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

Percentage Accurate: 97.5% → 98.9%

Time: 7.9s

Alternatives: 13

Speedup: 1.0×

• 32.3% 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: 97.5% 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 98.4%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
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. +-commutative 98.4%

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

   3. associate--l+ 98.4%

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

   4. associate-*l/ 98.4%

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

   5. *-commutative 98.4%

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

   6. fma-def 98.4%

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

   7. fma-neg 100.0%

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

   8. neg-sub0 100.0%

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

   9. associate-+l- 100.0%

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

   10. neg-sub0 100.0%

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

   11. +-commutative 100.0%

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

   12. unsub-neg 100.0%

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

   13. *-commutative 100.0%

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

   14. associate-*r/ 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 97.9% 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 98.4%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
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 98.8%

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

   8. associate-/l* 98.8%

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

   9. metadata-eval 98.8%

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

   10. *-lft-identity 98.8%

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

   11. associate-/l* 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. Final simplification 98.7%

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

Alternative 3: 42.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -1.4 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -4.7 \cdot 10^{+16}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq -1.2 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -4.4 \cdot 10^{-259}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 8.2 \cdot 10^{-114}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625\\ \mathbf{elif}\;b \cdot a \leq 4.2 \cdot 10^{+14}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 4.2 \cdot 10^{+131}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) -0.25)))
   (if (<= (* b a) -1.4e+162)
     t_1
     (if (<= (* b a) -4.7e+16)
       c
       (if (<= (* b a) -1.2e-45)
         t_1
         (if (<= (* b a) -4.4e-259)
           (* x y)
           (if (<= (* b a) 8.2e-114)
             (* (* t z) 0.0625)
             (if (<= (* b a) 4.2e+14)
               (* x y)
               (if (<= (* b a) 4.2e+131) c 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) <= -1.4e+162) {
		tmp = t_1;
	} else if ((b * a) <= -4.7e+16) {
		tmp = c;
	} else if ((b * a) <= -1.2e-45) {
		tmp = t_1;
	} else if ((b * a) <= -4.4e-259) {
		tmp = x * y;
	} else if ((b * a) <= 8.2e-114) {
		tmp = (t * z) * 0.0625;
	} else if ((b * a) <= 4.2e+14) {
		tmp = x * y;
	} else if ((b * a) <= 4.2e+131) {
		tmp = c;
	} 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) <= (-1.4d+162)) then
        tmp = t_1
    else if ((b * a) <= (-4.7d+16)) then
        tmp = c
    else if ((b * a) <= (-1.2d-45)) then
        tmp = t_1
    else if ((b * a) <= (-4.4d-259)) then
        tmp = x * y
    else if ((b * a) <= 8.2d-114) then
        tmp = (t * z) * 0.0625d0
    else if ((b * a) <= 4.2d+14) then
        tmp = x * y
    else if ((b * a) <= 4.2d+131) then
        tmp = c
    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) <= -1.4e+162) {
		tmp = t_1;
	} else if ((b * a) <= -4.7e+16) {
		tmp = c;
	} else if ((b * a) <= -1.2e-45) {
		tmp = t_1;
	} else if ((b * a) <= -4.4e-259) {
		tmp = x * y;
	} else if ((b * a) <= 8.2e-114) {
		tmp = (t * z) * 0.0625;
	} else if ((b * a) <= 4.2e+14) {
		tmp = x * y;
	} else if ((b * a) <= 4.2e+131) {
		tmp = c;
	} 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) <= -1.4e+162:
		tmp = t_1
	elif (b * a) <= -4.7e+16:
		tmp = c
	elif (b * a) <= -1.2e-45:
		tmp = t_1
	elif (b * a) <= -4.4e-259:
		tmp = x * y
	elif (b * a) <= 8.2e-114:
		tmp = (t * z) * 0.0625
	elif (b * a) <= 4.2e+14:
		tmp = x * y
	elif (b * a) <= 4.2e+131:
		tmp = c
	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) <= -1.4e+162)
		tmp = t_1;
	elseif (Float64(b * a) <= -4.7e+16)
		tmp = c;
	elseif (Float64(b * a) <= -1.2e-45)
		tmp = t_1;
	elseif (Float64(b * a) <= -4.4e-259)
		tmp = Float64(x * y);
	elseif (Float64(b * a) <= 8.2e-114)
		tmp = Float64(Float64(t * z) * 0.0625);
	elseif (Float64(b * a) <= 4.2e+14)
		tmp = Float64(x * y);
	elseif (Float64(b * a) <= 4.2e+131)
		tmp = c;
	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) <= -1.4e+162)
		tmp = t_1;
	elseif ((b * a) <= -4.7e+16)
		tmp = c;
	elseif ((b * a) <= -1.2e-45)
		tmp = t_1;
	elseif ((b * a) <= -4.4e-259)
		tmp = x * y;
	elseif ((b * a) <= 8.2e-114)
		tmp = (t * z) * 0.0625;
	elseif ((b * a) <= 4.2e+14)
		tmp = x * y;
	elseif ((b * a) <= 4.2e+131)
		tmp = c;
	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], -1.4e+162], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -4.7e+16], c, If[LessEqual[N[(b * a), $MachinePrecision], -1.2e-45], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -4.4e-259], N[(x * y), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 8.2e-114], N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 4.2e+14], N[(x * y), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 4.2e+131], c, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1.39999999999999995e162 or -4.7e16 < (*.f64 a b) < -1.19999999999999995e-45 or 4.19999999999999971e131 < (*.f64 a b)

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0 85.8%

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

   3. Taylor expanded in a around inf 74.8%

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

      1. *-commutative 74.8%

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

   5. Simplified 74.8%

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

   if -1.39999999999999995e162 < (*.f64 a b) < -4.7e16 or 4.2e14 < (*.f64 a b) < 4.19999999999999971e131

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 45.9%

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

   if -1.19999999999999995e-45 < (*.f64 a b) < -4.40000000000000019e-259 or 8.1999999999999993e-114 < (*.f64 a b) < 4.2e14

   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 78.1%

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

   3. Taylor expanded in y around inf 52.3%

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

   if -4.40000000000000019e-259 < (*.f64 a b) < 8.1999999999999993e-114

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 64.4%

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

      1. associate-*r* 64.4%

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

      2. metadata-eval 64.4%

         \[\leadsto \left(\color{blue}{\frac{1}{16}} \cdot t\right) \cdot z + c \]

      3. associate-/r/ 64.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{16}{t}}} \cdot z + c \]

      4. associate-*l/ 64.3%

         \[\leadsto \color{blue}{\frac{1 \cdot z}{\frac{16}{t}}} + c \]

      5. *-commutative 64.3%

         \[\leadsto \frac{\color{blue}{z \cdot 1}}{\frac{16}{t}} + c \]

      6. *-rgt-identity 64.3%

         \[\leadsto \frac{\color{blue}{z}}{\frac{16}{t}} + c \]

      7. associate-/r/ 64.4%

         \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + c \]

      8. *-commutative 64.4%

         \[\leadsto \color{blue}{t \cdot \frac{z}{16}} + c \]

   4. Simplified 64.4%

      \[\leadsto \color{blue}{t \cdot \frac{z}{16}} + c \]

   5. Taylor expanded in t around inf 44.5%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.4 \cdot 10^{+162}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq -4.7 \cdot 10^{+16}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq -1.2 \cdot 10^{-45}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq -4.4 \cdot 10^{-259}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 8.2 \cdot 10^{-114}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625\\ \mathbf{elif}\;b \cdot a \leq 4.2 \cdot 10^{+14}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 4.2 \cdot 10^{+131}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 4: 63.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-119}:\\ \;\;\;\;c + t \cdot \frac{z}{16}\\ \mathbf{elif}\;b \cdot a \leq 4 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (+ c (* b (* a -0.25)))))
   (if (<= (* b a) -1e-45)
     t_2
     (if (<= (* b a) -2e-251)
       t_1
       (if (<= (* b a) 5e-119)
         (+ c (* t (/ z 16.0)))
         (if (<= (* b a) 4e+93) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if ((b * a) <= -1e-45) {
		tmp = t_2;
	} else if ((b * a) <= -2e-251) {
		tmp = t_1;
	} else if ((b * a) <= 5e-119) {
		tmp = c + (t * (z / 16.0));
	} else if ((b * a) <= 4e+93) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = c + (b * (a * (-0.25d0)))
    if ((b * a) <= (-1d-45)) then
        tmp = t_2
    else if ((b * a) <= (-2d-251)) then
        tmp = t_1
    else if ((b * a) <= 5d-119) then
        tmp = c + (t * (z / 16.0d0))
    else if ((b * a) <= 4d+93) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if ((b * a) <= -1e-45) {
		tmp = t_2;
	} else if ((b * a) <= -2e-251) {
		tmp = t_1;
	} else if ((b * a) <= 5e-119) {
		tmp = c + (t * (z / 16.0));
	} else if ((b * a) <= 4e+93) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = c + (b * (a * -0.25))
	tmp = 0
	if (b * a) <= -1e-45:
		tmp = t_2
	elif (b * a) <= -2e-251:
		tmp = t_1
	elif (b * a) <= 5e-119:
		tmp = c + (t * (z / 16.0))
	elif (b * a) <= 4e+93:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (Float64(b * a) <= -1e-45)
		tmp = t_2;
	elseif (Float64(b * a) <= -2e-251)
		tmp = t_1;
	elseif (Float64(b * a) <= 5e-119)
		tmp = Float64(c + Float64(t * Float64(z / 16.0)));
	elseif (Float64(b * a) <= 4e+93)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = c + (b * (a * -0.25));
	tmp = 0.0;
	if ((b * a) <= -1e-45)
		tmp = t_2;
	elseif ((b * a) <= -2e-251)
		tmp = t_1;
	elseif ((b * a) <= 5e-119)
		tmp = c + (t * (z / 16.0));
	elseif ((b * a) <= 4e+93)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -1e-45], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -2e-251], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 5e-119], N[(c + N[(t * N[(z / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 4e+93], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.99999999999999984e-46 or 4.00000000000000017e93 < (*.f64 a b)

   1. Initial program 96.4%

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

   2. Taylor expanded in a around inf 77.0%

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

      1. *-commutative 77.0%

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

      2. *-commutative 77.0%

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

      3. associate-*r* 77.0%

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

   4. Simplified 77.0%

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

   if -9.99999999999999984e-46 < (*.f64 a b) < -2.00000000000000003e-251 or 4.99999999999999993e-119 < (*.f64 a b) < 4.00000000000000017e93

   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 x around inf 76.0%

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

   if -2.00000000000000003e-251 < (*.f64 a b) < 4.99999999999999993e-119

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 64.4%

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

      1. associate-*r* 64.4%

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

      2. metadata-eval 64.4%

         \[\leadsto \left(\color{blue}{\frac{1}{16}} \cdot t\right) \cdot z + c \]

      3. associate-/r/ 64.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{16}{t}}} \cdot z + c \]

      4. associate-*l/ 64.3%

         \[\leadsto \color{blue}{\frac{1 \cdot z}{\frac{16}{t}}} + c \]

      5. *-commutative 64.3%

         \[\leadsto \frac{\color{blue}{z \cdot 1}}{\frac{16}{t}} + c \]

      6. *-rgt-identity 64.3%

         \[\leadsto \frac{\color{blue}{z}}{\frac{16}{t}} + c \]

      7. associate-/r/ 64.4%

         \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + c \]

      8. *-commutative 64.4%

         \[\leadsto \color{blue}{t \cdot \frac{z}{16}} + c \]

   4. Simplified 64.4%

      \[\leadsto \color{blue}{t \cdot \frac{z}{16}} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{-45}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-251}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-119}:\\ \;\;\;\;c + t \cdot \frac{z}{16}\\ \mathbf{elif}\;b \cdot a \leq 4 \cdot 10^{+93}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 5: 64.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-88}:\\ \;\;\;\;x \cdot y + \left(t \cdot z\right) \cdot 0.0625\\ \mathbf{elif}\;b \cdot a \leq 4 \cdot 10^{+93}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* b (* a -0.25)))))
   (if (<= (* b a) -1e-45)
     t_1
     (if (<= (* b a) 5e-88)
       (+ (* x y) (* (* t z) 0.0625))
       (if (<= (* b a) 4e+93) (+ c (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double tmp;
	if ((b * a) <= -1e-45) {
		tmp = t_1;
	} else if ((b * a) <= 5e-88) {
		tmp = (x * y) + ((t * z) * 0.0625);
	} else if ((b * a) <= 4e+93) {
		tmp = c + (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 = c + (b * (a * (-0.25d0)))
    if ((b * a) <= (-1d-45)) then
        tmp = t_1
    else if ((b * a) <= 5d-88) then
        tmp = (x * y) + ((t * z) * 0.0625d0)
    else if ((b * a) <= 4d+93) then
        tmp = c + (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 = c + (b * (a * -0.25));
	double tmp;
	if ((b * a) <= -1e-45) {
		tmp = t_1;
	} else if ((b * a) <= 5e-88) {
		tmp = (x * y) + ((t * z) * 0.0625);
	} else if ((b * a) <= 4e+93) {
		tmp = c + (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (b * (a * -0.25))
	tmp = 0
	if (b * a) <= -1e-45:
		tmp = t_1
	elif (b * a) <= 5e-88:
		tmp = (x * y) + ((t * z) * 0.0625)
	elif (b * a) <= 4e+93:
		tmp = c + (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (Float64(b * a) <= -1e-45)
		tmp = t_1;
	elseif (Float64(b * a) <= 5e-88)
		tmp = Float64(Float64(x * y) + Float64(Float64(t * z) * 0.0625));
	elseif (Float64(b * a) <= 4e+93)
		tmp = Float64(c + 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 = c + (b * (a * -0.25));
	tmp = 0.0;
	if ((b * a) <= -1e-45)
		tmp = t_1;
	elseif ((b * a) <= 5e-88)
		tmp = (x * y) + ((t * z) * 0.0625);
	elseif ((b * a) <= 4e+93)
		tmp = c + (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[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -1e-45], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 5e-88], N[(N[(x * y), $MachinePrecision] + N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 4e+93], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.99999999999999984e-46 or 4.00000000000000017e93 < (*.f64 a b)

   1. Initial program 96.4%

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

   2. Taylor expanded in a around inf 77.0%

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

      1. *-commutative 77.0%

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

      2. *-commutative 77.0%

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

      3. associate-*r* 77.0%

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

   4. Simplified 77.0%

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

   if -9.99999999999999984e-46 < (*.f64 a b) < 5.00000000000000009e-88

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 97.2%

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

   3. Taylor expanded in c around 0 76.6%

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

   if 5.00000000000000009e-88 < (*.f64 a b) < 4.00000000000000017e93

   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 x around inf 82.7%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{-45}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-88}:\\ \;\;\;\;x \cdot y + \left(t \cdot z\right) \cdot 0.0625\\ \mathbf{elif}\;b \cdot a \leq 4 \cdot 10^{+93}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 6: 85.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -4 \cdot 10^{+152} \lor \neg \left(b \cdot a \leq 5 \cdot 10^{+133}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(t \cdot z\right) \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -4e+152) (not (<= (* b a) 5e+133)))
   (+ c (* 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) <= -4e+152) || !((b * a) <= 5e+133)) {
		tmp = c + (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) <= (-4d+152)) .or. (.not. ((b * a) <= 5d+133))) then
        tmp = c + (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) <= -4e+152) || !((b * a) <= 5e+133)) {
		tmp = c + (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) <= -4e+152) or not ((b * a) <= 5e+133):
		tmp = c + (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) <= -4e+152) || !(Float64(b * a) <= 5e+133))
		tmp = Float64(c + Float64(b * Float64(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) <= -4e+152) || ~(((b * a) <= 5e+133)))
		tmp = c + (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], -4e+152], N[Not[LessEqual[N[(b * a), $MachinePrecision], 5e+133]], $MachinePrecision]], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $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) < -4.0000000000000002e152 or 4.99999999999999961e133 < (*.f64 a b)

   1. Initial program 94.5%

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

   2. Taylor expanded in a around inf 85.8%

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

      1. *-commutative 85.8%

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

      2. *-commutative 85.8%

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

      3. associate-*r* 85.8%

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

   4. Simplified 85.8%

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

   if -4.0000000000000002e152 < (*.f64 a b) < 4.99999999999999961e133

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 93.1%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -4 \cdot 10^{+152} \lor \neg \left(b \cdot a \leq 5 \cdot 10^{+133}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(t \cdot z\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 7: 89.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+110} \lor \neg \left(b \cdot a \leq 4 \cdot 10^{+99}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(t \cdot z\right) \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -2e+110) (not (<= (* b a) 4e+99)))
   (- (+ 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) <= -2e+110) || !((b * a) <= 4e+99)) {
		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) <= (-2d+110)) .or. (.not. ((b * a) <= 4d+99))) 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) <= -2e+110) || !((b * a) <= 4e+99)) {
		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) <= -2e+110) or not ((b * a) <= 4e+99):
		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) <= -2e+110) || !(Float64(b * a) <= 4e+99))
		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) <= -2e+110) || ~(((b * a) <= 4e+99)))
		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], -2e+110], N[Not[LessEqual[N[(b * a), $MachinePrecision], 4e+99]], $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) < -2e110 or 3.9999999999999999e99 < (*.f64 a b)

   1. Initial program 95.3%

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

   2. Taylor expanded in z around 0 86.4%

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

   if -2e110 < (*.f64 a b) < 3.9999999999999999e99

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 94.2%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+110} \lor \neg \left(b \cdot a \leq 4 \cdot 10^{+99}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(t \cdot z\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 8: 97.5% 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 98.4%

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

2. Final simplification 98.4%

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

Alternative 9: 63.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{-45} \lor \neg \left(b \cdot a \leq 4 \cdot 10^{+93}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -1e-45) (not (<= (* b a) 4e+93)))
   (+ c (* b (* a -0.25)))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -1e-45) || !((b * a) <= 4e+93)) {
		tmp = c + (b * (a * -0.25));
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((b * a) <= (-1d-45)) .or. (.not. ((b * a) <= 4d+93))) then
        tmp = c + (b * (a * (-0.25d0)))
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -1e-45) || !((b * a) <= 4e+93)) {
		tmp = c + (b * (a * -0.25));
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -1e-45) or not ((b * a) <= 4e+93):
		tmp = c + (b * (a * -0.25))
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -1e-45) || !(Float64(b * a) <= 4e+93))
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -1e-45) || ~(((b * a) <= 4e+93)))
		tmp = c + (b * (a * -0.25));
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -1e-45], N[Not[LessEqual[N[(b * a), $MachinePrecision], 4e+93]], $MachinePrecision]], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -9.99999999999999984e-46 or 4.00000000000000017e93 < (*.f64 a b)

   1. Initial program 96.4%

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

   2. Taylor expanded in a around inf 77.0%

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

      1. *-commutative 77.0%

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

      2. *-commutative 77.0%

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

      3. associate-*r* 77.0%

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

   4. Simplified 77.0%

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

   if -9.99999999999999984e-46 < (*.f64 a b) < 4.00000000000000017e93

   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 x around inf 67.7%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{-45} \lor \neg \left(b \cdot a \leq 4 \cdot 10^{+93}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 10: 62.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -3.8 \cdot 10^{+162} \lor \neg \left(b \cdot a \leq 2.8 \cdot 10^{+132}\right):\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -3.8e+162) (not (<= (* b a) 2.8e+132)))
   (* (* b a) -0.25)
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -3.8e+162) || !((b * a) <= 2.8e+132)) {
		tmp = (b * a) * -0.25;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((b * a) <= (-3.8d+162)) .or. (.not. ((b * a) <= 2.8d+132))) then
        tmp = (b * a) * (-0.25d0)
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -3.8e+162) || !((b * a) <= 2.8e+132)) {
		tmp = (b * a) * -0.25;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -3.8e+162) or not ((b * a) <= 2.8e+132):
		tmp = (b * a) * -0.25
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -3.8e+162) || !(Float64(b * a) <= 2.8e+132))
		tmp = Float64(Float64(b * a) * -0.25);
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -3.8e+162) || ~(((b * a) <= 2.8e+132)))
		tmp = (b * a) * -0.25;
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -3.8e+162], N[Not[LessEqual[N[(b * a), $MachinePrecision], 2.8e+132]], $MachinePrecision]], N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -3.80000000000000024e162 or 2.7999999999999999e132 < (*.f64 a b)

   1. Initial program 94.4%

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

   2. Taylor expanded in z around 0 85.1%

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

   3. Taylor expanded in a around inf 78.6%

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

      1. *-commutative 78.6%

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

   5. Simplified 78.6%

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

   if -3.80000000000000024e162 < (*.f64 a b) < 2.7999999999999999e132

   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 x around inf 65.5%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -3.8 \cdot 10^{+162} \lor \neg \left(b \cdot a \leq 2.8 \cdot 10^{+132}\right):\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 11: 37.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot z\right) \cdot 0.0625\\ \mathbf{if}\;t \leq -1 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-241}:\\ \;\;\;\;c\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+148}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* t z) 0.0625)))
   (if (<= t -1e-62)
     t_1
     (if (<= t -5.5e-241) c (if (<= t 1.18e+148) (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * z) * 0.0625;
	double tmp;
	if (t <= -1e-62) {
		tmp = t_1;
	} else if (t <= -5.5e-241) {
		tmp = c;
	} else if (t <= 1.18e+148) {
		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 = (t * z) * 0.0625d0
    if (t <= (-1d-62)) then
        tmp = t_1
    else if (t <= (-5.5d-241)) then
        tmp = c
    else if (t <= 1.18d+148) 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 = (t * z) * 0.0625;
	double tmp;
	if (t <= -1e-62) {
		tmp = t_1;
	} else if (t <= -5.5e-241) {
		tmp = c;
	} else if (t <= 1.18e+148) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (t * z) * 0.0625
	tmp = 0
	if t <= -1e-62:
		tmp = t_1
	elif t <= -5.5e-241:
		tmp = c
	elif t <= 1.18e+148:
		tmp = x * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(t * z) * 0.0625)
	tmp = 0.0
	if (t <= -1e-62)
		tmp = t_1;
	elseif (t <= -5.5e-241)
		tmp = c;
	elseif (t <= 1.18e+148)
		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 = (t * z) * 0.0625;
	tmp = 0.0;
	if (t <= -1e-62)
		tmp = t_1;
	elseif (t <= -5.5e-241)
		tmp = c;
	elseif (t <= 1.18e+148)
		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[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]}, If[LessEqual[t, -1e-62], t$95$1, If[LessEqual[t, -5.5e-241], c, If[LessEqual[t, 1.18e+148], N[(x * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1e-62 or 1.18e148 < t

   1. Initial program 98.3%

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

   2. Taylor expanded in z around inf 57.9%

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

      1. associate-*r* 57.9%

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

      2. metadata-eval 57.9%

         \[\leadsto \left(\color{blue}{\frac{1}{16}} \cdot t\right) \cdot z + c \]

      3. associate-/r/ 57.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{16}{t}}} \cdot z + c \]

      4. associate-*l/ 57.9%

         \[\leadsto \color{blue}{\frac{1 \cdot z}{\frac{16}{t}}} + c \]

      5. *-commutative 57.9%

         \[\leadsto \frac{\color{blue}{z \cdot 1}}{\frac{16}{t}} + c \]

      6. *-rgt-identity 57.9%

         \[\leadsto \frac{\color{blue}{z}}{\frac{16}{t}} + c \]

      7. associate-/r/ 57.9%

         \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + c \]

      8. *-commutative 57.9%

         \[\leadsto \color{blue}{t \cdot \frac{z}{16}} + c \]

   4. Simplified 57.9%

      \[\leadsto \color{blue}{t \cdot \frac{z}{16}} + c \]

   5. Taylor expanded in t around inf 42.2%

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

   if -1e-62 < t < -5.4999999999999998e-241

   1. Initial program 94.1%

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

   2. Taylor expanded in c around inf 42.8%

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

   if -5.4999999999999998e-241 < t < 1.18e148

   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 87.7%

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

   3. Taylor expanded in y around inf 33.2%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-62}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-241}:\\ \;\;\;\;c\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+148}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625\\ \end{array} \]

Alternative 12: 37.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.15 \cdot 10^{+63}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+81}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -2.15e+63) c (if (<= c 1.8e+81) (* x y) c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -2.15e+63) {
		tmp = c;
	} else if (c <= 1.8e+81) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= (-2.15d+63)) then
        tmp = c
    else if (c <= 1.8d+81) then
        tmp = x * y
    else
        tmp = c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -2.15e+63) {
		tmp = c;
	} else if (c <= 1.8e+81) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -2.15e+63:
		tmp = c
	elif c <= 1.8e+81:
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -2.15e+63)
		tmp = c;
	elseif (c <= 1.8e+81)
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -2.15e+63)
		tmp = c;
	elseif (c <= 1.8e+81)
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -2.15e+63], c, If[LessEqual[c, 1.8e+81], N[(x * y), $MachinePrecision], c]]

Derivation

1. Split input into 2 regimes

2. if c < -2.15e63 or 1.80000000000000003e81 < c

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 49.7%

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

   if -2.15e63 < c < 1.80000000000000003e81

   1. Initial program 97.4%

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

   2. Taylor expanded in z around 0 72.4%

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

   3. Taylor expanded in y around inf 38.4%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.15 \cdot 10^{+63}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+81}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 13: 21.5% 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 98.4%

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

2. Taylor expanded in c around inf 23.9%

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

3. Final simplification 23.9%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023229 
(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))