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

Percentage Accurate: 97.6% → 98.8%

Time: 10.5s

Alternatives: 16

Speedup: 0.5×

• 32.7% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    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: 97.6% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    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: 98.8% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c)))
   (if (<= t_1 INFINITY) t_1 (fma (* -0.25 a) b (fma y x c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma((-0.25 * a), b, fma(y, x, c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(Float64(-0.25 * a), b, fma(y, x, c));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64))) c) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64))) c)

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 37.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 62.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.25 \cdot a, b, \mathsf{fma}\left(y, x, c\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 66.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ t_2 := \mathsf{fma}\left(-0.25 \cdot a, b, y \cdot x\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-318}:\\ \;\;\;\;\mathsf{fma}\left(0.0625 \cdot z, t, c\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-101}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, 0.0625, c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) 4.0)) (t_2 (fma (* -0.25 a) b (* y x))))
   (if (<= t_1 -5e+130)
     t_2
     (if (<= t_1 -2e-16)
       (fma y x c)
       (if (<= t_1 1e-318)
         (fma (* 0.0625 z) t c)
         (if (<= t_1 5e-101)
           (fma y x c)
           (if (<= t_1 1e-8) (fma (* t z) 0.0625 c) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double t_2 = fma((-0.25 * a), b, (y * x));
	double tmp;
	if (t_1 <= -5e+130) {
		tmp = t_2;
	} else if (t_1 <= -2e-16) {
		tmp = fma(y, x, c);
	} else if (t_1 <= 1e-318) {
		tmp = fma((0.0625 * z), t, c);
	} else if (t_1 <= 5e-101) {
		tmp = fma(y, x, c);
	} else if (t_1 <= 1e-8) {
		tmp = fma((t * z), 0.0625, c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	t_2 = fma(Float64(-0.25 * a), b, Float64(y * x))
	tmp = 0.0
	if (t_1 <= -5e+130)
		tmp = t_2;
	elseif (t_1 <= -2e-16)
		tmp = fma(y, x, c);
	elseif (t_1 <= 1e-318)
		tmp = fma(Float64(0.0625 * z), t, c);
	elseif (t_1 <= 5e-101)
		tmp = fma(y, x, c);
	elseif (t_1 <= 1e-8)
		tmp = fma(Float64(t * z), 0.0625, c);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-0.25 * a), $MachinePrecision] * b + N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+130], t$95$2, If[LessEqual[t$95$1, -2e-16], N[(y * x + c), $MachinePrecision], If[LessEqual[t$95$1, 1e-318], N[(N[(0.0625 * z), $MachinePrecision] * t + c), $MachinePrecision], If[LessEqual[t$95$1, 5e-101], N[(y * x + c), $MachinePrecision], If[LessEqual[t$95$1, 1e-8], N[(N[(t * z), $MachinePrecision] * 0.0625 + c), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -4.9999999999999996e130 or 1e-8 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 92.7%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 79.3%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 83.8%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(\frac{-1}{4} \cdot a, b, x \cdot y\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 79.0%

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

   if -4.9999999999999996e130 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -2e-16 or 9.9999875e-319 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 5.0000000000000001e-101

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 80.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 81.9%

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

   9. Taylor expanded in a around 0

      \[\leadsto c + \color{blue}{x \cdot y} \]
   10. Step-by-step derivation

   11. Applied rewrites 76.6%

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{x}, c\right) \]

   if -2e-16 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 9.9999875e-319

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 83.7%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 62.6%

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

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 96.2%

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

   12. Taylor expanded in x around 0

       \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot z, t, c\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 75.4%

       \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, c\right) \]

   if 5.0000000000000001e-101 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 1e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(c + \frac{1}{16} \cdot \left(t \cdot z\right)\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 86.6%

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

   6. Taylor expanded in a around 0

      \[\leadsto c + \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 78.0%

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

Alternative 3: 94.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-39} \lor \neg \left(t\_1 \leq 10^{+74}\right):\\ \;\;\;\;\mathsf{fma}\left(0.0625, t, \frac{\mathsf{fma}\left(-0.25, b \cdot a, \mathsf{fma}\left(y, x, c\right)\right)}{z}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot a, b, \mathsf{fma}\left(y, x, c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)))
   (if (or (<= t_1 -1e-39) (not (<= t_1 1e+74)))
     (* (fma 0.0625 t (/ (fma -0.25 (* b a) (fma y x c)) z)) z)
     (fma (* -0.25 a) b (fma y x c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) / 16.0;
	double tmp;
	if ((t_1 <= -1e-39) || !(t_1 <= 1e+74)) {
		tmp = fma(0.0625, t, (fma(-0.25, (b * a), fma(y, x, c)) / z)) * z;
	} else {
		tmp = fma((-0.25 * a), b, fma(y, x, c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * t) / 16.0)
	tmp = 0.0
	if ((t_1 <= -1e-39) || !(t_1 <= 1e+74))
		tmp = Float64(fma(0.0625, t, Float64(fma(-0.25, Float64(b * a), fma(y, x, c)) / z)) * z);
	else
		tmp = fma(Float64(-0.25 * a), b, fma(y, x, c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-39], N[Not[LessEqual[t$95$1, 1e+74]], $MachinePrecision]], N[(N[(0.0625 * t + N[(N[(-0.25 * N[(b * a), $MachinePrecision] + N[(y * x + c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(-0.25 * a), $MachinePrecision] * b + N[(y * x + c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -9.99999999999999929e-40 or 9.99999999999999952e73 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 95.8%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 92.7%

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

   if -9.99999999999999929e-40 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 9.99999999999999952e73

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 72.7%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 94.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.25 \cdot a, b, \mathsf{fma}\left(y, x, c\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot t}{16} \leq -1 \cdot 10^{-39} \lor \neg \left(\frac{z \cdot t}{16} \leq 10^{+74}\right):\\ \;\;\;\;\mathsf{fma}\left(0.0625, t, \frac{\mathsf{fma}\left(-0.25, b \cdot a, \mathsf{fma}\left(y, x, c\right)\right)}{z}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot a, b, \mathsf{fma}\left(y, x, c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot a, b, \mathsf{fma}\left(y, x, c\right)\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+220}:\\ \;\;\;\;\mathsf{fma}\left(0.0625 \cdot z, t, \mathsf{fma}\left(y, x, c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, \left(t \cdot z\right) \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) 4.0)))
   (if (<= t_1 -5e+75)
     (fma (* -0.25 a) b (fma y x c))
     (if (<= t_1 2e+220)
       (fma (* 0.0625 z) t (fma y x c))
       (fma -0.25 (* b a) (* (* t z) 0.0625))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double tmp;
	if (t_1 <= -5e+75) {
		tmp = fma((-0.25 * a), b, fma(y, x, c));
	} else if (t_1 <= 2e+220) {
		tmp = fma((0.0625 * z), t, fma(y, x, c));
	} else {
		tmp = fma(-0.25, (b * a), ((t * z) * 0.0625));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	tmp = 0.0
	if (t_1 <= -5e+75)
		tmp = fma(Float64(-0.25 * a), b, fma(y, x, c));
	elseif (t_1 <= 2e+220)
		tmp = fma(Float64(0.0625 * z), t, fma(y, x, c));
	else
		tmp = fma(-0.25, Float64(b * a), Float64(Float64(t * z) * 0.0625));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+75], N[(N[(-0.25 * a), $MachinePrecision] * b + N[(y * x + c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+220], N[(N[(0.0625 * z), $MachinePrecision] * t + N[(y * x + c), $MachinePrecision]), $MachinePrecision], N[(-0.25 * N[(b * a), $MachinePrecision] + N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -5.0000000000000002e75

   1. Initial program 88.9%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 89.2%

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

   if -5.0000000000000002e75 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 2e220

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 85.0%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 70.0%

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

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 91.9%

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

   if 2e220 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 95.2%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(c + \frac{1}{16} \cdot \left(t \cdot z\right)\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.9%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\frac{-1}{4}, b \cdot a, \frac{1}{16} \cdot \left(t \cdot z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 97.9%

      \[\leadsto \mathsf{fma}\left(-0.25, b \cdot a, \left(t \cdot z\right) \cdot 0.0625\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot a, b, \mathsf{fma}\left(y, x, c\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+222}:\\ \;\;\;\;\mathsf{fma}\left(0.0625 \cdot z, t, \mathsf{fma}\left(y, x, c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot a, b, c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) 4.0)))
   (if (<= t_1 -5e+75)
     (fma (* -0.25 a) b (fma y x c))
     (if (<= t_1 5e+222)
       (fma (* 0.0625 z) t (fma y x c))
       (fma (* -0.25 a) b c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double tmp;
	if (t_1 <= -5e+75) {
		tmp = fma((-0.25 * a), b, fma(y, x, c));
	} else if (t_1 <= 5e+222) {
		tmp = fma((0.0625 * z), t, fma(y, x, c));
	} else {
		tmp = fma((-0.25 * a), b, c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	tmp = 0.0
	if (t_1 <= -5e+75)
		tmp = fma(Float64(-0.25 * a), b, fma(y, x, c));
	elseif (t_1 <= 5e+222)
		tmp = fma(Float64(0.0625 * z), t, fma(y, x, c));
	else
		tmp = fma(Float64(-0.25 * a), b, c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+75], N[(N[(-0.25 * a), $MachinePrecision] * b + N[(y * x + c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+222], N[(N[(0.0625 * z), $MachinePrecision] * t + N[(y * x + c), $MachinePrecision]), $MachinePrecision], N[(N[(-0.25 * a), $MachinePrecision] * b + c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -5.0000000000000002e75

   1. Initial program 88.9%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 89.2%

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

   if -5.0000000000000002e75 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 5.00000000000000023e222

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 85.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 69.6%

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

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 91.9%

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

   if 5.00000000000000023e222 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 72.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 90.0%

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

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{-1}{4} \cdot a, b, c\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 92.8%

       \[\leadsto \mathsf{fma}\left(-0.25 \cdot a, b, c\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot a, b, \mathsf{fma}\left(y, x, c\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+222}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \mathsf{fma}\left(t \cdot z, 0.0625, c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot a, b, c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) 4.0)))
   (if (<= t_1 -5e+75)
     (fma (* -0.25 a) b (fma y x c))
     (if (<= t_1 5e+222)
       (fma y x (fma (* t z) 0.0625 c))
       (fma (* -0.25 a) b c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double tmp;
	if (t_1 <= -5e+75) {
		tmp = fma((-0.25 * a), b, fma(y, x, c));
	} else if (t_1 <= 5e+222) {
		tmp = fma(y, x, fma((t * z), 0.0625, c));
	} else {
		tmp = fma((-0.25 * a), b, c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	tmp = 0.0
	if (t_1 <= -5e+75)
		tmp = fma(Float64(-0.25 * a), b, fma(y, x, c));
	elseif (t_1 <= 5e+222)
		tmp = fma(y, x, fma(Float64(t * z), 0.0625, c));
	else
		tmp = fma(Float64(-0.25 * a), b, c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+75], N[(N[(-0.25 * a), $MachinePrecision] * b + N[(y * x + c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+222], N[(y * x + N[(N[(t * z), $MachinePrecision] * 0.0625 + c), $MachinePrecision]), $MachinePrecision], N[(N[(-0.25 * a), $MachinePrecision] * b + c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -5.0000000000000002e75

   1. Initial program 88.9%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 89.2%

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

   if -5.0000000000000002e75 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 5.00000000000000023e222

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 91.3%

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

   if 5.00000000000000023e222 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 72.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 90.0%

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

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{-1}{4} \cdot a, b, c\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 92.8%

       \[\leadsto \mathsf{fma}\left(-0.25 \cdot a, b, c\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, \mathsf{fma}\left(y, x, c\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+222}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \mathsf{fma}\left(t \cdot z, 0.0625, c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot a, b, c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) 4.0)))
   (if (<= t_1 -5e+75)
     (fma -0.25 (* b a) (fma y x c))
     (if (<= t_1 5e+222)
       (fma y x (fma (* t z) 0.0625 c))
       (fma (* -0.25 a) b c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double tmp;
	if (t_1 <= -5e+75) {
		tmp = fma(-0.25, (b * a), fma(y, x, c));
	} else if (t_1 <= 5e+222) {
		tmp = fma(y, x, fma((t * z), 0.0625, c));
	} else {
		tmp = fma((-0.25 * a), b, c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	tmp = 0.0
	if (t_1 <= -5e+75)
		tmp = fma(-0.25, Float64(b * a), fma(y, x, c));
	elseif (t_1 <= 5e+222)
		tmp = fma(y, x, fma(Float64(t * z), 0.0625, c));
	else
		tmp = fma(Float64(-0.25 * a), b, c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+75], N[(-0.25 * N[(b * a), $MachinePrecision] + N[(y * x + c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+222], N[(y * x + N[(N[(t * z), $MachinePrecision] * 0.0625 + c), $MachinePrecision]), $MachinePrecision], N[(N[(-0.25 * a), $MachinePrecision] * b + c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -5.0000000000000002e75

   1. Initial program 88.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 85.5%

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

   if -5.0000000000000002e75 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 5.00000000000000023e222

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 91.3%

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

   if 5.00000000000000023e222 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 72.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 90.0%

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

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{-1}{4} \cdot a, b, c\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 92.8%

       \[\leadsto \mathsf{fma}\left(-0.25 \cdot a, b, c\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+182}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, \mathsf{fma}\left(y, x, c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, 0.0625, c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)))
   (if (<= t_1 (- INFINITY))
     (* (* t z) 0.0625)
     (if (<= t_1 5e+182)
       (fma -0.25 (* b a) (fma y x c))
       (fma (* t z) 0.0625 c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) / 16.0;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (t * z) * 0.0625;
	} else if (t_1 <= 5e+182) {
		tmp = fma(-0.25, (b * a), fma(y, x, c));
	} else {
		tmp = fma((t * z), 0.0625, c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * t) / 16.0)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(t * z) * 0.0625);
	elseif (t_1 <= 5e+182)
		tmp = fma(-0.25, Float64(b * a), fma(y, x, c));
	else
		tmp = fma(Float64(t * z), 0.0625, c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision], If[LessEqual[t$95$1, 5e+182], N[(-0.25 * N[(b * a), $MachinePrecision] + N[(y * x + c), $MachinePrecision]), $MachinePrecision], N[(N[(t * z), $MachinePrecision] * 0.0625 + c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -inf.0

   1. Initial program 83.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 83.3%

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

   if -inf.0 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 4.99999999999999973e182

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 83.3%

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

   if 4.99999999999999973e182 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(c + \frac{1}{16} \cdot \left(t \cdot z\right)\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 91.6%

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

   6. Taylor expanded in a around 0

      \[\leadsto c + \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 87.6%

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

Alternative 9: 65.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-0.25 \cdot a, b, c\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-214}:\\ \;\;\;\;\mathsf{fma}\left(0.0625 \cdot z, t, c\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (fma (* -0.25 a) b c)))
   (if (<= (* x y) -1e+109)
     (fma y x c)
     (if (<= (* x y) -2e+61)
       t_1
       (if (<= (* x y) 5e-214)
         (fma (* 0.0625 z) t c)
         (if (<= (* x y) 5e+61) t_1 (fma y x c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((-0.25 * a), b, c);
	double tmp;
	if ((x * y) <= -1e+109) {
		tmp = fma(y, x, c);
	} else if ((x * y) <= -2e+61) {
		tmp = t_1;
	} else if ((x * y) <= 5e-214) {
		tmp = fma((0.0625 * z), t, c);
	} else if ((x * y) <= 5e+61) {
		tmp = t_1;
	} else {
		tmp = fma(y, x, c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = fma(Float64(-0.25 * a), b, c)
	tmp = 0.0
	if (Float64(x * y) <= -1e+109)
		tmp = fma(y, x, c);
	elseif (Float64(x * y) <= -2e+61)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-214)
		tmp = fma(Float64(0.0625 * z), t, c);
	elseif (Float64(x * y) <= 5e+61)
		tmp = t_1;
	else
		tmp = fma(y, x, c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-0.25 * a), $MachinePrecision] * b + c), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+109], N[(y * x + c), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e+61], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-214], N[(N[(0.0625 * z), $MachinePrecision] * t + c), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+61], t$95$1, N[(y * x + c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999982e108 or 5.00000000000000018e61 < (*.f64 x y)

   1. Initial program 92.1%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 76.7%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 88.0%

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

   9. Taylor expanded in a around 0

      \[\leadsto c + \color{blue}{x \cdot y} \]
   10. Step-by-step derivation

   11. Applied rewrites 78.2%

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{x}, c\right) \]

   if -9.99999999999999982e108 < (*.f64 x y) < -1.9999999999999999e61 or 4.9999999999999998e-214 < (*.f64 x y) < 5.00000000000000018e61

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 80.2%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 77.9%

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

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{-1}{4} \cdot a, b, c\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 74.4%

       \[\leadsto \mathsf{fma}\left(-0.25 \cdot a, b, c\right) \]

   if -1.9999999999999999e61 < (*.f64 x y) < 4.9999999999999998e-214

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 86.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 64.4%

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

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 72.9%

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

   12. Taylor expanded in x around 0

       \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot z, t, c\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 68.7%

       \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, c\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 65.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-0.25 \cdot a, b, c\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-214}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, 0.0625, c\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (fma (* -0.25 a) b c)))
   (if (<= (* x y) -1e+109)
     (fma y x c)
     (if (<= (* x y) -2e+61)
       t_1
       (if (<= (* x y) 5e-214)
         (fma (* t z) 0.0625 c)
         (if (<= (* x y) 5e+61) t_1 (fma y x c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((-0.25 * a), b, c);
	double tmp;
	if ((x * y) <= -1e+109) {
		tmp = fma(y, x, c);
	} else if ((x * y) <= -2e+61) {
		tmp = t_1;
	} else if ((x * y) <= 5e-214) {
		tmp = fma((t * z), 0.0625, c);
	} else if ((x * y) <= 5e+61) {
		tmp = t_1;
	} else {
		tmp = fma(y, x, c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = fma(Float64(-0.25 * a), b, c)
	tmp = 0.0
	if (Float64(x * y) <= -1e+109)
		tmp = fma(y, x, c);
	elseif (Float64(x * y) <= -2e+61)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-214)
		tmp = fma(Float64(t * z), 0.0625, c);
	elseif (Float64(x * y) <= 5e+61)
		tmp = t_1;
	else
		tmp = fma(y, x, c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-0.25 * a), $MachinePrecision] * b + c), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+109], N[(y * x + c), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e+61], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-214], N[(N[(t * z), $MachinePrecision] * 0.0625 + c), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+61], t$95$1, N[(y * x + c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999982e108 or 5.00000000000000018e61 < (*.f64 x y)

   1. Initial program 92.1%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 76.7%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 88.0%

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

   9. Taylor expanded in a around 0

      \[\leadsto c + \color{blue}{x \cdot y} \]
   10. Step-by-step derivation

   11. Applied rewrites 78.2%

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{x}, c\right) \]

   if -9.99999999999999982e108 < (*.f64 x y) < -1.9999999999999999e61 or 4.9999999999999998e-214 < (*.f64 x y) < 5.00000000000000018e61

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 80.2%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 77.9%

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

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{-1}{4} \cdot a, b, c\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 74.4%

       \[\leadsto \mathsf{fma}\left(-0.25 \cdot a, b, c\right) \]

   if -1.9999999999999999e61 < (*.f64 x y) < 4.9999999999999998e-214

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(c + \frac{1}{16} \cdot \left(t \cdot z\right)\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 95.8%

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

   6. Taylor expanded in a around 0

      \[\leadsto c + \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 68.6%

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

Alternative 11: 62.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+144} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+222}\right):\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) 4.0)))
   (if (or (<= t_1 -2e+144) (not (<= t_1 5e+222)))
     (* -0.25 (* b a))
     (fma y x c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double tmp;
	if ((t_1 <= -2e+144) || !(t_1 <= 5e+222)) {
		tmp = -0.25 * (b * a);
	} else {
		tmp = fma(y, x, c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	tmp = 0.0
	if ((t_1 <= -2e+144) || !(t_1 <= 5e+222))
		tmp = Float64(-0.25 * Float64(b * a));
	else
		tmp = fma(y, x, c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+144], N[Not[LessEqual[t$95$1, 5e+222]], $MachinePrecision]], N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision], N[(y * x + c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -2.00000000000000005e144 or 5.00000000000000023e222 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 88.5%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 79.9%

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

   if -2.00000000000000005e144 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 5.00000000000000023e222

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 84.6%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 71.1%

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

   9. Taylor expanded in a around 0

      \[\leadsto c + \color{blue}{x \cdot y} \]
   10. Step-by-step derivation

   11. Applied rewrites 61.5%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a \cdot b}{4} \leq -2 \cdot 10^{+144} \lor \neg \left(\frac{a \cdot b}{4} \leq 5 \cdot 10^{+222}\right):\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot a, b, \mathsf{fma}\left(y, x, c\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, \mathsf{fma}\left(t \cdot z, 0.0625, c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.0625 \cdot z, t, \mathsf{fma}\left(y, x, c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -2e+61)
   (fma (* -0.25 a) b (fma y x c))
   (if (<= (* x y) 5e+61)
     (fma -0.25 (* b a) (fma (* t z) 0.0625 c))
     (fma (* 0.0625 z) t (fma y x c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -2e+61) {
		tmp = fma((-0.25 * a), b, fma(y, x, c));
	} else if ((x * y) <= 5e+61) {
		tmp = fma(-0.25, (b * a), fma((t * z), 0.0625, c));
	} else {
		tmp = fma((0.0625 * z), t, fma(y, x, c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -2e+61)
		tmp = fma(Float64(-0.25 * a), b, fma(y, x, c));
	elseif (Float64(x * y) <= 5e+61)
		tmp = fma(-0.25, Float64(b * a), fma(Float64(t * z), 0.0625, c));
	else
		tmp = fma(Float64(0.0625 * z), t, fma(y, x, c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+61], N[(N[(-0.25 * a), $MachinePrecision] * b + N[(y * x + c), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+61], N[(-0.25 * N[(b * a), $MachinePrecision] + N[(N[(t * z), $MachinePrecision] * 0.0625 + c), $MachinePrecision]), $MachinePrecision], N[(N[(0.0625 * z), $MachinePrecision] * t + N[(y * x + c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.9999999999999999e61

   1. Initial program 88.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 88.8%

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

   if -1.9999999999999999e61 < (*.f64 x y) < 5.00000000000000018e61

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(c + \frac{1}{16} \cdot \left(t \cdot z\right)\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 96.3%

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

   if 5.00000000000000018e61 < (*.f64 x y)

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 76.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 87.6%

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

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 91.8%

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

Alternative 13: 64.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+95} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+61}\right):\\ \;\;\;\;\mathsf{fma}\left(y, x, c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, 0.0625, c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1e+95) (not (<= (* x y) 5e+61)))
   (fma y x c)
   (fma (* t z) 0.0625 c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1e+95) || !((x * y) <= 5e+61)) {
		tmp = fma(y, x, c);
	} else {
		tmp = fma((t * z), 0.0625, c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1e+95) || !(Float64(x * y) <= 5e+61))
		tmp = fma(y, x, c);
	else
		tmp = fma(Float64(t * z), 0.0625, c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+95], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+61]], $MachinePrecision]], N[(y * x + c), $MachinePrecision], N[(N[(t * z), $MachinePrecision] * 0.0625 + c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.00000000000000002e95 or 5.00000000000000018e61 < (*.f64 x y)

   1. Initial program 92.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 77.7%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 88.5%

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

   9. Taylor expanded in a around 0

      \[\leadsto c + \color{blue}{x \cdot y} \]
   10. Step-by-step derivation

   11. Applied rewrites 76.0%

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{x}, c\right) \]

   if -1.00000000000000002e95 < (*.f64 x y) < 5.00000000000000018e61

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(c + \frac{1}{16} \cdot \left(t \cdot z\right)\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 95.3%

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

   6. Taylor expanded in a around 0

      \[\leadsto c + \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 65.1%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+95} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+61}\right):\\ \;\;\;\;\mathsf{fma}\left(y, x, c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, 0.0625, c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+107} \lor \neg \left(x \cdot y \leq 10^{+77}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1e+107) (not (<= (* x y) 1e+77))) (* y x) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1e+107) || !((x * y) <= 1e+77)) {
		tmp = y * x;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-1d+107)) .or. (.not. ((x * y) <= 1d+77))) then
        tmp = y * x
    else
        tmp = c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1e+107) || !((x * y) <= 1e+77)) {
		tmp = y * x;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1e+107) or not ((x * y) <= 1e+77):
		tmp = y * x
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1e+107) || !(Float64(x * y) <= 1e+77))
		tmp = Float64(y * x);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1e+107) || ~(((x * y) <= 1e+77)))
		tmp = y * x;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+107], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+77]], $MachinePrecision]], N[(y * x), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.9999999999999997e106 or 9.99999999999999983e76 < (*.f64 x y)

   1. Initial program 92.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

   5. Applied rewrites 68.7%

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

   if -9.9999999999999997e106 < (*.f64 x y) < 9.99999999999999983e76

   1. Initial program 99.4%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c} \]
   4. Step-by-step derivation

   5. Applied rewrites 33.2%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+107} \lor \neg \left(x \cdot y \leq 10^{+77}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.6% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, x, c\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in z around inf

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

5. Applied rewrites 82.0%

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

6. Taylor expanded in z around 0

   \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
7. Step-by-step derivation

8. Applied rewrites 75.3%

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

9. Taylor expanded in a around 0

   \[\leadsto c + \color{blue}{x \cdot y} \]
10. Step-by-step derivation

11. Applied rewrites 50.8%

    \[\leadsto \mathsf{fma}\left(y, \color{blue}{x}, c\right) \]
12. Add Preprocessing

Alternative 16: 22.3% accurate, 47.0× 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in c around inf

   \[\leadsto \color{blue}{c} \]
4. Step-by-step derivation

5. Applied rewrites 24.9%

   \[\leadsto \color{blue}{c} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2025022 
(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))