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

Percentage Accurate: 98.0% → 98.0%

Time: 5.7s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

   \[x + y \cdot \frac{z - t}{a - t} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 80.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \frac{z}{a - t} \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{t}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-111}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-6}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+40}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* (/ z (- a t)) y)))
   (if (<= t_1 -1e+123)
     t_2
     (if (<= t_1 -4e+21)
       (fma (/ (- z) t) y x)
       (if (<= t_1 4e-111)
         (fma (/ z a) y x)
         (if (<= t_1 1e-6)
           (* (- z t) (/ y a))
           (if (<= t_1 2e+40) (+ y x) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (z / (a - t)) * y;
	double tmp;
	if (t_1 <= -1e+123) {
		tmp = t_2;
	} else if (t_1 <= -4e+21) {
		tmp = fma((-z / t), y, x);
	} else if (t_1 <= 4e-111) {
		tmp = fma((z / a), y, x);
	} else if (t_1 <= 1e-6) {
		tmp = (z - t) * (y / a);
	} else if (t_1 <= 2e+40) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(Float64(z / Float64(a - t)) * y)
	tmp = 0.0
	if (t_1 <= -1e+123)
		tmp = t_2;
	elseif (t_1 <= -4e+21)
		tmp = fma(Float64(Float64(-z) / t), y, x);
	elseif (t_1 <= 4e-111)
		tmp = fma(Float64(z / a), y, x);
	elseif (t_1 <= 1e-6)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	elseif (t_1 <= 2e+40)
		tmp = Float64(y + x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+123], t$95$2, If[LessEqual[t$95$1, -4e+21], N[(N[((-z) / t), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 4e-111], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 1e-6], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+40], N[(y + x), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -9.99999999999999978e122 or 2.00000000000000006e40 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 77.5

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

   5. Applied rewrites 77.5%

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

   if -9.99999999999999978e122 < (/.f64 (-.f64 z t) (-.f64 a t)) < -4e21

   1. Initial program 99.5%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

   5. Applied rewrites 87.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 87.2%

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

   if -4e21 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4.00000000000000035e-111

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 91.4

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

   5. Applied rewrites 91.4%

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

   if 4.00000000000000035e-111 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999955e-7

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 78.2

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

   5. Applied rewrites 78.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.6%

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

   if 9.99999999999999955e-7 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2.00000000000000006e40

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 94.3

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

   5. Applied rewrites 94.3%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -1 \cdot 10^{+123}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq -4 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{t}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{-111}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 10^{-6}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 2 \cdot 10^{+40}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{t}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+184}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* (- z t) (/ y (- a t)))))
   (if (<= t_1 -1e+123)
     t_2
     (if (<= t_1 -4e+21)
       (fma (/ (- z) t) y x)
       (if (<= t_1 1e-6)
         (fma y (/ (- z t) a) x)
         (if (<= t_1 5e+184) (+ x (* y (- 1.0 (/ z t)))) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (z - t) * (y / (a - t));
	double tmp;
	if (t_1 <= -1e+123) {
		tmp = t_2;
	} else if (t_1 <= -4e+21) {
		tmp = fma((-z / t), y, x);
	} else if (t_1 <= 1e-6) {
		tmp = fma(y, ((z - t) / a), x);
	} else if (t_1 <= 5e+184) {
		tmp = x + (y * (1.0 - (z / t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(Float64(z - t) * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -1e+123)
		tmp = t_2;
	elseif (t_1 <= -4e+21)
		tmp = fma(Float64(Float64(-z) / t), y, x);
	elseif (t_1 <= 1e-6)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	elseif (t_1 <= 5e+184)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / t))));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+123], t$95$2, If[LessEqual[t$95$1, -4e+21], N[(N[((-z) / t), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 1e-6], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 5e+184], N[(x + N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -9.99999999999999978e122 or 4.9999999999999999e184 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 90.3

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

   5. Applied rewrites 90.3%

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

   if -9.99999999999999978e122 < (/.f64 (-.f64 z t) (-.f64 a t)) < -4e21

   1. Initial program 99.5%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

   5. Applied rewrites 87.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 87.2%

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

   if -4e21 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999955e-7

   1. Initial program 98.8%

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

   3. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   5. Applied rewrites 85.3%

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

   6. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 98.6

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

   8. Applied rewrites 98.6%

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

   if 9.99999999999999955e-7 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4.9999999999999999e184

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. *-lft-identity N/A

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

      4. metadata-eval N/A

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

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

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. distribute-lft-neg-out N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. mul-1-neg N/A

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

      14. div-add-rev N/A

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

      15. *-inverses N/A

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

      16. associate-*r/ N/A

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

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

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. lower--.f64 N/A

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

      21. lower-/.f64 92.0

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

   5. Applied rewrites 92.0%

      \[\leadsto x + y \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -1 \cdot 10^{+123}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq -4 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{t}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 5 \cdot 10^{+184}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{t}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+184}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* (- z t) (/ y (- a t)))))
   (if (<= t_1 -1e+123)
     t_2
     (if (<= t_1 -4e+21)
       (fma (/ (- z) t) y x)
       (if (<= t_1 1e-6)
         (fma y (/ (- z t) a) x)
         (if (<= t_1 5e+184) (fma (- 1.0 (/ z t)) y x) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (z - t) * (y / (a - t));
	double tmp;
	if (t_1 <= -1e+123) {
		tmp = t_2;
	} else if (t_1 <= -4e+21) {
		tmp = fma((-z / t), y, x);
	} else if (t_1 <= 1e-6) {
		tmp = fma(y, ((z - t) / a), x);
	} else if (t_1 <= 5e+184) {
		tmp = fma((1.0 - (z / t)), y, x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(Float64(z - t) * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -1e+123)
		tmp = t_2;
	elseif (t_1 <= -4e+21)
		tmp = fma(Float64(Float64(-z) / t), y, x);
	elseif (t_1 <= 1e-6)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	elseif (t_1 <= 5e+184)
		tmp = fma(Float64(1.0 - Float64(z / t)), y, x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+123], t$95$2, If[LessEqual[t$95$1, -4e+21], N[(N[((-z) / t), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 1e-6], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 5e+184], N[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -9.99999999999999978e122 or 4.9999999999999999e184 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 90.3

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

   5. Applied rewrites 90.3%

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

   if -9.99999999999999978e122 < (/.f64 (-.f64 z t) (-.f64 a t)) < -4e21

   1. Initial program 99.5%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

   5. Applied rewrites 87.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 87.2%

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

   if -4e21 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999955e-7

   1. Initial program 98.8%

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

   3. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   5. Applied rewrites 85.3%

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

   6. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 98.6

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

   8. Applied rewrites 98.6%

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

   if 9.99999999999999955e-7 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4.9999999999999999e184

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

   5. Applied rewrites 92.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - \frac{z}{t}, y, x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -1 \cdot 10^{+123}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq -4 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{t}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 5 \cdot 10^{+184}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \frac{z}{a - t} \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{t}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+184}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* (/ z (- a t)) y)))
   (if (<= t_1 -1e+123)
     t_2
     (if (<= t_1 -4e+21)
       (fma (/ (- z) t) y x)
       (if (<= t_1 1e-6)
         (fma y (/ (- z t) a) x)
         (if (<= t_1 5e+184) (fma (- 1.0 (/ z t)) y x) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (z / (a - t)) * y;
	double tmp;
	if (t_1 <= -1e+123) {
		tmp = t_2;
	} else if (t_1 <= -4e+21) {
		tmp = fma((-z / t), y, x);
	} else if (t_1 <= 1e-6) {
		tmp = fma(y, ((z - t) / a), x);
	} else if (t_1 <= 5e+184) {
		tmp = fma((1.0 - (z / t)), y, x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(Float64(z / Float64(a - t)) * y)
	tmp = 0.0
	if (t_1 <= -1e+123)
		tmp = t_2;
	elseif (t_1 <= -4e+21)
		tmp = fma(Float64(Float64(-z) / t), y, x);
	elseif (t_1 <= 1e-6)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	elseif (t_1 <= 5e+184)
		tmp = fma(Float64(1.0 - Float64(z / t)), y, x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+123], t$95$2, If[LessEqual[t$95$1, -4e+21], N[(N[((-z) / t), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 1e-6], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 5e+184], N[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -9.99999999999999978e122 or 4.9999999999999999e184 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 96.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 87.4

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

   5. Applied rewrites 87.4%

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

   if -9.99999999999999978e122 < (/.f64 (-.f64 z t) (-.f64 a t)) < -4e21

   1. Initial program 99.5%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

   5. Applied rewrites 87.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 87.2%

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

   if -4e21 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999955e-7

   1. Initial program 98.8%

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

   3. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   5. Applied rewrites 85.3%

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

   6. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 98.6

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

   8. Applied rewrites 98.6%

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

   if 9.99999999999999955e-7 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4.9999999999999999e184

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

   5. Applied rewrites 92.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - \frac{z}{t}, y, x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -1 \cdot 10^{+123}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq -4 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{t}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 5 \cdot 10^{+184}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \frac{z}{a - t} \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{t}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+40}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* (/ z (- a t)) y)))
   (if (<= t_1 -1e+123)
     t_2
     (if (<= t_1 -4e+21)
       (fma (/ (- z) t) y x)
       (if (<= t_1 1e-6)
         (fma y (/ (- z t) a) x)
         (if (<= t_1 2e+40) (+ y x) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (z / (a - t)) * y;
	double tmp;
	if (t_1 <= -1e+123) {
		tmp = t_2;
	} else if (t_1 <= -4e+21) {
		tmp = fma((-z / t), y, x);
	} else if (t_1 <= 1e-6) {
		tmp = fma(y, ((z - t) / a), x);
	} else if (t_1 <= 2e+40) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(Float64(z / Float64(a - t)) * y)
	tmp = 0.0
	if (t_1 <= -1e+123)
		tmp = t_2;
	elseif (t_1 <= -4e+21)
		tmp = fma(Float64(Float64(-z) / t), y, x);
	elseif (t_1 <= 1e-6)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	elseif (t_1 <= 2e+40)
		tmp = Float64(y + x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+123], t$95$2, If[LessEqual[t$95$1, -4e+21], N[(N[((-z) / t), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 1e-6], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2e+40], N[(y + x), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -9.99999999999999978e122 or 2.00000000000000006e40 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 77.5

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

   5. Applied rewrites 77.5%

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

   if -9.99999999999999978e122 < (/.f64 (-.f64 z t) (-.f64 a t)) < -4e21

   1. Initial program 99.5%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

   5. Applied rewrites 87.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 87.2%

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

   if -4e21 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999955e-7

   1. Initial program 98.8%

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

   3. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   5. Applied rewrites 85.3%

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

   6. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 98.6

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

   8. Applied rewrites 98.6%

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

   if 9.99999999999999955e-7 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2.00000000000000006e40

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 94.3

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

   5. Applied rewrites 94.3%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -1 \cdot 10^{+123}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq -4 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{t}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 2 \cdot 10^{+40}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \frac{z}{a - t} \cdot y\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-111}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-6}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+40}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* (/ z (- a t)) y)))
   (if (<= t_1 -4e+21)
     t_2
     (if (<= t_1 4e-111)
       (fma (/ z a) y x)
       (if (<= t_1 1e-6)
         (* (- z t) (/ y a))
         (if (<= t_1 2e+40) (+ y x) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (z / (a - t)) * y;
	double tmp;
	if (t_1 <= -4e+21) {
		tmp = t_2;
	} else if (t_1 <= 4e-111) {
		tmp = fma((z / a), y, x);
	} else if (t_1 <= 1e-6) {
		tmp = (z - t) * (y / a);
	} else if (t_1 <= 2e+40) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(Float64(z / Float64(a - t)) * y)
	tmp = 0.0
	if (t_1 <= -4e+21)
		tmp = t_2;
	elseif (t_1 <= 4e-111)
		tmp = fma(Float64(z / a), y, x);
	elseif (t_1 <= 1e-6)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	elseif (t_1 <= 2e+40)
		tmp = Float64(y + x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+21], t$95$2, If[LessEqual[t$95$1, 4e-111], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 1e-6], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+40], N[(y + x), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -4e21 or 2.00000000000000006e40 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 72.7

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

   5. Applied rewrites 72.7%

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

   if -4e21 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4.00000000000000035e-111

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 91.4

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

   5. Applied rewrites 91.4%

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

   if 4.00000000000000035e-111 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999955e-7

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 78.2

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

   5. Applied rewrites 78.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.6%

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

   if 9.99999999999999955e-7 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2.00000000000000006e40

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 94.3

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

   5. Applied rewrites 94.3%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -4 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{-111}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 10^{-6}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 2 \cdot 10^{+40}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{-111}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-6}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t\_1 \leq 5000000000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 4e-111)
     (fma (/ z a) y x)
     (if (<= t_1 1e-6)
       (* (- z t) (/ y a))
       (if (<= t_1 5000000000000.0) (+ y x) (fma z (/ y a) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 4e-111) {
		tmp = fma((z / a), y, x);
	} else if (t_1 <= 1e-6) {
		tmp = (z - t) * (y / a);
	} else if (t_1 <= 5000000000000.0) {
		tmp = y + x;
	} else {
		tmp = fma(z, (y / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= 4e-111)
		tmp = fma(Float64(z / a), y, x);
	elseif (t_1 <= 1e-6)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	elseif (t_1 <= 5000000000000.0)
		tmp = Float64(y + x);
	else
		tmp = fma(z, Float64(y / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e-111], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 1e-6], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5000000000000.0], N[(y + x), $MachinePrecision], N[(z * N[(y / a), $MachinePrecision] + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 4.00000000000000035e-111

   1. Initial program 98.1%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 76.2

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

   5. Applied rewrites 76.2%

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

   if 4.00000000000000035e-111 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999955e-7

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 78.2

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

   5. Applied rewrites 78.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.6%

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

   if 9.99999999999999955e-7 < (/.f64 (-.f64 z t) (-.f64 a t)) < 5e12

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 95.9

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

   5. Applied rewrites 95.9%

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

   if 5e12 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 93.4

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

   4. Applied rewrites 93.4%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 54.5

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

   7. Applied rewrites 54.5%

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

   9. Applied rewrites 54.6%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{-111}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 10^{-6}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 5000000000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+117}:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-111}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+184}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 -5e+117)
     (* (/ z a) y)
     (if (<= t_1 4e-111)
       (* (- x) -1.0)
       (if (<= t_1 5e+184) (+ y x) (/ (* y z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e+117) {
		tmp = (z / a) * y;
	} else if (t_1 <= 4e-111) {
		tmp = -x * -1.0;
	} else if (t_1 <= 5e+184) {
		tmp = y + x;
	} else {
		tmp = (y * z) / a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if (t_1 <= (-5d+117)) then
        tmp = (z / a) * y
    else if (t_1 <= 4d-111) then
        tmp = -x * (-1.0d0)
    else if (t_1 <= 5d+184) then
        tmp = y + x
    else
        tmp = (y * z) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e+117) {
		tmp = (z / a) * y;
	} else if (t_1 <= 4e-111) {
		tmp = -x * -1.0;
	} else if (t_1 <= 5e+184) {
		tmp = y + x;
	} else {
		tmp = (y * z) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= -5e+117:
		tmp = (z / a) * y
	elif t_1 <= 4e-111:
		tmp = -x * -1.0
	elif t_1 <= 5e+184:
		tmp = y + x
	else:
		tmp = (y * z) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -5e+117)
		tmp = Float64(Float64(z / a) * y);
	elseif (t_1 <= 4e-111)
		tmp = Float64(Float64(-x) * -1.0);
	elseif (t_1 <= 5e+184)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(y * z) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= -5e+117)
		tmp = (z / a) * y;
	elseif (t_1 <= 4e-111)
		tmp = -x * -1.0;
	elseif (t_1 <= 5e+184)
		tmp = y + x;
	else
		tmp = (y * z) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+117], N[(N[(z / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 4e-111], N[((-x) * -1.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+184], N[(y + x), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -4.99999999999999983e117

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 81.5

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

   5. Applied rewrites 81.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 63.1%

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

   if -4.99999999999999983e117 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4.00000000000000035e-111

   1. Initial program 98.8%

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

   3. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   5. Applied rewrites 92.2%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(-x\right) \cdot -1 \]
   7. Step-by-step derivation

   8. Applied rewrites 70.4%

      \[\leadsto \left(-x\right) \cdot -1 \]

   if 4.00000000000000035e-111 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4.9999999999999999e184

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 75.9

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

   5. Applied rewrites 75.9%

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

   if 4.9999999999999999e184 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 99.7%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 87.6

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

   4. Applied rewrites 87.6%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 64.1

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

   7. Applied rewrites 64.1%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 64.4%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -5 \cdot 10^{+117}:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{-111}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 5 \cdot 10^{+184}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \frac{z}{a} \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+117}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-111}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+184}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* (/ z a) y)))
   (if (<= t_1 -5e+117)
     t_2
     (if (<= t_1 4e-111) (* (- x) -1.0) (if (<= t_1 5e+184) (+ y x) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (z / a) * y;
	double tmp;
	if (t_1 <= -5e+117) {
		tmp = t_2;
	} else if (t_1 <= 4e-111) {
		tmp = -x * -1.0;
	} else if (t_1 <= 5e+184) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
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 = (z - t) / (a - t)
    t_2 = (z / a) * y
    if (t_1 <= (-5d+117)) then
        tmp = t_2
    else if (t_1 <= 4d-111) then
        tmp = -x * (-1.0d0)
    else if (t_1 <= 5d+184) then
        tmp = y + x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (z / a) * y;
	double tmp;
	if (t_1 <= -5e+117) {
		tmp = t_2;
	} else if (t_1 <= 4e-111) {
		tmp = -x * -1.0;
	} else if (t_1 <= 5e+184) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	t_2 = (z / a) * y
	tmp = 0
	if t_1 <= -5e+117:
		tmp = t_2
	elif t_1 <= 4e-111:
		tmp = -x * -1.0
	elif t_1 <= 5e+184:
		tmp = y + x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(Float64(z / a) * y)
	tmp = 0.0
	if (t_1 <= -5e+117)
		tmp = t_2;
	elseif (t_1 <= 4e-111)
		tmp = Float64(Float64(-x) * -1.0);
	elseif (t_1 <= 5e+184)
		tmp = Float64(y + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	t_2 = (z / a) * y;
	tmp = 0.0;
	if (t_1 <= -5e+117)
		tmp = t_2;
	elseif (t_1 <= 4e-111)
		tmp = -x * -1.0;
	elseif (t_1 <= 5e+184)
		tmp = y + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / a), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+117], t$95$2, If[LessEqual[t$95$1, 4e-111], N[((-x) * -1.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+184], N[(y + x), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -4.99999999999999983e117 or 4.9999999999999999e184 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 87.8

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

   5. Applied rewrites 87.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 63.5%

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

   if -4.99999999999999983e117 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4.00000000000000035e-111

   1. Initial program 98.8%

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

   3. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   5. Applied rewrites 92.2%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(-x\right) \cdot -1 \]
   7. Step-by-step derivation

   8. Applied rewrites 70.4%

      \[\leadsto \left(-x\right) \cdot -1 \]

   if 4.00000000000000035e-111 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4.9999999999999999e184

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 75.9

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

   5. Applied rewrites 75.9%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -5 \cdot 10^{+117}:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{-111}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 5 \cdot 10^{+184}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 10^{-6} \lor \neg \left(t\_1 \leq 5000000000000\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (or (<= t_1 1e-6) (not (<= t_1 5000000000000.0)))
     (fma (/ z a) y x)
     (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if ((t_1 <= 1e-6) || !(t_1 <= 5000000000000.0)) {
		tmp = fma((z / a), y, x);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if ((t_1 <= 1e-6) || !(t_1 <= 5000000000000.0))
		tmp = fma(Float64(z / a), y, x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, 1e-6], N[Not[LessEqual[t$95$1, 5000000000000.0]], $MachinePrecision]], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999955e-7 or 5e12 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 68.2

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

   5. Applied rewrites 68.2%

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

   if 9.99999999999999955e-7 < (/.f64 (-.f64 z t) (-.f64 a t)) < 5e12

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 95.9

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

   5. Applied rewrites 95.9%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 10^{-6} \lor \neg \left(\frac{z - t}{a - t} \leq 5000000000000\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 81.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 5000000000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 1e-6)
     (fma (/ z a) y x)
     (if (<= t_1 5000000000000.0) (+ y x) (fma z (/ y a) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 1e-6) {
		tmp = fma((z / a), y, x);
	} else if (t_1 <= 5000000000000.0) {
		tmp = y + x;
	} else {
		tmp = fma(z, (y / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= 1e-6)
		tmp = fma(Float64(z / a), y, x);
	elseif (t_1 <= 5000000000000.0)
		tmp = Float64(y + x);
	else
		tmp = fma(z, Float64(y / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-6], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 5000000000000.0], N[(y + x), $MachinePrecision], N[(z * N[(y / a), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999955e-7

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 72.0

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

   5. Applied rewrites 72.0%

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

   if 9.99999999999999955e-7 < (/.f64 (-.f64 z t) (-.f64 a t)) < 5e12

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 95.9

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

   5. Applied rewrites 95.9%

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

   if 5e12 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 93.4

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

   4. Applied rewrites 93.4%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 54.5

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

   7. Applied rewrites 54.5%

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

   9. Applied rewrites 54.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 5000000000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 1.22 \cdot 10^{-105}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (/ (- z t) (- a t)) 1.22e-105) (* (- x) -1.0) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) / (a - t)) <= 1.22e-105) {
		tmp = -x * -1.0;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((z - t) / (a - t)) <= 1.22d-105) then
        tmp = -x * (-1.0d0)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) / (a - t)) <= 1.22e-105) {
		tmp = -x * -1.0;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((z - t) / (a - t)) <= 1.22e-105:
		tmp = -x * -1.0
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(z - t) / Float64(a - t)) <= 1.22e-105)
		tmp = Float64(Float64(-x) * -1.0);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z - t) / (a - t)) <= 1.22e-105)
		tmp = -x * -1.0;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], 1.22e-105], N[((-x) * -1.0), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 1.22000000000000001e-105

   1. Initial program 98.1%

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

   3. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   5. Applied rewrites 90.3%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(-x\right) \cdot -1 \]
   7. Step-by-step derivation

   8. Applied rewrites 60.2%

      \[\leadsto \left(-x\right) \cdot -1 \]

   if 1.22000000000000001e-105 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 70.5

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

   5. Applied rewrites 70.5%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 1.22 \cdot 10^{-105}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.2% accurate, 6.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

3. Taylor expanded in t around inf

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

   1. +-commutative N/A

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

   2. lower-+.f64 60.3

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

5. Applied rewrites 60.3%

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

6. Final simplification 60.3%

   \[\leadsto y + x \]
7. Add Preprocessing

Developer Target 1: 99.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (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 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2025016 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -8508084860551241/100000000000000000000000000000000) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t)))))))

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