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

Percentage Accurate: 77.9% → 93.7%

Time: 7.6s

Alternatives: 12

Speedup: 1.1×

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: 77.9% 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: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}, y, x\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (fma (- (+ (/ t (- a t)) 1.0) (/ z (- a t))) y x))

C

double code(double x, double y, double z, double t, double a) {
	return fma((((t / (a - t)) + 1.0) - (z / (a - t))), y, x);
}

Julia

function code(x, y, z, t, a)
	return fma(Float64(Float64(Float64(t / Float64(a - t)) + 1.0) - Float64(z / Float64(a - t))), y, x)
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]

Derivation

1. Initial program 74.9%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lower--.f64 N/A

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

   5. +-commutative N/A

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

   6. lower-+.f64 N/A

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

   7. lower-/.f64 N/A

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

   8. lower--.f64 N/A

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

   9. lower-/.f64 N/A

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

   10. lower--.f64 94.3

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

5. Applied rewrites 94.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}, y, x\right)} \]
6. Add Preprocessing

Alternative 2: 65.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-283}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_1 -1e-283)
     (+ y x)
     (if (<= t_1 0.0) x (if (<= t_1 5e+301) (+ y x) (* (/ z t) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -1e-283) {
		tmp = y + x;
	} else if (t_1 <= 0.0) {
		tmp = x;
	} else if (t_1 <= 5e+301) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - (((z - t) * y) / (a - t))
    if (t_1 <= (-1d-283)) then
        tmp = y + x
    else if (t_1 <= 0.0d0) then
        tmp = x
    else if (t_1 <= 5d+301) 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 t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -1e-283) {
		tmp = y + x;
	} else if (t_1 <= 0.0) {
		tmp = x;
	} else if (t_1 <= 5e+301) {
		tmp = y + x;
	} else {
		tmp = (z / t) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_1 <= -1e-283:
		tmp = y + x
	elif t_1 <= 0.0:
		tmp = x
	elif t_1 <= 5e+301:
		tmp = y + x
	else:
		tmp = (z / t) * y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -1e-283)
		tmp = Float64(y + x);
	elseif (t_1 <= 0.0)
		tmp = x;
	elseif (t_1 <= 5e+301)
		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)
	t_1 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_1 <= -1e-283)
		tmp = y + x;
	elseif (t_1 <= 0.0)
		tmp = x;
	elseif (t_1 <= 5e+301)
		tmp = y + x;
	else
		tmp = (z / t) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-283], N[(y + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], x, If[LessEqual[t$95$1, 5e+301], N[(y + x), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -9.99999999999999947e-284 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 5.0000000000000004e301

   1. Initial program 87.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 95.3

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

   5. Applied rewrites 95.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 78.3%

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

   9. Taylor expanded in a around inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 74.0

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

   11. Applied rewrites 74.0%

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

   if -9.99999999999999947e-284 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 4.4%

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

   3. Taylor expanded in a around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 4.4

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

   5. Applied rewrites 4.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 66.2%

      \[\leadsto \mathsf{fma}\left(0, \color{blue}{y}, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 66.2%

       \[\leadsto x \]

   if 5.0000000000000004e301 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 42.4%

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

   3. Taylor expanded in a around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 47.6

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

   5. Applied rewrites 47.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 38.5%

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

   10. Applied rewrites 53.0%

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

Alternative 3: 65.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-283}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_1 -1e-283)
     (+ y x)
     (if (<= t_1 0.0) x (if (<= t_1 5e+301) (+ y x) (* z (/ y t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -1e-283) {
		tmp = y + x;
	} else if (t_1 <= 0.0) {
		tmp = x;
	} else if (t_1 <= 5e+301) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - (((z - t) * y) / (a - t))
    if (t_1 <= (-1d-283)) then
        tmp = y + x
    else if (t_1 <= 0.0d0) then
        tmp = x
    else if (t_1 <= 5d+301) 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 t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -1e-283) {
		tmp = y + x;
	} else if (t_1 <= 0.0) {
		tmp = x;
	} else if (t_1 <= 5e+301) {
		tmp = y + x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_1 <= -1e-283:
		tmp = y + x
	elif t_1 <= 0.0:
		tmp = x
	elif t_1 <= 5e+301:
		tmp = y + x
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -1e-283)
		tmp = Float64(y + x);
	elseif (t_1 <= 0.0)
		tmp = x;
	elseif (t_1 <= 5e+301)
		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)
	t_1 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_1 <= -1e-283)
		tmp = y + x;
	elseif (t_1 <= 0.0)
		tmp = x;
	elseif (t_1 <= 5e+301)
		tmp = y + x;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-283], N[(y + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], x, If[LessEqual[t$95$1, 5e+301], N[(y + x), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -9.99999999999999947e-284 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 5.0000000000000004e301

   1. Initial program 87.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 95.3

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

   5. Applied rewrites 95.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 78.3%

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

   9. Taylor expanded in a around inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 74.0

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

   11. Applied rewrites 74.0%

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

   if -9.99999999999999947e-284 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 4.4%

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

   3. Taylor expanded in a around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 4.4

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

   5. Applied rewrites 4.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 66.2%

      \[\leadsto \mathsf{fma}\left(0, \color{blue}{y}, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 66.2%

       \[\leadsto x \]

   if 5.0000000000000004e301 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 42.4%

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

   3. Taylor expanded in a around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 47.6

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

   5. Applied rewrites 47.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 38.5%

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

   10. Applied rewrites 53.0%

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

Alternative 4: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-141} \lor \neg \left(a \leq 7 \cdot 10^{-96}\right):\\ \;\;\;\;\left(x + y\right) - \frac{z}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.8e-141) (not (<= a 7e-96)))
   (- (+ x y) (* (/ z (- a t)) y))
   (- x (/ (* y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-141) || !(a <= 7e-96)) {
		tmp = (x + y) - ((z / (a - t)) * y);
	} else {
		tmp = x - ((y * (a - z)) / 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 ((a <= (-4.8d-141)) .or. (.not. (a <= 7d-96))) then
        tmp = (x + y) - ((z / (a - t)) * y)
    else
        tmp = x - ((y * (a - z)) / 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 ((a <= -4.8e-141) || !(a <= 7e-96)) {
		tmp = (x + y) - ((z / (a - t)) * y);
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.8e-141) or not (a <= 7e-96):
		tmp = (x + y) - ((z / (a - t)) * y)
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.8e-141) || !(a <= 7e-96))
		tmp = Float64(Float64(x + y) - Float64(Float64(z / Float64(a - t)) * y));
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.8e-141) || ~((a <= 7e-96)))
		tmp = (x + y) - ((z / (a - t)) * y);
	else
		tmp = x - ((y * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.8e-141], N[Not[LessEqual[a, 7e-96]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.8000000000000002e-141 or 6.9999999999999998e-96 < a

   1. Initial program 75.8%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 89.5

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

   5. Applied rewrites 89.5%

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

   if -4.8000000000000002e-141 < a < 6.9999999999999998e-96

   1. Initial program 73.1%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. +-commutative N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

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

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

      12. distribute-lft-out-- N/A

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

      13. mul-1-neg N/A

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

      14. distribute-neg-frac N/A

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

      15. fp-cancel-sub-sign N/A

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

   5. Applied rewrites 90.8%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-141} \lor \neg \left(a \leq 7 \cdot 10^{-96}\right):\\ \;\;\;\;\left(x + y\right) - \frac{z}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+115} \lor \neg \left(a \leq 2.6 \cdot 10^{-49}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a - z}{-t}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.5e+115) (not (<= a 2.6e-49)))
   (fma (- 1.0 (/ z a)) y x)
   (fma (/ (- a z) (- t)) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.5e+115) || !(a <= 2.6e-49)) {
		tmp = fma((1.0 - (z / a)), y, x);
	} else {
		tmp = fma(((a - z) / -t), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.5e+115) || !(a <= 2.6e-49))
		tmp = fma(Float64(1.0 - Float64(z / a)), y, x);
	else
		tmp = fma(Float64(Float64(a - z) / Float64(-t)), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.5e+115], N[Not[LessEqual[a, 2.6e-49]], $MachinePrecision]], N[(N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(N[(a - z), $MachinePrecision] / (-t)), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.50000000000000005e115 or 2.59999999999999995e-49 < a

   1. Initial program 76.5%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 96.6

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

   5. Applied rewrites 96.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 93.5%

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

   if -3.50000000000000005e115 < a < 2.59999999999999995e-49

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 92.5

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

   5. Applied rewrites 92.5%

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

   6. Taylor expanded in t around -inf

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

   8. Applied rewrites 83.2%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+115} \lor \neg \left(a \leq 2.6 \cdot 10^{-49}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a - z}{-t}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-95} \lor \neg \left(a \leq 1.35 \cdot 10^{-49}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3e-95) (not (<= a 1.35e-49)))
   (fma (- 1.0 (/ z a)) y x)
   (- x (/ (* y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3e-95) || !(a <= 1.35e-49)) {
		tmp = fma((1.0 - (z / a)), y, x);
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3e-95) || !(a <= 1.35e-49))
		tmp = fma(Float64(1.0 - Float64(z / a)), y, x);
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3e-95], N[Not[LessEqual[a, 1.35e-49]], $MachinePrecision]], N[(N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3e-95 or 1.35e-49 < a

   1. Initial program 75.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 95.2

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

   5. Applied rewrites 95.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 86.8%

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

   if -3e-95 < a < 1.35e-49

   1. Initial program 74.3%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. +-commutative N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

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

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

      12. distribute-lft-out-- N/A

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

      13. mul-1-neg N/A

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

      14. distribute-neg-frac N/A

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

      15. fp-cancel-sub-sign N/A

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

   5. Applied rewrites 89.3%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-95} \lor \neg \left(a \leq 1.35 \cdot 10^{-49}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{a}, y, x\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-49}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a - z}{-t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.5e+115)
   (fma (- 1.0 (/ z a)) y x)
   (if (<= a 1.35e-49) (fma (/ (- a z) (- t)) y x) (- (+ x y) (* (/ y a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+115) {
		tmp = fma((1.0 - (z / a)), y, x);
	} else if (a <= 1.35e-49) {
		tmp = fma(((a - z) / -t), y, x);
	} else {
		tmp = (x + y) - ((y / a) * z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.5e+115)
		tmp = fma(Float64(1.0 - Float64(z / a)), y, x);
	elseif (a <= 1.35e-49)
		tmp = fma(Float64(Float64(a - z) / Float64(-t)), y, x);
	else
		tmp = Float64(Float64(x + y) - Float64(Float64(y / a) * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.5e+115], N[(N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[a, 1.35e-49], N[(N[(N[(a - z), $MachinePrecision] / (-t)), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.50000000000000005e115

   1. Initial program 72.2%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 96.0

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

   5. Applied rewrites 96.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 96.1%

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

   if -3.50000000000000005e115 < a < 1.35e-49

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 92.5

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

   5. Applied rewrites 92.5%

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

   6. Taylor expanded in t around -inf

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

   8. Applied rewrites 83.2%

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

   if 1.35e-49 < a

   1. Initial program 79.7%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 82.9

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

   5. Applied rewrites 82.9%

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

   7. Applied rewrites 93.0%

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

Alternative 8: 81.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-114} \lor \neg \left(a \leq 2.45 \cdot 10^{-49}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.05e-114) (not (<= a 2.45e-49)))
   (fma (- 1.0 (/ z a)) y x)
   (fma y (/ z t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.05e-114) || !(a <= 2.45e-49)) {
		tmp = fma((1.0 - (z / a)), y, x);
	} else {
		tmp = fma(y, (z / t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.05e-114) || !(a <= 2.45e-49))
		tmp = fma(Float64(1.0 - Float64(z / a)), y, x);
	else
		tmp = fma(y, Float64(z / t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.05e-114], N[Not[LessEqual[a, 2.45e-49]], $MachinePrecision]], N[(N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.04999999999999996e-114 or 2.4500000000000001e-49 < a

   1. Initial program 75.2%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 94.8

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

   5. Applied rewrites 94.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 86.4%

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

   if -1.04999999999999996e-114 < a < 2.4500000000000001e-49

   1. Initial program 74.5%

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

   3. Taylor expanded in a around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 68.2

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

   5. Applied rewrites 68.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 88.1%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-114} \lor \neg \left(a \leq 2.45 \cdot 10^{-49}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+42} \lor \neg \left(a \leq 6.5 \cdot 10^{-46}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.8e+42) (not (<= a 6.5e-46))) (+ y x) (fma y (/ z t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e+42) || !(a <= 6.5e-46)) {
		tmp = y + x;
	} else {
		tmp = fma(y, (z / t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.8e+42) || !(a <= 6.5e-46))
		tmp = Float64(y + x);
	else
		tmp = fma(y, Float64(z / t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.8e+42], N[Not[LessEqual[a, 6.5e-46]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.7999999999999999e42 or 6.49999999999999966e-46 < a

   1. Initial program 74.6%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 95.5

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

   5. Applied rewrites 95.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 81.4%

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

   9. Taylor expanded in a around inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 79.6

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

   11. Applied rewrites 79.6%

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

   if -2.7999999999999999e42 < a < 6.49999999999999966e-46

   1. Initial program 75.2%

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

   3. Taylor expanded in a around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 66.4

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

   5. Applied rewrites 66.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 83.6%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+42} \lor \neg \left(a \leq 6.5 \cdot 10^{-46}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(1 - \frac{z - t}{a - t}, y, x\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (fma (- 1.0 (/ (- z t) (- a t))) y x))

C

double code(double x, double y, double z, double t, double a) {
	return fma((1.0 - ((z - t) / (a - t))), y, x);
}

Julia

function code(x, y, z, t, a)
	return fma(Float64(1.0 - Float64(Float64(z - t) / Float64(a - t))), y, x)
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(1.0 - N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]

Derivation

1. Initial program 74.9%

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

3. Taylor expanded in x around 0

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

   1. associate--l+ N/A

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

   2. +-commutative N/A

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

   3. *-lft-identity N/A

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

   4. associate-/l* N/A

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

   5. *-commutative N/A

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

   6. fp-cancel-sub-sign N/A

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

   7. mul-1-neg N/A

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

   8. distribute-rgt-in N/A

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

   9. *-commutative N/A

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

   10. lower-fma.f64 N/A

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

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

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

   12. metadata-eval N/A

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

   13. *-lft-identity N/A

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

   14. lower--.f64 N/A

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

   15. lower-/.f64 N/A

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

   16. lower--.f64 N/A

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

   17. lower--.f64 91.0

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

5. Applied rewrites 91.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(1 - \frac{z - t}{a - t}, y, x\right)} \]
6. Add Preprocessing

Alternative 11: 64.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -16000 \lor \neg \left(a \leq 7.6 \cdot 10^{-48}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -16000.0) (not (<= a 7.6e-48))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -16000.0) || !(a <= 7.6e-48)) {
		tmp = y + x;
	} else {
		tmp = 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 <= (-16000.0d0)) .or. (.not. (a <= 7.6d-48))) then
        tmp = y + x
    else
        tmp = 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 <= -16000.0) || !(a <= 7.6e-48)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -16000.0) or not (a <= 7.6e-48):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -16000.0) || !(a <= 7.6e-48))
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -16000.0) || ~((a <= 7.6e-48)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -16000.0], N[Not[LessEqual[a, 7.6e-48]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -16000 or 7.60000000000000005e-48 < a

   1. Initial program 74.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 95.6

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

   5. Applied rewrites 95.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 81.2%

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

   9. Taylor expanded in a around inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 78.7

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

   11. Applied rewrites 78.7%

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

   if -16000 < a < 7.60000000000000005e-48

   1. Initial program 75.1%

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

   3. Taylor expanded in a around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 66.9

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

   5. Applied rewrites 66.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 56.5%

      \[\leadsto \mathsf{fma}\left(0, \color{blue}{y}, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 56.5%

       \[\leadsto x \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -16000 \lor \neg \left(a \leq 7.6 \cdot 10^{-48}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.6% accurate, 29.0× 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 74.9%

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

3. Taylor expanded in a around 0

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

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

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

   2. +-commutative N/A

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

   3. metadata-eval N/A

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

   4. *-lft-identity N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 N/A

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

   9. lower--.f64 N/A

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

   10. +-commutative N/A

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

   11. lower-+.f64 50.7

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

5. Applied rewrites 50.7%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 49.2%

   \[\leadsto \mathsf{fma}\left(0, \color{blue}{y}, x\right) \]
9. Step-by-step derivation

10. Applied rewrites 49.2%

    \[\leadsto x \]
11. Add Preprocessing

Developer Target 1: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (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) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (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 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024363 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -13664970889390727/100000000000000000000000) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 14754293444577233/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)))))

  (- (+ x y) (/ (* (- z t) y) (- a t))))