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

Percentage Accurate: 97.7% → 99.0%

Time: 13.0s

Alternatives: 17

Speedup: 1.0×

• 33.2% 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: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 0.1× speedup

Math

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

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 98.0%

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

   1. associate--l+ 98.0%

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

   2. associate-+l+ 98.0%

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

   3. fma-def 98.8%

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

   4. associate-+l- 98.8%

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

   5. associate-*l/ 98.8%

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

   6. fma-neg 98.8%

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

   7. neg-sub0 98.8%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{0 - \left(\frac{a \cdot b}{4} - c\right)}\right)\right) \]

   8. div0 98.8%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{0}{\frac{4}{b}}} - \left(\frac{a \cdot b}{4} - c\right)\right)\right) \]

   9. associate-+l- 98.8%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(\frac{0}{\frac{4}{b}} - \frac{a \cdot b}{4}\right) + c}\right)\right) \]

   10. associate-/l* 98.8%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(\frac{0}{\frac{4}{b}} - \color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

   11. div-sub 98.8%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{0 - a}{\frac{4}{b}}} + c\right)\right) \]

   12. neg-sub0 98.8%

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

   13. associate-/r/ 98.8%

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

   14. fma-def 98.8%

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

   15. neg-mul-1 98.8%

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

   16. *-commutative 98.8%

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

   17. associate-/l* 98.8%

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

   18. metadata-eval 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 98.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ c + \mathsf{fma}\left(a, b \cdot -0.25, \mathsf{fma}\left(0.0625, z \cdot t, x \cdot y\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ c (fma a (* b -0.25) (fma 0.0625 (* z t) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + fma(a, (b * -0.25), fma(0.0625, (z * t), (x * y)));
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(c + fma(a, Float64(b * -0.25), fma(0.0625, Float64(z * t), Float64(x * y))))
end

Wolfram

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

Derivation

1. Initial program 98.0%

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

2. Taylor expanded in x around 0 98.0%

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

   1. cancel-sign-sub-inv 98.0%

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

   2. metadata-eval 98.0%

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

   3. +-commutative 98.0%

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

   4. *-commutative 98.0%

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

   5. associate-*r* 98.0%

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

   6. +-commutative 98.0%

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

   7. associate-*r* 98.0%

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

   8. *-commutative 98.0%

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

   9. *-commutative 98.0%

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

   10. fma-def 98.4%

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

   11. fma-def 99.2%

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

   12. fma-def 98.8%

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

   13. +-commutative 98.8%

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

   14. associate-*r* 98.8%

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

   15. *-commutative 98.8%

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

   16. fma-def 98.8%

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

   17. *-commutative 98.8%

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

4. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 3: 97.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot y + \mathsf{fma}\left(a, b \cdot -0.25, c\right)\right) + z \cdot \left(t \cdot 0.0625\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (+ (* x y) (fma a (* b -0.25) c)) (* z (* t 0.0625))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((x * y) + fma(a, (b * -0.25), c)) + (z * (t * 0.0625));
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(x * y) + fma(a, Float64(b * -0.25), c)) + Float64(z * Float64(t * 0.0625)))
end

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. associate--l+ 98.0%

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

   2. associate-+l+ 98.0%

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

   3. fma-def 98.8%

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

   4. associate-+l- 98.8%

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

   5. associate-*l/ 98.8%

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

   6. fma-neg 98.8%

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

   7. neg-sub0 98.8%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{0 - \left(\frac{a \cdot b}{4} - c\right)}\right)\right) \]

   8. div0 98.8%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{0}{\frac{4}{b}}} - \left(\frac{a \cdot b}{4} - c\right)\right)\right) \]

   9. associate-+l- 98.8%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(\frac{0}{\frac{4}{b}} - \frac{a \cdot b}{4}\right) + c}\right)\right) \]

   10. associate-/l* 98.8%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(\frac{0}{\frac{4}{b}} - \color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

   11. div-sub 98.8%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{0 - a}{\frac{4}{b}}} + c\right)\right) \]

   12. neg-sub0 98.8%

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

   13. associate-/r/ 98.8%

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

   14. fma-def 98.8%

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

   15. neg-mul-1 98.8%

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

   16. *-commutative 98.8%

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

   17. associate-/l* 98.8%

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

   18. metadata-eval 98.8%

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

3. Simplified 98.8%

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

   1. fma-udef 98.0%

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

   2. fma-udef 98.0%

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

   3. associate-/r/ 98.0%

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

   4. fma-udef 98.0%

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

   5. associate-*l/ 98.0%

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

   6. associate-+r+ 98.0%

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

   7. +-commutative 98.0%

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

   8. associate-+r+ 98.0%

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

   9. div-inv 98.0%

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

   10. fma-def 98.0%

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

   11. clear-num 98.0%

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

   12. div-inv 98.0%

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

   13. metadata-eval 98.0%

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

   14. div-inv 98.0%

       \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\left(z \cdot t\right) \cdot \frac{1}{16}} \]

   15. associate-*l* 98.0%

       \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{z \cdot \left(t \cdot \frac{1}{16}\right)} \]

   16. metadata-eval 98.0%

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

5. Applied egg-rr 98.0%

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

6. Final simplification 98.0%

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

Alternative 4: 98.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. associate-+l- 98.0%

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

   2. sub-neg 98.0%

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

   3. fma-def 98.4%

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

   4. associate-*l/ 98.4%

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

   5. neg-sub0 98.4%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \color{blue}{\left(0 - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

   6. div0 98.4%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{0}{\frac{4}{b}}} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

   7. associate-+l- 98.4%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \color{blue}{\left(\left(\frac{0}{\frac{4}{b}} - \frac{a \cdot b}{4}\right) + c\right)} \]

   8. associate-/l* 98.4%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\left(\frac{0}{\frac{4}{b}} - \color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right) \]

   9. div-sub 98.4%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{16} \cdot t\right) + \left(\color{blue}{\frac{0 - a}{\frac{4}{b}}} + c\right) \]

   10. neg-sub0 98.4%

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

   11. associate-/r/ 98.4%

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

   12. neg-mul-1 98.4%

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

   13. *-commutative 98.4%

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

   14. associate-/l* 98.4%

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

   15. associate-/r/ 98.4%

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

   16. metadata-eval 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 5: 65.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + -0.25 \cdot \left(a \cdot b\right)\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+37}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -4.4 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.3 \cdot 10^{+66}:\\ \;\;\;\;c + t_2\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* -0.25 (* a b))))
        (t_2 (* 0.0625 (* z t)))
        (t_3 (+ c (* x y))))
   (if (<= (* x y) -3.2e+37)
     t_3
     (if (<= (* x y) -4.4e-111)
       t_1
       (if (<= (* x y) 3.3e+66)
         (+ c t_2)
         (if (<= (* x y) 2.5e+101) t_1 (if (<= (* x y) 4e+123) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (-0.25 * (a * b));
	double t_2 = 0.0625 * (z * t);
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -3.2e+37) {
		tmp = t_3;
	} else if ((x * y) <= -4.4e-111) {
		tmp = t_1;
	} else if ((x * y) <= 3.3e+66) {
		tmp = c + t_2;
	} else if ((x * y) <= 2.5e+101) {
		tmp = t_1;
	} else if ((x * y) <= 4e+123) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c + ((-0.25d0) * (a * b))
    t_2 = 0.0625d0 * (z * t)
    t_3 = c + (x * y)
    if ((x * y) <= (-3.2d+37)) then
        tmp = t_3
    else if ((x * y) <= (-4.4d-111)) then
        tmp = t_1
    else if ((x * y) <= 3.3d+66) then
        tmp = c + t_2
    else if ((x * y) <= 2.5d+101) then
        tmp = t_1
    else if ((x * y) <= 4d+123) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (-0.25 * (a * b));
	double t_2 = 0.0625 * (z * t);
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -3.2e+37) {
		tmp = t_3;
	} else if ((x * y) <= -4.4e-111) {
		tmp = t_1;
	} else if ((x * y) <= 3.3e+66) {
		tmp = c + t_2;
	} else if ((x * y) <= 2.5e+101) {
		tmp = t_1;
	} else if ((x * y) <= 4e+123) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (-0.25 * (a * b))
	t_2 = 0.0625 * (z * t)
	t_3 = c + (x * y)
	tmp = 0
	if (x * y) <= -3.2e+37:
		tmp = t_3
	elif (x * y) <= -4.4e-111:
		tmp = t_1
	elif (x * y) <= 3.3e+66:
		tmp = c + t_2
	elif (x * y) <= 2.5e+101:
		tmp = t_1
	elif (x * y) <= 4e+123:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(-0.25 * Float64(a * b)))
	t_2 = Float64(0.0625 * Float64(z * t))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -3.2e+37)
		tmp = t_3;
	elseif (Float64(x * y) <= -4.4e-111)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.3e+66)
		tmp = Float64(c + t_2);
	elseif (Float64(x * y) <= 2.5e+101)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e+123)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (-0.25 * (a * b));
	t_2 = 0.0625 * (z * t);
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -3.2e+37)
		tmp = t_3;
	elseif ((x * y) <= -4.4e-111)
		tmp = t_1;
	elseif ((x * y) <= 3.3e+66)
		tmp = c + t_2;
	elseif ((x * y) <= 2.5e+101)
		tmp = t_1;
	elseif ((x * y) <= 4e+123)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.2e+37], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -4.4e-111], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.3e+66], N[(c + t$95$2), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.5e+101], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e+123], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -3.20000000000000014e37 or 3.99999999999999991e123 < (*.f64 x y)

   1. Initial program 94.8%

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

   2. Taylor expanded in x around inf 70.8%

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

   if -3.20000000000000014e37 < (*.f64 x y) < -4.4e-111 or 3.3000000000000001e66 < (*.f64 x y) < 2.49999999999999994e101

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 79.7%

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

   if -4.4e-111 < (*.f64 x y) < 3.3000000000000001e66

   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 z around inf 73.9%

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

   if 2.49999999999999994e101 < (*.f64 x y) < 3.99999999999999991e123

   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%

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

      2. associate-+l+ 100.0%

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

      3. fma-def 100.0%

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

      4. associate-+l- 100.0%

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

      5. associate-*l/ 100.0%

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

      6. fma-neg 100.0%

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

      7. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{0 - \left(\frac{a \cdot b}{4} - c\right)}\right)\right) \]

      8. div0 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{0}{\frac{4}{b}}} - \left(\frac{a \cdot b}{4} - c\right)\right)\right) \]

      9. associate-+l- 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(\frac{0}{\frac{4}{b}} - \frac{a \cdot b}{4}\right) + c}\right)\right) \]

      10. associate-/l* 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(\frac{0}{\frac{4}{b}} - \color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      11. div-sub 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{0 - a}{\frac{4}{b}}} + c\right)\right) \]

      12. neg-sub0 100.0%

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

      13. associate-/r/ 100.0%

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

      14. fma-def 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. 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%

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

      3. associate-/r/ 100.0%

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

      4. fma-udef 100.0%

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

      5. associate-*l/ 100.0%

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

      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. +-commutative 100.0%

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

      8. associate-+r+ 100.0%

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

      9. div-inv 100.0%

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

      10. fma-def 100.0%

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

      11. clear-num 100.0%

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

      12. div-inv 100.0%

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

      13. metadata-eval 100.0%

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

      14. div-inv 100.0%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\left(z \cdot t\right) \cdot \frac{1}{16}} \]

      15. associate-*l* 100.0%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{z \cdot \left(t \cdot \frac{1}{16}\right)} \]

      16. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in z around inf 69.0%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+37}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4.4 \cdot 10^{-111}:\\ \;\;\;\;c + -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq 3.3 \cdot 10^{+66}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+101}:\\ \;\;\;\;c + -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+123}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 6: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \cdot b \leq -2.05 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -8 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -2.8 \cdot 10^{+60}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 1.65 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (+ c (* -0.25 (* a b)))))
   (if (<= (* a b) -2.05e+116)
     t_2
     (if (<= (* a b) -8e+82)
       t_1
       (if (<= (* a b) -2.8e+60)
         (* 0.0625 (* z t))
         (if (<= (* a b) 1.65e+74) 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 = c + (-0.25 * (a * b));
	double tmp;
	if ((a * b) <= -2.05e+116) {
		tmp = t_2;
	} else if ((a * b) <= -8e+82) {
		tmp = t_1;
	} else if ((a * b) <= -2.8e+60) {
		tmp = 0.0625 * (z * t);
	} else if ((a * b) <= 1.65e+74) {
		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 = c + ((-0.25d0) * (a * b))
    if ((a * b) <= (-2.05d+116)) then
        tmp = t_2
    else if ((a * b) <= (-8d+82)) then
        tmp = t_1
    else if ((a * b) <= (-2.8d+60)) then
        tmp = 0.0625d0 * (z * t)
    else if ((a * b) <= 1.65d+74) 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 = c + (-0.25 * (a * b));
	double tmp;
	if ((a * b) <= -2.05e+116) {
		tmp = t_2;
	} else if ((a * b) <= -8e+82) {
		tmp = t_1;
	} else if ((a * b) <= -2.8e+60) {
		tmp = 0.0625 * (z * t);
	} else if ((a * b) <= 1.65e+74) {
		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 = c + (-0.25 * (a * b))
	tmp = 0
	if (a * b) <= -2.05e+116:
		tmp = t_2
	elif (a * b) <= -8e+82:
		tmp = t_1
	elif (a * b) <= -2.8e+60:
		tmp = 0.0625 * (z * t)
	elif (a * b) <= 1.65e+74:
		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(c + Float64(-0.25 * Float64(a * b)))
	tmp = 0.0
	if (Float64(a * b) <= -2.05e+116)
		tmp = t_2;
	elseif (Float64(a * b) <= -8e+82)
		tmp = t_1;
	elseif (Float64(a * b) <= -2.8e+60)
		tmp = Float64(0.0625 * Float64(z * t));
	elseif (Float64(a * b) <= 1.65e+74)
		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 = c + (-0.25 * (a * b));
	tmp = 0.0;
	if ((a * b) <= -2.05e+116)
		tmp = t_2;
	elseif ((a * b) <= -8e+82)
		tmp = t_1;
	elseif ((a * b) <= -2.8e+60)
		tmp = 0.0625 * (z * t);
	elseif ((a * b) <= 1.65e+74)
		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[(c + N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2.05e+116], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -8e+82], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -2.8e+60], N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.65e+74], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.0499999999999999e116 or 1.6500000000000001e74 < (*.f64 a b)

   1. Initial program 96.2%

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

   2. Taylor expanded in a around inf 75.5%

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

   if -2.0499999999999999e116 < (*.f64 a b) < -7.9999999999999997e82 or -2.8e60 < (*.f64 a b) < 1.6500000000000001e74

   1. Initial program 98.8%

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

   2. Taylor expanded in x around inf 64.6%

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

   if -7.9999999999999997e82 < (*.f64 a b) < -2.8e60

   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%

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

      2. associate-+l+ 100.0%

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

      3. fma-def 100.0%

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

      4. associate-+l- 100.0%

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

      5. associate-*l/ 100.0%

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

      6. fma-neg 100.0%

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

      7. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{0 - \left(\frac{a \cdot b}{4} - c\right)}\right)\right) \]

      8. div0 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{0}{\frac{4}{b}}} - \left(\frac{a \cdot b}{4} - c\right)\right)\right) \]

      9. associate-+l- 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(\frac{0}{\frac{4}{b}} - \frac{a \cdot b}{4}\right) + c}\right)\right) \]

      10. associate-/l* 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(\frac{0}{\frac{4}{b}} - \color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      11. div-sub 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{0 - a}{\frac{4}{b}}} + c\right)\right) \]

      12. neg-sub0 100.0%

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

      13. associate-/r/ 100.0%

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

      14. fma-def 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. 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%

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

      3. associate-/r/ 100.0%

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

      4. fma-udef 100.0%

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

      5. associate-*l/ 100.0%

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

      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. +-commutative 100.0%

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

      8. associate-+r+ 100.0%

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

      9. div-inv 100.0%

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

      10. fma-def 100.0%

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

      11. clear-num 100.0%

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

      12. div-inv 100.0%

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

      13. metadata-eval 100.0%

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

      14. div-inv 100.0%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\left(z \cdot t\right) \cdot \frac{1}{16}} \]

      15. associate-*l* 100.0%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{z \cdot \left(t \cdot \frac{1}{16}\right)} \]

      16. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in z around inf 75.5%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.05 \cdot 10^{+116}:\\ \;\;\;\;c + -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \cdot b \leq -8 \cdot 10^{+82}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -2.8 \cdot 10^{+60}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 1.65 \cdot 10^{+74}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + -0.25 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 7: 65.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.5 \cdot 10^{+37}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.8 \cdot 10^{-110}:\\ \;\;\;\;c + -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-33}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -9.5e+37)
   (+ c (* x y))
   (if (<= (* x y) -2.8e-110)
     (+ c (* -0.25 (* a b)))
     (if (<= (* x y) 5e-33)
       (+ c (* 0.0625 (* z t)))
       (+ (* x y) (* z (* t 0.0625)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -9.5e+37) {
		tmp = c + (x * y);
	} else if ((x * y) <= -2.8e-110) {
		tmp = c + (-0.25 * (a * b));
	} else if ((x * y) <= 5e-33) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = (x * y) + (z * (t * 0.0625));
	}
	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) <= (-9.5d+37)) then
        tmp = c + (x * y)
    else if ((x * y) <= (-2.8d-110)) then
        tmp = c + ((-0.25d0) * (a * b))
    else if ((x * y) <= 5d-33) then
        tmp = c + (0.0625d0 * (z * t))
    else
        tmp = (x * y) + (z * (t * 0.0625d0))
    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) <= -9.5e+37) {
		tmp = c + (x * y);
	} else if ((x * y) <= -2.8e-110) {
		tmp = c + (-0.25 * (a * b));
	} else if ((x * y) <= 5e-33) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = (x * y) + (z * (t * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -9.5e+37:
		tmp = c + (x * y)
	elif (x * y) <= -2.8e-110:
		tmp = c + (-0.25 * (a * b))
	elif (x * y) <= 5e-33:
		tmp = c + (0.0625 * (z * t))
	else:
		tmp = (x * y) + (z * (t * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -9.5e+37)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(x * y) <= -2.8e-110)
		tmp = Float64(c + Float64(-0.25 * Float64(a * b)));
	elseif (Float64(x * y) <= 5e-33)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	else
		tmp = Float64(Float64(x * y) + Float64(z * Float64(t * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -9.5e+37)
		tmp = c + (x * y);
	elseif ((x * y) <= -2.8e-110)
		tmp = c + (-0.25 * (a * b));
	elseif ((x * y) <= 5e-33)
		tmp = c + (0.0625 * (z * t));
	else
		tmp = (x * y) + (z * (t * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -9.5e+37], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.8e-110], N[(c + N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-33], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.4999999999999995e37

   1. Initial program 94.3%

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

   2. Taylor expanded in x around inf 71.8%

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

   if -9.4999999999999995e37 < (*.f64 x y) < -2.8e-110

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 83.7%

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

   if -2.8e-110 < (*.f64 x y) < 5.00000000000000028e-33

   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 z around inf 76.0%

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

   if 5.00000000000000028e-33 < (*.f64 x y)

   1. Initial program 97.4%

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

      1. associate--l+ 97.4%

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

      2. associate-+l+ 97.4%

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

      3. fma-def 98.7%

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

      4. associate-+l- 98.7%

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

      5. associate-*l/ 98.7%

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

      6. fma-neg 98.7%

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

      7. neg-sub0 98.7%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{0 - \left(\frac{a \cdot b}{4} - c\right)}\right)\right) \]

      8. div0 98.7%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{0}{\frac{4}{b}}} - \left(\frac{a \cdot b}{4} - c\right)\right)\right) \]

      9. associate-+l- 98.7%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(\frac{0}{\frac{4}{b}} - \frac{a \cdot b}{4}\right) + c}\right)\right) \]

      10. associate-/l* 98.7%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(\frac{0}{\frac{4}{b}} - \color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      11. div-sub 98.7%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{0 - a}{\frac{4}{b}}} + c\right)\right) \]

      12. neg-sub0 98.7%

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

      13. associate-/r/ 98.7%

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

      14. fma-def 98.7%

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

      15. neg-mul-1 98.7%

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

      16. *-commutative 98.7%

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

      17. associate-/l* 98.7%

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

      18. metadata-eval 98.7%

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

   3. Simplified 98.7%

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

      1. fma-udef 97.4%

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

      2. fma-udef 97.4%

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

      3. associate-/r/ 97.4%

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

      4. fma-udef 97.4%

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

      5. associate-*l/ 97.4%

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

      6. associate-+r+ 97.4%

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

      7. +-commutative 97.4%

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

      8. associate-+r+ 97.4%

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

      9. div-inv 97.4%

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

      10. fma-def 97.4%

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

      11. clear-num 97.4%

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

      12. div-inv 97.4%

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

      13. metadata-eval 97.4%

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

      14. div-inv 97.4%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\left(z \cdot t\right) \cdot \frac{1}{16}} \]

      15. associate-*l* 97.4%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{z \cdot \left(t \cdot \frac{1}{16}\right)} \]

      16. metadata-eval 97.4%

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

   5. Applied egg-rr 97.4%

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

   6. Taylor expanded in x around inf 67.2%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.5 \cdot 10^{+37}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.8 \cdot 10^{-110}:\\ \;\;\;\;c + -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-33}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]

Alternative 8: 66.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -9.8 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-109}:\\ \;\;\;\;c + -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq 7.9 \cdot 10^{+68}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* a b) 0.25))))
   (if (<= (* x y) -9.8e+42)
     t_1
     (if (<= (* x y) -4e-109)
       (+ c (* -0.25 (* a b)))
       (if (<= (* x y) 7.9e+68) (+ c (* 0.0625 (* z t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((x * y) <= -9.8e+42) {
		tmp = t_1;
	} else if ((x * y) <= -4e-109) {
		tmp = c + (-0.25 * (a * b));
	} else if ((x * y) <= 7.9e+68) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - ((a * b) * 0.25d0)
    if ((x * y) <= (-9.8d+42)) then
        tmp = t_1
    else if ((x * y) <= (-4d-109)) then
        tmp = c + ((-0.25d0) * (a * b))
    else if ((x * y) <= 7.9d+68) then
        tmp = c + (0.0625d0 * (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((x * y) <= -9.8e+42) {
		tmp = t_1;
	} else if ((x * y) <= -4e-109) {
		tmp = c + (-0.25 * (a * b));
	} else if ((x * y) <= 7.9e+68) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) - ((a * b) * 0.25)
	tmp = 0
	if (x * y) <= -9.8e+42:
		tmp = t_1
	elif (x * y) <= -4e-109:
		tmp = c + (-0.25 * (a * b))
	elif (x * y) <= 7.9e+68:
		tmp = c + (0.0625 * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25))
	tmp = 0.0
	if (Float64(x * y) <= -9.8e+42)
		tmp = t_1;
	elseif (Float64(x * y) <= -4e-109)
		tmp = Float64(c + Float64(-0.25 * Float64(a * b)));
	elseif (Float64(x * y) <= 7.9e+68)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) - ((a * b) * 0.25);
	tmp = 0.0;
	if ((x * y) <= -9.8e+42)
		tmp = t_1;
	elseif ((x * y) <= -4e-109)
		tmp = c + (-0.25 * (a * b));
	elseif ((x * y) <= 7.9e+68)
		tmp = c + (0.0625 * (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -9.8e+42], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -4e-109], N[(c + N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7.9e+68], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.8000000000000004e42 or 7.9e68 < (*.f64 x y)

   1. Initial program 95.2%

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

   2. Taylor expanded in z around 0 83.3%

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

   3. Taylor expanded in c around 0 72.2%

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

   if -9.8000000000000004e42 < (*.f64 x y) < -4e-109

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 81.2%

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

   if -4e-109 < (*.f64 x y) < 7.9e68

   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 z around inf 73.5%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.8 \cdot 10^{+42}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-109}:\\ \;\;\;\;c + -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq 7.9 \cdot 10^{+68}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 9: 89.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -2.05 \cdot 10^{+116} \lor \neg \left(a \cdot b \leq 1.5 \cdot 10^{+74}\right):\\ \;\;\;\;\left(c + t_1\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (or (<= (* a b) -2.05e+116) (not (<= (* a b) 1.5e+74)))
     (- (+ c t_1) (* (* a b) 0.25))
     (+ c (+ (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if (((a * b) <= -2.05e+116) || !((a * b) <= 1.5e+74)) {
		tmp = (c + t_1) - ((a * b) * 0.25);
	} else {
		tmp = c + ((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) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if (((a * b) <= (-2.05d+116)) .or. (.not. ((a * b) <= 1.5d+74))) then
        tmp = (c + t_1) - ((a * b) * 0.25d0)
    else
        tmp = c + ((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 = 0.0625 * (z * t);
	double tmp;
	if (((a * b) <= -2.05e+116) || !((a * b) <= 1.5e+74)) {
		tmp = (c + t_1) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if ((a * b) <= -2.05e+116) or not ((a * b) <= 1.5e+74):
		tmp = (c + t_1) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if ((Float64(a * b) <= -2.05e+116) || !(Float64(a * b) <= 1.5e+74))
		tmp = Float64(Float64(c + t_1) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if (((a * b) <= -2.05e+116) || ~(((a * b) <= 1.5e+74)))
		tmp = (c + t_1) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(a * b), $MachinePrecision], -2.05e+116], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.5e+74]], $MachinePrecision]], N[(N[(c + t$95$1), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.0499999999999999e116 or 1.5e74 < (*.f64 a b)

   1. Initial program 96.2%

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

   2. Taylor expanded in x around 0 90.7%

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

   if -2.0499999999999999e116 < (*.f64 a b) < 1.5e74

   1. Initial program 98.8%

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

   2. Taylor expanded in a around 0 93.5%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.05 \cdot 10^{+116} \lor \neg \left(a \cdot b \leq 1.5 \cdot 10^{+74}\right):\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 10: 86.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+165} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+234}\right):\\ \;\;\;\;t_1 - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (or (<= (* a b) -1e+165) (not (<= (* a b) 5e+234)))
     (- t_1 (* (* a b) 0.25))
     (+ c (+ (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if (((a * b) <= -1e+165) || !((a * b) <= 5e+234)) {
		tmp = t_1 - ((a * b) * 0.25);
	} else {
		tmp = c + ((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) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if (((a * b) <= (-1d+165)) .or. (.not. ((a * b) <= 5d+234))) then
        tmp = t_1 - ((a * b) * 0.25d0)
    else
        tmp = c + ((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 = 0.0625 * (z * t);
	double tmp;
	if (((a * b) <= -1e+165) || !((a * b) <= 5e+234)) {
		tmp = t_1 - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if ((a * b) <= -1e+165) or not ((a * b) <= 5e+234):
		tmp = t_1 - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if ((Float64(a * b) <= -1e+165) || !(Float64(a * b) <= 5e+234))
		tmp = Float64(t_1 - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if (((a * b) <= -1e+165) || ~(((a * b) <= 5e+234)))
		tmp = t_1 - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(a * b), $MachinePrecision], -1e+165], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5e+234]], $MachinePrecision]], N[(t$95$1 - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -9.99999999999999899e164 or 5.0000000000000003e234 < (*.f64 a b)

   1. Initial program 94.6%

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

   2. Taylor expanded in x around 0 94.6%

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

   3. Taylor expanded in c around 0 90.9%

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

   if -9.99999999999999899e164 < (*.f64 a b) < 5.0000000000000003e234

   1. Initial program 99.0%

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

   2. Taylor expanded in a around 0 89.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+165} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+234}\right):\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 11: 85.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.05 \cdot 10^{+116}:\\ \;\;\;\;c + -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+239}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -2.05e+116)
   (+ c (* -0.25 (* a b)))
   (if (<= (* a b) 2e+239)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (- (* x y) (* (* a b) 0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2.05e+116) {
		tmp = c + (-0.25 * (a * b));
	} else if ((a * b) <= 2e+239) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a * b) <= (-2.05d+116)) then
        tmp = c + ((-0.25d0) * (a * b))
    else if ((a * b) <= 2d+239) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = (x * y) - ((a * b) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2.05e+116) {
		tmp = c + (-0.25 * (a * b));
	} else if ((a * b) <= 2e+239) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -2.05e+116:
		tmp = c + (-0.25 * (a * b))
	elif (a * b) <= 2e+239:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = (x * y) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -2.05e+116)
		tmp = Float64(c + Float64(-0.25 * Float64(a * b)));
	elseif (Float64(a * b) <= 2e+239)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -2.05e+116)
		tmp = c + (-0.25 * (a * b));
	elseif ((a * b) <= 2e+239)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = (x * y) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -2.05e+116], N[(c + N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+239], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.0499999999999999e116

   1. Initial program 94.4%

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

   2. Taylor expanded in a around inf 85.3%

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

   if -2.0499999999999999e116 < (*.f64 a b) < 1.99999999999999998e239

   1. Initial program 99.0%

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

   2. Taylor expanded in a around 0 90.3%

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

   if 1.99999999999999998e239 < (*.f64 a b)

   1. Initial program 95.6%

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

   2. Taylor expanded in z around 0 87.5%

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

   3. Taylor expanded in c around 0 84.6%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.05 \cdot 10^{+116}:\\ \;\;\;\;c + -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+239}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 12: 88.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+165}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;a \cdot b \leq 10^{+66}:\\ \;\;\;\;c + \left(x \cdot y + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* 0.0625 (* z t))))
   (if (<= (* a b) -1e+165)
     (- t_2 t_1)
     (if (<= (* a b) 1e+66) (+ c (+ (* x y) t_2)) (- (+ c (* 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);
	double tmp;
	if ((a * b) <= -1e+165) {
		tmp = t_2 - t_1;
	} else if ((a * b) <= 1e+66) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (c + (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)
    if ((a * b) <= (-1d+165)) then
        tmp = t_2 - t_1
    else if ((a * b) <= 1d+66) then
        tmp = c + ((x * y) + t_2)
    else
        tmp = (c + (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);
	double tmp;
	if ((a * b) <= -1e+165) {
		tmp = t_2 - t_1;
	} else if ((a * b) <= 1e+66) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (c + (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)
	tmp = 0
	if (a * b) <= -1e+165:
		tmp = t_2 - t_1
	elif (a * b) <= 1e+66:
		tmp = c + ((x * y) + t_2)
	else:
		tmp = (c + (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(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -1e+165)
		tmp = Float64(t_2 - t_1);
	elseif (Float64(a * b) <= 1e+66)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	else
		tmp = Float64(Float64(c + 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);
	tmp = 0.0;
	if ((a * b) <= -1e+165)
		tmp = t_2 - t_1;
	elseif ((a * b) <= 1e+66)
		tmp = c + ((x * y) + t_2);
	else
		tmp = (c + (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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e+165], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+66], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.99999999999999899e164

   1. Initial program 93.5%

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

   2. Taylor expanded in x around 0 96.8%

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

   3. Taylor expanded in c around 0 92.5%

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

   if -9.99999999999999899e164 < (*.f64 a b) < 9.99999999999999945e65

   1. Initial program 98.9%

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

   2. Taylor expanded in a around 0 92.3%

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

   if 9.99999999999999945e65 < (*.f64 a b)

   1. Initial program 97.8%

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

   2. Taylor expanded in z around 0 78.7%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+165}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 10^{+66}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 13: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. associate-/l* 98.0%

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

   2. associate-/r/ 98.0%

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

3. Applied egg-rr 98.0%

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

   1. associate-*l/ 98.0%

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

   2. associate-/l* 98.0%

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

5. Simplified 98.0%

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

6. Final simplification 98.0%

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

Alternative 14: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

2. Final simplification 98.0%

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

Alternative 15: 36.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-130} \lor \neg \left(t \leq 440000000000\right):\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -5e-130) (not (<= t 440000000000.0))) (* 0.0625 (* z t)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -5e-130) || !(t <= 440000000000.0)) {
		tmp = 0.0625 * (z * t);
	} 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 ((t <= (-5d-130)) .or. (.not. (t <= 440000000000.0d0))) then
        tmp = 0.0625d0 * (z * t)
    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 ((t <= -5e-130) || !(t <= 440000000000.0)) {
		tmp = 0.0625 * (z * t);
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -5e-130) or not (t <= 440000000000.0):
		tmp = 0.0625 * (z * t)
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -5e-130) || !(t <= 440000000000.0))
		tmp = Float64(0.0625 * Float64(z * t));
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -5e-130) || ~((t <= 440000000000.0)))
		tmp = 0.0625 * (z * t);
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -5e-130], N[Not[LessEqual[t, 440000000000.0]], $MachinePrecision]], N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if t < -4.9999999999999996e-130 or 4.4e11 < t

   1. Initial program 98.0%

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

      1. associate--l+ 98.0%

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

      2. associate-+l+ 98.0%

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

      3. fma-def 98.7%

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

      4. associate-+l- 98.7%

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

      5. associate-*l/ 98.7%

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

      6. fma-neg 98.7%

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

      7. neg-sub0 98.7%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{0 - \left(\frac{a \cdot b}{4} - c\right)}\right)\right) \]

      8. div0 98.7%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{0}{\frac{4}{b}}} - \left(\frac{a \cdot b}{4} - c\right)\right)\right) \]

      9. associate-+l- 98.7%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(\frac{0}{\frac{4}{b}} - \frac{a \cdot b}{4}\right) + c}\right)\right) \]

      10. associate-/l* 98.7%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(\frac{0}{\frac{4}{b}} - \color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      11. div-sub 98.7%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{0 - a}{\frac{4}{b}}} + c\right)\right) \]

      12. neg-sub0 98.7%

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

      13. associate-/r/ 98.7%

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

      14. fma-def 98.7%

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

      15. neg-mul-1 98.7%

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

      16. *-commutative 98.7%

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

      17. associate-/l* 98.7%

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

      18. metadata-eval 98.7%

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

   3. Simplified 98.7%

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

      1. fma-udef 98.1%

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

      2. fma-udef 98.1%

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

      3. associate-/r/ 98.0%

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

      4. fma-udef 98.0%

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

      5. associate-*l/ 98.0%

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

      6. associate-+r+ 98.0%

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

      7. +-commutative 98.0%

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

      8. associate-+r+ 98.0%

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

      9. div-inv 98.0%

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

      10. fma-def 98.0%

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

      11. clear-num 98.1%

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

      12. div-inv 98.1%

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

      13. metadata-eval 98.1%

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

      14. div-inv 98.1%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\left(z \cdot t\right) \cdot \frac{1}{16}} \]

      15. associate-*l* 98.1%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{z \cdot \left(t \cdot \frac{1}{16}\right)} \]

      16. metadata-eval 98.1%

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

   5. Applied egg-rr 98.1%

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

   6. Taylor expanded in z around inf 40.8%

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

   if -4.9999999999999996e-130 < t < 4.4e11

   1. Initial program 97.9%

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

   2. Taylor expanded in c around inf 38.7%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-130} \lor \neg \left(t \leq 440000000000\right):\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 16: 54.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+157} \lor \neg \left(z \leq 4.1 \cdot 10^{-16}\right):\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -3.3e+157) (not (<= z 4.1e-16)))
   (* 0.0625 (* z t))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.3e+157) || !(z <= 4.1e-16)) {
		tmp = 0.0625 * (z * t);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-3.3d+157)) .or. (.not. (z <= 4.1d-16))) then
        tmp = 0.0625d0 * (z * t)
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.3e+157) || !(z <= 4.1e-16)) {
		tmp = 0.0625 * (z * t);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -3.3e+157) or not (z <= 4.1e-16):
		tmp = 0.0625 * (z * t)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -3.3e+157) || !(z <= 4.1e-16))
		tmp = Float64(0.0625 * Float64(z * t));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -3.3e+157) || ~((z <= 4.1e-16)))
		tmp = 0.0625 * (z * t);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -3.3e+157], N[Not[LessEqual[z, 4.1e-16]], $MachinePrecision]], N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3000000000000002e157 or 4.10000000000000006e-16 < z

   1. Initial program 98.0%

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

      1. associate--l+ 98.0%

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

      2. associate-+l+ 98.0%

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

      3. fma-def 99.0%

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

      4. associate-+l- 99.0%

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

      5. associate-*l/ 99.0%

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

      6. fma-neg 99.0%

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

      7. neg-sub0 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{0 - \left(\frac{a \cdot b}{4} - c\right)}\right)\right) \]

      8. div0 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{0}{\frac{4}{b}}} - \left(\frac{a \cdot b}{4} - c\right)\right)\right) \]

      9. associate-+l- 99.0%

         \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(\frac{0}{\frac{4}{b}} - \frac{a \cdot b}{4}\right) + c}\right)\right) \]

      10. associate-/l* 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(\frac{0}{\frac{4}{b}} - \color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

      11. div-sub 99.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{0 - a}{\frac{4}{b}}} + c\right)\right) \]

      12. neg-sub0 99.0%

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

      13. associate-/r/ 99.0%

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

      14. fma-def 99.0%

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

      15. neg-mul-1 99.0%

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

      16. *-commutative 99.0%

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

      17. associate-/l* 99.0%

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

      18. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

      1. fma-udef 98.0%

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

      2. fma-udef 98.0%

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

      3. associate-/r/ 98.0%

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

      4. fma-udef 98.0%

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

      5. associate-*l/ 98.0%

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

      6. associate-+r+ 98.0%

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

      7. +-commutative 98.0%

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

      8. associate-+r+ 98.0%

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

      9. div-inv 97.9%

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

      10. fma-def 97.9%

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

      11. clear-num 98.0%

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

      12. div-inv 98.0%

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

      13. metadata-eval 98.0%

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

      14. div-inv 98.0%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{\left(z \cdot t\right) \cdot \frac{1}{16}} \]

      15. associate-*l* 98.0%

          \[\leadsto \left(\mathsf{fma}\left(a, b \cdot -0.25, c\right) + x \cdot y\right) + \color{blue}{z \cdot \left(t \cdot \frac{1}{16}\right)} \]

      16. metadata-eval 98.0%

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

   5. Applied egg-rr 98.0%

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

   6. Taylor expanded in z around inf 51.6%

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

   if -3.3000000000000002e157 < z < 4.10000000000000006e-16

   1. Initial program 98.0%

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

   2. Taylor expanded in x around inf 56.6%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+157} \lor \neg \left(z \leq 4.1 \cdot 10^{-16}\right):\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 17: 22.2% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

2. Taylor expanded in c around inf 25.0%

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

3. Final simplification 25.0%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023301 
(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))