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

Percentage Accurate: 97.3% → 98.3%

Time: 10.7s

Alternatives: 16

Speedup: 1.0×

• 34.2% 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: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(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)) + Float64(t * Float64(z * 0.0625)));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. associate--l+ 100.0%

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

      3. fma-def 100.0%

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

      4. associate-*l/ 100.0%

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

      5. fma-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. associate-/l* 99.9%

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

      10. distribute-frac-neg 99.9%

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

      11. associate-/r/ 100.0%

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

      12. fma-def 100.0%

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

      13. neg-mul-1 100.0%

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

      14. *-commutative 100.0%

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

      15. associate-/l* 100.0%

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

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

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

   5. 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 40.0%

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

      4. associate-*l/ 40.0%

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

      5. fma-neg 40.0%

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

      6. sub-neg 40.0%

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

      7. distribute-neg-in 40.0%

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

      8. remove-double-neg 40.0%

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

      9. associate-/l* 40.0%

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

      10. distribute-frac-neg 40.0%

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

      11. associate-/r/ 40.0%

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

      12. fma-def 40.0%

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

      13. neg-mul-1 40.0%

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

      14. *-commutative 40.0%

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

      15. associate-/l* 40.0%

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

      16. metadata-eval 40.0%

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

   3. Simplified 40.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
   4. 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 10.0%

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

      9. +-commutative 10.0%

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

      10. fma-udef 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%

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

   5. Applied egg-rr 0.0%

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

   6. Taylor expanded in x around inf 40.6%

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

4. Final simplification 97.7%

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

Alternative 2: 98.7% 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 96.1%

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

   1. associate-+l- 96.1%

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

   2. associate--l+ 96.1%

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

   3. fma-def 97.6%

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

   4. associate-*l/ 97.6%

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

   5. fma-neg 97.6%

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

   6. sub-neg 97.6%

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

   7. distribute-neg-in 97.6%

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

   8. remove-double-neg 97.6%

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

   9. associate-/l* 97.6%

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

   10. distribute-frac-neg 97.6%

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

   11. associate-/r/ 97.6%

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

   12. fma-def 97.7%

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

   13. neg-mul-1 97.7%

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

   14. *-commutative 97.7%

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

   15. associate-/l* 97.7%

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

   16. metadata-eval 97.7%

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

3. Simplified 97.7%

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

4. Final simplification 97.7%

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

Alternative 3: 97.9% 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 96.1%

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

   1. sub-neg 96.1%

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

   2. associate-+l+ 96.1%

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

   3. fma-def 96.5%

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

   4. associate-*l/ 96.5%

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

   5. distribute-frac-neg 96.5%

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

   6. distribute-rgt-neg-out 96.5%

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

   7. associate-/l* 96.4%

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

   8. neg-mul-1 96.4%

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

   9. associate-/r* 96.4%

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

   10. metadata-eval 96.4%

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

3. Simplified 96.4%

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

4. Final simplification 96.4%

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

Alternative 4: 98.1% accurate, 0.5× speedup

Math

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

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) (* x y))))

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 = x * y;
	}
	return tmp;
}

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   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 40.0%

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

      4. associate-*l/ 40.0%

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

      5. fma-neg 40.0%

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

      6. sub-neg 40.0%

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

      7. distribute-neg-in 40.0%

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

      8. remove-double-neg 40.0%

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

      9. associate-/l* 40.0%

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

      10. distribute-frac-neg 40.0%

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

      11. associate-/r/ 40.0%

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

      12. fma-def 40.0%

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

      13. neg-mul-1 40.0%

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

      14. *-commutative 40.0%

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

      15. associate-/l* 40.0%

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

      16. metadata-eval 40.0%

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

   3. Simplified 40.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
   4. 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 10.0%

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

      9. +-commutative 10.0%

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

      10. fma-udef 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%

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

   5. Applied egg-rr 0.0%

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

   6. Taylor expanded in x around inf 40.6%

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

4. Final simplification 97.7%

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

Alternative 5: 43.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.6 \cdot 10^{+90}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.2 \cdot 10^{-97}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq -6.2 \cdot 10^{-131}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.7 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 1.35 \cdot 10^{+112}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -6.6e+90)
   (* x y)
   (if (<= (* x y) -5.2e-97)
     c
     (if (<= (* x y) -6.2e-131)
       (* a (* b -0.25))
       (if (<= (* x y) 1.7e-90)
         (* t (* z 0.0625))
         (if (<= (* x y) 1.35e+112) 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) <= -6.6e+90) {
		tmp = x * y;
	} else if ((x * y) <= -5.2e-97) {
		tmp = c;
	} else if ((x * y) <= -6.2e-131) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 1.7e-90) {
		tmp = t * (z * 0.0625);
	} else if ((x * y) <= 1.35e+112) {
		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) <= (-6.6d+90)) then
        tmp = x * y
    else if ((x * y) <= (-5.2d-97)) then
        tmp = c
    else if ((x * y) <= (-6.2d-131)) then
        tmp = a * (b * (-0.25d0))
    else if ((x * y) <= 1.7d-90) then
        tmp = t * (z * 0.0625d0)
    else if ((x * y) <= 1.35d+112) 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) <= -6.6e+90) {
		tmp = x * y;
	} else if ((x * y) <= -5.2e-97) {
		tmp = c;
	} else if ((x * y) <= -6.2e-131) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 1.7e-90) {
		tmp = t * (z * 0.0625);
	} else if ((x * y) <= 1.35e+112) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -6.6e+90:
		tmp = x * y
	elif (x * y) <= -5.2e-97:
		tmp = c
	elif (x * y) <= -6.2e-131:
		tmp = a * (b * -0.25)
	elif (x * y) <= 1.7e-90:
		tmp = t * (z * 0.0625)
	elif (x * y) <= 1.35e+112:
		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) <= -6.6e+90)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -5.2e-97)
		tmp = c;
	elseif (Float64(x * y) <= -6.2e-131)
		tmp = Float64(a * Float64(b * -0.25));
	elseif (Float64(x * y) <= 1.7e-90)
		tmp = Float64(t * Float64(z * 0.0625));
	elseif (Float64(x * y) <= 1.35e+112)
		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) <= -6.6e+90)
		tmp = x * y;
	elseif ((x * y) <= -5.2e-97)
		tmp = c;
	elseif ((x * y) <= -6.2e-131)
		tmp = a * (b * -0.25);
	elseif ((x * y) <= 1.7e-90)
		tmp = t * (z * 0.0625);
	elseif ((x * y) <= 1.35e+112)
		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], -6.6e+90], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5.2e-97], c, If[LessEqual[N[(x * y), $MachinePrecision], -6.2e-131], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.7e-90], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.35e+112], c, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -6.60000000000000016e90 or 1.3500000000000001e112 < (*.f64 x y)

   1. Initial program 90.9%

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

      1. associate-+l- 90.9%

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

      2. associate--l+ 90.9%

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

      3. fma-def 94.9%

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

      4. associate-*l/ 94.9%

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

      5. fma-neg 94.9%

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

      6. sub-neg 94.9%

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

      7. distribute-neg-in 94.9%

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

      8. remove-double-neg 94.9%

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

      9. associate-/l* 94.9%

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

      10. distribute-frac-neg 94.9%

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

      11. associate-/r/ 94.9%

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

      12. fma-def 94.9%

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

      13. neg-mul-1 94.9%

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

      14. *-commutative 94.9%

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

      15. associate-/l* 94.9%

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

      16. metadata-eval 94.9%

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

   3. Simplified 94.9%

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

      1. fma-udef 90.9%

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

      2. fma-udef 90.9%

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

      3. associate-*l/ 90.9%

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

      4. fma-udef 90.9%

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

      5. associate-/r/ 90.8%

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

      6. associate-+r+ 90.8%

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

      7. associate-*l/ 90.8%

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

      8. fma-udef 91.9%

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

      9. +-commutative 91.9%

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

      10. fma-udef 90.8%

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

      11. associate-*l/ 90.8%

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

      12. associate-+r+ 90.8%

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

      13. div-inv 90.9%

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

      14. fma-def 90.9%

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

      15. clear-num 90.9%

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

      16. div-inv 90.9%

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

      17. metadata-eval 90.9%

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

      18. associate-*l/ 90.9%

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

   5. Applied egg-rr 90.9%

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

   6. Taylor expanded in x around inf 66.7%

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

   if -6.60000000000000016e90 < (*.f64 x y) < -5.20000000000000014e-97 or 1.69999999999999997e-90 < (*.f64 x y) < 1.3500000000000001e112

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 40.2%

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

   if -5.20000000000000014e-97 < (*.f64 x y) < -6.20000000000000041e-131

   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* 99.7%

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

      10. distribute-frac-neg 99.7%

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

      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. 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/ 99.7%

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

      6. associate-+r+ 99.7%

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

      7. associate-*l/ 99.7%

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

      8. fma-udef 99.7%

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

      9. +-commutative 99.7%

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

      10. fma-udef 99.7%

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

      11. associate-*l/ 99.7%

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

      12. associate-+r+ 99.7%

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

      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%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in a around inf 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-*r* 83.8%

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

      3. *-commutative 83.8%

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

   8. Simplified 83.8%

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

   if -6.20000000000000041e-131 < (*.f64 x y) < 1.69999999999999997e-90

   1. Initial program 98.9%

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

      1. associate-+l- 98.9%

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

      2. associate--l+ 98.9%

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

      3. fma-def 98.9%

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

      4. associate-*l/ 98.9%

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

      5. fma-neg 98.9%

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

      6. sub-neg 98.9%

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

      7. distribute-neg-in 98.9%

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

      8. remove-double-neg 98.9%

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

      9. associate-/l* 98.8%

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

      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/ 98.9%

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

      12. fma-def 98.9%

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

      13. neg-mul-1 98.9%

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

      14. *-commutative 98.9%

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

      15. associate-/l* 98.9%

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

      16. metadata-eval 98.9%

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

   3. Simplified 98.9%

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

      1. fma-udef 98.9%

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

      2. fma-udef 98.9%

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

      3. associate-*l/ 98.9%

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

      4. fma-udef 98.9%

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

      5. associate-/r/ 98.8%

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

      6. associate-+r+ 98.8%

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

      7. associate-*l/ 98.8%

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

      8. fma-udef 98.8%

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

      9. +-commutative 98.8%

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

      10. fma-udef 98.8%

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

      11. associate-*l/ 98.8%

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

      12. associate-+r+ 98.8%

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

      13. div-inv 98.8%

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

      14. fma-def 98.8%

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

      15. clear-num 98.9%

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

      16. div-inv 98.9%

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

      17. metadata-eval 98.9%

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

      18. associate-*l/ 98.9%

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

   5. Applied egg-rr 98.9%

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

   6. Taylor expanded in t around inf 44.7%

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

      1. *-commutative 44.7%

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

      2. associate-*r* 44.7%

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

      3. *-commutative 44.7%

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

   8. Simplified 44.7%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.6 \cdot 10^{+90}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.2 \cdot 10^{-97}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq -6.2 \cdot 10^{-131}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.7 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 1.35 \cdot 10^{+112}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -1.65 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{-188}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 1.15 \cdot 10^{+112}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* a b) 0.25))))
   (if (<= (* x y) -1.65e+168)
     t_1
     (if (<= (* x y) 1.6e-188)
       (+ c (* 0.0625 (* z t)))
       (if (<= (* x y) 1.15e+112) (+ c (* a (* b -0.25))) 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 ((x * y) <= -1.65e+168) {
		tmp = t_1;
	} else if ((x * y) <= 1.6e-188) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 1.15e+112) {
		tmp = c + (a * (b * -0.25));
	} 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 ((x * y) <= (-1.65d+168)) then
        tmp = t_1
    else if ((x * y) <= 1.6d-188) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((x * y) <= 1.15d+112) then
        tmp = c + (a * (b * (-0.25d0)))
    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 ((x * y) <= -1.65e+168) {
		tmp = t_1;
	} else if ((x * y) <= 1.6e-188) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 1.15e+112) {
		tmp = c + (a * (b * -0.25));
	} 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 (x * y) <= -1.65e+168:
		tmp = t_1
	elif (x * y) <= 1.6e-188:
		tmp = c + (0.0625 * (z * t))
	elif (x * y) <= 1.15e+112:
		tmp = c + (a * (b * -0.25))
	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(x * y) <= -1.65e+168)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.6e-188)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(x * y) <= 1.15e+112)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	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 ((x * y) <= -1.65e+168)
		tmp = t_1;
	elseif ((x * y) <= 1.6e-188)
		tmp = c + (0.0625 * (z * t));
	elseif ((x * y) <= 1.15e+112)
		tmp = c + (a * (b * -0.25));
	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[(x * y), $MachinePrecision], -1.65e+168], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.6e-188], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.15e+112], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.6499999999999999e168 or 1.15e112 < (*.f64 x y)

   1. Initial program 89.8%

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

   2. Taylor expanded in z around 0 83.6%

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

   3. Taylor expanded in c around 0 80.0%

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

   if -1.6499999999999999e168 < (*.f64 x y) < 1.60000000000000011e-188

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 65.5%

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

   if 1.60000000000000011e-188 < (*.f64 x y) < 1.15e112

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-*r* 70.7%

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

   4. Simplified 70.7%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.65 \cdot 10^{+168}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{-188}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 1.15 \cdot 10^{+112}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 7: 88.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -4.6 \cdot 10^{+157} \lor \neg \left(x \cdot y \leq 4.3 \cdot 10^{+102}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)))
   (if (or (<= (* x y) -4.6e+157) (not (<= (* x y) 4.3e+102)))
     (- (+ c (* x y)) t_1)
     (- (+ c (* 0.0625 (* z t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double tmp;
	if (((x * y) <= -4.6e+157) || !((x * y) <= 4.3e+102)) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (c + (0.0625 * (z * t))) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    if (((x * y) <= (-4.6d+157)) .or. (.not. ((x * y) <= 4.3d+102))) then
        tmp = (c + (x * y)) - t_1
    else
        tmp = (c + (0.0625d0 * (z * t))) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double tmp;
	if (((x * y) <= -4.6e+157) || !((x * y) <= 4.3e+102)) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (c + (0.0625 * (z * t))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	tmp = 0
	if ((x * y) <= -4.6e+157) or not ((x * y) <= 4.3e+102):
		tmp = (c + (x * y)) - t_1
	else:
		tmp = (c + (0.0625 * (z * t))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if ((Float64(x * y) <= -4.6e+157) || !(Float64(x * y) <= 4.3e+102))
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	else
		tmp = Float64(Float64(c + Float64(0.0625 * Float64(z * t))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	tmp = 0.0;
	if (((x * y) <= -4.6e+157) || ~(((x * y) <= 4.3e+102)))
		tmp = (c + (x * y)) - t_1;
	else
		tmp = (c + (0.0625 * (z * t))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[Or[LessEqual[N[(x * y), $MachinePrecision], -4.6e+157], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.3e+102]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.60000000000000008e157 or 4.3000000000000001e102 < (*.f64 x y)

   1. Initial program 90.5%

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

   2. Taylor expanded in z around 0 83.8%

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

   if -4.60000000000000008e157 < (*.f64 x y) < 4.3000000000000001e102

   1. Initial program 99.4%

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

   2. Taylor expanded in x around 0 96.4%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.6 \cdot 10^{+157} \lor \neg \left(x \cdot y \leq 4.3 \cdot 10^{+102}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 8: 76.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+30}:\\ \;\;\;\;c + t_2\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+40} \lor \neg \left(t \leq 4.8 \cdot 10^{+118}\right) \land t \leq 5.8 \cdot 10^{+169}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* 0.0625 (* z t))))
   (if (<= t -2.5e+30)
     (+ c t_2)
     (if (or (<= t 7.8e+40) (and (not (<= t 4.8e+118)) (<= t 5.8e+169)))
       (- (+ c (* x y)) t_1)
       (- t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if (t <= -2.5e+30) {
		tmp = c + t_2;
	} else if ((t <= 7.8e+40) || (!(t <= 4.8e+118) && (t <= 5.8e+169))) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = t_2 - 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) :: t_2
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    t_2 = 0.0625d0 * (z * t)
    if (t <= (-2.5d+30)) then
        tmp = c + t_2
    else if ((t <= 7.8d+40) .or. (.not. (t <= 4.8d+118)) .and. (t <= 5.8d+169)) then
        tmp = (c + (x * y)) - t_1
    else
        tmp = t_2 - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if (t <= -2.5e+30) {
		tmp = c + t_2;
	} else if ((t <= 7.8e+40) || (!(t <= 4.8e+118) && (t <= 5.8e+169))) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = 0.0625 * (z * t)
	tmp = 0
	if t <= -2.5e+30:
		tmp = c + t_2
	elif (t <= 7.8e+40) or (not (t <= 4.8e+118) and (t <= 5.8e+169)):
		tmp = (c + (x * y)) - t_1
	else:
		tmp = t_2 - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (t <= -2.5e+30)
		tmp = Float64(c + t_2);
	elseif ((t <= 7.8e+40) || (!(t <= 4.8e+118) && (t <= 5.8e+169)))
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	else
		tmp = Float64(t_2 - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	t_2 = 0.0625 * (z * t);
	tmp = 0.0;
	if (t <= -2.5e+30)
		tmp = c + t_2;
	elseif ((t <= 7.8e+40) || (~((t <= 4.8e+118)) && (t <= 5.8e+169)))
		tmp = (c + (x * y)) - t_1;
	else
		tmp = t_2 - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+30], N[(c + t$95$2), $MachinePrecision], If[Or[LessEqual[t, 7.8e+40], And[N[Not[LessEqual[t, 4.8e+118]], $MachinePrecision], LessEqual[t, 5.8e+169]]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4999999999999999e30

   1. Initial program 92.9%

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

   2. Taylor expanded in z around inf 69.4%

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

   if -2.4999999999999999e30 < t < 7.8000000000000002e40 or 4.8e118 < t < 5.8000000000000001e169

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 92.1%

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

   if 7.8000000000000002e40 < t < 4.8e118 or 5.8000000000000001e169 < t

   1. Initial program 93.6%

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

   2. Taylor expanded in x around 0 79.3%

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

   3. Taylor expanded in c around 0 72.3%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+30}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+40} \lor \neg \left(t \leq 4.8 \cdot 10^{+118}\right) \land t \leq 5.8 \cdot 10^{+169}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 9: 59.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right) - t_1\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{-107}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-221}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-138}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (- (* 0.0625 (* z t)) t_1)))
   (if (<= y -3.1e-107)
     (+ c (* x y))
     (if (<= y 1.3e-221)
       t_2
       (if (<= y 5.2e-138)
         (+ c (* a (* b -0.25)))
         (if (<= y 5.8e+142) t_2 (- (* x y) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = (0.0625 * (z * t)) - t_1;
	double tmp;
	if (y <= -3.1e-107) {
		tmp = c + (x * y);
	} else if (y <= 1.3e-221) {
		tmp = t_2;
	} else if (y <= 5.2e-138) {
		tmp = c + (a * (b * -0.25));
	} else if (y <= 5.8e+142) {
		tmp = t_2;
	} else {
		tmp = (x * y) - 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) :: t_2
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    t_2 = (0.0625d0 * (z * t)) - t_1
    if (y <= (-3.1d-107)) then
        tmp = c + (x * y)
    else if (y <= 1.3d-221) then
        tmp = t_2
    else if (y <= 5.2d-138) then
        tmp = c + (a * (b * (-0.25d0)))
    else if (y <= 5.8d+142) then
        tmp = t_2
    else
        tmp = (x * y) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = (0.0625 * (z * t)) - t_1;
	double tmp;
	if (y <= -3.1e-107) {
		tmp = c + (x * y);
	} else if (y <= 1.3e-221) {
		tmp = t_2;
	} else if (y <= 5.2e-138) {
		tmp = c + (a * (b * -0.25));
	} else if (y <= 5.8e+142) {
		tmp = t_2;
	} else {
		tmp = (x * y) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = (0.0625 * (z * t)) - t_1
	tmp = 0
	if y <= -3.1e-107:
		tmp = c + (x * y)
	elif y <= 1.3e-221:
		tmp = t_2
	elif y <= 5.2e-138:
		tmp = c + (a * (b * -0.25))
	elif y <= 5.8e+142:
		tmp = t_2
	else:
		tmp = (x * y) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(Float64(0.0625 * Float64(z * t)) - t_1)
	tmp = 0.0
	if (y <= -3.1e-107)
		tmp = Float64(c + Float64(x * y));
	elseif (y <= 1.3e-221)
		tmp = t_2;
	elseif (y <= 5.2e-138)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (y <= 5.8e+142)
		tmp = t_2;
	else
		tmp = Float64(Float64(x * y) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	t_2 = (0.0625 * (z * t)) - t_1;
	tmp = 0.0;
	if (y <= -3.1e-107)
		tmp = c + (x * y);
	elseif (y <= 1.3e-221)
		tmp = t_2;
	elseif (y <= 5.2e-138)
		tmp = c + (a * (b * -0.25));
	elseif (y <= 5.8e+142)
		tmp = t_2;
	else
		tmp = (x * y) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[y, -3.1e-107], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-221], t$95$2, If[LessEqual[y, 5.2e-138], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+142], t$95$2, N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.10000000000000022e-107

   1. Initial program 93.4%

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

   2. Taylor expanded in x around inf 54.4%

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

   if -3.10000000000000022e-107 < y < 1.3000000000000001e-221 or 5.2e-138 < y < 5.80000000000000027e142

   1. Initial program 98.2%

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

   2. Taylor expanded in x around 0 88.0%

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

   3. Taylor expanded in c around 0 70.8%

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

   if 1.3000000000000001e-221 < y < 5.2e-138

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 87.5%

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

      1. *-commutative 87.5%

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

      2. associate-*r* 87.5%

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

   4. Simplified 87.5%

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

   if 5.80000000000000027e142 < y

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0 94.7%

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

   3. Taylor expanded in c around 0 81.0%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-107}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-221}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-138}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+142}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 10: 63.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.32 \cdot 10^{+156}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.15 \cdot 10^{-188}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2.4 \cdot 10^{+113}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -1.32e+156)
   (+ c (* x y))
   (if (<= (* x y) 2.15e-188)
     (+ c (* 0.0625 (* z t)))
     (if (<= (* x y) 2.4e+113) (+ c (* a (* b -0.25))) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -1.32e+156) {
		tmp = c + (x * y);
	} else if ((x * y) <= 2.15e-188) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 2.4e+113) {
		tmp = c + (a * (b * -0.25));
	} 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) <= (-1.32d+156)) then
        tmp = c + (x * y)
    else if ((x * y) <= 2.15d-188) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((x * y) <= 2.4d+113) then
        tmp = c + (a * (b * (-0.25d0)))
    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) <= -1.32e+156) {
		tmp = c + (x * y);
	} else if ((x * y) <= 2.15e-188) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 2.4e+113) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -1.32e+156:
		tmp = c + (x * y)
	elif (x * y) <= 2.15e-188:
		tmp = c + (0.0625 * (z * t))
	elif (x * y) <= 2.4e+113:
		tmp = c + (a * (b * -0.25))
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -1.32e+156)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(x * y) <= 2.15e-188)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(x * y) <= 2.4e+113)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	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) <= -1.32e+156)
		tmp = c + (x * y);
	elseif ((x * y) <= 2.15e-188)
		tmp = c + (0.0625 * (z * t));
	elseif ((x * y) <= 2.4e+113)
		tmp = c + (a * (b * -0.25));
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -1.32e+156], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.15e-188], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.4e+113], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.3199999999999999e156

   1. Initial program 92.9%

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

   2. Taylor expanded in x around inf 81.3%

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

   if -1.3199999999999999e156 < (*.f64 x y) < 2.14999999999999994e-188

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 65.4%

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

   if 2.14999999999999994e-188 < (*.f64 x y) < 2.39999999999999983e113

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-*r* 70.7%

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

   4. Simplified 70.7%

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

   if 2.39999999999999983e113 < (*.f64 x y)

   1. Initial program 87.7%

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

      1. associate-+l- 87.7%

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

      2. associate--l+ 87.7%

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

      3. fma-def 91.8%

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

      4. associate-*l/ 91.8%

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

      5. fma-neg 91.8%

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

      6. sub-neg 91.8%

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

      7. distribute-neg-in 91.8%

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

      8. remove-double-neg 91.8%

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

      9. associate-/l* 91.8%

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

      10. distribute-frac-neg 91.8%

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

      11. associate-/r/ 91.8%

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

      12. fma-def 91.8%

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

      13. neg-mul-1 91.8%

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

      14. *-commutative 91.8%

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

      15. associate-/l* 91.8%

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

      16. metadata-eval 91.8%

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

   3. Simplified 91.8%

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

      1. fma-udef 87.8%

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

      2. fma-udef 87.8%

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

      3. associate-*l/ 87.8%

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

      4. fma-udef 87.7%

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

      5. associate-/r/ 87.7%

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

      6. associate-+r+ 87.7%

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

      7. associate-*l/ 87.7%

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

      8. fma-udef 89.7%

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

      9. +-commutative 89.7%

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

      10. fma-udef 87.7%

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

      11. associate-*l/ 87.7%

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

      12. associate-+r+ 87.7%

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

      13. div-inv 87.7%

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

      14. fma-def 87.7%

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

      15. clear-num 87.8%

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

      16. div-inv 87.8%

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

      17. metadata-eval 87.8%

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

      18. associate-*l/ 87.8%

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

   5. Applied egg-rr 87.8%

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

   6. Taylor expanded in x around inf 67.8%

      \[\leadsto \color{blue}{x \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.32 \cdot 10^{+156}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.15 \cdot 10^{-188}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2.4 \cdot 10^{+113}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 11: 44.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.6 \cdot 10^{+88}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.8 \cdot 10^{-99}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -5.6e+88)
   (* x y)
   (if (<= (* x y) -5.8e-99)
     c
     (if (<= (* x y) 3.5e+110) (* a (* b -0.25)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -5.6e+88) {
		tmp = x * y;
	} else if ((x * y) <= -5.8e-99) {
		tmp = c;
	} else if ((x * y) <= 3.5e+110) {
		tmp = a * (b * -0.25);
	} 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) <= (-5.6d+88)) then
        tmp = x * y
    else if ((x * y) <= (-5.8d-99)) then
        tmp = c
    else if ((x * y) <= 3.5d+110) then
        tmp = a * (b * (-0.25d0))
    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) <= -5.6e+88) {
		tmp = x * y;
	} else if ((x * y) <= -5.8e-99) {
		tmp = c;
	} else if ((x * y) <= 3.5e+110) {
		tmp = a * (b * -0.25);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -5.6e+88:
		tmp = x * y
	elif (x * y) <= -5.8e-99:
		tmp = c
	elif (x * y) <= 3.5e+110:
		tmp = a * (b * -0.25)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -5.6e+88)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -5.8e-99)
		tmp = c;
	elseif (Float64(x * y) <= 3.5e+110)
		tmp = Float64(a * Float64(b * -0.25));
	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) <= -5.6e+88)
		tmp = x * y;
	elseif ((x * y) <= -5.8e-99)
		tmp = c;
	elseif ((x * y) <= 3.5e+110)
		tmp = a * (b * -0.25);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -5.6e+88], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5.8e-99], c, If[LessEqual[N[(x * y), $MachinePrecision], 3.5e+110], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.59999999999999977e88 or 3.4999999999999999e110 < (*.f64 x y)

   1. Initial program 91.1%

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

      1. associate-+l- 91.1%

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

      2. associate--l+ 91.1%

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

      3. fma-def 95.0%

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

      4. associate-*l/ 95.0%

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

      5. fma-neg 95.0%

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

      6. sub-neg 95.0%

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

      7. distribute-neg-in 95.0%

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

      8. remove-double-neg 95.0%

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

      9. associate-/l* 95.0%

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

      10. distribute-frac-neg 95.0%

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

      11. associate-/r/ 95.0%

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

      12. fma-def 95.0%

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

      13. neg-mul-1 95.0%

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

      14. *-commutative 95.0%

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

      15. associate-/l* 95.0%

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

      16. metadata-eval 95.0%

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

   3. Simplified 95.0%

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

      1. fma-udef 91.1%

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

      2. fma-udef 91.1%

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

      3. associate-*l/ 91.1%

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

      4. fma-udef 91.1%

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

      5. associate-/r/ 91.0%

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

      6. associate-+r+ 91.0%

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

      7. associate-*l/ 91.0%

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

      8. fma-udef 92.0%

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

      9. +-commutative 92.0%

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

      10. fma-udef 91.0%

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

      11. associate-*l/ 91.0%

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

      12. associate-+r+ 91.0%

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

      13. div-inv 91.0%

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

      14. fma-def 91.0%

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

      15. clear-num 91.1%

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

      16. div-inv 91.1%

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

      17. metadata-eval 91.1%

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

      18. associate-*l/ 91.1%

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

   5. Applied egg-rr 91.1%

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

   6. Taylor expanded in x around inf 65.4%

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

   if -5.59999999999999977e88 < (*.f64 x y) < -5.79999999999999971e-99

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 42.3%

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

   if -5.79999999999999971e-99 < (*.f64 x y) < 3.4999999999999999e110

   1. Initial program 99.2%

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

      1. associate-+l- 99.2%

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

      2. associate--l+ 99.2%

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

      3. fma-def 99.2%

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

      4. associate-*l/ 99.2%

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

      5. fma-neg 99.2%

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

      6. sub-neg 99.2%

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

      7. distribute-neg-in 99.2%

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

      8. remove-double-neg 99.2%

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

      9. associate-/l* 99.1%

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

      10. distribute-frac-neg 99.1%

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

      11. associate-/r/ 99.2%

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

      12. fma-def 99.2%

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

      13. neg-mul-1 99.2%

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

      14. *-commutative 99.2%

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

      15. associate-/l* 99.2%

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

      16. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

      1. fma-udef 99.2%

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

      2. fma-udef 99.2%

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

      3. associate-*l/ 99.2%

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

      4. fma-udef 99.2%

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

      5. associate-/r/ 99.1%

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

      6. associate-+r+ 99.1%

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

      7. associate-*l/ 99.1%

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

      8. fma-udef 99.1%

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

      9. +-commutative 99.1%

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

      10. fma-udef 99.1%

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

      11. associate-*l/ 99.1%

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

      12. associate-+r+ 99.1%

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

      13. div-inv 99.2%

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

      14. fma-def 99.2%

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

      15. clear-num 99.2%

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

      16. div-inv 99.2%

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

      17. metadata-eval 99.2%

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

      18. associate-*l/ 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in a around inf 37.6%

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

      1. *-commutative 37.6%

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

      2. associate-*r* 37.6%

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

      3. *-commutative 37.6%

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

   8. Simplified 37.6%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.6 \cdot 10^{+88}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.8 \cdot 10^{-99}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 12: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (a / ((-4.0d0) / b))) + ((x * y) + (t * (z * 0.0625d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

   1. sub-neg 96.1%

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

   2. associate-+l+ 96.1%

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

   3. fma-def 96.5%

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

   4. associate-*l/ 96.5%

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

   5. distribute-frac-neg 96.5%

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

   6. distribute-rgt-neg-out 96.5%

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

   7. associate-/l* 96.4%

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

   8. neg-mul-1 96.4%

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

   9. associate-/r* 96.4%

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

   10. metadata-eval 96.4%

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

3. Simplified 96.4%

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

   1. fma-udef 96.0%

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

   2. *-commutative 96.0%

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

   3. div-inv 96.0%

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

   4. metadata-eval 96.0%

      \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

5. Applied egg-rr 96.0%

   \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} + \left(\frac{a}{\frac{-4}{b}} + c\right) \]

6. Final simplification 96.0%

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

Alternative 13: 65.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.65 \cdot 10^{+155} \lor \neg \left(x \cdot y \leq 2.05 \cdot 10^{+107}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -3.65e+155) (not (<= (* x y) 2.05e+107)))
   (+ c (* x y))
   (+ c (* 0.0625 (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -3.65e+155) || !((x * y) <= 2.05e+107)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-3.65d+155)) .or. (.not. ((x * y) <= 2.05d+107))) then
        tmp = c + (x * y)
    else
        tmp = c + (0.0625d0 * (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -3.65e+155) || !((x * y) <= 2.05e+107)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -3.65e+155) or not ((x * y) <= 2.05e+107):
		tmp = c + (x * y)
	else:
		tmp = c + (0.0625 * (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -3.65e+155) || !(Float64(x * y) <= 2.05e+107))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -3.65e+155) || ~(((x * y) <= 2.05e+107)))
		tmp = c + (x * y);
	else
		tmp = c + (0.0625 * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -3.65e+155], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.05e+107]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.65000000000000019e155 or 2.05e107 < (*.f64 x y)

   1. Initial program 90.5%

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

   2. Taylor expanded in x around inf 73.9%

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

   if -3.65000000000000019e155 < (*.f64 x y) < 2.05e107

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf 63.7%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.65 \cdot 10^{+155} \lor \neg \left(x \cdot y \leq 2.05 \cdot 10^{+107}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 14: 54.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-182}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* a (* b -0.25))))
   (if (<= a -2.9e+108)
     t_2
     (if (<= a -2.7e-129)
       t_1
       (if (<= a -1.1e-182)
         (* t (* z 0.0625))
         (if (<= a 1.55e+61) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = a * (b * -0.25);
	double tmp;
	if (a <= -2.9e+108) {
		tmp = t_2;
	} else if (a <= -2.7e-129) {
		tmp = t_1;
	} else if (a <= -1.1e-182) {
		tmp = t * (z * 0.0625);
	} else if (a <= 1.55e+61) {
		tmp = t_1;
	} 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 = c + (x * y)
    t_2 = a * (b * (-0.25d0))
    if (a <= (-2.9d+108)) then
        tmp = t_2
    else if (a <= (-2.7d-129)) then
        tmp = t_1
    else if (a <= (-1.1d-182)) then
        tmp = t * (z * 0.0625d0)
    else if (a <= 1.55d+61) then
        tmp = t_1
    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 = c + (x * y);
	double t_2 = a * (b * -0.25);
	double tmp;
	if (a <= -2.9e+108) {
		tmp = t_2;
	} else if (a <= -2.7e-129) {
		tmp = t_1;
	} else if (a <= -1.1e-182) {
		tmp = t * (z * 0.0625);
	} else if (a <= 1.55e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = a * (b * -0.25)
	tmp = 0
	if a <= -2.9e+108:
		tmp = t_2
	elif a <= -2.7e-129:
		tmp = t_1
	elif a <= -1.1e-182:
		tmp = t * (z * 0.0625)
	elif a <= 1.55e+61:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (a <= -2.9e+108)
		tmp = t_2;
	elseif (a <= -2.7e-129)
		tmp = t_1;
	elseif (a <= -1.1e-182)
		tmp = Float64(t * Float64(z * 0.0625));
	elseif (a <= 1.55e+61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = a * (b * -0.25);
	tmp = 0.0;
	if (a <= -2.9e+108)
		tmp = t_2;
	elseif (a <= -2.7e-129)
		tmp = t_1;
	elseif (a <= -1.1e-182)
		tmp = t * (z * 0.0625);
	elseif (a <= 1.55e+61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.9e+108], t$95$2, If[LessEqual[a, -2.7e-129], t$95$1, If[LessEqual[a, -1.1e-182], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+61], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.90000000000000007e108 or 1.55e61 < a

   1. Initial program 94.0%

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

      1. associate-+l- 94.0%

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

      2. associate--l+ 94.0%

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

      3. fma-def 97.6%

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

      4. associate-*l/ 97.6%

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

      5. fma-neg 97.6%

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

      6. sub-neg 97.6%

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

      7. distribute-neg-in 97.6%

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

      8. remove-double-neg 97.6%

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

      9. associate-/l* 97.5%

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

      10. distribute-frac-neg 97.5%

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

      11. associate-/r/ 97.6%

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

      12. fma-def 97.6%

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

      13. neg-mul-1 97.6%

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

      14. *-commutative 97.6%

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

      15. associate-/l* 97.6%

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

      16. metadata-eval 97.6%

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

   3. Simplified 97.6%

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

      1. fma-udef 94.0%

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

      2. fma-udef 94.0%

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

      3. associate-*l/ 94.0%

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

      4. fma-udef 94.0%

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

      5. associate-/r/ 93.9%

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

      6. associate-+r+ 93.9%

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

      7. associate-*l/ 93.9%

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

      8. fma-udef 93.9%

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

      9. +-commutative 93.9%

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

      10. fma-udef 93.9%

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

      11. associate-*l/ 93.9%

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

      12. associate-+r+ 93.9%

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

      13. div-inv 93.9%

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

      14. fma-def 94.0%

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

      15. clear-num 94.0%

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

      16. div-inv 94.0%

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

      17. metadata-eval 94.0%

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

      18. associate-*l/ 94.0%

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

   5. Applied egg-rr 94.0%

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

   6. Taylor expanded in a around inf 51.9%

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

      1. *-commutative 51.9%

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

      2. associate-*r* 51.9%

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

      3. *-commutative 51.9%

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

   8. Simplified 51.9%

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

   if -2.90000000000000007e108 < a < -2.69999999999999999e-129 or -1.1e-182 < a < 1.55e61

   1. Initial program 96.8%

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

   2. Taylor expanded in x around inf 56.6%

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

   if -2.69999999999999999e-129 < a < -1.1e-182

   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. 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%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in t around inf 51.3%

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

      1. *-commutative 51.3%

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

      2. associate-*r* 51.3%

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

      3. *-commutative 51.3%

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

   8. Simplified 51.3%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+108}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-129}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-182}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+61}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]

Alternative 15: 41.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.06 \cdot 10^{+89} \lor \neg \left(x \cdot y \leq 1.2 \cdot 10^{+112}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.06e+89) (not (<= (* x y) 1.2e+112))) (* x y) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.06e+89) || !((x * y) <= 1.2e+112)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-1.06d+89)) .or. (.not. ((x * y) <= 1.2d+112))) then
        tmp = x * y
    else
        tmp = c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.06e+89) || !((x * y) <= 1.2e+112)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.06e+89) or not ((x * y) <= 1.2e+112):
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.06e+89) || !(Float64(x * y) <= 1.2e+112))
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1.06e+89) || ~(((x * y) <= 1.2e+112)))
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.06e+89], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.2e+112]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.05999999999999997e89 or 1.2e112 < (*.f64 x y)

   1. Initial program 90.9%

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

      1. associate-+l- 90.9%

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

      2. associate--l+ 90.9%

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

      3. fma-def 94.9%

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

      4. associate-*l/ 94.9%

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

      5. fma-neg 94.9%

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

      6. sub-neg 94.9%

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

      7. distribute-neg-in 94.9%

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

      8. remove-double-neg 94.9%

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

      9. associate-/l* 94.9%

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

      10. distribute-frac-neg 94.9%

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

      11. associate-/r/ 94.9%

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

      12. fma-def 94.9%

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

      13. neg-mul-1 94.9%

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

      14. *-commutative 94.9%

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

      15. associate-/l* 94.9%

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

      16. metadata-eval 94.9%

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

   3. Simplified 94.9%

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

      1. fma-udef 90.9%

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

      2. fma-udef 90.9%

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

      3. associate-*l/ 90.9%

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

      4. fma-udef 90.9%

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

      5. associate-/r/ 90.8%

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

      6. associate-+r+ 90.8%

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

      7. associate-*l/ 90.8%

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

      8. fma-udef 91.9%

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

      9. +-commutative 91.9%

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

      10. fma-udef 90.8%

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

      11. associate-*l/ 90.8%

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

      12. associate-+r+ 90.8%

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

      13. div-inv 90.9%

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

      14. fma-def 90.9%

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

      15. clear-num 90.9%

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

      16. div-inv 90.9%

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

      17. metadata-eval 90.9%

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

      18. associate-*l/ 90.9%

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

   5. Applied egg-rr 90.9%

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

   6. Taylor expanded in x around inf 66.7%

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

   if -1.05999999999999997e89 < (*.f64 x y) < 1.2e112

   1. Initial program 99.4%

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

   2. Taylor expanded in c around inf 29.4%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.06 \cdot 10^{+89} \lor \neg \left(x \cdot y \leq 1.2 \cdot 10^{+112}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 16: 22.1% 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 96.1%

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

2. Taylor expanded in c around inf 20.5%

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

3. Final simplification 20.5%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023312 
(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))