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

Percentage Accurate: 97.9% → 99.0%

Time: 15.8s

Alternatives: 19

Speedup: 1.0×

• 32.6% 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: 97.9% 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: 99.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;\left(x \cdot y + \mathsf{fma}\left(a, b \cdot -0.25, c\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t\_1\right)\\ \end{array} \end{array} \]

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)
     (fma y x t_1))))

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 = fma(y, x, t_1);
	}
	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 = fma(y, x, t_1);
	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[(y * x + t$95$1), $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* 100.0%

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

      10. distribute-frac-neg 100.0%

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

      11. associate-/r/ 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 99.9%

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

      14. fma-def 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 50.0%

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

      4. associate-*l/ 50.0%

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

      5. fma-neg 50.0%

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

      6. sub-neg 50.0%

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

      7. distribute-neg-in 50.0%

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

      8. remove-double-neg 50.0%

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

      9. associate-/l* 50.0%

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

      10. distribute-frac-neg 50.0%

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

      11. associate-/r/ 50.0%

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

      12. fma-def 50.0%

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

      13. neg-mul-1 50.0%

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

      14. *-commutative 50.0%

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

      15. associate-/l* 50.0%

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

      16. metadata-eval 50.0%

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

   3. Simplified 50.0%

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

      1. fma-udef 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 33.3%

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

      9. +-commutative 33.3%

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

      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 x around inf 50.0%

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

      1. *-commutative 50.0%

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

      2. fma-def 83.3%

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

      3. *-commutative 83.3%

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

   9. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, t \cdot \left(0.0625 \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

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

Alternative 2: 98.9% 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 97.6%

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

   1. associate-+l- 97.6%

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

   2. associate--l+ 97.6%

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

   3. fma-def 98.8%

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

   4. associate-*l/ 98.8%

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

   5. fma-neg 98.8%

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

   6. sub-neg 98.8%

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

   7. distribute-neg-in 98.8%

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

   8. remove-double-neg 98.8%

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

   9. associate-/l* 98.8%

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

   10. distribute-frac-neg 98.8%

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

   11. associate-/r/ 98.8%

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

   12. fma-def 98.8%

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

   13. neg-mul-1 98.8%

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

   14. *-commutative 98.8%

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

   15. associate-/l* 98.8%

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

   16. metadata-eval 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 3: 98.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;c + t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot \left(z \cdot 0.0625\right)\right)\\ \end{array} \end{array} \]

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) (fma y x (* t (* z 0.0625))))))

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 = fma(y, x, (t * (z * 0.0625)));
	}
	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 = fma(y, x, Float64(t * Float64(z * 0.0625)));
	end
	return 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[(y * x + N[(t * N[(z * 0.0625), $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 50.0%

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

      4. associate-*l/ 50.0%

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

      5. fma-neg 50.0%

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

      6. sub-neg 50.0%

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

      7. distribute-neg-in 50.0%

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

      8. remove-double-neg 50.0%

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

      9. associate-/l* 50.0%

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

      10. distribute-frac-neg 50.0%

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

      11. associate-/r/ 50.0%

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

      12. fma-def 50.0%

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

      13. neg-mul-1 50.0%

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

      14. *-commutative 50.0%

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

      15. associate-/l* 50.0%

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

      16. metadata-eval 50.0%

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

   3. Simplified 50.0%

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

      1. fma-udef 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 33.3%

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

      9. +-commutative 33.3%

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

      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 x around inf 50.0%

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

      1. *-commutative 50.0%

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

      2. fma-def 83.3%

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

      3. *-commutative 83.3%

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

   9. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, t \cdot \left(0.0625 \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

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

Alternative 4: 98.3% 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 97.6%

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

   1. sub-neg 97.6%

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

   2. associate-+l+ 97.6%

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

   3. fma-def 98.4%

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

   4. associate-*l/ 98.4%

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

   5. distribute-frac-neg 98.4%

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

   6. distribute-rgt-neg-out 98.4%

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

   7. associate-/l* 98.4%

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

   8. neg-mul-1 98.4%

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

   9. associate-/r* 98.4%

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

   10. metadata-eval 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 5: 64.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := z \cdot \left(t \cdot 0.0625\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -7.5 \cdot 10^{+41}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.3 \cdot 10^{-289}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{+147}:\\ \;\;\;\;c + t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25))))
        (t_2 (* z (* t 0.0625)))
        (t_3 (+ c (* x y))))
   (if (<= (* x y) -7.5e+41)
     t_3
     (if (<= (* x y) 0.0)
       t_1
       (if (<= (* x y) 1.3e-289)
         t_2
         (if (<= (* x y) 1.6e-119)
           t_1
           (if (<= (* x y) 3.2e+147) (+ c t_2) t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = z * (t * 0.0625);
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -7.5e+41) {
		tmp = t_3;
	} else if ((x * y) <= 0.0) {
		tmp = t_1;
	} else if ((x * y) <= 1.3e-289) {
		tmp = t_2;
	} else if ((x * y) <= 1.6e-119) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e+147) {
		tmp = c + t_2;
	} 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 = c + (a * (b * (-0.25d0)))
    t_2 = z * (t * 0.0625d0)
    t_3 = c + (x * y)
    if ((x * y) <= (-7.5d+41)) then
        tmp = t_3
    else if ((x * y) <= 0.0d0) then
        tmp = t_1
    else if ((x * y) <= 1.3d-289) then
        tmp = t_2
    else if ((x * y) <= 1.6d-119) then
        tmp = t_1
    else if ((x * y) <= 3.2d+147) then
        tmp = c + t_2
    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 = c + (a * (b * -0.25));
	double t_2 = z * (t * 0.0625);
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -7.5e+41) {
		tmp = t_3;
	} else if ((x * y) <= 0.0) {
		tmp = t_1;
	} else if ((x * y) <= 1.3e-289) {
		tmp = t_2;
	} else if ((x * y) <= 1.6e-119) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e+147) {
		tmp = c + t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = z * (t * 0.0625)
	t_3 = c + (x * y)
	tmp = 0
	if (x * y) <= -7.5e+41:
		tmp = t_3
	elif (x * y) <= 0.0:
		tmp = t_1
	elif (x * y) <= 1.3e-289:
		tmp = t_2
	elif (x * y) <= 1.6e-119:
		tmp = t_1
	elif (x * y) <= 3.2e+147:
		tmp = c + t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_2 = Float64(z * Float64(t * 0.0625))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -7.5e+41)
		tmp = t_3;
	elseif (Float64(x * y) <= 0.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.3e-289)
		tmp = t_2;
	elseif (Float64(x * y) <= 1.6e-119)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.2e+147)
		tmp = Float64(c + t_2);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (a * (b * -0.25));
	t_2 = z * (t * 0.0625);
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -7.5e+41)
		tmp = t_3;
	elseif ((x * y) <= 0.0)
		tmp = t_1;
	elseif ((x * y) <= 1.3e-289)
		tmp = t_2;
	elseif ((x * y) <= 1.6e-119)
		tmp = t_1;
	elseif ((x * y) <= 3.2e+147)
		tmp = c + t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -7.5e+41], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 0.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.3e-289], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1.6e-119], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.2e+147], N[(c + t$95$2), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -7.50000000000000072e41 or 3.19999999999999979e147 < (*.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. Add Preprocessing

   3. Taylor expanded in x around inf 77.4%

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

   if -7.50000000000000072e41 < (*.f64 x y) < 0.0 or 1.2999999999999999e-289 < (*.f64 x y) < 1.59999999999999997e-119

   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 68.8%

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

      1. *-commutative 68.8%

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

      2. associate-*r* 68.8%

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

   5. Simplified 68.8%

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

   if 0.0 < (*.f64 x y) < 1.2999999999999999e-289

   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* 100.0%

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

      10. distribute-frac-neg 100.0%

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

      11. associate-/r/ 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/ 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-*l/ 100.0%

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

      8. fma-udef 100.0%

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

      9. +-commutative 100.0%

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

      10. fma-udef 100.0%

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

      11. associate-*l/ 100.0%

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

      12. associate-+r+ 100.0%

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

      13. div-inv 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%

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

   7. Taylor expanded in t around inf 88.1%

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

      1. associate-*r* 88.1%

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

      2. *-commutative 88.1%

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

      3. *-commutative 88.1%

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

      4. *-commutative 88.1%

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

   9. Simplified 88.1%

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

   if 1.59999999999999997e-119 < (*.f64 x y) < 3.19999999999999979e147

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 73.8%

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

      1. associate-*r* 73.8%

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

   5. Simplified 73.8%

      \[\leadsto \color{blue}{\left(0.0625 \cdot t\right) \cdot z} + c \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.5 \cdot 10^{+41}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.3 \cdot 10^{-289}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{-119}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{+147}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 44.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right)\\ t_2 := z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;x \cdot y \leq -4.3 \cdot 10^{+77}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{-286}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 1.95 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{+147}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (* a -0.25))) (t_2 (* z (* t 0.0625))))
   (if (<= (* x y) -4.3e+77)
     (* x y)
     (if (<= (* x y) 0.0)
       t_1
       (if (<= (* x y) 4.1e-286)
         t_2
         (if (<= (* x y) 1.95e-129)
           t_1
           (if (<= (* x y) 3.2e+147) t_2 (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (a * -0.25);
	double t_2 = z * (t * 0.0625);
	double tmp;
	if ((x * y) <= -4.3e+77) {
		tmp = x * y;
	} else if ((x * y) <= 0.0) {
		tmp = t_1;
	} else if ((x * y) <= 4.1e-286) {
		tmp = t_2;
	} else if ((x * y) <= 1.95e-129) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e+147) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * (-0.25d0))
    t_2 = z * (t * 0.0625d0)
    if ((x * y) <= (-4.3d+77)) then
        tmp = x * y
    else if ((x * y) <= 0.0d0) then
        tmp = t_1
    else if ((x * y) <= 4.1d-286) then
        tmp = t_2
    else if ((x * y) <= 1.95d-129) then
        tmp = t_1
    else if ((x * y) <= 3.2d+147) then
        tmp = t_2
    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 t_1 = b * (a * -0.25);
	double t_2 = z * (t * 0.0625);
	double tmp;
	if ((x * y) <= -4.3e+77) {
		tmp = x * y;
	} else if ((x * y) <= 0.0) {
		tmp = t_1;
	} else if ((x * y) <= 4.1e-286) {
		tmp = t_2;
	} else if ((x * y) <= 1.95e-129) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e+147) {
		tmp = t_2;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * (a * -0.25)
	t_2 = z * (t * 0.0625)
	tmp = 0
	if (x * y) <= -4.3e+77:
		tmp = x * y
	elif (x * y) <= 0.0:
		tmp = t_1
	elif (x * y) <= 4.1e-286:
		tmp = t_2
	elif (x * y) <= 1.95e-129:
		tmp = t_1
	elif (x * y) <= 3.2e+147:
		tmp = t_2
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(a * -0.25))
	t_2 = Float64(z * Float64(t * 0.0625))
	tmp = 0.0
	if (Float64(x * y) <= -4.3e+77)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 0.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.1e-286)
		tmp = t_2;
	elseif (Float64(x * y) <= 1.95e-129)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.2e+147)
		tmp = t_2;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b * (a * -0.25);
	t_2 = z * (t * 0.0625);
	tmp = 0.0;
	if ((x * y) <= -4.3e+77)
		tmp = x * y;
	elseif ((x * y) <= 0.0)
		tmp = t_1;
	elseif ((x * y) <= 4.1e-286)
		tmp = t_2;
	elseif ((x * y) <= 1.95e-129)
		tmp = t_1;
	elseif ((x * y) <= 3.2e+147)
		tmp = t_2;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.3e+77], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.1e-286], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1.95e-129], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.2e+147], t$95$2, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.29999999999999991e77 or 3.19999999999999979e147 < (*.f64 x y)

   1. Initial program 94.6%

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

      1. associate-+l- 94.6%

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

      2. associate--l+ 94.6%

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

      3. fma-def 97.8%

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

      4. associate-*l/ 97.8%

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

      5. fma-neg 97.8%

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

      6. sub-neg 97.8%

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

      7. distribute-neg-in 97.8%

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

      8. remove-double-neg 97.8%

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

      9. associate-/l* 97.8%

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

      10. distribute-frac-neg 97.8%

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

      11. associate-/r/ 97.8%

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

      12. fma-def 97.8%

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

      13. neg-mul-1 97.8%

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

      14. *-commutative 97.8%

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

      15. associate-/l* 97.8%

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

      16. metadata-eval 97.8%

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

   3. Simplified 97.8%

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

      1. fma-udef 94.6%

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

      2. fma-udef 94.6%

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

      3. associate-*l/ 94.6%

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

      4. fma-udef 94.6%

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

      5. associate-/r/ 94.6%

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

      6. associate-+r+ 94.6%

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

      7. associate-*l/ 94.6%

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

      8. fma-udef 96.8%

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

      9. +-commutative 96.8%

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

      10. fma-udef 94.6%

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

      11. associate-*l/ 94.6%

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

      12. associate-+r+ 94.6%

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

      13. div-inv 94.6%

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

      14. fma-def 94.6%

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

      15. clear-num 94.6%

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

      16. div-inv 94.6%

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

      17. metadata-eval 94.6%

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

      18. associate-*l/ 94.6%

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

   6. Applied egg-rr 94.6%

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

   7. Taylor expanded in x around inf 82.3%

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

   8. Taylor expanded in x around inf 72.0%

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

   if -4.29999999999999991e77 < (*.f64 x y) < 0.0 or 4.1e-286 < (*.f64 x y) < 1.95000000000000005e-129

   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 99.9%

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

      14. fma-def 99.9%

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

      15. clear-num 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%

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

   7. Taylor expanded in a around inf 78.2%

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

      1. *-commutative 78.2%

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

      2. associate-*r* 78.2%

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

      3. *-commutative 78.2%

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

   9. Simplified 78.2%

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

   10. Taylor expanded in a around inf 51.1%

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

       1. *-commutative 51.1%

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

       2. *-commutative 51.1%

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

       3. associate-*l* 51.1%

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

       4. *-commutative 51.1%

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

   12. Simplified 51.1%

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

   if 0.0 < (*.f64 x y) < 4.1e-286 or 1.95000000000000005e-129 < (*.f64 x y) < 3.19999999999999979e147

   1. Initial program 98.1%

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

      1. associate-+l- 98.1%

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

      2. associate--l+ 98.1%

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

      3. fma-def 98.1%

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

      4. associate-*l/ 98.1%

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

      5. fma-neg 98.1%

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

      6. sub-neg 98.1%

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

      7. distribute-neg-in 98.1%

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

      8. remove-double-neg 98.1%

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

      9. associate-/l* 98.1%

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

      10. distribute-frac-neg 98.1%

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

      11. associate-/r/ 98.1%

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

      12. fma-def 98.1%

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

      13. neg-mul-1 98.1%

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

      14. *-commutative 98.1%

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

      15. associate-/l* 98.1%

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

      16. metadata-eval 98.1%

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

   3. Simplified 98.1%

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

      1. fma-udef 98.1%

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

      2. fma-udef 98.1%

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

      3. associate-*l/ 98.1%

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

      4. fma-udef 98.1%

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

      5. associate-/r/ 98.1%

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

      6. associate-+r+ 98.1%

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

      7. associate-*l/ 98.1%

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

      8. fma-udef 98.1%

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

      9. +-commutative 98.1%

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

      10. fma-udef 98.1%

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

      11. associate-*l/ 98.1%

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

      12. associate-+r+ 98.1%

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

      13. div-inv 98.1%

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

      14. fma-def 98.1%

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

      15. clear-num 98.1%

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

      16. div-inv 98.1%

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

      17. metadata-eval 98.1%

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

      18. associate-*l/ 98.1%

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

   6. Applied egg-rr 98.1%

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

   7. Taylor expanded in t around inf 54.3%

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

      1. associate-*r* 54.3%

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

      2. *-commutative 54.3%

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

      3. *-commutative 54.3%

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

      4. *-commutative 54.3%

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

   9. Simplified 54.3%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.3 \cdot 10^{+77}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{-286}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 1.95 \cdot 10^{-129}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{+147}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right)\\ t_2 := z \cdot \left(t \cdot 0.0625\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -2.65 \cdot 10^{+42}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.85 \cdot 10^{-287}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{+147}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (* a -0.25))) (t_2 (* z (* t 0.0625))) (t_3 (+ c (* x y))))
   (if (<= (* x y) -2.65e+42)
     t_3
     (if (<= (* x y) 0.0)
       t_1
       (if (<= (* x y) 1.85e-287)
         t_2
         (if (<= (* x y) 6e-120) t_1 (if (<= (* x y) 3.2e+147) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (a * -0.25);
	double t_2 = z * (t * 0.0625);
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -2.65e+42) {
		tmp = t_3;
	} else if ((x * y) <= 0.0) {
		tmp = t_1;
	} else if ((x * y) <= 1.85e-287) {
		tmp = t_2;
	} else if ((x * y) <= 6e-120) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e+147) {
		tmp = t_2;
	} 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 = b * (a * (-0.25d0))
    t_2 = z * (t * 0.0625d0)
    t_3 = c + (x * y)
    if ((x * y) <= (-2.65d+42)) then
        tmp = t_3
    else if ((x * y) <= 0.0d0) then
        tmp = t_1
    else if ((x * y) <= 1.85d-287) then
        tmp = t_2
    else if ((x * y) <= 6d-120) then
        tmp = t_1
    else if ((x * y) <= 3.2d+147) then
        tmp = t_2
    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 = b * (a * -0.25);
	double t_2 = z * (t * 0.0625);
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -2.65e+42) {
		tmp = t_3;
	} else if ((x * y) <= 0.0) {
		tmp = t_1;
	} else if ((x * y) <= 1.85e-287) {
		tmp = t_2;
	} else if ((x * y) <= 6e-120) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e+147) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * (a * -0.25)
	t_2 = z * (t * 0.0625)
	t_3 = c + (x * y)
	tmp = 0
	if (x * y) <= -2.65e+42:
		tmp = t_3
	elif (x * y) <= 0.0:
		tmp = t_1
	elif (x * y) <= 1.85e-287:
		tmp = t_2
	elif (x * y) <= 6e-120:
		tmp = t_1
	elif (x * y) <= 3.2e+147:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(a * -0.25))
	t_2 = Float64(z * Float64(t * 0.0625))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -2.65e+42)
		tmp = t_3;
	elseif (Float64(x * y) <= 0.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.85e-287)
		tmp = t_2;
	elseif (Float64(x * y) <= 6e-120)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.2e+147)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b * (a * -0.25);
	t_2 = z * (t * 0.0625);
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -2.65e+42)
		tmp = t_3;
	elseif ((x * y) <= 0.0)
		tmp = t_1;
	elseif ((x * y) <= 1.85e-287)
		tmp = t_2;
	elseif ((x * y) <= 6e-120)
		tmp = t_1;
	elseif ((x * y) <= 3.2e+147)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.65e+42], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 0.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.85e-287], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 6e-120], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.2e+147], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.65000000000000014e42 or 3.19999999999999979e147 < (*.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. Add Preprocessing

   3. Taylor expanded in x around inf 77.4%

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

   if -2.65000000000000014e42 < (*.f64 x y) < 0.0 or 1.85000000000000013e-287 < (*.f64 x y) < 6.00000000000000022e-120

   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 99.9%

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

      14. fma-def 99.9%

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

      15. clear-num 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%

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

   7. Taylor expanded in a around inf 79.9%

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

      1. *-commutative 79.9%

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

      2. associate-*r* 79.9%

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

      3. *-commutative 79.9%

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

   9. Simplified 79.9%

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

   10. Taylor expanded in a around inf 52.5%

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

       1. *-commutative 52.5%

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

       2. *-commutative 52.5%

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

       3. associate-*l* 52.5%

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

       4. *-commutative 52.5%

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

   12. Simplified 52.5%

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

   if 0.0 < (*.f64 x y) < 1.85000000000000013e-287 or 6.00000000000000022e-120 < (*.f64 x y) < 3.19999999999999979e147

   1. Initial program 98.1%

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

      1. associate-+l- 98.1%

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

      2. associate--l+ 98.1%

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

      3. fma-def 98.1%

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

      4. associate-*l/ 98.1%

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

      5. fma-neg 98.1%

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

      6. sub-neg 98.1%

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

      7. distribute-neg-in 98.1%

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

      8. remove-double-neg 98.1%

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

      9. associate-/l* 98.1%

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

      10. distribute-frac-neg 98.1%

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

      11. associate-/r/ 98.1%

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

      12. fma-def 98.1%

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

      13. neg-mul-1 98.1%

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

      14. *-commutative 98.1%

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

      15. associate-/l* 98.1%

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

      16. metadata-eval 98.1%

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

   3. Simplified 98.1%

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

      1. fma-udef 98.1%

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

      2. fma-udef 98.1%

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

      3. associate-*l/ 98.1%

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

      4. fma-udef 98.1%

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

      5. associate-/r/ 98.1%

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

      6. associate-+r+ 98.1%

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

      7. associate-*l/ 98.1%

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

      8. fma-udef 98.1%

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

      9. +-commutative 98.1%

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

      10. fma-udef 98.1%

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

      11. associate-*l/ 98.1%

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

      12. associate-+r+ 98.1%

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

      13. div-inv 98.1%

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

      14. fma-def 98.1%

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

      15. clear-num 98.1%

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

      16. div-inv 98.1%

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

      17. metadata-eval 98.1%

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

      18. associate-*l/ 98.1%

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

   6. Applied egg-rr 98.1%

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

   7. Taylor expanded in t around inf 54.3%

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

      1. associate-*r* 54.3%

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

      2. *-commutative 54.3%

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

      3. *-commutative 54.3%

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

      4. *-commutative 54.3%

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

   9. Simplified 54.3%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.65 \cdot 10^{+42}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.85 \cdot 10^{-287}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{-120}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{+147}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := z \cdot \left(t \cdot 0.0625\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -9.5 \cdot 10^{+40}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{-286}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 8.2 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25))))
        (t_2 (* z (* t 0.0625)))
        (t_3 (+ c (* x y))))
   (if (<= (* x y) -9.5e+40)
     t_3
     (if (<= (* x y) 0.0)
       t_1
       (if (<= (* x y) 2.2e-286)
         t_2
         (if (<= (* x y) 8.2e-22) t_1 (if (<= (* x y) 5.4e+149) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = z * (t * 0.0625);
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -9.5e+40) {
		tmp = t_3;
	} else if ((x * y) <= 0.0) {
		tmp = t_1;
	} else if ((x * y) <= 2.2e-286) {
		tmp = t_2;
	} else if ((x * y) <= 8.2e-22) {
		tmp = t_1;
	} else if ((x * y) <= 5.4e+149) {
		tmp = t_2;
	} 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 = c + (a * (b * (-0.25d0)))
    t_2 = z * (t * 0.0625d0)
    t_3 = c + (x * y)
    if ((x * y) <= (-9.5d+40)) then
        tmp = t_3
    else if ((x * y) <= 0.0d0) then
        tmp = t_1
    else if ((x * y) <= 2.2d-286) then
        tmp = t_2
    else if ((x * y) <= 8.2d-22) then
        tmp = t_1
    else if ((x * y) <= 5.4d+149) then
        tmp = t_2
    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 = c + (a * (b * -0.25));
	double t_2 = z * (t * 0.0625);
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -9.5e+40) {
		tmp = t_3;
	} else if ((x * y) <= 0.0) {
		tmp = t_1;
	} else if ((x * y) <= 2.2e-286) {
		tmp = t_2;
	} else if ((x * y) <= 8.2e-22) {
		tmp = t_1;
	} else if ((x * y) <= 5.4e+149) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = z * (t * 0.0625)
	t_3 = c + (x * y)
	tmp = 0
	if (x * y) <= -9.5e+40:
		tmp = t_3
	elif (x * y) <= 0.0:
		tmp = t_1
	elif (x * y) <= 2.2e-286:
		tmp = t_2
	elif (x * y) <= 8.2e-22:
		tmp = t_1
	elif (x * y) <= 5.4e+149:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_2 = Float64(z * Float64(t * 0.0625))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -9.5e+40)
		tmp = t_3;
	elseif (Float64(x * y) <= 0.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 2.2e-286)
		tmp = t_2;
	elseif (Float64(x * y) <= 8.2e-22)
		tmp = t_1;
	elseif (Float64(x * y) <= 5.4e+149)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (a * (b * -0.25));
	t_2 = z * (t * 0.0625);
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -9.5e+40)
		tmp = t_3;
	elseif ((x * y) <= 0.0)
		tmp = t_1;
	elseif ((x * y) <= 2.2e-286)
		tmp = t_2;
	elseif ((x * y) <= 8.2e-22)
		tmp = t_1;
	elseif ((x * y) <= 5.4e+149)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -9.5e+40], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 0.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2.2e-286], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 8.2e-22], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5.4e+149], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.5000000000000003e40 or 5.4000000000000002e149 < (*.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. Add Preprocessing

   3. Taylor expanded in x around inf 77.4%

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

   if -9.5000000000000003e40 < (*.f64 x y) < 0.0 or 2.1999999999999999e-286 < (*.f64 x y) < 8.1999999999999999e-22

   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 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-*r* 67.3%

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

   5. Simplified 67.3%

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

   if 0.0 < (*.f64 x y) < 2.1999999999999999e-286 or 8.1999999999999999e-22 < (*.f64 x y) < 5.4000000000000002e149

   1. Initial program 97.3%

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

      1. associate-+l- 97.3%

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

      2. associate--l+ 97.3%

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

      3. fma-def 97.3%

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

      4. associate-*l/ 97.3%

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

      5. fma-neg 97.3%

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

      6. sub-neg 97.3%

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

      7. distribute-neg-in 97.3%

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

      8. remove-double-neg 97.3%

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

      9. associate-/l* 97.3%

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

      10. distribute-frac-neg 97.3%

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

      11. associate-/r/ 97.3%

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

      12. fma-def 97.3%

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

      13. neg-mul-1 97.3%

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

      14. *-commutative 97.3%

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

      15. associate-/l* 97.3%

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

      16. metadata-eval 97.3%

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

   3. Simplified 97.3%

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

      1. fma-udef 97.3%

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

      2. fma-udef 97.3%

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

      3. associate-*l/ 97.3%

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

      4. fma-udef 97.3%

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

      5. associate-/r/ 97.3%

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

      6. associate-+r+ 97.3%

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

      7. associate-*l/ 97.3%

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

      8. fma-udef 97.3%

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

      9. +-commutative 97.3%

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

      10. fma-udef 97.3%

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

      11. associate-*l/ 97.3%

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

      12. associate-+r+ 97.3%

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

      13. div-inv 97.3%

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

      14. fma-def 97.3%

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

      15. clear-num 97.3%

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

      16. div-inv 97.3%

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

      17. metadata-eval 97.3%

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

      18. associate-*l/ 97.3%

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

   6. Applied egg-rr 97.3%

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

   7. Taylor expanded in t around inf 58.4%

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

      1. associate-*r* 58.4%

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

      2. *-commutative 58.4%

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

      3. *-commutative 58.4%

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

      4. *-commutative 58.4%

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

   9. Simplified 58.4%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.5 \cdot 10^{+40}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{-286}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 8.2 \cdot 10^{-22}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+236}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{+105} \lor \neg \left(a \cdot b \leq -1 \cdot 10^{-14}\right) \land a \cdot b \leq 4 \cdot 10^{+154}:\\ \;\;\;\;x \cdot y + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -2e+236)
   (* b (* a -0.25))
   (if (or (<= (* a b) -2e+105)
           (and (not (<= (* a b) -1e-14)) (<= (* a b) 4e+154)))
     (+ (* x y) (* t (* z 0.0625)))
     (+ c (* a (* b -0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2e+236) {
		tmp = b * (a * -0.25);
	} else if (((a * b) <= -2e+105) || (!((a * b) <= -1e-14) && ((a * b) <= 4e+154))) {
		tmp = (x * y) + (t * (z * 0.0625));
	} else {
		tmp = c + (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) :: tmp
    if ((a * b) <= (-2d+236)) then
        tmp = b * (a * (-0.25d0))
    else if (((a * b) <= (-2d+105)) .or. (.not. ((a * b) <= (-1d-14))) .and. ((a * b) <= 4d+154)) then
        tmp = (x * y) + (t * (z * 0.0625d0))
    else
        tmp = c + (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 tmp;
	if ((a * b) <= -2e+236) {
		tmp = b * (a * -0.25);
	} else if (((a * b) <= -2e+105) || (!((a * b) <= -1e-14) && ((a * b) <= 4e+154))) {
		tmp = (x * y) + (t * (z * 0.0625));
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -2e+236:
		tmp = b * (a * -0.25)
	elif ((a * b) <= -2e+105) or (not ((a * b) <= -1e-14) and ((a * b) <= 4e+154)):
		tmp = (x * y) + (t * (z * 0.0625))
	else:
		tmp = c + (a * (b * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -2e+236)
		tmp = Float64(b * Float64(a * -0.25));
	elseif ((Float64(a * b) <= -2e+105) || (!(Float64(a * b) <= -1e-14) && (Float64(a * b) <= 4e+154)))
		tmp = Float64(Float64(x * y) + Float64(t * Float64(z * 0.0625)));
	else
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -2e+236)
		tmp = b * (a * -0.25);
	elseif (((a * b) <= -2e+105) || (~(((a * b) <= -1e-14)) && ((a * b) <= 4e+154)))
		tmp = (x * y) + (t * (z * 0.0625));
	else
		tmp = c + (a * (b * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -2e+236], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * b), $MachinePrecision], -2e+105], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], -1e-14]], $MachinePrecision], LessEqual[N[(a * b), $MachinePrecision], 4e+154]]], N[(N[(x * y), $MachinePrecision] + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.00000000000000011e236

   1. Initial program 96.3%

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

      1. associate-+l- 96.3%

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

      2. associate--l+ 96.3%

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

      3. fma-def 96.3%

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

      4. associate-*l/ 96.3%

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

      5. fma-neg 96.3%

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

      6. sub-neg 96.3%

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

      7. distribute-neg-in 96.3%

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

      8. remove-double-neg 96.3%

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

      9. associate-/l* 96.2%

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

      10. distribute-frac-neg 96.2%

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

      11. associate-/r/ 96.3%

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

      12. fma-def 96.3%

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

      13. neg-mul-1 96.3%

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

      14. *-commutative 96.3%

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

      15. associate-/l* 96.3%

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

      16. metadata-eval 96.3%

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

   3. Simplified 96.3%

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

      1. fma-udef 96.3%

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

      2. fma-udef 96.3%

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

      3. associate-*l/ 96.3%

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

      4. fma-udef 96.3%

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

      5. associate-/r/ 96.2%

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

      6. associate-+r+ 96.2%

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

      7. associate-*l/ 96.2%

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

      8. fma-udef 96.2%

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

      9. +-commutative 96.2%

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

      10. fma-udef 96.2%

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

      11. associate-*l/ 96.2%

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

      12. associate-+r+ 96.2%

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

      13. div-inv 96.2%

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

      14. fma-def 96.2%

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

      15. clear-num 96.3%

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

      16. div-inv 96.3%

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

      17. metadata-eval 96.3%

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

      18. associate-*l/ 96.3%

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

   6. Applied egg-rr 96.3%

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

   7. Taylor expanded in a around inf 96.3%

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

      1. *-commutative 96.3%

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

      2. associate-*r* 96.3%

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

      3. *-commutative 96.3%

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

   9. Simplified 96.3%

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

   10. Taylor expanded in a around inf 93.8%

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

       1. *-commutative 93.8%

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

       2. *-commutative 93.8%

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

       3. associate-*l* 93.8%

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

       4. *-commutative 93.8%

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

   12. Simplified 93.8%

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

   if -2.00000000000000011e236 < (*.f64 a b) < -1.9999999999999999e105 or -9.99999999999999999e-15 < (*.f64 a b) < 4.00000000000000015e154

   1. Initial program 99.4%

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

      1. associate-+l- 99.4%

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

      2. associate--l+ 99.4%

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

      3. fma-def 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* 100.0%

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

      10. distribute-frac-neg 100.0%

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

      11. associate-/r/ 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 99.4%

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

      2. fma-udef 99.4%

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

      3. associate-*l/ 99.4%

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

      4. fma-udef 99.4%

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

      5. associate-/r/ 99.4%

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

      6. associate-+r+ 99.4%

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

      7. associate-*l/ 99.4%

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

      8. fma-udef 100.0%

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

      9. +-commutative 100.0%

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

      10. fma-udef 99.4%

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

      11. associate-*l/ 99.4%

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

      12. associate-+r+ 99.4%

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

      13. div-inv 99.4%

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

      14. fma-def 99.4%

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

      15. clear-num 99.4%

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

      16. div-inv 99.4%

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

      17. metadata-eval 99.4%

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

      18. associate-*l/ 99.4%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in x around inf 75.1%

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

   if -1.9999999999999999e105 < (*.f64 a b) < -9.99999999999999999e-15 or 4.00000000000000015e154 < (*.f64 a b)

   1. Initial program 93.2%

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

   3. Taylor expanded in a around inf 70.4%

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

      1. *-commutative 70.4%

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

      2. associate-*r* 70.4%

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

   5. Simplified 70.4%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+236}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{+105} \lor \neg \left(a \cdot b \leq -1 \cdot 10^{-14}\right) \land a \cdot b \leq 4 \cdot 10^{+154}:\\ \;\;\;\;x \cdot y + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -20000000:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-14}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x \cdot y + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* a b) 0.25))))
   (if (<= (* a b) -2e+71)
     t_1
     (if (<= (* a b) -20000000.0)
       (+ c (* z (* t 0.0625)))
       (if (<= (* a b) -1e-14)
         (+ c (* a (* b -0.25)))
         (if (<= (* a b) 2e+152) (+ (* x y) (* t (* z 0.0625))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((a * b) <= -2e+71) {
		tmp = t_1;
	} else if ((a * b) <= -20000000.0) {
		tmp = c + (z * (t * 0.0625));
	} else if ((a * b) <= -1e-14) {
		tmp = c + (a * (b * -0.25));
	} else if ((a * b) <= 2e+152) {
		tmp = (x * y) + (t * (z * 0.0625));
	} 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) - ((a * b) * 0.25d0)
    if ((a * b) <= (-2d+71)) then
        tmp = t_1
    else if ((a * b) <= (-20000000.0d0)) then
        tmp = c + (z * (t * 0.0625d0))
    else if ((a * b) <= (-1d-14)) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((a * b) <= 2d+152) then
        tmp = (x * y) + (t * (z * 0.0625d0))
    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) - ((a * b) * 0.25);
	double tmp;
	if ((a * b) <= -2e+71) {
		tmp = t_1;
	} else if ((a * b) <= -20000000.0) {
		tmp = c + (z * (t * 0.0625));
	} else if ((a * b) <= -1e-14) {
		tmp = c + (a * (b * -0.25));
	} else if ((a * b) <= 2e+152) {
		tmp = (x * y) + (t * (z * 0.0625));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) - ((a * b) * 0.25)
	tmp = 0
	if (a * b) <= -2e+71:
		tmp = t_1
	elif (a * b) <= -20000000.0:
		tmp = c + (z * (t * 0.0625))
	elif (a * b) <= -1e-14:
		tmp = c + (a * (b * -0.25))
	elif (a * b) <= 2e+152:
		tmp = (x * y) + (t * (z * 0.0625))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25))
	tmp = 0.0
	if (Float64(a * b) <= -2e+71)
		tmp = t_1;
	elseif (Float64(a * b) <= -20000000.0)
		tmp = Float64(c + Float64(z * Float64(t * 0.0625)));
	elseif (Float64(a * b) <= -1e-14)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(a * b) <= 2e+152)
		tmp = Float64(Float64(x * y) + Float64(t * Float64(z * 0.0625)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) - ((a * b) * 0.25);
	tmp = 0.0;
	if ((a * b) <= -2e+71)
		tmp = t_1;
	elseif ((a * b) <= -20000000.0)
		tmp = c + (z * (t * 0.0625));
	elseif ((a * b) <= -1e-14)
		tmp = c + (a * (b * -0.25));
	elseif ((a * b) <= 2e+152)
		tmp = (x * y) + (t * (z * 0.0625));
	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[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+71], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -20000000.0], N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1e-14], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+152], N[(N[(x * y), $MachinePrecision] + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -2.0000000000000001e71 or 2.0000000000000001e152 < (*.f64 a b)

   1. Initial program 95.0%

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

   3. Taylor expanded in z around 0 85.8%

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

   4. Taylor expanded in c around 0 78.6%

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

   if -2.0000000000000001e71 < (*.f64 a b) < -2e7

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf 69.9%

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

      1. associate-*r* 69.9%

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

   5. Simplified 69.9%

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

   if -2e7 < (*.f64 a b) < -9.99999999999999999e-15

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf 68.5%

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

      1. *-commutative 68.5%

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

      2. associate-*r* 68.5%

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

   5. Simplified 68.5%

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

   if -9.99999999999999999e-15 < (*.f64 a b) < 2.0000000000000001e152

   1. Initial program 99.3%

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

      1. associate-+l- 99.3%

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

      2. associate--l+ 99.3%

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

      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* 100.0%

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

      10. distribute-frac-neg 100.0%

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

      11. associate-/r/ 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 99.3%

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

      2. fma-udef 99.3%

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

      3. associate-*l/ 99.3%

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

      4. fma-udef 99.3%

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

      5. associate-/r/ 99.3%

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

      6. associate-+r+ 99.3%

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

      7. associate-*l/ 99.3%

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

      8. fma-udef 100.0%

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

      9. +-commutative 100.0%

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

      10. fma-udef 99.3%

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

      11. associate-*l/ 99.3%

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

      12. associate-+r+ 99.3%

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

      13. div-inv 99.3%

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

      14. fma-def 99.3%

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

      15. clear-num 99.3%

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

      16. div-inv 99.3%

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

      17. metadata-eval 99.3%

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

      18. associate-*l/ 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in x around inf 75.3%

      \[\leadsto \color{blue}{x \cdot y} + t \cdot \left(z \cdot 0.0625\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+71}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq -20000000:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-14}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x \cdot y + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 0.0625\right)\\ t_2 := x \cdot y + t\_1\\ \mathbf{if}\;x \cdot y \leq -3.15 \cdot 10^{+75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 5.3 \cdot 10^{-120}:\\ \;\;\;\;t\_1 + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.05 \cdot 10^{+24}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* z 0.0625))) (t_2 (+ (* x y) t_1)))
   (if (<= (* x y) -3.15e+75)
     t_2
     (if (<= (* x y) 5.3e-120)
       (+ t_1 (* a (* b -0.25)))
       (if (<= (* x y) 1.05e+24) (+ c (* z (* t 0.0625))) t_2)))))

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 t_2 = (x * y) + t_1;
	double tmp;
	if ((x * y) <= -3.15e+75) {
		tmp = t_2;
	} else if ((x * y) <= 5.3e-120) {
		tmp = t_1 + (a * (b * -0.25));
	} else if ((x * y) <= 1.05e+24) {
		tmp = c + (z * (t * 0.0625));
	} else {
		tmp = t_2;
	}
	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) :: tmp
    t_1 = t * (z * 0.0625d0)
    t_2 = (x * y) + t_1
    if ((x * y) <= (-3.15d+75)) then
        tmp = t_2
    else if ((x * y) <= 5.3d-120) then
        tmp = t_1 + (a * (b * (-0.25d0)))
    else if ((x * y) <= 1.05d+24) then
        tmp = c + (z * (t * 0.0625d0))
    else
        tmp = t_2
    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 = t * (z * 0.0625);
	double t_2 = (x * y) + t_1;
	double tmp;
	if ((x * y) <= -3.15e+75) {
		tmp = t_2;
	} else if ((x * y) <= 5.3e-120) {
		tmp = t_1 + (a * (b * -0.25));
	} else if ((x * y) <= 1.05e+24) {
		tmp = c + (z * (t * 0.0625));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = t * (z * 0.0625)
	t_2 = (x * y) + t_1
	tmp = 0
	if (x * y) <= -3.15e+75:
		tmp = t_2
	elif (x * y) <= 5.3e-120:
		tmp = t_1 + (a * (b * -0.25))
	elif (x * y) <= 1.05e+24:
		tmp = c + (z * (t * 0.0625))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(z * 0.0625))
	t_2 = Float64(Float64(x * y) + t_1)
	tmp = 0.0
	if (Float64(x * y) <= -3.15e+75)
		tmp = t_2;
	elseif (Float64(x * y) <= 5.3e-120)
		tmp = Float64(t_1 + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 1.05e+24)
		tmp = Float64(c + Float64(z * Float64(t * 0.0625)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (z * 0.0625);
	t_2 = (x * y) + t_1;
	tmp = 0.0;
	if ((x * y) <= -3.15e+75)
		tmp = t_2;
	elseif ((x * y) <= 5.3e-120)
		tmp = t_1 + (a * (b * -0.25));
	elseif ((x * y) <= 1.05e+24)
		tmp = c + (z * (t * 0.0625));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.15e+75], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5.3e-120], N[(t$95$1 + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.05e+24], N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.15000000000000018e75 or 1.0500000000000001e24 < (*.f64 x y)

   1. Initial program 95.4%

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

      1. associate-+l- 95.4%

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

      2. associate--l+ 95.4%

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

      3. fma-def 98.2%

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

      4. associate-*l/ 98.2%

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

      5. fma-neg 98.2%

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

      6. sub-neg 98.2%

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

      7. distribute-neg-in 98.2%

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

      8. remove-double-neg 98.2%

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

      9. associate-/l* 98.2%

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

      10. distribute-frac-neg 98.2%

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

      11. associate-/r/ 98.2%

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

      12. fma-def 98.2%

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

      13. neg-mul-1 98.2%

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

      14. *-commutative 98.2%

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

      15. associate-/l* 98.2%

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

      16. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

      1. fma-udef 95.4%

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

      2. fma-udef 95.4%

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

      3. associate-*l/ 95.4%

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

      4. fma-udef 95.4%

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

      5. associate-/r/ 95.4%

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

      6. associate-+r+ 95.4%

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

      7. associate-*l/ 95.4%

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

      8. fma-udef 97.2%

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

      9. +-commutative 97.2%

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

      10. fma-udef 95.4%

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

      11. associate-*l/ 95.4%

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

      12. associate-+r+ 95.4%

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

      13. div-inv 95.4%

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

      14. fma-def 95.4%

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

      15. clear-num 95.4%

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

      16. div-inv 95.4%

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

      17. metadata-eval 95.4%

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

      18. associate-*l/ 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in x around inf 82.2%

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

   if -3.15000000000000018e75 < (*.f64 x y) < 5.29999999999999997e-120

   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 99.9%

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

      14. fma-def 99.9%

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

      15. clear-num 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%

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

   7. Taylor expanded in a around inf 79.1%

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

      1. *-commutative 79.1%

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

      2. associate-*r* 79.1%

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

      3. *-commutative 79.1%

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

   9. Simplified 79.1%

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

   if 5.29999999999999997e-120 < (*.f64 x y) < 1.0500000000000001e24

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 78.7%

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

      1. associate-*r* 78.7%

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

   5. Simplified 78.7%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.15 \cdot 10^{+75}:\\ \;\;\;\;x \cdot y + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 5.3 \cdot 10^{-120}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right) + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.05 \cdot 10^{+24}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -2.6 \cdot 10^{+43} \lor \neg \left(x \cdot y \leq 8.2 \cdot 10^{-22}\right):\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + t\_1\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (or (<= (* x y) -2.6e+43) (not (<= (* x y) 8.2e-22)))
     (+ 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) <= -2.6e+43) || !((x * y) <= 8.2e-22)) {
		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) <= (-2.6d+43)) .or. (.not. ((x * y) <= 8.2d-22))) 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) <= -2.6e+43) || !((x * y) <= 8.2e-22)) {
		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) <= -2.6e+43) or not ((x * y) <= 8.2e-22):
		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) <= -2.6e+43) || !(Float64(x * y) <= 8.2e-22))
		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) <= -2.6e+43) || ~(((x * y) <= 8.2e-22)))
		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], -2.6e+43], N[Not[LessEqual[N[(x * y), $MachinePrecision], 8.2e-22]], $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) < -2.60000000000000021e43 or 8.1999999999999999e-22 < (*.f64 x y)

   1. Initial program 95.4%

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

   3. Taylor expanded in a around 0 88.1%

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

   if -2.60000000000000021e43 < (*.f64 x y) < 8.1999999999999999e-22

   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 x around 0 97.1%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.6 \cdot 10^{+43} \lor \neg \left(x \cdot y \leq 8.2 \cdot 10^{-22}\right):\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 86.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.8 \cdot 10^{+71} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+189}\right):\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right) + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -1.8e+71) (not (<= (* a b) 2e+189)))
   (+ (* t (* z 0.0625)) (* a (* b -0.25)))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1.8e+71) || !((a * b) <= 2e+189)) {
		tmp = (t * (z * 0.0625)) + (a * (b * -0.25));
	} else {
		tmp = c + ((x * y) + (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 (((a * b) <= (-1.8d+71)) .or. (.not. ((a * b) <= 2d+189))) then
        tmp = (t * (z * 0.0625d0)) + (a * (b * (-0.25d0)))
    else
        tmp = c + ((x * y) + (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 (((a * b) <= -1.8e+71) || !((a * b) <= 2e+189)) {
		tmp = (t * (z * 0.0625)) + (a * (b * -0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -1.8e+71) or not ((a * b) <= 2e+189):
		tmp = (t * (z * 0.0625)) + (a * (b * -0.25))
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -1.8e+71) || !(Float64(a * b) <= 2e+189))
		tmp = Float64(Float64(t * Float64(z * 0.0625)) + Float64(a * Float64(b * -0.25)));
	else
		tmp = Float64(c + Float64(Float64(x * y) + 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 (((a * b) <= -1.8e+71) || ~(((a * b) <= 2e+189)))
		tmp = (t * (z * 0.0625)) + (a * (b * -0.25));
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.8e+71], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e+189]], $MachinePrecision]], N[(N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.8e71 or 2e189 < (*.f64 a b)

   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 96.0%

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

      4. associate-*l/ 96.0%

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

      5. fma-neg 96.0%

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

      6. sub-neg 96.0%

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

      7. distribute-neg-in 96.0%

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

      8. remove-double-neg 96.0%

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

      9. associate-/l* 96.0%

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

      10. distribute-frac-neg 96.0%

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

      11. associate-/r/ 96.0%

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

      12. fma-def 96.1%

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

      13. neg-mul-1 96.1%

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

      14. *-commutative 96.1%

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

      15. associate-/l* 96.1%

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

      16. metadata-eval 96.1%

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

   3. Simplified 96.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
   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/ 93.3%

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

      6. associate-+r+ 93.3%

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

      7. associate-*l/ 93.3%

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

      8. fma-udef 94.7%

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

      9. +-commutative 94.7%

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

      10. fma-udef 93.3%

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

      11. associate-*l/ 93.3%

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

      12. associate-+r+ 93.3%

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

      13. div-inv 93.3%

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

      14. fma-def 93.3%

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

      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 a around inf 82.9%

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

      1. *-commutative 82.9%

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

      2. associate-*r* 82.9%

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

      3. *-commutative 82.9%

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

   9. Simplified 82.9%

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

   if -1.8e71 < (*.f64 a b) < 2e189

   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 a around 0 88.2%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.8 \cdot 10^{+71} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+189}\right):\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right) + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{-13}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+189}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right) + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -2e-13)
   (- (+ c (* x y)) (* (* a b) 0.25))
   (if (<= (* a b) 2e+189)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (+ (* 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 tmp;
	if ((a * b) <= -2e-13) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else if ((a * b) <= 2e+189) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (t * (z * 0.0625)) + (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) :: tmp
    if ((a * b) <= (-2d-13)) then
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    else if ((a * b) <= 2d+189) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = (t * (z * 0.0625d0)) + (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 tmp;
	if ((a * b) <= -2e-13) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else if ((a * b) <= 2e+189) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (t * (z * 0.0625)) + (a * (b * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -2e-13:
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	elif (a * b) <= 2e+189:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = (t * (z * 0.0625)) + (a * (b * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -2e-13)
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	elseif (Float64(a * b) <= 2e+189)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	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)
	tmp = 0.0;
	if ((a * b) <= -2e-13)
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	elseif ((a * b) <= 2e+189)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = (t * (z * 0.0625)) + (a * (b * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -2e-13], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+189], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.0000000000000001e-13

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 82.6%

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

   if -2.0000000000000001e-13 < (*.f64 a b) < 2e189

   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 a around 0 90.2%

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

   if 2e189 < (*.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. Step-by-step derivation

      1. associate-+l- 89.3%

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

      2. associate--l+ 89.3%

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

      3. fma-def 92.9%

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

      4. associate-*l/ 92.9%

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

      5. fma-neg 92.9%

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

      6. sub-neg 92.9%

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

      7. distribute-neg-in 92.9%

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

      8. remove-double-neg 92.9%

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

      9. associate-/l* 92.9%

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

      10. distribute-frac-neg 92.9%

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

      11. associate-/r/ 92.9%

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

      12. fma-def 92.9%

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

      13. neg-mul-1 92.9%

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

      14. *-commutative 92.9%

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

      15. associate-/l* 92.9%

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

      16. metadata-eval 92.9%

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

   3. Simplified 92.9%

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

      1. fma-udef 89.3%

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

      2. fma-udef 89.3%

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

      3. associate-*l/ 89.3%

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

      4. fma-udef 89.3%

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

      5. associate-/r/ 89.3%

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

      6. associate-+r+ 89.3%

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

      7. associate-*l/ 89.3%

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

      8. fma-udef 89.3%

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

      9. +-commutative 89.3%

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

      10. fma-udef 89.3%

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

      11. associate-*l/ 89.3%

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

      12. associate-+r+ 89.3%

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

      13. div-inv 89.2%

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

      14. fma-def 89.2%

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

      15. clear-num 89.3%

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

      16. div-inv 89.3%

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

      17. metadata-eval 89.3%

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

      18. associate-*l/ 89.3%

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

   6. Applied egg-rr 89.3%

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

   7. Taylor expanded in a around inf 85.7%

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

      1. *-commutative 85.7%

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

      2. associate-*r* 85.7%

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

      3. *-commutative 85.7%

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

   9. Simplified 85.7%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{-13}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+189}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right) + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.1 \cdot 10^{+75}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{-105}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 5.2 \cdot 10^{+24}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -4.1e+75)
   (* x y)
   (if (<= (* x y) 3.6e-105)
     (* b (* a -0.25))
     (if (<= (* x y) 5.2e+24) c (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -4.1e+75) {
		tmp = x * y;
	} else if ((x * y) <= 3.6e-105) {
		tmp = b * (a * -0.25);
	} else if ((x * y) <= 5.2e+24) {
		tmp = c;
	} 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) <= (-4.1d+75)) then
        tmp = x * y
    else if ((x * y) <= 3.6d-105) then
        tmp = b * (a * (-0.25d0))
    else if ((x * y) <= 5.2d+24) then
        tmp = c
    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) <= -4.1e+75) {
		tmp = x * y;
	} else if ((x * y) <= 3.6e-105) {
		tmp = b * (a * -0.25);
	} else if ((x * y) <= 5.2e+24) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -4.1e+75:
		tmp = x * y
	elif (x * y) <= 3.6e-105:
		tmp = b * (a * -0.25)
	elif (x * y) <= 5.2e+24:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -4.1e+75)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 3.6e-105)
		tmp = Float64(b * Float64(a * -0.25));
	elseif (Float64(x * y) <= 5.2e+24)
		tmp = c;
	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) <= -4.1e+75)
		tmp = x * y;
	elseif ((x * y) <= 3.6e-105)
		tmp = b * (a * -0.25);
	elseif ((x * y) <= 5.2e+24)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -4.1e+75], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.6e-105], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5.2e+24], c, N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.0999999999999998e75 or 5.1999999999999997e24 < (*.f64 x y)

   1. Initial program 95.4%

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

      1. associate-+l- 95.4%

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

      2. associate--l+ 95.4%

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

      3. fma-def 98.2%

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

      4. associate-*l/ 98.2%

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

      5. fma-neg 98.2%

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

      6. sub-neg 98.2%

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

      7. distribute-neg-in 98.2%

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

      8. remove-double-neg 98.2%

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

      9. associate-/l* 98.2%

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

      10. distribute-frac-neg 98.2%

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

      11. associate-/r/ 98.2%

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

      12. fma-def 98.2%

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

      13. neg-mul-1 98.2%

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

      14. *-commutative 98.2%

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

      15. associate-/l* 98.2%

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

      16. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

      1. fma-udef 95.4%

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

      2. fma-udef 95.4%

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

      3. associate-*l/ 95.4%

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

      4. fma-udef 95.4%

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

      5. associate-/r/ 95.4%

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

      6. associate-+r+ 95.4%

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

      7. associate-*l/ 95.4%

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

      8. fma-udef 97.2%

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

      9. +-commutative 97.2%

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

      10. fma-udef 95.4%

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

      11. associate-*l/ 95.4%

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

      12. associate-+r+ 95.4%

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

      13. div-inv 95.4%

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

      14. fma-def 95.4%

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

      15. clear-num 95.4%

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

      16. div-inv 95.4%

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

      17. metadata-eval 95.4%

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

      18. associate-*l/ 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in x around inf 82.2%

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

   8. Taylor expanded in x around inf 65.4%

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

   if -4.0999999999999998e75 < (*.f64 x y) < 3.59999999999999964e-105

   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 99.9%

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

      14. fma-def 99.9%

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

      15. clear-num 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%

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

   7. Taylor expanded in a around inf 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-*r* 79.8%

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

      3. *-commutative 79.8%

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

   9. Simplified 79.8%

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

   10. Taylor expanded in a around inf 47.6%

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

       1. *-commutative 47.6%

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

       2. *-commutative 47.6%

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

       3. associate-*l* 47.6%

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

       4. *-commutative 47.6%

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

   12. Simplified 47.6%

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

   if 3.59999999999999964e-105 < (*.f64 x y) < 5.1999999999999997e24

   1. Initial program 96.4%

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

   3. Taylor expanded in c around inf 37.0%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.1 \cdot 10^{+75}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{-105}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 5.2 \cdot 10^{+24}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.9 \cdot 10^{+61} \lor \neg \left(x \cdot y \leq 4.1 \cdot 10^{+24}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -3.9e+61) (not (<= (* x y) 4.1e+24))) (* 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) <= -3.9e+61) || !((x * y) <= 4.1e+24)) {
		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) <= (-3.9d+61)) .or. (.not. ((x * y) <= 4.1d+24))) 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) <= -3.9e+61) || !((x * y) <= 4.1e+24)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -3.9e+61) or not ((x * y) <= 4.1e+24):
		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) <= -3.9e+61) || !(Float64(x * y) <= 4.1e+24))
		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) <= -3.9e+61) || ~(((x * y) <= 4.1e+24)))
		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], -3.9e+61], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.1e+24]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.89999999999999987e61 or 4.1000000000000001e24 < (*.f64 x y)

   1. Initial program 95.4%

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

      1. associate-+l- 95.4%

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

      2. associate--l+ 95.4%

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

      3. fma-def 98.2%

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

      4. associate-*l/ 98.2%

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

      5. fma-neg 98.2%

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

      6. sub-neg 98.2%

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

      7. distribute-neg-in 98.2%

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

      8. remove-double-neg 98.2%

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

      9. associate-/l* 98.2%

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

      10. distribute-frac-neg 98.2%

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

      11. associate-/r/ 98.2%

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

      12. fma-def 98.2%

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

      13. neg-mul-1 98.2%

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

      14. *-commutative 98.2%

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

      15. associate-/l* 98.2%

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

      16. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

      1. fma-udef 95.5%

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

      2. fma-udef 95.5%

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

      3. associate-*l/ 95.5%

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

      4. fma-udef 95.4%

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

      5. associate-/r/ 95.4%

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

      6. associate-+r+ 95.4%

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

      7. associate-*l/ 95.4%

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

      8. fma-udef 97.3%

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

      9. +-commutative 97.3%

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

      10. fma-udef 95.4%

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

      11. associate-*l/ 95.4%

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

      12. associate-+r+ 95.4%

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

      13. div-inv 95.4%

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

      14. fma-def 95.5%

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

      15. clear-num 95.5%

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

      16. div-inv 95.5%

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

      17. metadata-eval 95.5%

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

      18. associate-*l/ 95.5%

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

   6. Applied egg-rr 95.5%

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

   7. Taylor expanded in x around inf 82.4%

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

   8. Taylor expanded in x around inf 64.9%

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

   if -3.89999999999999987e61 < (*.f64 x y) < 4.1000000000000001e24

   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 21.2%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.9 \cdot 10^{+61} \lor \neg \left(x \cdot y \leq 4.1 \cdot 10^{+24}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot y + \left(t \cdot \left(z \cdot 0.0625\right) - \left(\frac{a}{\frac{4}{b}} - c\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (* x y) (- (* t (* z 0.0625)) (- (/ a (/ 4.0 b)) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (x * y) + ((t * (z * 0.0625)) - ((a / (4.0 / b)) - 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) + ((t * (z * 0.0625d0)) - ((a / (4.0d0 / b)) - 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) + ((t * (z * 0.0625)) - ((a / (4.0 / b)) - c));
}

Python

def code(x, y, z, t, a, b, c):
	return (x * y) + ((t * (z * 0.0625)) - ((a / (4.0 / b)) - c))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(x * y) + Float64(Float64(t * Float64(z * 0.0625)) - Float64(Float64(a / Float64(4.0 / b)) - c)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (x * y) + ((t * (z * 0.0625)) - ((a / (4.0 / b)) - c));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(x * y), $MachinePrecision] + N[(N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision] - N[(N[(a / N[(4.0 / b), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.6%

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

   1. associate-+l- 97.6%

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

   2. associate--l+ 97.6%

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

   3. fma-def 98.8%

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

   4. associate-*l/ 98.8%

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

   5. fma-neg 98.8%

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

   6. sub-neg 98.8%

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

   7. distribute-neg-in 98.8%

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

   8. remove-double-neg 98.8%

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

   9. associate-/l* 98.8%

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

   10. distribute-frac-neg 98.8%

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

   11. associate-/r/ 98.8%

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

   12. fma-def 98.8%

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

   13. neg-mul-1 98.8%

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

   14. *-commutative 98.8%

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

   15. associate-/l* 98.8%

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

   16. metadata-eval 98.8%

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

3. Simplified 98.8%

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

   1. fma-udef 97.6%

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

   2. fma-udef 97.6%

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

   3. associate-*l/ 97.6%

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

   4. fma-udef 97.6%

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

   5. associate-/r/ 97.6%

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

   6. associate-+r+ 97.6%

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

   7. frac-2neg 97.6%

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

   8. distribute-neg-frac 97.6%

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

   9. metadata-eval 97.6%

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

   10. distribute-frac-neg 97.6%

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

   11. associate-/l* 97.6%

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

   12. associate-+l+ 97.6%

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

   13. sub-neg 97.6%

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

   14. associate-+l- 97.6%

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

   15. associate--l+ 97.6%

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

6. Applied egg-rr 97.6%

   \[\leadsto \color{blue}{x \cdot y + \left(t \cdot \left(z \cdot 0.0625\right) - \left(\frac{a}{\frac{4}{b}} - c\right)\right)} \]

7. Final simplification 97.6%

   \[\leadsto x \cdot y + \left(t \cdot \left(z \cdot 0.0625\right) - \left(\frac{a}{\frac{4}{b}} - c\right)\right) \]
8. Add Preprocessing

Alternative 18: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

3. Final simplification 97.6%

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

Alternative 19: 22.9% 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 97.6%

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

3. Taylor expanded in c around inf 15.9%

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

4. Final simplification 15.9%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024040 
(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))