Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Percentage Accurate: 77.4% → 92.5%

Time: 3.9s

Alternatives: 11

Speedup: 0.9×

Specification

Math

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

FPCore

(FPCore (x y z t a) :precision binary64 (- (+ x y) (/ (* (- z t) y) (- a t))))

C

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

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)
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
    code = (x + y) - (((z - t) * y) / (a - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.4% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a) :precision binary64 (- (+ x y) (/ (* (- z t) y) (- a t))))

C

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

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)
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
    code = (x + y) - (((z - t) * y) / (a - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\frac{t}{a - t} + 1\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y\\ \mathbf{if}\;y \leq -4 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-65}:\\ \;\;\;\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- (+ (+ (/ t (- a t)) 1.0) (/ x y)) (/ z (- a t))) y)))
   (if (<= y -4e-79)
     t_1
     (if (<= y 4.8e-65) (- (+ x y) (/ (* (- z t) y) (- a t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((((t / (a - t)) + 1.0) + (x / y)) - (z / (a - t))) * y;
	double tmp;
	if (y <= -4e-79) {
		tmp = t_1;
	} else if (y <= 4.8e-65) {
		tmp = (x + y) - (((z - t) * y) / (a - t));
	} else {
		tmp = t_1;
	}
	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)
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) :: t_1
    real(8) :: tmp
    t_1 = ((((t / (a - t)) + 1.0d0) + (x / y)) - (z / (a - t))) * y
    if (y <= (-4d-79)) then
        tmp = t_1
    else if (y <= 4.8d-65) then
        tmp = (x + y) - (((z - t) * y) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((((t / (a - t)) + 1.0) + (x / y)) - (z / (a - t))) * y;
	double tmp;
	if (y <= -4e-79) {
		tmp = t_1;
	} else if (y <= 4.8e-65) {
		tmp = (x + y) - (((z - t) * y) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((((t / (a - t)) + 1.0) + (x / y)) - (z / (a - t))) * y
	tmp = 0
	if y <= -4e-79:
		tmp = t_1
	elif y <= 4.8e-65:
		tmp = (x + y) - (((z - t) * y) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(Float64(Float64(t / Float64(a - t)) + 1.0) + Float64(x / y)) - Float64(z / Float64(a - t))) * y)
	tmp = 0.0
	if (y <= -4e-79)
		tmp = t_1;
	elseif (y <= 4.8e-65)
		tmp = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((((t / (a - t)) + 1.0) + (x / y)) - (z / (a - t))) * y;
	tmp = 0.0;
	if (y <= -4e-79)
		tmp = t_1;
	elseif (y <= 4.8e-65)
		tmp = (x + y) - (((z - t) * y) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4e-79], t$95$1, If[LessEqual[y, 4.8e-65], N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4e-79 or 4.8000000000000003e-65 < y

   1. Initial program 66.6%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 91.0

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

   4. Applied rewrites 91.0%

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

   if -4e-79 < y < 4.8000000000000003e-65

   1. Initial program 94.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 89.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - a}{t} \cdot y + x\\ \mathbf{if}\;t \leq -5 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+114}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* (/ (- z a) t) y) x)))
   (if (<= t -5e+160)
     t_1
     (if (<= t 1.3e+114) (- (+ x y) (* y (/ z (- a t)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (((z - a) / t) * y) + x;
	double tmp;
	if (t <= -5e+160) {
		tmp = t_1;
	} else if (t <= 1.3e+114) {
		tmp = (x + y) - (y * (z / (a - t)));
	} else {
		tmp = t_1;
	}
	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)
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) :: t_1
    real(8) :: tmp
    t_1 = (((z - a) / t) * y) + x
    if (t <= (-5d+160)) then
        tmp = t_1
    else if (t <= 1.3d+114) then
        tmp = (x + y) - (y * (z / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (((z - a) / t) * y) + x;
	double tmp;
	if (t <= -5e+160) {
		tmp = t_1;
	} else if (t <= 1.3e+114) {
		tmp = (x + y) - (y * (z / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (((z - a) / t) * y) + x
	tmp = 0
	if t <= -5e+160:
		tmp = t_1
	elif t <= 1.3e+114:
		tmp = (x + y) - (y * (z / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(Float64(z - a) / t) * y) + x)
	tmp = 0.0
	if (t <= -5e+160)
		tmp = t_1;
	elseif (t <= 1.3e+114)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (((z - a) / t) * y) + x;
	tmp = 0.0;
	if (t <= -5e+160)
		tmp = t_1;
	elseif (t <= 1.3e+114)
		tmp = (x + y) - (y * (z / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -5e+160], t$95$1, If[LessEqual[t, 1.3e+114], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.0000000000000002e160 or 1.3e114 < t

   1. Initial program 52.3%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot y - y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{a \cdot y - y \cdot z}{t}\right)\right) + x \]

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 77.2

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

   4. Applied rewrites 77.2%

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

   5. Taylor expanded in y around 0

      \[\leadsto y \cdot \left(\frac{z}{t} - \frac{a}{t}\right) + x \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

         \[\leadsto \frac{z - a}{t} \cdot y + x \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{z - a}{t} \cdot y + x \]

      5. lower--.f64 89.6

         \[\leadsto \frac{z - a}{t} \cdot y + x \]

   7. Applied rewrites 89.6%

      \[\leadsto \frac{z - a}{t} \cdot y + x \]

   if -5.0000000000000002e160 < t < 1.3e114

   1. Initial program 86.8%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 88.9

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

   4. Applied rewrites 88.9%

      \[\leadsto \left(x + y\right) - \color{blue}{y \cdot \frac{z}{a - t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 78.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -16600000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-115}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -16600000.0)
   (+ y x)
   (if (<= a -8.8e-115)
     (- x (/ (* (- z t) y) (- a t)))
     (if (<= a 4.2e-39) (fma z (/ y t) x) (- (+ x y) (/ (* z y) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -16600000.0) {
		tmp = y + x;
	} else if (a <= -8.8e-115) {
		tmp = x - (((z - t) * y) / (a - t));
	} else if (a <= 4.2e-39) {
		tmp = fma(z, (y / t), x);
	} else {
		tmp = (x + y) - ((z * y) / a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -16600000.0)
		tmp = Float64(y + x);
	elseif (a <= -8.8e-115)
		tmp = Float64(x - Float64(Float64(Float64(z - t) * y) / Float64(a - t)));
	elseif (a <= 4.2e-39)
		tmp = fma(z, Float64(y / t), x);
	else
		tmp = Float64(Float64(x + y) - Float64(Float64(z * y) / a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -16600000.0], N[(y + x), $MachinePrecision], If[LessEqual[a, -8.8e-115], N[(x - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e-39], N[(z * N[(y / t), $MachinePrecision] + x), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.66e7

   1. Initial program 79.4%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 75.2

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

   4. Applied rewrites 75.2%

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

   if -1.66e7 < a < -8.7999999999999997e-115

   1. Initial program 74.8%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 64.4%

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

   if -8.7999999999999997e-115 < a < 4.19999999999999987e-39

   1. Initial program 74.1%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot y - y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{a \cdot y - y \cdot z}{t}\right)\right) + x \]

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 82.0

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

   4. Applied rewrites 82.0%

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

   5. Taylor expanded in a around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot z}{t} + x \]

      2. associate-/l* N/A

         \[\leadsto y \cdot \frac{z}{t} + x \]

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 80.5

         \[\leadsto \mathsf{fma}\left(y, \frac{z}{t}, x\right) \]

   7. Applied rewrites 80.5%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{z}{t}}, x\right) \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{z}{t}, x\right) \]

      2. lift-fma.f64 N/A

         \[\leadsto y \cdot \frac{z}{t} + x \]

      3. associate-*r/ N/A

         \[\leadsto \frac{y \cdot z}{t} + x \]

      4. *-commutative N/A

         \[\leadsto \frac{z \cdot y}{t} + x \]

      5. associate-/l* N/A

         \[\leadsto z \cdot \frac{y}{t} + x \]

      6. lower-fma.f64 N/A

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

      7. lift-/.f64 80.6

         \[\leadsto \mathsf{fma}\left(z, \frac{y}{t}, x\right) \]

   9. Applied rewrites 80.6%

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

   if 4.19999999999999987e-39 < a

   1. Initial program 81.0%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

         \[\leadsto \left(x + y\right) - \frac{z \cdot y}{a} \]

      3. lower-*.f64 80.0

         \[\leadsto \left(x + y\right) - \frac{z \cdot y}{a} \]

   4. Applied rewrites 80.0%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z \cdot y}{a}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{z \cdot y}{a}\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* z y) a))))
   (if (<= a -2.4e-79) t_1 (if (<= a 4.2e-39) (fma z (/ y t) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((z * y) / a);
	double tmp;
	if (a <= -2.4e-79) {
		tmp = t_1;
	} else if (a <= 4.2e-39) {
		tmp = fma(z, (y / t), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(z * y) / a))
	tmp = 0.0
	if (a <= -2.4e-79)
		tmp = t_1;
	elseif (a <= 4.2e-39)
		tmp = fma(z, Float64(y / t), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.4e-79], t$95$1, If[LessEqual[a, 4.2e-39], N[(z * N[(y / t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.40000000000000006e-79 or 4.19999999999999987e-39 < a

   1. Initial program 79.6%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

         \[\leadsto \left(x + y\right) - \frac{z \cdot y}{a} \]

      3. lower-*.f64 78.0

         \[\leadsto \left(x + y\right) - \frac{z \cdot y}{a} \]

   4. Applied rewrites 78.0%

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

   if -2.40000000000000006e-79 < a < 4.19999999999999987e-39

   1. Initial program 74.2%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot y - y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{a \cdot y - y \cdot z}{t}\right)\right) + x \]

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 81.6

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

   4. Applied rewrites 81.6%

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

   5. Taylor expanded in a around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot z}{t} + x \]

      2. associate-/l* N/A

         \[\leadsto y \cdot \frac{z}{t} + x \]

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 80.1

         \[\leadsto \mathsf{fma}\left(y, \frac{z}{t}, x\right) \]

   7. Applied rewrites 80.1%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{z}{t}}, x\right) \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{z}{t}, x\right) \]

      2. lift-fma.f64 N/A

         \[\leadsto y \cdot \frac{z}{t} + x \]

      3. associate-*r/ N/A

         \[\leadsto \frac{y \cdot z}{t} + x \]

      4. *-commutative N/A

         \[\leadsto \frac{z \cdot y}{t} + x \]

      5. associate-/l* N/A

         \[\leadsto z \cdot \frac{y}{t} + x \]

      6. lower-fma.f64 N/A

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

      7. lift-/.f64 80.3

         \[\leadsto \mathsf{fma}\left(z, \frac{y}{t}, x\right) \]

   9. Applied rewrites 80.3%

      \[\leadsto \mathsf{fma}\left(z, \frac{y}{\color{blue}{t}}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 76.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+134}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-77}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.2e+134)
   (+ y x)
   (if (<= a -2.4e-77)
     (- x (/ (* z y) a))
     (if (<= a 3.4e+28) (fma z (/ y t) x) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.2e+134) {
		tmp = y + x;
	} else if (a <= -2.4e-77) {
		tmp = x - ((z * y) / a);
	} else if (a <= 3.4e+28) {
		tmp = fma(z, (y / t), x);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.2e+134)
		tmp = Float64(y + x);
	elseif (a <= -2.4e-77)
		tmp = Float64(x - Float64(Float64(z * y) / a));
	elseif (a <= 3.4e+28)
		tmp = fma(z, Float64(y / t), x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.2e+134], N[(y + x), $MachinePrecision], If[LessEqual[a, -2.4e-77], N[(x - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e+28], N[(z * N[(y / t), $MachinePrecision] + x), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.1999999999999992e134 or 3.4e28 < a

   1. Initial program 80.1%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 80.6

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

   4. Applied rewrites 80.6%

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

   if -9.1999999999999992e134 < a < -2.3999999999999999e-77

   1. Initial program 77.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 62.0%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 51.2%

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

   8. Taylor expanded in z around inf

      \[\leadsto x - \frac{\color{blue}{z} \cdot y}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 60.4%

       \[\leadsto x - \frac{\color{blue}{z} \cdot y}{a} \]

   if -2.3999999999999999e-77 < a < 3.4e28

   1. Initial program 75.0%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot y - y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{a \cdot y - y \cdot z}{t}\right)\right) + x \]

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 79.2

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

   4. Applied rewrites 79.2%

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

   5. Taylor expanded in a around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot z}{t} + x \]

      2. associate-/l* N/A

         \[\leadsto y \cdot \frac{z}{t} + x \]

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 77.6

         \[\leadsto \mathsf{fma}\left(y, \frac{z}{t}, x\right) \]

   7. Applied rewrites 77.6%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{z}{t}}, x\right) \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{z}{t}, x\right) \]

      2. lift-fma.f64 N/A

         \[\leadsto y \cdot \frac{z}{t} + x \]

      3. associate-*r/ N/A

         \[\leadsto \frac{y \cdot z}{t} + x \]

      4. *-commutative N/A

         \[\leadsto \frac{z \cdot y}{t} + x \]

      5. associate-/l* N/A

         \[\leadsto z \cdot \frac{y}{t} + x \]

      6. lower-fma.f64 N/A

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

      7. lift-/.f64 77.7

         \[\leadsto \mathsf{fma}\left(z, \frac{y}{t}, x\right) \]

   9. Applied rewrites 77.7%

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

Alternative 6: 76.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -46000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -46000.0) (+ y x) (if (<= a 3.4e+28) (fma z (/ y t) x) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -46000.0) {
		tmp = y + x;
	} else if (a <= 3.4e+28) {
		tmp = fma(z, (y / t), x);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -46000.0)
		tmp = Float64(y + x);
	elseif (a <= 3.4e+28)
		tmp = fma(z, Float64(y / t), x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -46000.0], N[(y + x), $MachinePrecision], If[LessEqual[a, 3.4e+28], N[(z * N[(y / t), $MachinePrecision] + x), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -46000 or 3.4e28 < a

   1. Initial program 80.0%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 76.6

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

   4. Applied rewrites 76.6%

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

   if -46000 < a < 3.4e28

   1. Initial program 75.0%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot y - y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{a \cdot y - y \cdot z}{t}\right)\right) + x \]

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 77.4

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

   4. Applied rewrites 77.4%

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

   5. Taylor expanded in a around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot z}{t} + x \]

      2. associate-/l* N/A

         \[\leadsto y \cdot \frac{z}{t} + x \]

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 75.5

         \[\leadsto \mathsf{fma}\left(y, \frac{z}{t}, x\right) \]

   7. Applied rewrites 75.5%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{z}{t}}, x\right) \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{z}{t}, x\right) \]

      2. lift-fma.f64 N/A

         \[\leadsto y \cdot \frac{z}{t} + x \]

      3. associate-*r/ N/A

         \[\leadsto \frac{y \cdot z}{t} + x \]

      4. *-commutative N/A

         \[\leadsto \frac{z \cdot y}{t} + x \]

      5. associate-/l* N/A

         \[\leadsto z \cdot \frac{y}{t} + x \]

      6. lower-fma.f64 N/A

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

      7. lift-/.f64 75.6

         \[\leadsto \mathsf{fma}\left(z, \frac{y}{t}, x\right) \]

   9. Applied rewrites 75.6%

      \[\leadsto \mathsf{fma}\left(z, \frac{y}{\color{blue}{t}}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 75.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -46000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -46000.0) (+ y x) (if (<= a 3.4e+28) (fma y (/ z t) x) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -46000.0) {
		tmp = y + x;
	} else if (a <= 3.4e+28) {
		tmp = fma(y, (z / t), x);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -46000.0)
		tmp = Float64(y + x);
	elseif (a <= 3.4e+28)
		tmp = fma(y, Float64(z / t), x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -46000.0], N[(y + x), $MachinePrecision], If[LessEqual[a, 3.4e+28], N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -46000 or 3.4e28 < a

   1. Initial program 80.0%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 76.6

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

   4. Applied rewrites 76.6%

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

   if -46000 < a < 3.4e28

   1. Initial program 75.0%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot y - y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{a \cdot y - y \cdot z}{t}\right)\right) + x \]

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 77.4

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

   4. Applied rewrites 77.4%

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

   5. Taylor expanded in a around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot z}{t} + x \]

      2. associate-/l* N/A

         \[\leadsto y \cdot \frac{z}{t} + x \]

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 75.5

         \[\leadsto \mathsf{fma}\left(y, \frac{z}{t}, x\right) \]

   7. Applied rewrites 75.5%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{z}{t}}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq 10^{+291}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- (+ x y) (/ (* (- z t) y) (- a t))) 1e+291) (+ y x) (* (/ z t) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x + y) - (((z - t) * y) / (a - t))) <= 1e+291) {
		tmp = y + x;
	} else {
		tmp = (z / t) * y;
	}
	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)
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) :: tmp
    if (((x + y) - (((z - t) * y) / (a - t))) <= 1d+291) then
        tmp = y + x
    else
        tmp = (z / t) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x + y) - (((z - t) * y) / (a - t))) <= 1e+291) {
		tmp = y + x;
	} else {
		tmp = (z / t) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((x + y) - (((z - t) * y) / (a - t))) <= 1e+291:
		tmp = y + x
	else:
		tmp = (z / t) * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t))) <= 1e+291)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(z / t) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x + y) - (((z - t) * y) / (a - t))) <= 1e+291)
		tmp = y + x;
	else
		tmp = (z / t) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1e+291], N[(y + x), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.9999999999999996e290

   1. Initial program 81.9%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 64.5

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

   4. Applied rewrites 64.5%

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

   if 9.9999999999999996e290 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 47.1%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a - t}} \]
   3. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(y\right)\right) \cdot z}{a - t} \]

      6. lower-neg.f64 N/A

         \[\leadsto \frac{\left(-y\right) \cdot z}{a - t} \]

      7. lift--.f64 39.4

         \[\leadsto \frac{\left(-y\right) \cdot z}{a - \color{blue}{t}} \]

   4. Applied rewrites 39.4%

      \[\leadsto \color{blue}{\frac{\left(-y\right) \cdot z}{a - t}} \]

   5. Taylor expanded in t around inf

      \[\leadsto \frac{y \cdot z}{\color{blue}{t}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot z}{t} \]

      2. *-commutative N/A

         \[\leadsto \frac{z \cdot y}{t} \]

      3. lift-*.f64 30.7

         \[\leadsto \frac{z \cdot y}{t} \]

   7. Applied rewrites 30.7%

      \[\leadsto \frac{z \cdot y}{\color{blue}{t}} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot y}{t} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z \cdot y}{t} \]

      3. *-commutative N/A

         \[\leadsto \frac{y \cdot z}{t} \]

      4. associate-*r/ N/A

         \[\leadsto y \cdot \frac{z}{\color{blue}{t}} \]

      5. *-commutative N/A

         \[\leadsto \frac{z}{t} \cdot y \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{z}{t} \cdot y \]

      7. lift-/.f64 38.7

         \[\leadsto \frac{z}{t} \cdot y \]

   9. Applied rewrites 38.7%

      \[\leadsto \frac{z}{t} \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq 10^{+291}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- (+ x y) (/ (* (- z t) y) (- a t))) 1e+291) (+ y x) (* z (/ y t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x + y) - (((z - t) * y) / (a - t))) <= 1e+291) {
		tmp = y + x;
	} else {
		tmp = z * (y / t);
	}
	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)
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) :: tmp
    if (((x + y) - (((z - t) * y) / (a - t))) <= 1d+291) then
        tmp = y + x
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x + y) - (((z - t) * y) / (a - t))) <= 1e+291) {
		tmp = y + x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((x + y) - (((z - t) * y) / (a - t))) <= 1e+291:
		tmp = y + x
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t))) <= 1e+291)
		tmp = Float64(y + x);
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x + y) - (((z - t) * y) / (a - t))) <= 1e+291)
		tmp = y + x;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1e+291], N[(y + x), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.9999999999999996e290

   1. Initial program 81.9%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 64.5

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

   4. Applied rewrites 64.5%

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

   if 9.9999999999999996e290 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 47.1%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a - t}} \]
   3. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(y\right)\right) \cdot z}{a - t} \]

      6. lower-neg.f64 N/A

         \[\leadsto \frac{\left(-y\right) \cdot z}{a - t} \]

      7. lift--.f64 39.4

         \[\leadsto \frac{\left(-y\right) \cdot z}{a - \color{blue}{t}} \]

   4. Applied rewrites 39.4%

      \[\leadsto \color{blue}{\frac{\left(-y\right) \cdot z}{a - t}} \]

   5. Taylor expanded in t around inf

      \[\leadsto \frac{y \cdot z}{\color{blue}{t}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot z}{t} \]

      2. *-commutative N/A

         \[\leadsto \frac{z \cdot y}{t} \]

      3. lift-*.f64 30.7

         \[\leadsto \frac{z \cdot y}{t} \]

   7. Applied rewrites 30.7%

      \[\leadsto \frac{z \cdot y}{\color{blue}{t}} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot y}{t} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z \cdot y}{t} \]

      3. associate-/l* N/A

         \[\leadsto z \cdot \frac{y}{\color{blue}{t}} \]

      4. lower-*.f64 N/A

         \[\leadsto z \cdot \frac{y}{\color{blue}{t}} \]

      5. lift-/.f64 39.1

         \[\leadsto z \cdot \frac{y}{t} \]

   9. Applied rewrites 39.1%

      \[\leadsto z \cdot \frac{y}{\color{blue}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 61.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+134}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.2e+134) (+ y x) (if (<= a 7.8e-140) x (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.2e+134) {
		tmp = y + x;
	} else if (a <= 7.8e-140) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	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)
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) :: tmp
    if (a <= (-9.2d+134)) then
        tmp = y + x
    else if (a <= 7.8d-140) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.2e+134) {
		tmp = y + x;
	} else if (a <= 7.8e-140) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.2e+134:
		tmp = y + x
	elif a <= 7.8e-140:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.2e+134)
		tmp = Float64(y + x);
	elseif (a <= 7.8e-140)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.2e+134)
		tmp = y + x;
	elseif (a <= 7.8e-140)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.2e+134], N[(y + x), $MachinePrecision], If[LessEqual[a, 7.8e-140], x, N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -9.1999999999999992e134 or 7.80000000000000038e-140 < a

   1. Initial program 79.8%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 72.4

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

   4. Applied rewrites 72.4%

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

   if -9.1999999999999992e134 < a < 7.80000000000000038e-140

   1. Initial program 75.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 49.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 50.1% accurate, 17.9× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

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

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)
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
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 77.4%

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

2. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
3. Step-by-step derivation

4. Applied rewrites 50.1%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025119 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64
  (- (+ x y) (/ (* (- z t) y) (- a t))))