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

Percentage Accurate: 97.6% → 97.6%

Time: 8.0s

Alternatives: 15

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

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: 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]

Derivation

1. Initial program 97.7%

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

Alternative 2: 62.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ t_2 := -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+99}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+154}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, 0.0625, c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) 4.0)) (t_2 (* -0.25 (* b a))))
   (if (<= t_1 -2e+99)
     t_2
     (if (<= t_1 5e+63)
       (fma y x c)
       (if (<= t_1 5e+154) (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 = -0.25 * (b * a);
	double tmp;
	if (t_1 <= -2e+99) {
		tmp = t_2;
	} else if (t_1 <= 5e+63) {
		tmp = fma(y, x, c);
	} else if (t_1 <= 5e+154) {
		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 = Float64(-0.25 * Float64(b * a))
	tmp = 0.0
	if (t_1 <= -2e+99)
		tmp = t_2;
	elseif (t_1 <= 5e+63)
		tmp = fma(y, x, c);
	elseif (t_1 <= 5e+154)
		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[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+99], t$95$2, If[LessEqual[t$95$1, 5e+63], N[(y * x + c), $MachinePrecision], If[LessEqual[t$95$1, 5e+154], N[(N[(t * z), $MachinePrecision] * 0.0625 + c), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -1.9999999999999999e99 or 5.00000000000000004e154 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 96.4%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 68.9%

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

   if -1.9999999999999999e99 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 5.00000000000000011e63

   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 76.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 68.0%

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

   if 5.00000000000000011e63 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 5.00000000000000004e154

   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 87.6%

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

   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 70.4%

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

Alternative 3: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ t_2 := -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+99}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+150}:\\ \;\;\;\;\left(0.0625 \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) 4.0)) (t_2 (* -0.25 (* b a))))
   (if (<= t_1 -2e+99)
     t_2
     (if (<= t_1 2e+77)
       (fma y x c)
       (if (<= t_1 5e+150) (* (* 0.0625 z) t) 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 = -0.25 * (b * a);
	double tmp;
	if (t_1 <= -2e+99) {
		tmp = t_2;
	} else if (t_1 <= 2e+77) {
		tmp = fma(y, x, c);
	} else if (t_1 <= 5e+150) {
		tmp = (0.0625 * z) * t;
	} 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 = Float64(-0.25 * Float64(b * a))
	tmp = 0.0
	if (t_1 <= -2e+99)
		tmp = t_2;
	elseif (t_1 <= 2e+77)
		tmp = fma(y, x, c);
	elseif (t_1 <= 5e+150)
		tmp = Float64(Float64(0.0625 * z) * t);
	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[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+99], t$95$2, If[LessEqual[t$95$1, 2e+77], N[(y * x + c), $MachinePrecision], If[LessEqual[t$95$1, 5e+150], N[(N[(0.0625 * z), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -1.9999999999999999e99 or 5.00000000000000009e150 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 96.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 68.1%

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

   if -1.9999999999999999e99 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 1.99999999999999997e77

   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 76.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 68.2%

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

   if 1.99999999999999997e77 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 5.00000000000000009e150

   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

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

   5. Applied rewrites 65.3%

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

   7. Applied rewrites 65.3%

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

Alternative 4: 89.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_1 \leq -100000 \lor \neg \left(t\_1 \leq 5 \cdot 10^{+111}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, \mathsf{fma}\left(t \cdot z, 0.0625, c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c + \left(b \cdot a\right) \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)))
   (if (or (<= t_1 -100000.0) (not (<= t_1 5e+111)))
     (fma -0.25 (* b a) (fma (* t z) 0.0625 c))
     (fma y x (+ c (* (* b a) -0.25))))))

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 <= -100000.0) || !(t_1 <= 5e+111)) {
		tmp = fma(-0.25, (b * a), fma((t * z), 0.0625, c));
	} else {
		tmp = fma(y, x, (c + ((b * a) * -0.25)));
	}
	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 <= -100000.0) || !(t_1 <= 5e+111))
		tmp = fma(-0.25, Float64(b * a), fma(Float64(t * z), 0.0625, c));
	else
		tmp = fma(y, x, Float64(c + Float64(Float64(b * a) * -0.25)));
	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, -100000.0], N[Not[LessEqual[t$95$1, 5e+111]], $MachinePrecision]], N[(-0.25 * N[(b * a), $MachinePrecision] + N[(N[(t * z), $MachinePrecision] * 0.0625 + c), $MachinePrecision]), $MachinePrecision], N[(y * x + N[(c + N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -1e5 or 4.9999999999999997e111 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 94.9%

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

   3. Taylor expanded in 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 84.8%

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

   if -1e5 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 4.9999999999999997e111

   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 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 95.6%

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

   7. Applied rewrites 95.6%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot t}{16} \leq -100000 \lor \neg \left(\frac{z \cdot t}{16} \leq 5 \cdot 10^{+111}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, \mathsf{fma}\left(t \cdot z, 0.0625, c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c + \left(b \cdot a\right) \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+233} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+135}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, \left(t \cdot z\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c + \left(b \cdot a\right) \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)))
   (if (or (<= t_1 -2e+233) (not (<= t_1 5e+135)))
     (fma -0.25 (* b a) (* (* t z) 0.0625))
     (fma y x (+ c (* (* b a) -0.25))))))

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 <= -2e+233) || !(t_1 <= 5e+135)) {
		tmp = fma(-0.25, (b * a), ((t * z) * 0.0625));
	} else {
		tmp = fma(y, x, (c + ((b * a) * -0.25)));
	}
	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 <= -2e+233) || !(t_1 <= 5e+135))
		tmp = fma(-0.25, Float64(b * a), Float64(Float64(t * z) * 0.0625));
	else
		tmp = fma(y, x, Float64(c + Float64(Float64(b * a) * -0.25)));
	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, -2e+233], N[Not[LessEqual[t$95$1, 5e+135]], $MachinePrecision]], N[(-0.25 * N[(b * a), $MachinePrecision] + N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision], N[(y * x + N[(c + N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -1.99999999999999995e233 or 5.00000000000000029e135 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 93.6%

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

   3. Taylor expanded in 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 86.0%

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

   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 86.0%

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

   if -1.99999999999999995e233 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 5.00000000000000029e135

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 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 92.4%

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

   7. Applied rewrites 92.9%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot t}{16} \leq -2 \cdot 10^{+233} \lor \neg \left(\frac{z \cdot t}{16} \leq 5 \cdot 10^{+135}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, \left(t \cdot z\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c + \left(b \cdot a\right) \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+233} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+190}\right):\\ \;\;\;\;\left(0.0625 \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c + \left(b \cdot a\right) \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)))
   (if (or (<= t_1 -2e+233) (not (<= t_1 5e+190)))
     (* (* 0.0625 z) t)
     (fma y x (+ c (* (* b a) -0.25))))))

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 <= -2e+233) || !(t_1 <= 5e+190)) {
		tmp = (0.0625 * z) * t;
	} else {
		tmp = fma(y, x, (c + ((b * a) * -0.25)));
	}
	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 <= -2e+233) || !(t_1 <= 5e+190))
		tmp = Float64(Float64(0.0625 * z) * t);
	else
		tmp = fma(y, x, Float64(c + Float64(Float64(b * a) * -0.25)));
	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, -2e+233], N[Not[LessEqual[t$95$1, 5e+190]], $MachinePrecision]], N[(N[(0.0625 * z), $MachinePrecision] * t), $MachinePrecision], N[(y * x + N[(c + N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -1.99999999999999995e233 or 5.00000000000000036e190 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 92.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 81.8%

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

   7. Applied rewrites 83.4%

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

   if -1.99999999999999995e233 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 5.00000000000000036e190

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 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 91.2%

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

   7. Applied rewrites 91.7%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot t}{16} \leq -2 \cdot 10^{+233} \lor \neg \left(\frac{z \cdot t}{16} \leq 5 \cdot 10^{+190}\right):\\ \;\;\;\;\left(0.0625 \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c + \left(b \cdot a\right) \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+233} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+190}\right):\\ \;\;\;\;\left(0.0625 \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, \mathsf{fma}\left(y, x, c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)))
   (if (or (<= t_1 -2e+233) (not (<= t_1 5e+190)))
     (* (* 0.0625 z) t)
     (fma -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 = (z * t) / 16.0;
	double tmp;
	if ((t_1 <= -2e+233) || !(t_1 <= 5e+190)) {
		tmp = (0.0625 * z) * t;
	} else {
		tmp = fma(-0.25, (b * a), 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 <= -2e+233) || !(t_1 <= 5e+190))
		tmp = Float64(Float64(0.0625 * z) * t);
	else
		tmp = fma(-0.25, Float64(b * a), 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, -2e+233], N[Not[LessEqual[t$95$1, 5e+190]], $MachinePrecision]], N[(N[(0.0625 * z), $MachinePrecision] * t), $MachinePrecision], N[(-0.25 * N[(b * a), $MachinePrecision] + N[(y * x + c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -1.99999999999999995e233 or 5.00000000000000036e190 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 92.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 81.8%

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

   7. Applied rewrites 83.4%

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

   if -1.99999999999999995e233 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 5.00000000000000036e190

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 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 91.2%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot t}{16} \leq -2 \cdot 10^{+233} \lor \neg \left(\frac{z \cdot t}{16} \leq 5 \cdot 10^{+190}\right):\\ \;\;\;\;\left(0.0625 \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, \mathsf{fma}\left(y, x, c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+295} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+190}\right):\\ \;\;\;\;\left(0.0625 \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, -0.25 \cdot \left(a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)))
   (if (or (<= t_1 -1e+295) (not (<= t_1 5e+190)))
     (* (* 0.0625 z) t)
     (fma y x (* -0.25 (* a b))))))

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+295) || !(t_1 <= 5e+190)) {
		tmp = (0.0625 * z) * t;
	} else {
		tmp = fma(y, x, (-0.25 * (a * b)));
	}
	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+295) || !(t_1 <= 5e+190))
		tmp = Float64(Float64(0.0625 * z) * t);
	else
		tmp = fma(y, x, Float64(-0.25 * Float64(a * b)));
	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+295], N[Not[LessEqual[t$95$1, 5e+190]], $MachinePrecision]], N[(N[(0.0625 * z), $MachinePrecision] * t), $MachinePrecision], N[(y * x + N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -9.9999999999999998e294 or 5.00000000000000036e190 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 91.7%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 85.7%

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

   7. Applied rewrites 87.6%

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

   if -9.9999999999999998e294 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 5.00000000000000036e190

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 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 90.1%

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

   7. Applied rewrites 90.6%

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

   8. Taylor expanded in a around inf

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

   10. Applied rewrites 70.4%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot t}{16} \leq -1 \cdot 10^{+295} \lor \neg \left(\frac{z \cdot t}{16} \leq 5 \cdot 10^{+190}\right):\\ \;\;\;\;\left(0.0625 \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, -0.25 \cdot \left(a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+295} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+190}\right):\\ \;\;\;\;\left(0.0625 \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)))
   (if (or (<= t_1 -1e+295) (not (<= t_1 5e+190)))
     (* (* 0.0625 z) t)
     (fma -0.25 (* b a) (* y x)))))

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+295) || !(t_1 <= 5e+190)) {
		tmp = (0.0625 * z) * t;
	} else {
		tmp = fma(-0.25, (b * a), (y * x));
	}
	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+295) || !(t_1 <= 5e+190))
		tmp = Float64(Float64(0.0625 * z) * t);
	else
		tmp = fma(-0.25, Float64(b * a), Float64(y * x));
	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+295], N[Not[LessEqual[t$95$1, 5e+190]], $MachinePrecision]], N[(N[(0.0625 * z), $MachinePrecision] * t), $MachinePrecision], N[(-0.25 * N[(b * a), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -9.9999999999999998e294 or 5.00000000000000036e190 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 91.7%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 85.7%

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

   7. Applied rewrites 87.6%

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

   if -9.9999999999999998e294 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 5.00000000000000036e190

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 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 90.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 69.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot t}{16} \leq -1 \cdot 10^{+295} \lor \neg \left(\frac{z \cdot t}{16} \leq 5 \cdot 10^{+190}\right):\\ \;\;\;\;\left(0.0625 \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+99} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+154}\right):\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) 4.0)))
   (if (or (<= t_1 -2e+99) (not (<= t_1 5e+154)))
     (* -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+99) || !(t_1 <= 5e+154)) {
		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+99) || !(t_1 <= 5e+154))
		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+99], N[Not[LessEqual[t$95$1, 5e+154]], $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)) < -1.9999999999999999e99 or 5.00000000000000004e154 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 96.4%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 68.9%

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

   if -1.9999999999999999e99 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 5.00000000000000004e154

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 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 73.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 64.4%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a \cdot b}{4} \leq -2 \cdot 10^{+99} \lor \neg \left(\frac{a \cdot b}{4} \leq 5 \cdot 10^{+154}\right):\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 94.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-53} \lor \neg \left(t \leq 27500000000000\right):\\ \;\;\;\;\mathsf{fma}\left(0.0625, z, \frac{\mathsf{fma}\left(-0.25, b \cdot a, \mathsf{fma}\left(y, x, c\right)\right)}{t}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c + \left(b \cdot a\right) \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -1.25e-53) (not (<= t 27500000000000.0)))
   (* (fma 0.0625 z (/ (fma -0.25 (* b a) (fma y x c)) t)) t)
   (fma y x (+ c (* (* b a) -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.25e-53) || !(t <= 27500000000000.0)) {
		tmp = fma(0.0625, z, (fma(-0.25, (b * a), fma(y, x, c)) / t)) * t;
	} else {
		tmp = fma(y, x, (c + ((b * a) * -0.25)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1.25e-53) || !(t <= 27500000000000.0))
		tmp = Float64(fma(0.0625, z, Float64(fma(-0.25, Float64(b * a), fma(y, x, c)) / t)) * t);
	else
		tmp = fma(y, x, Float64(c + Float64(Float64(b * a) * -0.25)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -1.25e-53], N[Not[LessEqual[t, 27500000000000.0]], $MachinePrecision]], N[(N[(0.0625 * z + N[(N[(-0.25 * N[(b * a), $MachinePrecision] + N[(y * x + c), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(y * x + N[(c + N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.25e-53 or 2.75e13 < t

   1. Initial program 96.6%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 98.5%

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

   if -1.25e-53 < t < 2.75e13

   1. Initial program 99.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 95.5%

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

   7. Applied rewrites 96.4%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-53} \lor \neg \left(t \leq 27500000000000\right):\\ \;\;\;\;\mathsf{fma}\left(0.0625, z, \frac{\mathsf{fma}\left(-0.25, b \cdot a, \mathsf{fma}\left(y, x, c\right)\right)}{t}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c + \left(b \cdot a\right) \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+22} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+105}\right):\\ \;\;\;\;\mathsf{fma}\left(y, x, c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1e+22) (not (<= (* x y) 5e+105)))
   (fma y x c)
   (fma -0.25 (* b a) c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1e+22) || !((x * y) <= 5e+105)) {
		tmp = fma(y, x, c);
	} else {
		tmp = fma(-0.25, (b * a), c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1e+22) || !(Float64(x * y) <= 5e+105))
		tmp = fma(y, x, c);
	else
		tmp = fma(-0.25, Float64(b * a), c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+22], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+105]], $MachinePrecision]], N[(y * x + c), $MachinePrecision], N[(-0.25 * N[(b * a), $MachinePrecision] + c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1e22 or 5.00000000000000046e105 < (*.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 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 85.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 78.1%

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

   if -1e22 < (*.f64 x y) < 5.00000000000000046e105

   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 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 71.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 65.2%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+22} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+105}\right):\\ \;\;\;\;\mathsf{fma}\left(y, x, c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 41.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+119} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -5e+119) (not (<= (* x y) 2e-18))) (* 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) <= -5e+119) || !((x * y) <= 2e-18)) {
		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) <= (-5d+119)) .or. (.not. ((x * y) <= 2d-18))) 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) <= -5e+119) || !((x * y) <= 2e-18)) {
		tmp = y * x;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -5e+119) or not ((x * y) <= 2e-18):
		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) <= -5e+119) || !(Float64(x * y) <= 2e-18))
		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) <= -5e+119) || ~(((x * y) <= 2e-18)))
		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], -5e+119], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e-18]], $MachinePrecision]], N[(y * x), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.9999999999999999e119 or 2.0000000000000001e-18 < (*.f64 x y)

   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 x around inf

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

   5. Applied rewrites 65.1%

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

   if -4.9999999999999999e119 < (*.f64 x y) < 2.0000000000000001e-18

   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 29.1%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+119} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.2% 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 97.7%

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

3. Taylor expanded in z around 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 78.1%

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

6. Taylor expanded in a around 0

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

8. Applied rewrites 52.0%

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

Alternative 15: 22.8% 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 97.7%

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

3. Taylor expanded in c around inf

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

5. Applied rewrites 18.5%

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

Reproduce

herbie shell --seed 2025021 
(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))