right)}\right)\right) \]

      13. neg-mul-1 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

      14. *-commutative 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

      15. associate-/l* 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

      16. metadata-eval 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{\color{blue}{-4}}, b, c\right)\right)\right) \]

   3. Simplified 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 94.1%

         \[\leadsto \color{blue}{x \cdot y + \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      2. fma-udef 94.1%

         \[\leadsto x \cdot y + \color{blue}{\left(\frac{z}{16} \cdot t + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      3. associate-*l/ 94.1%

         \[\leadsto x \cdot y + \left(\color{blue}{\frac{z \cdot t}{16}} + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right) \]

      4. fma-udef 94.1%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \color{blue}{\left(\frac{a}{-4} \cdot b + c\right)}\right) \]

      5. associate-/r/ 94.1%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \left(\color{blue}{\frac{a}{\frac{-4}{b}}} + c\right)\right) \]

      6. associate-+r+ 94.1%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]

      7. associate-*l/ 94.1%

         \[\leadsto \left(x \cdot y + \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      8. fma-udef 96.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      9. +-commutative 96.1%

         \[\leadsto \color{blue}{\left(\frac{a}{\frac{-4}{b}} + c\right) + \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} \]

      10. fma-udef 94.1%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} \]

      11. associate-*l/ 94.1%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) \]

      12. associate-+r+ 94.1%

          \[\leadsto \color{blue}{\left(\left(\frac{a}{\frac{-4}{b}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16}} \]

      13. div-inv 94.1%

          \[\leadsto \left(\left(\color{blue}{a \cdot \frac{1}{\frac{-4}{b}}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      14. fma-def 94.1%

          \[\leadsto \left(\color{blue}{\mathsf{fma}\left(a, \frac{1}{\frac{-4}{b}}, c\right)} + x \cdot y\right) + \frac{z \cdot t}{16} \]

      15. clear-num 94.1%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{\frac{b}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      16. div-inv 94.1%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{b \cdot \frac{1}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      17. metadata-eval 94.1%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot \color{blue}{-0.25}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      18. associate-*l/ 94.1%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\frac{z}{16} \cdot t} \]

   6. Applied egg-rr 94.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + t \cdot \left(z \cdot 0.0625\right)} \]

   7. Taylor expanded in x around inf 84.3%

      \[\leadsto \color{blue}{x \cdot y} + t \cdot \left(z \cdot 0.0625\right) \]

   if -1.60000000000000009e85 < (*.f64 x y) < -9.99989e-321

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 75.9%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 75.9%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

      2. associate-*r* 75.9%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   5. Simplified 75.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   if -9.99989e-321 < (*.f64 x y) < 6.4999999999999998e43

   1. Initial program 98.8%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 66.7%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.6 \cdot 10^{+85}:\\ \;\;\;\;x \cdot y + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-320}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 6.5 \cdot 10^{+43}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -3.5 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-320}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 7.2 \cdot 10^{+115}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))))
   (if (<= (* x y) -3.5e+87)
     t_1
     (if (<= (* x y) -1e-320)
       (+ c (* a (* b -0.25)))
       (if (<= (* x y) 7.2e+115) (+ c (* 0.0625 (* z t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if ((x * y) <= -3.5e+87) {
		tmp = t_1;
	} else if ((x * y) <= -1e-320) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 7.2e+115) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + (x * y)
    if ((x * y) <= (-3.5d+87)) then
        tmp = t_1
    else if ((x * y) <= (-1d-320)) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 7.2d+115) then
        tmp = c + (0.0625d0 * (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if ((x * y) <= -3.5e+87) {
		tmp = t_1;
	} else if ((x * y) <= -1e-320) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 7.2e+115) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	tmp = 0
	if (x * y) <= -3.5e+87:
		tmp = t_1
	elif (x * y) <= -1e-320:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 7.2e+115:
		tmp = c + (0.0625 * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -3.5e+87)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e-320)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 7.2e+115)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -3.5e+87)
		tmp = t_1;
	elseif ((x * y) <= -1e-320)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 7.2e+115)
		tmp = c + (0.0625 * (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.5e+87], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e-320], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7.2e+115], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.49999999999999986e87 or 7.2000000000000001e115 < (*.f64 x y)

   1. Initial program 93.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.8%

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

   if -3.49999999999999986e87 < (*.f64 x y) < -9.99989e-321

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 75.9%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 75.9%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

      2. associate-*r* 75.9%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   5. Simplified 75.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   if -9.99989e-321 < (*.f64 x y) < 7.2000000000000001e115

   1. Initial program 98.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 66.5%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.5 \cdot 10^{+87}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-320}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 7.2 \cdot 10^{+115}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -8.4 \cdot 10^{+113} \lor \neg \left(x \cdot y \leq 1.6 \cdot 10^{-65}\right):\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + t_1\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (or (<= (* x y) -8.4e+113) (not (<= (* x y) 1.6e-65)))
     (+ c (+ (* x y) t_1))
     (- (+ c t_1) (* (* a b) 0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if (((x * y) <= -8.4e+113) || !((x * y) <= 1.6e-65)) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + t_1) - ((a * b) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if (((x * y) <= (-8.4d+113)) .or. (.not. ((x * y) <= 1.6d-65))) then
        tmp = c + ((x * y) + t_1)
    else
        tmp = (c + t_1) - ((a * b) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if (((x * y) <= -8.4e+113) || !((x * y) <= 1.6e-65)) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + t_1) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if ((x * y) <= -8.4e+113) or not ((x * y) <= 1.6e-65):
		tmp = c + ((x * y) + t_1)
	else:
		tmp = (c + t_1) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if ((Float64(x * y) <= -8.4e+113) || !(Float64(x * y) <= 1.6e-65))
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	else
		tmp = Float64(Float64(c + t_1) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if (((x * y) <= -8.4e+113) || ~(((x * y) <= 1.6e-65)))
		tmp = c + ((x * y) + t_1);
	else
		tmp = (c + t_1) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(x * y), $MachinePrecision], -8.4e+113], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.6e-65]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(c + t$95$1), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -8.3999999999999996e113 or 1.6e-65 < (*.f64 x y)

   1. Initial program 94.8%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 90.9%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} + c \]

   if -8.3999999999999996e113 < (*.f64 x y) < 1.6e-65

   1. Initial program 99.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.4%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.4 \cdot 10^{+113} \lor \neg \left(x \cdot y \leq 1.6 \cdot 10^{-65}\right):\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.4 \cdot 10^{+113}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.3 \cdot 10^{-271}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -8.4e+113)
   (* x y)
   (if (<= (* x y) -2.3e-271)
     c
     (if (<= (* x y) 2e+115) (* t (* z 0.0625)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -8.4e+113) {
		tmp = x * y;
	} else if ((x * y) <= -2.3e-271) {
		tmp = c;
	} else if ((x * y) <= 2e+115) {
		tmp = t * (z * 0.0625);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x * y) <= (-8.4d+113)) then
        tmp = x * y
    else if ((x * y) <= (-2.3d-271)) then
        tmp = c
    else if ((x * y) <= 2d+115) then
        tmp = t * (z * 0.0625d0)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -8.4e+113) {
		tmp = x * y;
	} else if ((x * y) <= -2.3e-271) {
		tmp = c;
	} else if ((x * y) <= 2e+115) {
		tmp = t * (z * 0.0625);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -8.4e+113:
		tmp = x * y
	elif (x * y) <= -2.3e-271:
		tmp = c
	elif (x * y) <= 2e+115:
		tmp = t * (z * 0.0625)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -8.4e+113)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2.3e-271)
		tmp = c;
	elseif (Float64(x * y) <= 2e+115)
		tmp = Float64(t * Float64(z * 0.0625));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -8.4e+113)
		tmp = x * y;
	elseif ((x * y) <= -2.3e-271)
		tmp = c;
	elseif ((x * y) <= 2e+115)
		tmp = t * (z * 0.0625);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -8.4e+113], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.3e-271], c, If[LessEqual[N[(x * y), $MachinePrecision], 2e+115], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.3999999999999996e113 or 2e115 < (*.f64 x y)

   1. Initial program 93.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 93.4%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. associate--l+ 93.4%

         \[\leadsto \color{blue}{x \cdot y + \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. fma-def 98.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      4. associate-*l/ 98.9%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

      5. fma-neg 98.9%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

      6. sub-neg 98.9%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, -\color{blue}{\left(\frac{a \cdot b}{4} + \left(-c\right)\right)}\right)\right) \]

      7. distribute-neg-in 98.9%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(-\frac{a \cdot b}{4}\right) + \left(-\left(-c\right)\right)}\right)\right) \]

      8. remove-double-neg 98.9%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\frac{a \cdot b}{4}\right) + \color{blue}{c}\right)\right) \]

      9. associate-/l* 98.9%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      10. distribute-frac-neg 98.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{\frac{4}{b}}} + c\right)\right) \]

      11. associate-/r/ 98.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{4} \cdot b} + c\right)\right) \]

      12. fma-def 98.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\mathsf{fma}\left(\frac{-a}{4}, b, c\right)}\right)\right) \]

      13. neg-mul-1 98.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

      14. *-commutative 98.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

      15. associate-/l* 98.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

      16. metadata-eval 98.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{\color{blue}{-4}}, b, c\right)\right)\right) \]

   3. Simplified 98.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 93.4%

         \[\leadsto \color{blue}{x \cdot y + \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      2. fma-udef 93.4%

         \[\leadsto x \cdot y + \color{blue}{\left(\frac{z}{16} \cdot t + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      3. associate-*l/ 93.4%

         \[\leadsto x \cdot y + \left(\color{blue}{\frac{z \cdot t}{16}} + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right) \]

      4. fma-udef 93.4%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \color{blue}{\left(\frac{a}{-4} \cdot b + c\right)}\right) \]

      5. associate-/r/ 93.4%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \left(\color{blue}{\frac{a}{\frac{-4}{b}}} + c\right)\right) \]

      6. associate-+r+ 93.4%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]

      7. associate-*l/ 93.4%

         \[\leadsto \left(x \cdot y + \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      8. fma-udef 95.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      9. +-commutative 95.6%

         \[\leadsto \color{blue}{\left(\frac{a}{\frac{-4}{b}} + c\right) + \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} \]

      10. fma-udef 93.4%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} \]

      11. associate-*l/ 93.4%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) \]

      12. associate-+r+ 93.4%

          \[\leadsto \color{blue}{\left(\left(\frac{a}{\frac{-4}{b}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16}} \]

      13. div-inv 93.4%

          \[\leadsto \left(\left(\color{blue}{a \cdot \frac{1}{\frac{-4}{b}}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      14. fma-def 93.4%

          \[\leadsto \left(\color{blue}{\mathsf{fma}\left(a, \frac{1}{\frac{-4}{b}}, c\right)} + x \cdot y\right) + \frac{z \cdot t}{16} \]

      15. clear-num 93.4%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{\frac{b}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      16. div-inv 93.4%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{b \cdot \frac{1}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      17. metadata-eval 93.4%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot \color{blue}{-0.25}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      18. associate-*l/ 93.4%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\frac{z}{16} \cdot t} \]

   6. Applied egg-rr 93.4%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + t \cdot \left(z \cdot 0.0625\right)} \]

   7. Taylor expanded in x around inf 84.6%

      \[\leadsto \color{blue}{x \cdot y} + t \cdot \left(z \cdot 0.0625\right) \]

   8. Taylor expanded in x around inf 74.1%

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

   if -8.3999999999999996e113 < (*.f64 x y) < -2.30000000000000009e-271

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 49.0%

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

   if -2.30000000000000009e-271 < (*.f64 x y) < 2e115

   1. Initial program 99.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 99.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. associate--l+ 99.0%

         \[\leadsto \color{blue}{x \cdot y + \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. fma-def 99.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      4. associate-*l/ 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

      5. fma-neg 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

      6. sub-neg 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, -\color{blue}{\left(\frac{a \cdot b}{4} + \left(-c\right)\right)}\right)\right) \]

      7. distribute-neg-in 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(-\frac{a \cdot b}{4}\right) + \left(-\left(-c\right)\right)}\right)\right) \]

      8. remove-double-neg 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\frac{a \cdot b}{4}\right) + \color{blue}{c}\right)\right) \]

      9. associate-/l* 98.9%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      10. distribute-frac-neg 98.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{\frac{4}{b}}} + c\right)\right) \]

      11. associate-/r/ 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{4} \cdot b} + c\right)\right) \]

      12. fma-def 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\mathsf{fma}\left(\frac{-a}{4}, b, c\right)}\right)\right) \]

      13. neg-mul-1 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

      14. *-commutative 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

      15. associate-/l* 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

      16. metadata-eval 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{\color{blue}{-4}}, b, c\right)\right)\right) \]

   3. Simplified 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 99.0%

         \[\leadsto \color{blue}{x \cdot y + \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      2. fma-udef 99.0%

         \[\leadsto x \cdot y + \color{blue}{\left(\frac{z}{16} \cdot t + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      3. associate-*l/ 99.0%

         \[\leadsto x \cdot y + \left(\color{blue}{\frac{z \cdot t}{16}} + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right) \]

      4. fma-udef 99.0%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \color{blue}{\left(\frac{a}{-4} \cdot b + c\right)}\right) \]

      5. associate-/r/ 98.9%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \left(\color{blue}{\frac{a}{\frac{-4}{b}}} + c\right)\right) \]

      6. associate-+r+ 98.9%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]

      7. associate-*l/ 98.9%

         \[\leadsto \left(x \cdot y + \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      8. fma-udef 98.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      9. +-commutative 98.9%

         \[\leadsto \color{blue}{\left(\frac{a}{\frac{-4}{b}} + c\right) + \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} \]

      10. fma-udef 98.9%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} \]

      11. associate-*l/ 98.9%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) \]

      12. associate-+r+ 98.9%

          \[\leadsto \color{blue}{\left(\left(\frac{a}{\frac{-4}{b}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16}} \]

      13. div-inv 99.0%

          \[\leadsto \left(\left(\color{blue}{a \cdot \frac{1}{\frac{-4}{b}}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      14. fma-def 99.0%

          \[\leadsto \left(\color{blue}{\mathsf{fma}\left(a, \frac{1}{\frac{-4}{b}}, c\right)} + x \cdot y\right) + \frac{z \cdot t}{16} \]

      15. clear-num 99.0%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{\frac{b}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      16. div-inv 99.0%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{b \cdot \frac{1}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      17. metadata-eval 99.0%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot \color{blue}{-0.25}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      18. associate-*l/ 99.0%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\frac{z}{16} \cdot t} \]

   6. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + t \cdot \left(z \cdot 0.0625\right)} \]

   7. Taylor expanded in t around inf 45.5%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 45.5%

         \[\leadsto \color{blue}{\left(t \cdot z\right) \cdot 0.0625} \]

      2. associate-*r* 45.5%

         \[\leadsto \color{blue}{t \cdot \left(z \cdot 0.0625\right)} \]

      3. *-commutative 45.5%

         \[\leadsto t \cdot \color{blue}{\left(0.0625 \cdot z\right)} \]

   9. Simplified 45.5%

      \[\leadsto \color{blue}{t \cdot \left(0.0625 \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.4 \cdot 10^{+113}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.3 \cdot 10^{-271}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+263}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right) + t_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+190}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= (* a b) -2e+263)
     (+ (* t (* z 0.0625)) t_1)
     (if (<= (* a b) 2e+190) (+ c (+ (* x y) (* 0.0625 (* z t)))) (+ c t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double tmp;
	if ((a * b) <= -2e+263) {
		tmp = (t * (z * 0.0625)) + t_1;
	} else if ((a * b) <= 2e+190) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * (-0.25d0))
    if ((a * b) <= (-2d+263)) then
        tmp = (t * (z * 0.0625d0)) + t_1
    else if ((a * b) <= 2d+190) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = c + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double tmp;
	if ((a * b) <= -2e+263) {
		tmp = (t * (z * 0.0625)) + t_1;
	} else if ((a * b) <= 2e+190) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	tmp = 0
	if (a * b) <= -2e+263:
		tmp = (t * (z * 0.0625)) + t_1
	elif (a * b) <= 2e+190:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = c + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (Float64(a * b) <= -2e+263)
		tmp = Float64(Float64(t * Float64(z * 0.0625)) + t_1);
	elseif (Float64(a * b) <= 2e+190)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(c + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b * -0.25);
	tmp = 0.0;
	if ((a * b) <= -2e+263)
		tmp = (t * (z * 0.0625)) + t_1;
	elseif ((a * b) <= 2e+190)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = c + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+263], N[(N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+190], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.00000000000000003e263

   1. Initial program 88.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 88.2%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. associate--l+ 88.2%

         \[\leadsto \color{blue}{x \cdot y + \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. fma-def 88.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      4. associate-*l/ 88.2%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

      5. fma-neg 88.2%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

      6. sub-neg 88.2%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, -\color{blue}{\left(\frac{a \cdot b}{4} + \left(-c\right)\right)}\right)\right) \]

      7. distribute-neg-in 88.2%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(-\frac{a \cdot b}{4}\right) + \left(-\left(-c\right)\right)}\right)\right) \]

      8. remove-double-neg 88.2%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\frac{a \cdot b}{4}\right) + \color{blue}{c}\right)\right) \]

      9. associate-/l* 88.1%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      10. distribute-frac-neg 88.1%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{\frac{4}{b}}} + c\right)\right) \]

      11. associate-/r/ 88.2%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{4} \cdot b} + c\right)\right) \]

      12. fma-def 88.2%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\mathsf{fma}\left(\frac{-a}{4}, b, c\right)}\right)\right) \]

      13. neg-mul-1 88.2%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

      14. *-commutative 88.2%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

      15. associate-/l* 88.2%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

      16. metadata-eval 88.2%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{\color{blue}{-4}}, b, c\right)\right)\right) \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 88.2%

         \[\leadsto \color{blue}{x \cdot y + \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      2. fma-udef 88.2%

         \[\leadsto x \cdot y + \color{blue}{\left(\frac{z}{16} \cdot t + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      3. associate-*l/ 88.2%

         \[\leadsto x \cdot y + \left(\color{blue}{\frac{z \cdot t}{16}} + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right) \]

      4. fma-udef 88.2%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \color{blue}{\left(\frac{a}{-4} \cdot b + c\right)}\right) \]

      5. associate-/r/ 88.1%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \left(\color{blue}{\frac{a}{\frac{-4}{b}}} + c\right)\right) \]

      6. associate-+r+ 88.1%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]

      7. associate-*l/ 88.1%

         \[\leadsto \left(x \cdot y + \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      8. fma-udef 88.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      9. +-commutative 88.1%

         \[\leadsto \color{blue}{\left(\frac{a}{\frac{-4}{b}} + c\right) + \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} \]

      10. fma-udef 88.1%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} \]

      11. associate-*l/ 88.1%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) \]

      12. associate-+r+ 88.1%

          \[\leadsto \color{blue}{\left(\left(\frac{a}{\frac{-4}{b}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16}} \]

      13. div-inv 88.2%

          \[\leadsto \left(\left(\color{blue}{a \cdot \frac{1}{\frac{-4}{b}}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      14. fma-def 88.2%

          \[\leadsto \left(\color{blue}{\mathsf{fma}\left(a, \frac{1}{\frac{-4}{b}}, c\right)} + x \cdot y\right) + \frac{z \cdot t}{16} \]

      15. clear-num 88.2%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{\frac{b}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      16. div-inv 88.2%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{b \cdot \frac{1}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      17. metadata-eval 88.2%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot \color{blue}{-0.25}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      18. associate-*l/ 88.2%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\frac{z}{16} \cdot t} \]

   6. Applied egg-rr 88.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + t \cdot \left(z \cdot 0.0625\right)} \]

   7. Taylor expanded in a around inf 88.2%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + t \cdot \left(z \cdot 0.0625\right) \]
   8. Step-by-step derivation

      1. *-commutative 88.2%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + t \cdot \left(z \cdot 0.0625\right) \]

      2. associate-*r* 88.2%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + t \cdot \left(z \cdot 0.0625\right) \]

      3. *-commutative 88.2%

         \[\leadsto a \cdot \color{blue}{\left(-0.25 \cdot b\right)} + t \cdot \left(z \cdot 0.0625\right) \]

   9. Simplified 88.2%

      \[\leadsto \color{blue}{a \cdot \left(-0.25 \cdot b\right)} + t \cdot \left(z \cdot 0.0625\right) \]

   if -2.00000000000000003e263 < (*.f64 a b) < 2.0000000000000001e190

   1. Initial program 99.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 89.8%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} + c \]

   if 2.0000000000000001e190 < (*.f64 a b)

   1. Initial program 89.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 96.4%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 96.4%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

      2. associate-*r* 96.4%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   5. Simplified 96.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+263}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right) + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+190}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.02 \cdot 10^{+114} \lor \neg \left(x \cdot y \leq 7.2 \cdot 10^{+115}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.02e+114) (not (<= (* x y) 7.2e+115)))
   (+ c (* x y))
   (+ c (* 0.0625 (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.02e+114) || !((x * y) <= 7.2e+115)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-1.02d+114)) .or. (.not. ((x * y) <= 7.2d+115))) then
        tmp = c + (x * y)
    else
        tmp = c + (0.0625d0 * (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.02e+114) || !((x * y) <= 7.2e+115)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.02e+114) or not ((x * y) <= 7.2e+115):
		tmp = c + (x * y)
	else:
		tmp = c + (0.0625 * (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.02e+114) || !(Float64(x * y) <= 7.2e+115))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1.02e+114) || ~(((x * y) <= 7.2e+115)))
		tmp = c + (x * y);
	else
		tmp = c + (0.0625 * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.02e+114], N[Not[LessEqual[N[(x * y), $MachinePrecision], 7.2e+115]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.01999999999999999e114 or 7.2000000000000001e115 < (*.f64 x y)

   1. Initial program 93.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 78.1%

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

   if -1.01999999999999999e114 < (*.f64 x y) < 7.2000000000000001e115

   1. Initial program 99.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 66.8%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.02 \cdot 10^{+114} \lor \neg \left(x \cdot y \leq 7.2 \cdot 10^{+115}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 41.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.01 \cdot 10^{+114} \lor \neg \left(x \cdot y \leq 7.2 \cdot 10^{+39}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.01e+114) (not (<= (* x y) 7.2e+39))) (* x y) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.01e+114) || !((x * y) <= 7.2e+39)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-1.01d+114)) .or. (.not. ((x * y) <= 7.2d+39))) then
        tmp = x * y
    else
        tmp = c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.01e+114) || !((x * y) <= 7.2e+39)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.01e+114) or not ((x * y) <= 7.2e+39):
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.01e+114) || !(Float64(x * y) <= 7.2e+39))
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1.01e+114) || ~(((x * y) <= 7.2e+39)))
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.01e+114], N[Not[LessEqual[N[(x * y), $MachinePrecision], 7.2e+39]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.00999999999999993e114 or 7.19999999999999969e39 < (*.f64 x y)

   1. Initial program 94.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 94.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. associate--l+ 94.0%

         \[\leadsto \color{blue}{x \cdot y + \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. fma-def 99.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      4. associate-*l/ 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

      5. fma-neg 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

      6. sub-neg 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, -\color{blue}{\left(\frac{a \cdot b}{4} + \left(-c\right)\right)}\right)\right) \]

      7. distribute-neg-in 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(-\frac{a \cdot b}{4}\right) + \left(-\left(-c\right)\right)}\right)\right) \]

      8. remove-double-neg 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\frac{a \cdot b}{4}\right) + \color{blue}{c}\right)\right) \]

      9. associate-/l* 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      10. distribute-frac-neg 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{\frac{4}{b}}} + c\right)\right) \]

      11. associate-/r/ 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{4} \cdot b} + c\right)\right) \]

      12. fma-def 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\mathsf{fma}\left(\frac{-a}{4}, b, c\right)}\right)\right) \]

      13. neg-mul-1 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

      14. *-commutative 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

      15. associate-/l* 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

      16. metadata-eval 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{\color{blue}{-4}}, b, c\right)\right)\right) \]

   3. Simplified 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 94.0%

         \[\leadsto \color{blue}{x \cdot y + \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      2. fma-udef 94.0%

         \[\leadsto x \cdot y + \color{blue}{\left(\frac{z}{16} \cdot t + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      3. associate-*l/ 94.0%

         \[\leadsto x \cdot y + \left(\color{blue}{\frac{z \cdot t}{16}} + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right) \]

      4. fma-udef 94.0%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \color{blue}{\left(\frac{a}{-4} \cdot b + c\right)}\right) \]

      5. associate-/r/ 94.0%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \left(\color{blue}{\frac{a}{\frac{-4}{b}}} + c\right)\right) \]

      6. associate-+r+ 94.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]

      7. associate-*l/ 94.0%

         \[\leadsto \left(x \cdot y + \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      8. fma-udef 96.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      9. +-commutative 96.0%

         \[\leadsto \color{blue}{\left(\frac{a}{\frac{-4}{b}} + c\right) + \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} \]

      10. fma-udef 94.0%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} \]

      11. associate-*l/ 94.0%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) \]

      12. associate-+r+ 94.0%

          \[\leadsto \color{blue}{\left(\left(\frac{a}{\frac{-4}{b}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16}} \]

      13. div-inv 94.0%

          \[\leadsto \left(\left(\color{blue}{a \cdot \frac{1}{\frac{-4}{b}}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      14. fma-def 94.0%

          \[\leadsto \left(\color{blue}{\mathsf{fma}\left(a, \frac{1}{\frac{-4}{b}}, c\right)} + x \cdot y\right) + \frac{z \cdot t}{16} \]

      15. clear-num 94.0%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{\frac{b}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      16. div-inv 94.0%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{b \cdot \frac{1}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      17. metadata-eval 94.0%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot \color{blue}{-0.25}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      18. associate-*l/ 94.0%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\frac{z}{16} \cdot t} \]

   6. Applied egg-rr 94.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + t \cdot \left(z \cdot 0.0625\right)} \]

   7. Taylor expanded in x around inf 84.9%

      \[\leadsto \color{blue}{x \cdot y} + t \cdot \left(z \cdot 0.0625\right) \]

   8. Taylor expanded in x around inf 71.3%

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

   if -1.00999999999999993e114 < (*.f64 x y) < 7.19999999999999969e39

   1. Initial program 99.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 34.0%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.01 \cdot 10^{+114} \lor \neg \left(x \cdot y \leq 7.2 \cdot 10^{+39}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-53} \lor \neg \left(t \leq 5.4 \cdot 10^{+174}\right):\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -2.3e-53) (not (<= t 5.4e+174)))
   (* t (* z 0.0625))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.3e-53) || !(t <= 5.4e+174)) {
		tmp = t * (z * 0.0625);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-2.3d-53)) .or. (.not. (t <= 5.4d+174))) then
        tmp = t * (z * 0.0625d0)
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.3e-53) || !(t <= 5.4e+174)) {
		tmp = t * (z * 0.0625);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -2.3e-53) or not (t <= 5.4e+174):
		tmp = t * (z * 0.0625)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -2.3e-53) || !(t <= 5.4e+174))
		tmp = Float64(t * Float64(z * 0.0625));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -2.3e-53) || ~((t <= 5.4e+174)))
		tmp = t * (z * 0.0625);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -2.3e-53], N[Not[LessEqual[t, 5.4e+174]], $MachinePrecision]], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3000000000000001e-53 or 5.3999999999999998e174 < t

   1. Initial program 94.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 94.9%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. associate--l+ 94.9%

         \[\leadsto \color{blue}{x \cdot y + \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. fma-def 98.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

      4. associate-*l/ 98.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

      5. fma-neg 98.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

      6. sub-neg 98.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, -\color{blue}{\left(\frac{a \cdot b}{4} + \left(-c\right)\right)}\right)\right) \]

      7. distribute-neg-in 98.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(-\frac{a \cdot b}{4}\right) + \left(-\left(-c\right)\right)}\right)\right) \]

      8. remove-double-neg 98.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\frac{a \cdot b}{4}\right) + \color{blue}{c}\right)\right) \]

      9. associate-/l* 97.9%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      10. distribute-frac-neg 97.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{\frac{4}{b}}} + c\right)\right) \]

      11. associate-/r/ 98.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{4} \cdot b} + c\right)\right) \]

      12. fma-def 98.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\mathsf{fma}\left(\frac{-a}{4}, b, c\right)}\right)\right) \]

      13. neg-mul-1 98.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

      14. *-commutative 98.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

      15. associate-/l* 98.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

      16. metadata-eval 98.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{\color{blue}{-4}}, b, c\right)\right)\right) \]

   3. Simplified 98.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 94.9%

         \[\leadsto \color{blue}{x \cdot y + \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      2. fma-udef 94.9%

         \[\leadsto x \cdot y + \color{blue}{\left(\frac{z}{16} \cdot t + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)} \]

      3. associate-*l/ 94.9%

         \[\leadsto x \cdot y + \left(\color{blue}{\frac{z \cdot t}{16}} + \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right) \]

      4. fma-udef 94.9%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \color{blue}{\left(\frac{a}{-4} \cdot b + c\right)}\right) \]

      5. associate-/r/ 94.9%

         \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \left(\color{blue}{\frac{a}{\frac{-4}{b}}} + c\right)\right) \]

      6. associate-+r+ 94.9%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right)} \]

      7. associate-*l/ 94.9%

         \[\leadsto \left(x \cdot y + \color{blue}{\frac{z}{16} \cdot t}\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      8. fma-udef 96.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

      9. +-commutative 96.9%

         \[\leadsto \color{blue}{\left(\frac{a}{\frac{-4}{b}} + c\right) + \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right)} \]

      10. fma-udef 94.9%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \color{blue}{\left(x \cdot y + \frac{z}{16} \cdot t\right)} \]

      11. associate-*l/ 94.9%

          \[\leadsto \left(\frac{a}{\frac{-4}{b}} + c\right) + \left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) \]

      12. associate-+r+ 94.9%

          \[\leadsto \color{blue}{\left(\left(\frac{a}{\frac{-4}{b}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16}} \]

      13. div-inv 94.9%

          \[\leadsto \left(\left(\color{blue}{a \cdot \frac{1}{\frac{-4}{b}}} + c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      14. fma-def 94.9%

          \[\leadsto \left(\color{blue}{\mathsf{fma}\left(a, \frac{1}{\frac{-4}{b}}, c\right)} + x \cdot y\right) + \frac{z \cdot t}{16} \]

      15. clear-num 94.9%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{\frac{b}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      16. div-inv 94.9%

          \[\leadsto \left(\mathsf{fma}\left(a, \color{blue}{b \cdot \frac{1}{-4}}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      17. metadata-eval 94.9%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot \color{blue}{-0.25}, c\right) + x \cdot y\right) + \frac{z \cdot t}{16} \]

      18. associate-*l/ 94.9%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\frac{z}{16} \cdot t} \]

   6. Applied egg-rr 94.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + t \cdot \left(z \cdot 0.0625\right)} \]

   7. Taylor expanded in t around inf 52.3%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 52.3%

         \[\leadsto \color{blue}{\left(t \cdot z\right) \cdot 0.0625} \]

      2. associate-*r* 52.3%

         \[\leadsto \color{blue}{t \cdot \left(z \cdot 0.0625\right)} \]

      3. *-commutative 52.3%

         \[\leadsto t \cdot \color{blue}{\left(0.0625 \cdot z\right)} \]

   9. Simplified 52.3%

      \[\leadsto \color{blue}{t \cdot \left(0.0625 \cdot z\right)} \]

   if -2.3000000000000001e-53 < t < 5.3999999999999998e174

   1. Initial program 98.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 63.5%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-53} \lor \neg \left(t \leq 5.4 \cdot 10^{+174}\right):\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 22.2% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ c \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 c)

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return c;
}

Python

def code(x, y, z, t, a, b, c):
	return c

Julia

function code(x, y, z, t, a, b, c)
	return c
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := c

Derivation

1. Initial program 97.2%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Add Preprocessing

3. Taylor expanded in c around inf 23.4%

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

4. Final simplification 23.4%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))