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

Percentage Accurate: 97.8% → 98.9%

Time: 4.1s

Alternatives: 16

Speedup: 0.5×

• 32.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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: 97.8% 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: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot b, a, \left(t \cdot z\right) \cdot 0.0625\right) + c\\ \end{array} \end{array} \]

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 b) a (* (* 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 = (((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 * b), a, ((t * z) * 0.0625)) + 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 = Float64(fma(Float64(-0.25 * b), a, Float64(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[(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[(N[(-0.25 * b), $MachinePrecision] * a + N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision] + c), $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 99.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 x around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 48.2

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

   5. Applied rewrites 48.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0625 \cdot t, z, -0.25 \cdot \left(b \cdot a\right)\right)} + c \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate-*r* N/A

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

      4. +-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 51.2

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

   7. Applied rewrites 51.2%

      \[\leadsto \mathsf{fma}\left(-0.25 \cdot b, \color{blue}{a}, \left(t \cdot z\right) \cdot 0.0625\right) + c \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 95.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right)\\ t_2 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+34} \lor \neg \left(t\_2 \leq 4 \cdot 10^{-41}\right):\\ \;\;\;\;\mathsf{fma}\left(0.0625, t, \frac{t\_1}{z}\right) \cdot z + c\\ \mathbf{else}:\\ \;\;\;\;t\_1 + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (fma y x (* -0.25 (* b a)))) (t_2 (/ (* z t) 16.0)))
   (if (or (<= t_2 -2e+34) (not (<= t_2 4e-41)))
     (+ (* (fma 0.0625 t (/ t_1 z)) z) c)
     (+ t_1 c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(y, x, (-0.25 * (b * a)));
	double t_2 = (z * t) / 16.0;
	double tmp;
	if ((t_2 <= -2e+34) || !(t_2 <= 4e-41)) {
		tmp = (fma(0.0625, t, (t_1 / z)) * z) + c;
	} else {
		tmp = t_1 + c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = fma(y, x, Float64(-0.25 * Float64(b * a)))
	t_2 = Float64(Float64(z * t) / 16.0)
	tmp = 0.0
	if ((t_2 <= -2e+34) || !(t_2 <= 4e-41))
		tmp = Float64(Float64(fma(0.0625, t, Float64(t_1 / z)) * z) + c);
	else
		tmp = Float64(t_1 + c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * x + N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -2e+34], N[Not[LessEqual[t$95$2, 4e-41]], $MachinePrecision]], N[(N[(N[(0.0625 * t + N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + c), $MachinePrecision], N[(t$95$1 + c), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -1.99999999999999989e34 or 4.00000000000000002e-41 < (/.f64 (*.f64 z t) #s(literal 16 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 z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 94.4%

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

   if -1.99999999999999989e34 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 4.00000000000000002e-41

   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

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

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)}\right) + c \]

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right)} \cdot \left(a \cdot b\right)\right) + c \]

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 96.0

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

   5. Applied rewrites 96.0%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot t}{16} \leq -2 \cdot 10^{+34} \lor \neg \left(\frac{z \cdot t}{16} \leq 4 \cdot 10^{-41}\right):\\ \;\;\;\;\mathsf{fma}\left(0.0625, t, \frac{\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right)}{z}\right) \cdot z + c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right) + c\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ t_2 := \left(t \cdot z\right) \cdot 0.0625 + c\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+72}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-188}:\\ \;\;\;\;y \cdot x + c\\ \mathbf{elif}\;t\_1 \leq 3 \cdot 10^{+77}:\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right) + c\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)) (t_2 (+ (* (* t z) 0.0625) c)))
   (if (<= t_1 -5e+72)
     t_2
     (if (<= t_1 4e-188)
       (+ (* y x) c)
       (if (<= t_1 3e+77) (+ (* -0.25 (* b a)) c) t_2)))))

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 t_2 = ((t * z) * 0.0625) + c;
	double tmp;
	if (t_1 <= -5e+72) {
		tmp = t_2;
	} else if (t_1 <= 4e-188) {
		tmp = (y * x) + c;
	} else if (t_1 <= 3e+77) {
		tmp = (-0.25 * (b * a)) + c;
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * t) / 16.0d0
    t_2 = ((t * z) * 0.0625d0) + c
    if (t_1 <= (-5d+72)) then
        tmp = t_2
    else if (t_1 <= 4d-188) then
        tmp = (y * x) + c
    else if (t_1 <= 3d+77) then
        tmp = ((-0.25d0) * (b * a)) + c
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) / 16.0;
	double t_2 = ((t * z) * 0.0625) + c;
	double tmp;
	if (t_1 <= -5e+72) {
		tmp = t_2;
	} else if (t_1 <= 4e-188) {
		tmp = (y * x) + c;
	} else if (t_1 <= 3e+77) {
		tmp = (-0.25 * (b * a)) + c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (z * t) / 16.0
	t_2 = ((t * z) * 0.0625) + c
	tmp = 0
	if t_1 <= -5e+72:
		tmp = t_2
	elif t_1 <= 4e-188:
		tmp = (y * x) + c
	elif t_1 <= 3e+77:
		tmp = (-0.25 * (b * a)) + c
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * t) / 16.0)
	t_2 = Float64(Float64(Float64(t * z) * 0.0625) + c)
	tmp = 0.0
	if (t_1 <= -5e+72)
		tmp = t_2;
	elseif (t_1 <= 4e-188)
		tmp = Float64(Float64(y * x) + c);
	elseif (t_1 <= 3e+77)
		tmp = Float64(Float64(-0.25 * Float64(b * a)) + c);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (z * t) / 16.0;
	t_2 = ((t * z) * 0.0625) + c;
	tmp = 0.0;
	if (t_1 <= -5e+72)
		tmp = t_2;
	elseif (t_1 <= 4e-188)
		tmp = (y * x) + c;
	elseif (t_1 <= 3e+77)
		tmp = (-0.25 * (b * a)) + c;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision] + c), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+72], t$95$2, If[LessEqual[t$95$1, 4e-188], N[(N[(y * x), $MachinePrecision] + c), $MachinePrecision], If[LessEqual[t$95$1, 3e+77], N[(N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -4.99999999999999992e72 or 2.9999999999999998e77 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 95.6%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 70.2

         \[\leadsto \left(t \cdot z\right) \cdot 0.0625 + c \]

   5. Applied rewrites 70.2%

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

   if -4.99999999999999992e72 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 3.9999999999999998e-188

   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 x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 63.6

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

   5. Applied rewrites 63.6%

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

   if 3.9999999999999998e-188 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 2.9999999999999998e77

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 57.8

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

   5. Applied rewrites 57.8%

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

Alternative 4: 62.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ t_2 := \left(t \cdot z\right) \cdot 0.0625\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+72}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-188}:\\ \;\;\;\;y \cdot x + c\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+120}:\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right) + c\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)) (t_2 (* (* t z) 0.0625)))
   (if (<= t_1 -5e+72)
     t_2
     (if (<= t_1 4e-188)
       (+ (* y x) c)
       (if (<= t_1 2e+120) (+ (* -0.25 (* b a)) c) t_2)))))

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 t_2 = (t * z) * 0.0625;
	double tmp;
	if (t_1 <= -5e+72) {
		tmp = t_2;
	} else if (t_1 <= 4e-188) {
		tmp = (y * x) + c;
	} else if (t_1 <= 2e+120) {
		tmp = (-0.25 * (b * a)) + c;
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * t) / 16.0d0
    t_2 = (t * z) * 0.0625d0
    if (t_1 <= (-5d+72)) then
        tmp = t_2
    else if (t_1 <= 4d-188) then
        tmp = (y * x) + c
    else if (t_1 <= 2d+120) then
        tmp = ((-0.25d0) * (b * a)) + c
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) / 16.0;
	double t_2 = (t * z) * 0.0625;
	double tmp;
	if (t_1 <= -5e+72) {
		tmp = t_2;
	} else if (t_1 <= 4e-188) {
		tmp = (y * x) + c;
	} else if (t_1 <= 2e+120) {
		tmp = (-0.25 * (b * a)) + c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (z * t) / 16.0
	t_2 = (t * z) * 0.0625
	tmp = 0
	if t_1 <= -5e+72:
		tmp = t_2
	elif t_1 <= 4e-188:
		tmp = (y * x) + c
	elif t_1 <= 2e+120:
		tmp = (-0.25 * (b * a)) + c
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * t) / 16.0)
	t_2 = Float64(Float64(t * z) * 0.0625)
	tmp = 0.0
	if (t_1 <= -5e+72)
		tmp = t_2;
	elseif (t_1 <= 4e-188)
		tmp = Float64(Float64(y * x) + c);
	elseif (t_1 <= 2e+120)
		tmp = Float64(Float64(-0.25 * Float64(b * a)) + c);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (z * t) / 16.0;
	t_2 = (t * z) * 0.0625;
	tmp = 0.0;
	if (t_1 <= -5e+72)
		tmp = t_2;
	elseif (t_1 <= 4e-188)
		tmp = (y * x) + c;
	elseif (t_1 <= 2e+120)
		tmp = (-0.25 * (b * a)) + c;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+72], t$95$2, If[LessEqual[t$95$1, 4e-188], N[(N[(y * x), $MachinePrecision] + c), $MachinePrecision], If[LessEqual[t$95$1, 2e+120], N[(N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -4.99999999999999992e72 or 2e120 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 95.3%

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 64.3

         \[\leadsto \left(t \cdot z\right) \cdot 0.0625 \]

   5. Applied rewrites 64.3%

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

   if -4.99999999999999992e72 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 3.9999999999999998e-188

   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 x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 63.6

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

   5. Applied rewrites 63.6%

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

   if 3.9999999999999998e-188 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 2e120

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 56.0

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

   5. Applied rewrites 56.0%

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

Alternative 5: 89.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+72} \lor \neg \left(t\_1 \leq 500000\right):\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot b, a, \left(t \cdot z\right) \cdot 0.0625\right) + c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right) + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)))
   (if (or (<= t_1 -5e+72) (not (<= t_1 500000.0)))
     (+ (fma (* -0.25 b) a (* (* t z) 0.0625)) c)
     (+ (fma y x (* -0.25 (* b a))) 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 <= -5e+72) || !(t_1 <= 500000.0)) {
		tmp = fma((-0.25 * b), a, ((t * z) * 0.0625)) + c;
	} else {
		tmp = fma(y, x, (-0.25 * (b * a))) + 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 <= -5e+72) || !(t_1 <= 500000.0))
		tmp = Float64(fma(Float64(-0.25 * b), a, Float64(Float64(t * z) * 0.0625)) + c);
	else
		tmp = Float64(fma(y, x, Float64(-0.25 * Float64(b * a))) + 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, -5e+72], N[Not[LessEqual[t$95$1, 500000.0]], $MachinePrecision]], N[(N[(N[(-0.25 * b), $MachinePrecision] * a + N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision], N[(N[(y * x + N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -4.99999999999999992e72 or 5e5 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 96.1%

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

   3. Taylor expanded in x around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 83.1

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

   5. Applied rewrites 83.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0625 \cdot t, z, -0.25 \cdot \left(b \cdot a\right)\right)} + c \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate-*r* N/A

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

      4. +-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 83.1

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

   7. Applied rewrites 83.1%

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

   if -4.99999999999999992e72 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 5e5

   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

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

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)}\right) + c \]

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right)} \cdot \left(a \cdot b\right)\right) + c \]

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 94.8

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

   5. Applied rewrites 94.8%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot t}{16} \leq -5 \cdot 10^{+72} \lor \neg \left(\frac{z \cdot t}{16} \leq 500000\right):\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot b, a, \left(t \cdot z\right) \cdot 0.0625\right) + c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right) + c\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(0.0625 \cdot t, z, \mathsf{fma}\left(-0.25, b \cdot a, y \cdot x\right)\right)\\ \mathbf{elif}\;t\_1 \leq 500000:\\ \;\;\;\;\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right) + c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot b, a, \left(t \cdot z\right) \cdot 0.0625\right) + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)))
   (if (<= t_1 -4e+65)
     (fma (* 0.0625 t) z (fma -0.25 (* b a) (* y x)))
     (if (<= t_1 500000.0)
       (+ (fma y x (* -0.25 (* b a))) c)
       (+ (fma (* -0.25 b) a (* (* 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 <= -4e+65) {
		tmp = fma((0.0625 * t), z, fma(-0.25, (b * a), (y * x)));
	} else if (t_1 <= 500000.0) {
		tmp = fma(y, x, (-0.25 * (b * a))) + c;
	} else {
		tmp = fma((-0.25 * b), a, ((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 <= -4e+65)
		tmp = fma(Float64(0.0625 * t), z, fma(-0.25, Float64(b * a), Float64(y * x)));
	elseif (t_1 <= 500000.0)
		tmp = Float64(fma(y, x, Float64(-0.25 * Float64(b * a))) + c);
	else
		tmp = Float64(fma(Float64(-0.25 * b), a, Float64(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, -4e+65], N[(N[(0.0625 * t), $MachinePrecision] * z + N[(-0.25 * N[(b * a), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 500000.0], N[(N[(y * x + N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision], N[(N[(N[(-0.25 * b), $MachinePrecision] * a + N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -4e65

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 95.6%

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

   6. Taylor expanded in c around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-commutative N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 87.1

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

   8. Applied rewrites 87.1%

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

   if -4e65 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 5e5

   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

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

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)}\right) + c \]

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right)} \cdot \left(a \cdot b\right)\right) + c \]

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 94.9

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

   5. Applied rewrites 94.9%

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

   if 5e5 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 96.8%

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

   3. Taylor expanded in x around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 82.9

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

   5. Applied rewrites 82.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0625 \cdot t, z, -0.25 \cdot \left(b \cdot a\right)\right)} + c \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate-*r* N/A

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

      4. +-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 82.8

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

   7. Applied rewrites 82.8%

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

Alternative 7: 89.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.25 \cdot \left(b \cdot a\right)\\ t_2 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(0.0625 \cdot t, z, t\_1\right) + c\\ \mathbf{elif}\;t\_2 \leq 500000:\\ \;\;\;\;\mathsf{fma}\left(y, x, t\_1\right) + c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot b, a, \left(t \cdot z\right) \cdot 0.0625\right) + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -0.25 (* b a))) (t_2 (/ (* z t) 16.0)))
   (if (<= t_2 -5e+72)
     (+ (fma (* 0.0625 t) z t_1) c)
     (if (<= t_2 500000.0)
       (+ (fma y x t_1) c)
       (+ (fma (* -0.25 b) a (* (* 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 = -0.25 * (b * a);
	double t_2 = (z * t) / 16.0;
	double tmp;
	if (t_2 <= -5e+72) {
		tmp = fma((0.0625 * t), z, t_1) + c;
	} else if (t_2 <= 500000.0) {
		tmp = fma(y, x, t_1) + c;
	} else {
		tmp = fma((-0.25 * b), a, ((t * z) * 0.0625)) + c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-0.25 * Float64(b * a))
	t_2 = Float64(Float64(z * t) / 16.0)
	tmp = 0.0
	if (t_2 <= -5e+72)
		tmp = Float64(fma(Float64(0.0625 * t), z, t_1) + c);
	elseif (t_2 <= 500000.0)
		tmp = Float64(fma(y, x, t_1) + c);
	else
		tmp = Float64(fma(Float64(-0.25 * b), a, Float64(Float64(t * z) * 0.0625)) + c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+72], N[(N[(N[(0.0625 * t), $MachinePrecision] * z + t$95$1), $MachinePrecision] + c), $MachinePrecision], If[LessEqual[t$95$2, 500000.0], N[(N[(y * x + t$95$1), $MachinePrecision] + c), $MachinePrecision], N[(N[(N[(-0.25 * b), $MachinePrecision] * a + N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -4.99999999999999992e72

   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

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 83.3

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

   5. Applied rewrites 83.3%

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

   if -4.99999999999999992e72 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 5e5

   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

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

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)}\right) + c \]

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right)} \cdot \left(a \cdot b\right)\right) + c \]

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 94.8

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

   5. Applied rewrites 94.8%

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

   if 5e5 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 96.8%

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

   3. Taylor expanded in x around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 82.9

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

   5. Applied rewrites 82.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0625 \cdot t, z, -0.25 \cdot \left(b \cdot a\right)\right)} + c \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate-*r* N/A

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

      4. +-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 82.8

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

   7. Applied rewrites 82.8%

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

Alternative 8: 85.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+234} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+261}\right):\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625 + c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right) + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)))
   (if (or (<= t_1 -5e+234) (not (<= t_1 5e+261)))
     (+ (* (* t z) 0.0625) c)
     (+ (fma y x (* -0.25 (* b a))) 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 <= -5e+234) || !(t_1 <= 5e+261)) {
		tmp = ((t * z) * 0.0625) + c;
	} else {
		tmp = fma(y, x, (-0.25 * (b * a))) + 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 <= -5e+234) || !(t_1 <= 5e+261))
		tmp = Float64(Float64(Float64(t * z) * 0.0625) + c);
	else
		tmp = Float64(fma(y, x, Float64(-0.25 * Float64(b * a))) + 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, -5e+234], N[Not[LessEqual[t$95$1, 5e+261]], $MachinePrecision]], N[(N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision] + c), $MachinePrecision], N[(N[(y * x + N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -5.0000000000000003e234 or 5.0000000000000001e261 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 91.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 87.2

         \[\leadsto \left(t \cdot z\right) \cdot 0.0625 + c \]

   5. Applied rewrites 87.2%

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

   if -5.0000000000000003e234 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 5.0000000000000001e261

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0

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

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)}\right) + c \]

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right)} \cdot \left(a \cdot b\right)\right) + c \]

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 85.1

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

   5. Applied rewrites 85.1%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot t}{16} \leq -5 \cdot 10^{+234} \lor \neg \left(\frac{z \cdot t}{16} \leq 5 \cdot 10^{+261}\right):\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625 + c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right) + c\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.25 \cdot \left(b \cdot a\right)\\ t_2 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(0.0625 \cdot t, z, t\_1\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+261}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t\_1\right) + c\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625 + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -0.25 (* b a))) (t_2 (/ (* z t) 16.0)))
   (if (<= t_2 -5e+72)
     (fma (* 0.0625 t) z t_1)
     (if (<= t_2 5e+261) (+ (fma y x t_1) c) (+ (* (* 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 = -0.25 * (b * a);
	double t_2 = (z * t) / 16.0;
	double tmp;
	if (t_2 <= -5e+72) {
		tmp = fma((0.0625 * t), z, t_1);
	} else if (t_2 <= 5e+261) {
		tmp = fma(y, x, t_1) + c;
	} else {
		tmp = ((t * z) * 0.0625) + c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-0.25 * Float64(b * a))
	t_2 = Float64(Float64(z * t) / 16.0)
	tmp = 0.0
	if (t_2 <= -5e+72)
		tmp = fma(Float64(0.0625 * t), z, t_1);
	elseif (t_2 <= 5e+261)
		tmp = Float64(fma(y, x, t_1) + c);
	else
		tmp = Float64(Float64(Float64(t * z) * 0.0625) + c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+72], N[(N[(0.0625 * t), $MachinePrecision] * z + t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 5e+261], N[(N[(y * x + t$95$1), $MachinePrecision] + c), $MachinePrecision], N[(N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision] + c), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -4.99999999999999992e72

   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 z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 95.7%

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

   6. Taylor expanded in c around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-commutative N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 87.9

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

   8. Applied rewrites 87.9%

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

   9. Taylor expanded in x around 0

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

       1. lower-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lift-*.f64 74.3

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

   11. Applied rewrites 74.3%

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

   if -4.99999999999999992e72 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 5.0000000000000001e261

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0

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

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)}\right) + c \]

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right)} \cdot \left(a \cdot b\right)\right) + c \]

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 88.1

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

   5. Applied rewrites 88.1%

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

   if 5.0000000000000001e261 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 91.6%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 89.6

         \[\leadsto \left(t \cdot z\right) \cdot 0.0625 + c \]

   5. Applied rewrites 89.6%

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

Alternative 10: 62.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+72} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+200}\right):\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625\\ \mathbf{else}:\\ \;\;\;\;y \cdot x + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)))
   (if (or (<= t_1 -5e+72) (not (<= t_1 2e+200)))
     (* (* t z) 0.0625)
     (+ (* 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 <= -5e+72) || !(t_1 <= 2e+200)) {
		tmp = (t * z) * 0.0625;
	} else {
		tmp = (y * x) + 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) :: t_1
    real(8) :: tmp
    t_1 = (z * t) / 16.0d0
    if ((t_1 <= (-5d+72)) .or. (.not. (t_1 <= 2d+200))) then
        tmp = (t * z) * 0.0625d0
    else
        tmp = (y * x) + 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 t_1 = (z * t) / 16.0;
	double tmp;
	if ((t_1 <= -5e+72) || !(t_1 <= 2e+200)) {
		tmp = (t * z) * 0.0625;
	} else {
		tmp = (y * x) + c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (z * t) / 16.0
	tmp = 0
	if (t_1 <= -5e+72) or not (t_1 <= 2e+200):
		tmp = (t * z) * 0.0625
	else:
		tmp = (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 <= -5e+72) || !(t_1 <= 2e+200))
		tmp = Float64(Float64(t * z) * 0.0625);
	else
		tmp = Float64(Float64(y * x) + c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (z * t) / 16.0;
	tmp = 0.0;
	if ((t_1 <= -5e+72) || ~((t_1 <= 2e+200)))
		tmp = (t * z) * 0.0625;
	else
		tmp = (y * x) + c;
	end
	tmp_2 = 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, -5e+72], N[Not[LessEqual[t$95$1, 2e+200]], $MachinePrecision]], N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision], N[(N[(y * x), $MachinePrecision] + c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -4.99999999999999992e72 or 1.9999999999999999e200 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 94.6%

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 68.0

         \[\leadsto \left(t \cdot z\right) \cdot 0.0625 \]

   5. Applied rewrites 68.0%

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

   if -4.99999999999999992e72 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 1.9999999999999999e200

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 60.1

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

   5. Applied rewrites 60.1%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot t}{16} \leq -5 \cdot 10^{+72} \lor \neg \left(\frac{z \cdot t}{16} \leq 2 \cdot 10^{+200}\right):\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625\\ \mathbf{else}:\\ \;\;\;\;y \cdot x + c\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+283} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+120}\right):\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) 4.0)))
   (if (or (<= t_1 -1e+283) (not (<= t_1 5e+120)))
     (* -0.25 (* b a))
     (+ (* 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 <= -1e+283) || !(t_1 <= 5e+120)) {
		tmp = -0.25 * (b * a);
	} else {
		tmp = (y * x) + 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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) / 4.0d0
    if ((t_1 <= (-1d+283)) .or. (.not. (t_1 <= 5d+120))) then
        tmp = (-0.25d0) * (b * a)
    else
        tmp = (y * x) + 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 t_1 = (a * b) / 4.0;
	double tmp;
	if ((t_1 <= -1e+283) || !(t_1 <= 5e+120)) {
		tmp = -0.25 * (b * a);
	} else {
		tmp = (y * x) + c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / 4.0
	tmp = 0
	if (t_1 <= -1e+283) or not (t_1 <= 5e+120):
		tmp = -0.25 * (b * a)
	else:
		tmp = (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 <= -1e+283) || !(t_1 <= 5e+120))
		tmp = Float64(-0.25 * Float64(b * a));
	else
		tmp = Float64(Float64(y * x) + c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) / 4.0;
	tmp = 0.0;
	if ((t_1 <= -1e+283) || ~((t_1 <= 5e+120)))
		tmp = -0.25 * (b * a);
	else
		tmp = (y * x) + c;
	end
	tmp_2 = 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, -1e+283], N[Not[LessEqual[t$95$1, 5e+120]], $MachinePrecision]], N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] + c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -9.99999999999999955e282 or 5.00000000000000019e120 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 93.0%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

         \[\leadsto \frac{-1}{4} \cdot \color{blue}{\left(a \cdot b\right)} \]

      2. *-commutative N/A

         \[\leadsto \frac{-1}{4} \cdot \left(b \cdot \color{blue}{a}\right) \]

      3. lower-*.f64 75.5

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

   5. Applied rewrites 75.5%

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

   if -9.99999999999999955e282 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 5.00000000000000019e120

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 57.9

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

   5. Applied rewrites 57.9%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a \cdot b}{4} \leq -1 \cdot 10^{+283} \lor \neg \left(\frac{a \cdot b}{4} \leq 5 \cdot 10^{+120}\right):\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x + c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 90.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+52} \lor \neg \left(x \cdot y \leq 0.005\right):\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, \mathsf{fma}\left(t \cdot z, 0.0625, y \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.0625 \cdot t, z, -0.25 \cdot \left(b \cdot a\right)\right) + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1e+52) (not (<= (* x y) 0.005)))
   (fma -0.25 (* b a) (fma (* t z) 0.0625 (* y x)))
   (+ (fma (* 0.0625 t) z (* -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+52) || !((x * y) <= 0.005)) {
		tmp = fma(-0.25, (b * a), fma((t * z), 0.0625, (y * x)));
	} else {
		tmp = fma((0.0625 * t), z, (-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+52) || !(Float64(x * y) <= 0.005))
		tmp = fma(-0.25, Float64(b * a), fma(Float64(t * z), 0.0625, Float64(y * x)));
	else
		tmp = Float64(fma(Float64(0.0625 * t), z, Float64(-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+52], N[Not[LessEqual[N[(x * y), $MachinePrecision], 0.005]], $MachinePrecision]], N[(-0.25 * N[(b * a), $MachinePrecision] + N[(N[(t * z), $MachinePrecision] * 0.0625 + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(0.0625 * t), $MachinePrecision] * z + N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.9999999999999999e51 or 0.0050000000000000001 < (*.f64 x y)

   1. Initial program 96.2%

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

   3. Taylor expanded in c around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 84.4

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

   5. Applied rewrites 84.4%

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

   if -9.9999999999999999e51 < (*.f64 x y) < 0.0050000000000000001

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 95.3

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

   5. Applied rewrites 95.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0625 \cdot t, z, -0.25 \cdot \left(b \cdot a\right)\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+52} \lor \neg \left(x \cdot y \leq 0.005\right):\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, \mathsf{fma}\left(t \cdot z, 0.0625, y \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.0625 \cdot t, z, -0.25 \cdot \left(b \cdot a\right)\right) + c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+27} \lor \neg \left(x \cdot y \leq 0.05\right):\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625 + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1e+27) (not (<= (* x y) 0.05)))
   (fma -0.25 (* b a) (* y x))
   (+ (* (* 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+27) || !((x * y) <= 0.05)) {
		tmp = fma(-0.25, (b * a), (y * x));
	} else {
		tmp = ((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+27) || !(Float64(x * y) <= 0.05))
		tmp = fma(-0.25, Float64(b * a), Float64(y * x));
	else
		tmp = Float64(Float64(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+27], N[Not[LessEqual[N[(x * y), $MachinePrecision], 0.05]], $MachinePrecision]], N[(-0.25 * N[(b * a), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision] + c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1e27 or 0.050000000000000003 < (*.f64 x y)

   1. Initial program 96.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 81.6%

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

   6. Taylor expanded in c around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-commutative N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 85.0

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

   8. Applied rewrites 85.0%

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

   9. Taylor expanded in z around 0

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

       1. lower-fma.f64 N/A

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

       2. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{4}, b \cdot a, x \cdot y\right) \]

       3. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{4}, b \cdot a, x \cdot y\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{4}, b \cdot a, y \cdot x\right) \]

       5. lift-*.f64 68.8

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

   11. Applied rewrites 68.8%

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

   if -1e27 < (*.f64 x y) < 0.050000000000000003

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 63.6

         \[\leadsto \left(t \cdot z\right) \cdot 0.0625 + c \]

   5. Applied rewrites 63.6%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+27} \lor \neg \left(x \cdot y \leq 0.05\right):\\ \;\;\;\;\mathsf{fma}\left(-0.25, b \cdot a, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625 + c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.1 \lor \neg \left(x \cdot y \leq 0.05\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -0.1) (not (<= (* x y) 0.05))) (* 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) <= -0.1) || !((x * y) <= 0.05)) {
		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) <= (-0.1d0)) .or. (.not. ((x * y) <= 0.05d0))) 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) <= -0.1) || !((x * y) <= 0.05)) {
		tmp = y * x;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -0.1) or not ((x * y) <= 0.05):
		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) <= -0.1) || !(Float64(x * y) <= 0.05))
		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) <= -0.1) || ~(((x * y) <= 0.05)))
		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], -0.1], N[Not[LessEqual[N[(x * y), $MachinePrecision], 0.05]], $MachinePrecision]], N[(y * x), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -0.10000000000000001 or 0.050000000000000003 < (*.f64 x y)

   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 x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 50.5

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

   5. Applied rewrites 50.5%

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

   if -0.10000000000000001 < (*.f64 x y) < 0.050000000000000003

   1. Initial program 99.2%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 30.9%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.1 \lor \neg \left(x \cdot y \leq 0.05\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.9% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ y \cdot x + c \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (y * x) + 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 = (y * x) + c
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 48.9

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

5. Applied rewrites 48.9%

   \[\leadsto \color{blue}{y \cdot x} + c \]
6. 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 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 c around inf

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

5. Applied rewrites 22.3%

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

Reproduce

herbie shell --seed 2025086 
(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))