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

Percentage Accurate: 97.7% → 98.9%

Time: 8.4s

Alternatives: 14

Speedup: 1.0×

• 32.4% 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: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. associate-+l- 98.8%

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

   2. +-commutative 98.8%

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

   3. associate--l+ 98.8%

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

   4. associate-*l/ 98.8%

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

   5. *-commutative 98.8%

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

   6. fma-def 99.2%

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

   7. fma-neg 99.6%

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

   8. neg-sub0 99.6%

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

   9. associate-+l- 99.6%

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

   10. neg-sub0 99.6%

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

   11. +-commutative 99.6%

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

   12. unsub-neg 99.6%

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

   13. *-commutative 99.6%

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

   14. associate-*r/ 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 98.2% accurate, 0.1× speedup

Math

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

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(z / Float64(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[(z / N[(16.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c - N[(a / N[(4.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.8%

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

   1. associate-+l- 98.8%

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

   2. sub-neg 98.8%

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

   3. neg-mul-1 98.8%

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

   4. metadata-eval 98.8%

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

   5. metadata-eval 98.8%

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

   6. cancel-sign-sub-inv 98.8%

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

   7. fma-def 99.2%

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

   8. associate-/l* 99.1%

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

   9. metadata-eval 99.1%

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

   10. *-lft-identity 99.1%

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

   11. associate-/l* 99.1%

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

3. Simplified 99.1%

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

4. Final simplification 99.1%

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

Alternative 3: 65.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_3 := x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+158}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 0.0005:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 10^{+109}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y)))
        (t_2 (+ c (* t (* z 0.0625))))
        (t_3 (- (* x y) (* (* b a) 0.25))))
   (if (<= (* b a) -5e+158)
     t_3
     (if (<= (* b a) -1e-42)
       t_2
       (if (<= (* b a) -1e-197)
         t_1
         (if (<= (* b a) 1e-34)
           t_2
           (if (<= (* b a) 0.0005)
             t_3
             (if (<= (* b a) 5e+55)
               t_1
               (if (<= (* b a) 1e+109) 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 + (x * y);
	double t_2 = c + (t * (z * 0.0625));
	double t_3 = (x * y) - ((b * a) * 0.25);
	double tmp;
	if ((b * a) <= -5e+158) {
		tmp = t_3;
	} else if ((b * a) <= -1e-42) {
		tmp = t_2;
	} else if ((b * a) <= -1e-197) {
		tmp = t_1;
	} else if ((b * a) <= 1e-34) {
		tmp = t_2;
	} else if ((b * a) <= 0.0005) {
		tmp = t_3;
	} else if ((b * a) <= 5e+55) {
		tmp = t_1;
	} else if ((b * a) <= 1e+109) {
		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 + (x * y)
    t_2 = c + (t * (z * 0.0625d0))
    t_3 = (x * y) - ((b * a) * 0.25d0)
    if ((b * a) <= (-5d+158)) then
        tmp = t_3
    else if ((b * a) <= (-1d-42)) then
        tmp = t_2
    else if ((b * a) <= (-1d-197)) then
        tmp = t_1
    else if ((b * a) <= 1d-34) then
        tmp = t_2
    else if ((b * a) <= 0.0005d0) then
        tmp = t_3
    else if ((b * a) <= 5d+55) then
        tmp = t_1
    else if ((b * a) <= 1d+109) 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 + (x * y);
	double t_2 = c + (t * (z * 0.0625));
	double t_3 = (x * y) - ((b * a) * 0.25);
	double tmp;
	if ((b * a) <= -5e+158) {
		tmp = t_3;
	} else if ((b * a) <= -1e-42) {
		tmp = t_2;
	} else if ((b * a) <= -1e-197) {
		tmp = t_1;
	} else if ((b * a) <= 1e-34) {
		tmp = t_2;
	} else if ((b * a) <= 0.0005) {
		tmp = t_3;
	} else if ((b * a) <= 5e+55) {
		tmp = t_1;
	} else if ((b * a) <= 1e+109) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = c + (t * (z * 0.0625))
	t_3 = (x * y) - ((b * a) * 0.25)
	tmp = 0
	if (b * a) <= -5e+158:
		tmp = t_3
	elif (b * a) <= -1e-42:
		tmp = t_2
	elif (b * a) <= -1e-197:
		tmp = t_1
	elif (b * a) <= 1e-34:
		tmp = t_2
	elif (b * a) <= 0.0005:
		tmp = t_3
	elif (b * a) <= 5e+55:
		tmp = t_1
	elif (b * a) <= 1e+109:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(c + Float64(t * Float64(z * 0.0625)))
	t_3 = Float64(Float64(x * y) - Float64(Float64(b * a) * 0.25))
	tmp = 0.0
	if (Float64(b * a) <= -5e+158)
		tmp = t_3;
	elseif (Float64(b * a) <= -1e-42)
		tmp = t_2;
	elseif (Float64(b * a) <= -1e-197)
		tmp = t_1;
	elseif (Float64(b * a) <= 1e-34)
		tmp = t_2;
	elseif (Float64(b * a) <= 0.0005)
		tmp = t_3;
	elseif (Float64(b * a) <= 5e+55)
		tmp = t_1;
	elseif (Float64(b * a) <= 1e+109)
		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 + (x * y);
	t_2 = c + (t * (z * 0.0625));
	t_3 = (x * y) - ((b * a) * 0.25);
	tmp = 0.0;
	if ((b * a) <= -5e+158)
		tmp = t_3;
	elseif ((b * a) <= -1e-42)
		tmp = t_2;
	elseif ((b * a) <= -1e-197)
		tmp = t_1;
	elseif ((b * a) <= 1e-34)
		tmp = t_2;
	elseif ((b * a) <= 0.0005)
		tmp = t_3;
	elseif ((b * a) <= 5e+55)
		tmp = t_1;
	elseif ((b * a) <= 1e+109)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -5e+158], t$95$3, If[LessEqual[N[(b * a), $MachinePrecision], -1e-42], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -1e-197], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 1e-34], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 0.0005], t$95$3, If[LessEqual[N[(b * a), $MachinePrecision], 5e+55], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 1e+109], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.9999999999999996e158 or 9.99999999999999928e-35 < (*.f64 a b) < 5.0000000000000001e-4 or 9.99999999999999982e108 < (*.f64 a b)

   1. Initial program 99.0%

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

      1. associate-+l- 99.0%

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

      2. sub-neg 99.0%

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

      3. neg-mul-1 99.0%

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

      4. metadata-eval 99.0%

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

      5. metadata-eval 99.0%

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

      6. cancel-sign-sub-inv 99.0%

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

      7. fma-def 99.0%

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

      8. associate-/l* 99.0%

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

      9. metadata-eval 99.0%

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

      10. *-lft-identity 99.0%

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

      11. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 92.8%

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

   5. Taylor expanded in c around 0 86.3%

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

   if -4.9999999999999996e158 < (*.f64 a b) < -1.00000000000000004e-42 or -9.9999999999999999e-198 < (*.f64 a b) < 9.99999999999999928e-35 or 5.00000000000000046e55 < (*.f64 a b) < 9.99999999999999982e108

   1. Initial program 98.4%

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

      1. associate-+l- 98.4%

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

      2. sub-neg 98.4%

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

      3. neg-mul-1 98.4%

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

      4. metadata-eval 98.4%

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

      5. metadata-eval 98.4%

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

      6. cancel-sign-sub-inv 98.4%

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

      7. fma-def 99.2%

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

      8. associate-/l* 99.1%

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

      9. metadata-eval 99.1%

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

      10. *-lft-identity 99.1%

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

      11. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in a around 0 93.7%

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

   5. Taylor expanded in y around 0 69.9%

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

      1. *-commutative 69.9%

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

      2. associate-*l* 69.9%

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

   7. Simplified 69.9%

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

   if -1.00000000000000004e-42 < (*.f64 a b) < -9.9999999999999999e-198 or 5.0000000000000001e-4 < (*.f64 a b) < 5.00000000000000046e55

   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 0 86.9%

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

      1. associate-*r* 86.9%

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

      2. *-commutative 86.9%

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

      3. *-commutative 86.9%

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

      4. fma-neg 86.9%

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

      5. distribute-rgt-neg-in 86.9%

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

      6. distribute-rgt-neg-in 86.9%

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

      7. metadata-eval 86.9%

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

   4. Simplified 86.9%

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

   5. Taylor expanded in y around inf 83.0%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+158}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-42}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-197}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 10^{-34}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 0.0005:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{+55}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 10^{+109}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 4: 43.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 0.0625\right)\\ t_2 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -7.2 \cdot 10^{+139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -4.4 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -1.12 \cdot 10^{-133}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 2.35 \cdot 10^{-179}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq 9.5 \cdot 10^{+60}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 2.7 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* z 0.0625))) (t_2 (* (* b a) -0.25)))
   (if (<= (* b a) -7.2e+139)
     t_2
     (if (<= (* b a) -4.4e-48)
       t_1
       (if (<= (* b a) -1.12e-133)
         (* x y)
         (if (<= (* b a) 2.35e-179)
           c
           (if (<= (* b a) 9.5e+60)
             (* x y)
             (if (<= (* b a) 2.7e+108) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (z * 0.0625);
	double t_2 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -7.2e+139) {
		tmp = t_2;
	} else if ((b * a) <= -4.4e-48) {
		tmp = t_1;
	} else if ((b * a) <= -1.12e-133) {
		tmp = x * y;
	} else if ((b * a) <= 2.35e-179) {
		tmp = c;
	} else if ((b * a) <= 9.5e+60) {
		tmp = x * y;
	} else if ((b * a) <= 2.7e+108) {
		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 = t * (z * 0.0625d0)
    t_2 = (b * a) * (-0.25d0)
    if ((b * a) <= (-7.2d+139)) then
        tmp = t_2
    else if ((b * a) <= (-4.4d-48)) then
        tmp = t_1
    else if ((b * a) <= (-1.12d-133)) then
        tmp = x * y
    else if ((b * a) <= 2.35d-179) then
        tmp = c
    else if ((b * a) <= 9.5d+60) then
        tmp = x * y
    else if ((b * a) <= 2.7d+108) 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 = t * (z * 0.0625);
	double t_2 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -7.2e+139) {
		tmp = t_2;
	} else if ((b * a) <= -4.4e-48) {
		tmp = t_1;
	} else if ((b * a) <= -1.12e-133) {
		tmp = x * y;
	} else if ((b * a) <= 2.35e-179) {
		tmp = c;
	} else if ((b * a) <= 9.5e+60) {
		tmp = x * y;
	} else if ((b * a) <= 2.7e+108) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = t * (z * 0.0625)
	t_2 = (b * a) * -0.25
	tmp = 0
	if (b * a) <= -7.2e+139:
		tmp = t_2
	elif (b * a) <= -4.4e-48:
		tmp = t_1
	elif (b * a) <= -1.12e-133:
		tmp = x * y
	elif (b * a) <= 2.35e-179:
		tmp = c
	elif (b * a) <= 9.5e+60:
		tmp = x * y
	elif (b * a) <= 2.7e+108:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(z * 0.0625))
	t_2 = Float64(Float64(b * a) * -0.25)
	tmp = 0.0
	if (Float64(b * a) <= -7.2e+139)
		tmp = t_2;
	elseif (Float64(b * a) <= -4.4e-48)
		tmp = t_1;
	elseif (Float64(b * a) <= -1.12e-133)
		tmp = Float64(x * y);
	elseif (Float64(b * a) <= 2.35e-179)
		tmp = c;
	elseif (Float64(b * a) <= 9.5e+60)
		tmp = Float64(x * y);
	elseif (Float64(b * a) <= 2.7e+108)
		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 = t * (z * 0.0625);
	t_2 = (b * a) * -0.25;
	tmp = 0.0;
	if ((b * a) <= -7.2e+139)
		tmp = t_2;
	elseif ((b * a) <= -4.4e-48)
		tmp = t_1;
	elseif ((b * a) <= -1.12e-133)
		tmp = x * y;
	elseif ((b * a) <= 2.35e-179)
		tmp = c;
	elseif ((b * a) <= 9.5e+60)
		tmp = x * y;
	elseif ((b * a) <= 2.7e+108)
		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[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -7.2e+139], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -4.4e-48], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -1.12e-133], N[(x * y), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 2.35e-179], c, If[LessEqual[N[(b * a), $MachinePrecision], 9.5e+60], N[(x * y), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 2.7e+108], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -7.19999999999999971e139 or 2.7e108 < (*.f64 a b)

   1. Initial program 99.0%

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

      1. associate-+l- 99.0%

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

      2. sub-neg 99.0%

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

      3. neg-mul-1 99.0%

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

      4. metadata-eval 99.0%

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

      5. metadata-eval 99.0%

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

      6. cancel-sign-sub-inv 99.0%

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

      7. fma-def 99.0%

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

      8. associate-/l* 99.0%

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

      9. metadata-eval 99.0%

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

      10. *-lft-identity 99.0%

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

      11. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in x around 0 88.5%

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

   5. Taylor expanded in c around 0 80.3%

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

   6. Taylor expanded in t around 0 74.1%

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

   if -7.19999999999999971e139 < (*.f64 a b) < -4.40000000000000025e-48 or 9.49999999999999988e60 < (*.f64 a b) < 2.7e108

   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. neg-mul-1 98.0%

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

      4. metadata-eval 98.0%

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

      5. metadata-eval 98.0%

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

      6. cancel-sign-sub-inv 98.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-lft-identity 99.8%

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

      11. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 88.3%

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

   5. Taylor expanded in y around 0 69.6%

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

      1. *-commutative 69.6%

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

      2. associate-*l* 69.6%

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

   7. Simplified 69.6%

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

   8. Taylor expanded in c around 0 51.0%

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

      1. *-commutative 51.0%

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

      2. associate-*r* 51.0%

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

      3. *-commutative 51.0%

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

   10. Simplified 51.0%

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

   if -4.40000000000000025e-48 < (*.f64 a b) < -1.1199999999999999e-133 or 2.3500000000000001e-179 < (*.f64 a b) < 9.49999999999999988e60

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 99.9%

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

      9. metadata-eval 99.9%

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

      10. *-lft-identity 99.9%

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

      11. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 78.7%

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

   5. Taylor expanded in c around 0 60.9%

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

   6. Taylor expanded in y around inf 55.3%

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

   if -1.1199999999999999e-133 < (*.f64 a b) < 2.3500000000000001e-179

   1. Initial program 98.3%

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

      1. associate-+l- 98.3%

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

      2. sub-neg 98.3%

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

      3. neg-mul-1 98.3%

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

      4. metadata-eval 98.3%

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

      5. metadata-eval 98.3%

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

      6. cancel-sign-sub-inv 98.3%

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

      7. fma-def 98.3%

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

      8. associate-/l* 98.2%

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

      9. metadata-eval 98.2%

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

      10. *-lft-identity 98.2%

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

      11. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in c around inf 39.7%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -7.2 \cdot 10^{+139}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq -4.4 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq -1.12 \cdot 10^{-133}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 2.35 \cdot 10^{-179}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq 9.5 \cdot 10^{+60}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 2.7 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 5: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := t \cdot \left(z \cdot 0.0625\right)\\ t_3 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -3.2 \cdot 10^{+250}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot a \leq -2.75 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -9 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 7 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 3.4 \cdot 10^{+100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 7.6 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* t (* z 0.0625))) (t_3 (* (* b a) -0.25)))
   (if (<= (* b a) -3.2e+250)
     t_3
     (if (<= (* b a) -2.75e+140)
       t_1
       (if (<= (* b a) -9e+74)
         t_2
         (if (<= (* b a) 7e+62)
           t_1
           (if (<= (* b a) 3.4e+100)
             t_2
             (if (<= (* b a) 7.6e+122) t_1 t_3))))))))

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 = t * (z * 0.0625);
	double t_3 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -3.2e+250) {
		tmp = t_3;
	} else if ((b * a) <= -2.75e+140) {
		tmp = t_1;
	} else if ((b * a) <= -9e+74) {
		tmp = t_2;
	} else if ((b * a) <= 7e+62) {
		tmp = t_1;
	} else if ((b * a) <= 3.4e+100) {
		tmp = t_2;
	} else if ((b * a) <= 7.6e+122) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = t * (z * 0.0625d0)
    t_3 = (b * a) * (-0.25d0)
    if ((b * a) <= (-3.2d+250)) then
        tmp = t_3
    else if ((b * a) <= (-2.75d+140)) then
        tmp = t_1
    else if ((b * a) <= (-9d+74)) then
        tmp = t_2
    else if ((b * a) <= 7d+62) then
        tmp = t_1
    else if ((b * a) <= 3.4d+100) then
        tmp = t_2
    else if ((b * a) <= 7.6d+122) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = t * (z * 0.0625);
	double t_3 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -3.2e+250) {
		tmp = t_3;
	} else if ((b * a) <= -2.75e+140) {
		tmp = t_1;
	} else if ((b * a) <= -9e+74) {
		tmp = t_2;
	} else if ((b * a) <= 7e+62) {
		tmp = t_1;
	} else if ((b * a) <= 3.4e+100) {
		tmp = t_2;
	} else if ((b * a) <= 7.6e+122) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = t * (z * 0.0625)
	t_3 = (b * a) * -0.25
	tmp = 0
	if (b * a) <= -3.2e+250:
		tmp = t_3
	elif (b * a) <= -2.75e+140:
		tmp = t_1
	elif (b * a) <= -9e+74:
		tmp = t_2
	elif (b * a) <= 7e+62:
		tmp = t_1
	elif (b * a) <= 3.4e+100:
		tmp = t_2
	elif (b * a) <= 7.6e+122:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(t * Float64(z * 0.0625))
	t_3 = Float64(Float64(b * a) * -0.25)
	tmp = 0.0
	if (Float64(b * a) <= -3.2e+250)
		tmp = t_3;
	elseif (Float64(b * a) <= -2.75e+140)
		tmp = t_1;
	elseif (Float64(b * a) <= -9e+74)
		tmp = t_2;
	elseif (Float64(b * a) <= 7e+62)
		tmp = t_1;
	elseif (Float64(b * a) <= 3.4e+100)
		tmp = t_2;
	elseif (Float64(b * a) <= 7.6e+122)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = t * (z * 0.0625);
	t_3 = (b * a) * -0.25;
	tmp = 0.0;
	if ((b * a) <= -3.2e+250)
		tmp = t_3;
	elseif ((b * a) <= -2.75e+140)
		tmp = t_1;
	elseif ((b * a) <= -9e+74)
		tmp = t_2;
	elseif ((b * a) <= 7e+62)
		tmp = t_1;
	elseif ((b * a) <= 3.4e+100)
		tmp = t_2;
	elseif ((b * a) <= 7.6e+122)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -3.2e+250], t$95$3, If[LessEqual[N[(b * a), $MachinePrecision], -2.75e+140], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -9e+74], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 7e+62], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 3.4e+100], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 7.6e+122], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.1999999999999997e250 or 7.5999999999999996e122 < (*.f64 a b)

   1. Initial program 98.7%

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

      1. associate-+l- 98.7%

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

      2. sub-neg 98.7%

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

      3. neg-mul-1 98.7%

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

      4. metadata-eval 98.7%

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

      5. metadata-eval 98.7%

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

      6. cancel-sign-sub-inv 98.7%

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

      7. fma-def 98.7%

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

      8. associate-/l* 98.7%

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

      9. metadata-eval 98.7%

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

      10. *-lft-identity 98.7%

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

      11. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in x around 0 94.3%

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

   5. Taylor expanded in c around 0 90.4%

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

   6. Taylor expanded in t around 0 86.4%

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

   if -3.1999999999999997e250 < (*.f64 a b) < -2.75e140 or -8.9999999999999999e74 < (*.f64 a b) < 6.99999999999999967e62 or 3.39999999999999994e100 < (*.f64 a b) < 7.5999999999999996e122

   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 z around 0 72.1%

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

      1. associate-*r* 72.1%

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

      2. *-commutative 72.1%

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

      3. *-commutative 72.1%

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

      4. fma-neg 72.1%

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

      5. distribute-rgt-neg-in 72.1%

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

      6. distribute-rgt-neg-in 72.1%

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

      7. metadata-eval 72.1%

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

   4. Simplified 72.1%

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

   5. Taylor expanded in y around inf 67.0%

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

   if -2.75e140 < (*.f64 a b) < -8.9999999999999999e74 or 6.99999999999999967e62 < (*.f64 a b) < 3.39999999999999994e100

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. sub-neg 99.9%

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

      3. neg-mul-1 99.9%

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

      4. metadata-eval 99.9%

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

      5. metadata-eval 99.9%

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

      6. cancel-sign-sub-inv 99.9%

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

      7. fma-def 99.9%

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

      8. associate-/l* 99.7%

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

      9. metadata-eval 99.7%

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

      10. *-lft-identity 99.7%

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

      11. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 80.1%

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

   5. Taylor expanded in y around 0 74.6%

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

      1. *-commutative 74.6%

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

      2. associate-*l* 74.6%

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

   7. Simplified 74.6%

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

   8. Taylor expanded in c around 0 74.7%

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

      1. *-commutative 74.7%

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

      2. associate-*r* 74.7%

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

      3. *-commutative 74.7%

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

   10. Simplified 74.7%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -3.2 \cdot 10^{+250}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq -2.75 \cdot 10^{+140}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -9 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 7 \cdot 10^{+62}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 3.4 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 7.6 \cdot 10^{+122}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 6: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := c + x \cdot y\\ t_3 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -3.2 \cdot 10^{+250}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 2.3 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 1.9 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 7.6 \cdot 10^{+122}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625))))
        (t_2 (+ c (* x y)))
        (t_3 (* (* b a) -0.25)))
   (if (<= (* b a) -3.2e+250)
     t_3
     (if (<= (* b a) -2e-43)
       t_1
       (if (<= (* b a) 2.3e+62)
         t_2
         (if (<= (* b a) 1.9e+120) t_1 (if (<= (* b a) 7.6e+122) 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 + (t * (z * 0.0625));
	double t_2 = c + (x * y);
	double t_3 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -3.2e+250) {
		tmp = t_3;
	} else if ((b * a) <= -2e-43) {
		tmp = t_1;
	} else if ((b * a) <= 2.3e+62) {
		tmp = t_2;
	} else if ((b * a) <= 1.9e+120) {
		tmp = t_1;
	} else if ((b * a) <= 7.6e+122) {
		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 + (t * (z * 0.0625d0))
    t_2 = c + (x * y)
    t_3 = (b * a) * (-0.25d0)
    if ((b * a) <= (-3.2d+250)) then
        tmp = t_3
    else if ((b * a) <= (-2d-43)) then
        tmp = t_1
    else if ((b * a) <= 2.3d+62) then
        tmp = t_2
    else if ((b * a) <= 1.9d+120) then
        tmp = t_1
    else if ((b * a) <= 7.6d+122) 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 + (t * (z * 0.0625));
	double t_2 = c + (x * y);
	double t_3 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -3.2e+250) {
		tmp = t_3;
	} else if ((b * a) <= -2e-43) {
		tmp = t_1;
	} else if ((b * a) <= 2.3e+62) {
		tmp = t_2;
	} else if ((b * a) <= 1.9e+120) {
		tmp = t_1;
	} else if ((b * a) <= 7.6e+122) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (t * (z * 0.0625))
	t_2 = c + (x * y)
	t_3 = (b * a) * -0.25
	tmp = 0
	if (b * a) <= -3.2e+250:
		tmp = t_3
	elif (b * a) <= -2e-43:
		tmp = t_1
	elif (b * a) <= 2.3e+62:
		tmp = t_2
	elif (b * a) <= 1.9e+120:
		tmp = t_1
	elif (b * a) <= 7.6e+122:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(t * Float64(z * 0.0625)))
	t_2 = Float64(c + Float64(x * y))
	t_3 = Float64(Float64(b * a) * -0.25)
	tmp = 0.0
	if (Float64(b * a) <= -3.2e+250)
		tmp = t_3;
	elseif (Float64(b * a) <= -2e-43)
		tmp = t_1;
	elseif (Float64(b * a) <= 2.3e+62)
		tmp = t_2;
	elseif (Float64(b * a) <= 1.9e+120)
		tmp = t_1;
	elseif (Float64(b * a) <= 7.6e+122)
		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 + (t * (z * 0.0625));
	t_2 = c + (x * y);
	t_3 = (b * a) * -0.25;
	tmp = 0.0;
	if ((b * a) <= -3.2e+250)
		tmp = t_3;
	elseif ((b * a) <= -2e-43)
		tmp = t_1;
	elseif ((b * a) <= 2.3e+62)
		tmp = t_2;
	elseif ((b * a) <= 1.9e+120)
		tmp = t_1;
	elseif ((b * a) <= 7.6e+122)
		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[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -3.2e+250], t$95$3, If[LessEqual[N[(b * a), $MachinePrecision], -2e-43], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 2.3e+62], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 1.9e+120], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 7.6e+122], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.1999999999999997e250 or 7.5999999999999996e122 < (*.f64 a b)

   1. Initial program 98.7%

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

      1. associate-+l- 98.7%

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

      2. sub-neg 98.7%

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

      3. neg-mul-1 98.7%

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

      4. metadata-eval 98.7%

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

      5. metadata-eval 98.7%

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

      6. cancel-sign-sub-inv 98.7%

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

      7. fma-def 98.7%

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

      8. associate-/l* 98.7%

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

      9. metadata-eval 98.7%

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

      10. *-lft-identity 98.7%

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

      11. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in x around 0 94.3%

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

   5. Taylor expanded in c around 0 90.4%

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

   6. Taylor expanded in t around 0 86.4%

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

   if -3.1999999999999997e250 < (*.f64 a b) < -2.00000000000000015e-43 or 2.29999999999999984e62 < (*.f64 a b) < 1.8999999999999999e120

   1. Initial program 98.5%

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

      1. associate-+l- 98.5%

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

      2. sub-neg 98.5%

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

      3. neg-mul-1 98.5%

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

      4. metadata-eval 98.5%

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

      5. metadata-eval 98.5%

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

      6. cancel-sign-sub-inv 98.5%

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

      7. fma-def 100.0%

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

      8. associate-/l* 99.9%

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

      9. metadata-eval 99.9%

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

      10. *-lft-identity 99.9%

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

      11. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 84.3%

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

   5. Taylor expanded in y around 0 62.1%

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

      1. *-commutative 62.1%

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

      2. associate-*l* 62.1%

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

   7. Simplified 62.1%

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

   if -2.00000000000000015e-43 < (*.f64 a b) < 2.29999999999999984e62 or 1.8999999999999999e120 < (*.f64 a b) < 7.5999999999999996e122

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 73.6%

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

      1. associate-*r* 73.6%

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

      2. *-commutative 73.6%

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

      3. *-commutative 73.6%

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

      4. fma-neg 73.6%

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

      5. distribute-rgt-neg-in 73.6%

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

      6. distribute-rgt-neg-in 73.6%

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

      7. metadata-eval 73.6%

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

   4. Simplified 73.6%

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

   5. Taylor expanded in y around inf 70.8%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -3.2 \cdot 10^{+250}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-43}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 2.3 \cdot 10^{+62}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 1.9 \cdot 10^{+120}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 7.6 \cdot 10^{+122}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 7: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{+55}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625)))) (t_2 (+ c (* b (* a -0.25)))))
   (if (<= (* b a) -1e+141)
     t_2
     (if (<= (* b a) -1e-42)
       t_1
       (if (<= (* b a) 5e+55)
         (+ c (* x y))
         (if (<= (* b a) 1e+106) 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 + (t * (z * 0.0625));
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if ((b * a) <= -1e+141) {
		tmp = t_2;
	} else if ((b * a) <= -1e-42) {
		tmp = t_1;
	} else if ((b * a) <= 5e+55) {
		tmp = c + (x * y);
	} else if ((b * a) <= 1e+106) {
		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 + (t * (z * 0.0625d0))
    t_2 = c + (b * (a * (-0.25d0)))
    if ((b * a) <= (-1d+141)) then
        tmp = t_2
    else if ((b * a) <= (-1d-42)) then
        tmp = t_1
    else if ((b * a) <= 5d+55) then
        tmp = c + (x * y)
    else if ((b * a) <= 1d+106) 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 + (t * (z * 0.0625));
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if ((b * a) <= -1e+141) {
		tmp = t_2;
	} else if ((b * a) <= -1e-42) {
		tmp = t_1;
	} else if ((b * a) <= 5e+55) {
		tmp = c + (x * y);
	} else if ((b * a) <= 1e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (t * (z * 0.0625))
	t_2 = c + (b * (a * -0.25))
	tmp = 0
	if (b * a) <= -1e+141:
		tmp = t_2
	elif (b * a) <= -1e-42:
		tmp = t_1
	elif (b * a) <= 5e+55:
		tmp = c + (x * y)
	elif (b * a) <= 1e+106:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(t * Float64(z * 0.0625)))
	t_2 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (Float64(b * a) <= -1e+141)
		tmp = t_2;
	elseif (Float64(b * a) <= -1e-42)
		tmp = t_1;
	elseif (Float64(b * a) <= 5e+55)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(b * a) <= 1e+106)
		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 + (t * (z * 0.0625));
	t_2 = c + (b * (a * -0.25));
	tmp = 0.0;
	if ((b * a) <= -1e+141)
		tmp = t_2;
	elseif ((b * a) <= -1e-42)
		tmp = t_1;
	elseif ((b * a) <= 5e+55)
		tmp = c + (x * y);
	elseif ((b * a) <= 1e+106)
		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[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -1e+141], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -1e-42], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 5e+55], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 1e+106], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.00000000000000002e141 or 1.00000000000000009e106 < (*.f64 a b)

   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 inf 82.3%

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

      1. *-commutative 82.3%

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

      2. *-commutative 82.3%

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

      3. associate-*r* 82.3%

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

   4. Simplified 82.3%

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

   if -1.00000000000000002e141 < (*.f64 a b) < -1.00000000000000004e-42 or 5.00000000000000046e55 < (*.f64 a b) < 1.00000000000000009e106

   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. neg-mul-1 98.0%

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

      4. metadata-eval 98.0%

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

      5. metadata-eval 98.0%

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

      6. cancel-sign-sub-inv 98.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-lft-identity 99.8%

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

      11. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 88.3%

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

   5. Taylor expanded in y around 0 69.6%

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

      1. *-commutative 69.6%

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

      2. associate-*l* 69.6%

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

   7. Simplified 69.6%

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

   if -1.00000000000000004e-42 < (*.f64 a b) < 5.00000000000000046e55

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 73.1%

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

      1. associate-*r* 73.1%

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

      2. *-commutative 73.1%

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

      3. *-commutative 73.1%

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

      4. fma-neg 73.1%

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

      5. distribute-rgt-neg-in 73.1%

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

      6. distribute-rgt-neg-in 73.1%

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

      7. metadata-eval 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in y around inf 70.2%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+141}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-42}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{+55}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 10^{+106}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 8: 43.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -4.2 \cdot 10^{+196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -2.55 \cdot 10^{-105}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -4 \cdot 10^{-297}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) -0.25)))
   (if (<= (* b a) -4.2e+196)
     t_1
     (if (<= (* b a) -2.55e-105)
       (* x y)
       (if (<= (* b a) -4e-297) c (if (<= (* b a) 9.5e+58) (* x y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -4.2e+196) {
		tmp = t_1;
	} else if ((b * a) <= -2.55e-105) {
		tmp = x * y;
	} else if ((b * a) <= -4e-297) {
		tmp = c;
	} else if ((b * a) <= 9.5e+58) {
		tmp = x * y;
	} 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 = (b * a) * (-0.25d0)
    if ((b * a) <= (-4.2d+196)) then
        tmp = t_1
    else if ((b * a) <= (-2.55d-105)) then
        tmp = x * y
    else if ((b * a) <= (-4d-297)) then
        tmp = c
    else if ((b * a) <= 9.5d+58) then
        tmp = x * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -4.2e+196) {
		tmp = t_1;
	} else if ((b * a) <= -2.55e-105) {
		tmp = x * y;
	} else if ((b * a) <= -4e-297) {
		tmp = c;
	} else if ((b * a) <= 9.5e+58) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * -0.25
	tmp = 0
	if (b * a) <= -4.2e+196:
		tmp = t_1
	elif (b * a) <= -2.55e-105:
		tmp = x * y
	elif (b * a) <= -4e-297:
		tmp = c
	elif (b * a) <= 9.5e+58:
		tmp = x * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * -0.25)
	tmp = 0.0
	if (Float64(b * a) <= -4.2e+196)
		tmp = t_1;
	elseif (Float64(b * a) <= -2.55e-105)
		tmp = Float64(x * y);
	elseif (Float64(b * a) <= -4e-297)
		tmp = c;
	elseif (Float64(b * a) <= 9.5e+58)
		tmp = Float64(x * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b * a) * -0.25;
	tmp = 0.0;
	if ((b * a) <= -4.2e+196)
		tmp = t_1;
	elseif ((b * a) <= -2.55e-105)
		tmp = x * y;
	elseif ((b * a) <= -4e-297)
		tmp = c;
	elseif ((b * a) <= 9.5e+58)
		tmp = x * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -4.2e+196], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -2.55e-105], N[(x * y), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], -4e-297], c, If[LessEqual[N[(b * a), $MachinePrecision], 9.5e+58], N[(x * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.20000000000000029e196 or 9.5000000000000002e58 < (*.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. Step-by-step derivation

      1. associate-+l- 97.8%

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

      2. sub-neg 97.8%

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

      3. neg-mul-1 97.8%

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

      4. metadata-eval 97.8%

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

      5. metadata-eval 97.8%

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

      6. cancel-sign-sub-inv 97.8%

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

      7. fma-def 98.9%

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

      8. associate-/l* 98.9%

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

      9. metadata-eval 98.9%

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

      10. *-lft-identity 98.9%

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

      11. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in x around 0 92.3%

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

   5. Taylor expanded in c around 0 84.9%

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

   6. Taylor expanded in t around 0 74.4%

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

   if -4.20000000000000029e196 < (*.f64 a b) < -2.55000000000000004e-105 or -4.00000000000000016e-297 < (*.f64 a b) < 9.5000000000000002e58

   1. Initial program 99.3%

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

      1. associate-+l- 99.3%

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

      2. sub-neg 99.3%

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

      3. neg-mul-1 99.3%

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

      4. metadata-eval 99.3%

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

      5. metadata-eval 99.3%

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

      6. cancel-sign-sub-inv 99.3%

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

      7. fma-def 99.3%

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

      8. associate-/l* 99.2%

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

      9. metadata-eval 99.2%

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

      10. *-lft-identity 99.2%

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

      11. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in z around 0 68.2%

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

   5. Taylor expanded in c around 0 45.7%

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

   6. Taylor expanded in y around inf 40.2%

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

   if -2.55000000000000004e-105 < (*.f64 a b) < -4.00000000000000016e-297

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 99.9%

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

      9. metadata-eval 99.9%

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

      10. *-lft-identity 99.9%

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

      11. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in c around inf 54.6%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -4.2 \cdot 10^{+196}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq -2.55 \cdot 10^{-105}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -4 \cdot 10^{-297}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 9: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+141} \lor \neg \left(b \cdot a \leq 4 \cdot 10^{+100}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(t \cdot z\right) \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -1e+141) (not (<= (* b a) 4e+100)))
   (- (+ c (* x y)) (* (* b a) 0.25))
   (+ c (+ (* x y) (* (* t z) 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -1e+141) || !((b * a) <= 4e+100)) {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	} else {
		tmp = c + ((x * y) + ((t * z) * 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 (((b * a) <= (-1d+141)) .or. (.not. ((b * a) <= 4d+100))) then
        tmp = (c + (x * y)) - ((b * a) * 0.25d0)
    else
        tmp = c + ((x * y) + ((t * z) * 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 (((b * a) <= -1e+141) || !((b * a) <= 4e+100)) {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	} else {
		tmp = c + ((x * y) + ((t * z) * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -1e+141) or not ((b * a) <= 4e+100):
		tmp = (c + (x * y)) - ((b * a) * 0.25)
	else:
		tmp = c + ((x * y) + ((t * z) * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -1e+141) || !(Float64(b * a) <= 4e+100))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(b * a) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(t * z) * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -1e+141) || ~(((b * a) <= 4e+100)))
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	else
		tmp = c + ((x * y) + ((t * z) * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -1e+141], N[Not[LessEqual[N[(b * a), $MachinePrecision], 4e+100]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.00000000000000002e141 or 4.00000000000000006e100 < (*.f64 a b)

   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. neg-mul-1 98.0%

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

      4. metadata-eval 98.0%

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

      5. metadata-eval 98.0%

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

      6. cancel-sign-sub-inv 98.0%

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

      7. fma-def 99.0%

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

      8. associate-/l* 99.0%

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

      9. metadata-eval 99.0%

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

      10. *-lft-identity 99.0%

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

      11. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 92.0%

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

   if -1.00000000000000002e141 < (*.f64 a b) < 4.00000000000000006e100

   1. Initial program 99.3%

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

      1. associate-+l- 99.3%

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

      2. sub-neg 99.3%

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

      3. neg-mul-1 99.3%

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

      4. metadata-eval 99.3%

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

      5. metadata-eval 99.3%

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

      6. cancel-sign-sub-inv 99.3%

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

      7. fma-def 99.3%

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

      8. associate-/l* 99.2%

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

      9. metadata-eval 99.2%

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

      10. *-lft-identity 99.2%

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

      11. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in a around 0 94.1%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+141} \lor \neg \left(b \cdot a \leq 4 \cdot 10^{+100}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(t \cdot z\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 10: 85.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -4 \cdot 10^{+252}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+143}:\\ \;\;\;\;c + \left(x \cdot y + \left(t \cdot z\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* b a) -4e+252)
   (* (* b a) -0.25)
   (if (<= (* b a) 2e+143)
     (+ c (+ (* x y) (* (* t z) 0.0625)))
     (- (* x y) (* (* b a) 0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b * a) <= -4e+252) {
		tmp = (b * a) * -0.25;
	} else if ((b * a) <= 2e+143) {
		tmp = c + ((x * y) + ((t * z) * 0.0625));
	} else {
		tmp = (x * y) - ((b * a) * 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 ((b * a) <= (-4d+252)) then
        tmp = (b * a) * (-0.25d0)
    else if ((b * a) <= 2d+143) then
        tmp = c + ((x * y) + ((t * z) * 0.0625d0))
    else
        tmp = (x * y) - ((b * a) * 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 ((b * a) <= -4e+252) {
		tmp = (b * a) * -0.25;
	} else if ((b * a) <= 2e+143) {
		tmp = c + ((x * y) + ((t * z) * 0.0625));
	} else {
		tmp = (x * y) - ((b * a) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b * a) <= -4e+252:
		tmp = (b * a) * -0.25
	elif (b * a) <= 2e+143:
		tmp = c + ((x * y) + ((t * z) * 0.0625))
	else:
		tmp = (x * y) - ((b * a) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(b * a) <= -4e+252)
		tmp = Float64(Float64(b * a) * -0.25);
	elseif (Float64(b * a) <= 2e+143)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(t * z) * 0.0625)));
	else
		tmp = Float64(Float64(x * y) - Float64(Float64(b * a) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b * a) <= -4e+252)
		tmp = (b * a) * -0.25;
	elseif ((b * a) <= 2e+143)
		tmp = c + ((x * y) + ((t * z) * 0.0625));
	else
		tmp = (x * y) - ((b * a) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(b * a), $MachinePrecision], -4e+252], N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 2e+143], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.0000000000000004e252

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 100.0%

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

      9. metadata-eval 100.0%

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

      10. *-lft-identity 100.0%

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

      11. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 100.0%

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

   5. Taylor expanded in c around 0 100.0%

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

   6. Taylor expanded in t around 0 97.1%

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

   if -4.0000000000000004e252 < (*.f64 a b) < 2e143

   1. Initial program 98.9%

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

      1. associate-+l- 98.9%

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

      2. sub-neg 98.9%

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

      3. neg-mul-1 98.9%

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

      4. metadata-eval 98.9%

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

      5. metadata-eval 98.9%

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

      6. cancel-sign-sub-inv 98.9%

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

      7. fma-def 99.4%

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

      8. associate-/l* 99.4%

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

      9. metadata-eval 99.4%

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

      10. *-lft-identity 99.4%

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

      11. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in a around 0 90.7%

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

   if 2e143 < (*.f64 a b)

   1. Initial program 97.5%

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

      1. associate-+l- 97.5%

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

      2. sub-neg 97.5%

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

      3. neg-mul-1 97.5%

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

      4. metadata-eval 97.5%

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

      5. metadata-eval 97.5%

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

      6. cancel-sign-sub-inv 97.5%

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

      7. fma-def 97.5%

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

      8. associate-/l* 97.5%

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

      9. metadata-eval 97.5%

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

      10. *-lft-identity 97.5%

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

      11. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around 0 97.0%

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

   5. Taylor expanded in c around 0 89.7%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -4 \cdot 10^{+252}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+143}:\\ \;\;\;\;c + \left(x \cdot y + \left(t \cdot z\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 11: 85.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot 0.25\\ t_2 := \left(t \cdot z\right) \cdot 0.0625\\ \mathbf{if}\;b \cdot a \leq -4 \cdot 10^{+252}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+143}:\\ \;\;\;\;c + \left(x \cdot y + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) 0.25)) (t_2 (* (* t z) 0.0625)))
   (if (<= (* b a) -4e+252)
     (- t_2 t_1)
     (if (<= (* b a) 2e+143) (+ c (+ (* x y) t_2)) (- (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * 0.25;
	double t_2 = (t * z) * 0.0625;
	double tmp;
	if ((b * a) <= -4e+252) {
		tmp = t_2 - t_1;
	} else if ((b * a) <= 2e+143) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (x * y) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * a) * 0.25d0
    t_2 = (t * z) * 0.0625d0
    if ((b * a) <= (-4d+252)) then
        tmp = t_2 - t_1
    else if ((b * a) <= 2d+143) then
        tmp = c + ((x * y) + t_2)
    else
        tmp = (x * y) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * 0.25;
	double t_2 = (t * z) * 0.0625;
	double tmp;
	if ((b * a) <= -4e+252) {
		tmp = t_2 - t_1;
	} else if ((b * a) <= 2e+143) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (x * y) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * 0.25
	t_2 = (t * z) * 0.0625
	tmp = 0
	if (b * a) <= -4e+252:
		tmp = t_2 - t_1
	elif (b * a) <= 2e+143:
		tmp = c + ((x * y) + t_2)
	else:
		tmp = (x * y) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * 0.25)
	t_2 = Float64(Float64(t * z) * 0.0625)
	tmp = 0.0
	if (Float64(b * a) <= -4e+252)
		tmp = Float64(t_2 - t_1);
	elseif (Float64(b * a) <= 2e+143)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	else
		tmp = Float64(Float64(x * y) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b * a) * 0.25;
	t_2 = (t * z) * 0.0625;
	tmp = 0.0;
	if ((b * a) <= -4e+252)
		tmp = t_2 - t_1;
	elseif ((b * a) <= 2e+143)
		tmp = c + ((x * y) + t_2);
	else
		tmp = (x * y) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -4e+252], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 2e+143], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.0000000000000004e252

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 100.0%

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

      9. metadata-eval 100.0%

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

      10. *-lft-identity 100.0%

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

      11. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 100.0%

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

   5. Taylor expanded in c around 0 100.0%

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

   if -4.0000000000000004e252 < (*.f64 a b) < 2e143

   1. Initial program 98.9%

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

      1. associate-+l- 98.9%

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

      2. sub-neg 98.9%

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

      3. neg-mul-1 98.9%

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

      4. metadata-eval 98.9%

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

      5. metadata-eval 98.9%

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

      6. cancel-sign-sub-inv 98.9%

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

      7. fma-def 99.4%

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

      8. associate-/l* 99.4%

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

      9. metadata-eval 99.4%

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

      10. *-lft-identity 99.4%

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

      11. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in a around 0 90.7%

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

   if 2e143 < (*.f64 a b)

   1. Initial program 97.5%

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

      1. associate-+l- 97.5%

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

      2. sub-neg 97.5%

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

      3. neg-mul-1 97.5%

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

      4. metadata-eval 97.5%

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

      5. metadata-eval 97.5%

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

      6. cancel-sign-sub-inv 97.5%

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

      7. fma-def 97.5%

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

      8. associate-/l* 97.5%

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

      9. metadata-eval 97.5%

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

      10. *-lft-identity 97.5%

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

      11. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around 0 97.0%

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

   5. Taylor expanded in c around 0 89.7%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -4 \cdot 10^{+252}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625 - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+143}:\\ \;\;\;\;c + \left(x \cdot y + \left(t \cdot z\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 12: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + ((((t * z) / 16.0) + (x * y)) - ((b * a) / 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 + ((((t * z) / 16.0d0) + (x * y)) - ((b * a) / 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 + ((((t * z) / 16.0) + (x * y)) - ((b * a) / 4.0));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

2. Final simplification 98.8%

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

Alternative 13: 36.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -680000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+36}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -680000.0) (* x y) (if (<= y 2.2e+36) c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -680000.0) {
		tmp = x * y;
	} else if (y <= 2.2e+36) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-680000.0d0)) then
        tmp = x * y
    else if (y <= 2.2d+36) then
        tmp = c
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -680000.0) {
		tmp = x * y;
	} else if (y <= 2.2e+36) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -680000.0:
		tmp = x * y
	elif y <= 2.2e+36:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -680000.0)
		tmp = Float64(x * y);
	elseif (y <= 2.2e+36)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -680000.0)
		tmp = x * y;
	elseif (y <= 2.2e+36)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -680000.0], N[(x * y), $MachinePrecision], If[LessEqual[y, 2.2e+36], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8e5 or 2.2e36 < y

   1. Initial program 97.5%

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

      1. associate-+l- 97.5%

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

      2. sub-neg 97.5%

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

      3. neg-mul-1 97.5%

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

      4. metadata-eval 97.5%

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

      5. metadata-eval 97.5%

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

      6. cancel-sign-sub-inv 97.5%

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

      7. fma-def 98.3%

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

      8. associate-/l* 98.3%

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

      9. metadata-eval 98.3%

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

      10. *-lft-identity 98.3%

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

      11. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around 0 85.4%

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

   5. Taylor expanded in c around 0 70.7%

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

   6. Taylor expanded in y around inf 47.8%

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

   if -6.8e5 < y < 2.2e36

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 99.9%

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

      9. metadata-eval 99.9%

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

      10. *-lft-identity 99.9%

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

      11. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in c around inf 24.8%

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

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -680000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+36}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 14: 22.6% 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 98.8%

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

   1. associate-+l- 98.8%

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

   2. sub-neg 98.8%

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

   3. neg-mul-1 98.8%

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

   4. metadata-eval 98.8%

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

   5. metadata-eval 98.8%

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

   6. cancel-sign-sub-inv 98.8%

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

   7. fma-def 99.2%

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

   8. associate-/l* 99.1%

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

   9. metadata-eval 99.1%

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

   10. *-lft-identity 99.1%

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

   11. associate-/l* 99.1%

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

3. Simplified 99.1%

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

4. Taylor expanded in c around inf 21.1%

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

5. Final simplification 21.1%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023238 
(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))