Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Percentage Accurate: 97.2% → 99.6%

Time: 4.2s

Alternatives: 13

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

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 - z) + 1.0d0) / a))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

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

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

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

Initial Program: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z) + 1.0d0) / a))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

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

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

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

Alternative 1: 99.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

2. Taylor expanded in a around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. sub-div N/A

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

   5. lower-/.f64 N/A

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

   6. lower--.f64 N/A

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

   7. associate--l+ N/A

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

   8. +-commutative N/A

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

   9. associate-+l- N/A

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

   10. lower--.f64 N/A

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

   11. lower--.f64 99.6

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

4. Applied rewrites 99.6%

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

Alternative 2: 91.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{t}, a, x\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+105}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{1 - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) t) a x)))
   (if (<= t -3.5e+19)
     t_1
     (if (<= t 4.2e+105) (fma (/ (- z y) (- 1.0 z)) a x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - y) / t), a, x);
	double tmp;
	if (t <= -3.5e+19) {
		tmp = t_1;
	} else if (t <= 4.2e+105) {
		tmp = fma(((z - y) / (1.0 - z)), a, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - y) / t), a, x)
	tmp = 0.0
	if (t <= -3.5e+19)
		tmp = t_1;
	elseif (t <= 4.2e+105)
		tmp = fma(Float64(Float64(z - y) / Float64(1.0 - z)), a, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision] * a + x), $MachinePrecision]}, If[LessEqual[t, -3.5e+19], t$95$1, If[LessEqual[t, 4.2e+105], N[(N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5e19 or 4.2000000000000002e105 < t

   1. Initial program 96.8%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-div N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate-+l- N/A

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

      10. lower--.f64 N/A

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

      11. lower--.f64 99.2

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

   4. Applied rewrites 99.2%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lift--.f64 86.1

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

   7. Applied rewrites 86.1%

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

   if -3.5e19 < t < 4.2000000000000002e105

   1. Initial program 97.4%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-div N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate-+l- N/A

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

      10. lower--.f64 N/A

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

      11. lower--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in t around 0

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

      1. lower--.f64 95.2

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

   7. Applied rewrites 95.2%

      \[\leadsto \mathsf{fma}\left(\frac{z - y}{1 - z}, a, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+49}:\\ \;\;\;\;x - \frac{y - z}{\frac{-z}{a}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-18}:\\ \;\;\;\;x - a \cdot \frac{y}{1 + t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t - \left(z - 1\right)}, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+49)
   (- x (/ (- y z) (/ (- z) a)))
   (if (<= z 6e-18)
     (- x (* a (/ y (+ 1.0 t))))
     (fma (/ z (- t (- z 1.0))) a x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+49) {
		tmp = x - ((y - z) / (-z / a));
	} else if (z <= 6e-18) {
		tmp = x - (a * (y / (1.0 + t)));
	} else {
		tmp = fma((z / (t - (z - 1.0))), a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+49)
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(-z) / a)));
	elseif (z <= 6e-18)
		tmp = Float64(x - Float64(a * Float64(y / Float64(1.0 + t))));
	else
		tmp = fma(Float64(z / Float64(t - Float64(z - 1.0))), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+49], N[(x - N[(N[(y - z), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-18], N[(x - N[(a * N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(t - N[(z - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.20000000000000014e49

   1. Initial program 94.2%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 84.2

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

   4. Applied rewrites 84.2%

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

   if -3.20000000000000014e49 < z < 5.99999999999999966e-18

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 90.6

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

   4. Applied rewrites 90.6%

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

   if 5.99999999999999966e-18 < z

   1. Initial program 95.7%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-div N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate-+l- N/A

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

      10. lower--.f64 N/A

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

      11. lower--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 83.4%

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

Alternative 4: 87.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+49}:\\ \;\;\;\;x - \frac{y - z}{\frac{-z}{a}}\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-37}:\\ \;\;\;\;x - a \cdot \frac{y}{1 + t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t - z}, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+49)
   (- x (/ (- y z) (/ (- z) a)))
   (if (<= z 1.62e-37) (- x (* a (/ y (+ 1.0 t)))) (fma (/ z (- t z)) a x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+49) {
		tmp = x - ((y - z) / (-z / a));
	} else if (z <= 1.62e-37) {
		tmp = x - (a * (y / (1.0 + t)));
	} else {
		tmp = fma((z / (t - z)), a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+49)
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(-z) / a)));
	elseif (z <= 1.62e-37)
		tmp = Float64(x - Float64(a * Float64(y / Float64(1.0 + t))));
	else
		tmp = fma(Float64(z / Float64(t - z)), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+49], N[(x - N[(N[(y - z), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.62e-37], N[(x - N[(a * N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(t - z), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.20000000000000014e49

   1. Initial program 94.2%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 84.2

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

   4. Applied rewrites 84.2%

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

   if -3.20000000000000014e49 < z < 1.6199999999999999e-37

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 90.9

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

   4. Applied rewrites 90.9%

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

   if 1.6199999999999999e-37 < z

   1. Initial program 96.0%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-div N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate-+l- N/A

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

      10. lower--.f64 N/A

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

      11. lower--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 82.6%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 80.7%

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

Alternative 5: 86.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{t - z}, a, x\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-37}:\\ \;\;\;\;x - a \cdot \frac{y}{1 + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ z (- t z)) a x)))
   (if (<= z -3.2e+49)
     t_1
     (if (<= z 1.62e-37) (- x (* a (/ y (+ 1.0 t)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((z / (t - z)), a, x);
	double tmp;
	if (z <= -3.2e+49) {
		tmp = t_1;
	} else if (z <= 1.62e-37) {
		tmp = x - (a * (y / (1.0 + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(z / Float64(t - z)), a, x)
	tmp = 0.0
	if (z <= -3.2e+49)
		tmp = t_1;
	elseif (z <= 1.62e-37)
		tmp = Float64(x - Float64(a * Float64(y / Float64(1.0 + t))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / N[(t - z), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision]}, If[LessEqual[z, -3.2e+49], t$95$1, If[LessEqual[z, 1.62e-37], N[(x - N[(a * N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000014e49 or 1.6199999999999999e-37 < z

   1. Initial program 95.2%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-div N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate-+l- N/A

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

      10. lower--.f64 N/A

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

      11. lower--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 84.5%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 83.5%

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

   if -3.20000000000000014e49 < z < 1.6199999999999999e-37

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 90.9

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

   4. Applied rewrites 90.9%

      \[\leadsto x - \color{blue}{a \cdot \frac{y}{1 + t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{t - z}, a, x\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-237}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{t}, a, x\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-115}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ z (- t z)) a x)))
   (if (<= z -3.2e+49)
     t_1
     (if (<= z -3.3e-237)
       (fma (/ (- z y) t) a x)
       (if (<= z 4.6e-115) (- x (* a y)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((z / (t - z)), a, x);
	double tmp;
	if (z <= -3.2e+49) {
		tmp = t_1;
	} else if (z <= -3.3e-237) {
		tmp = fma(((z - y) / t), a, x);
	} else if (z <= 4.6e-115) {
		tmp = x - (a * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(z / Float64(t - z)), a, x)
	tmp = 0.0
	if (z <= -3.2e+49)
		tmp = t_1;
	elseif (z <= -3.3e-237)
		tmp = fma(Float64(Float64(z - y) / t), a, x);
	elseif (z <= 4.6e-115)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / N[(t - z), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision]}, If[LessEqual[z, -3.2e+49], t$95$1, If[LessEqual[z, -3.3e-237], N[(N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[z, 4.6e-115], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.20000000000000014e49 or 4.59999999999999969e-115 < z

   1. Initial program 95.6%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-div N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate-+l- N/A

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

      10. lower--.f64 N/A

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

      11. lower--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 81.7%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 79.7%

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

   if -3.20000000000000014e49 < z < -3.3000000000000001e-237

   1. Initial program 99.0%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-div N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate-+l- N/A

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

      10. lower--.f64 N/A

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

      11. lower--.f64 99.5

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

   4. Applied rewrites 99.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lift--.f64 65.8

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

   7. Applied rewrites 65.8%

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

   if -3.3000000000000001e-237 < z < 4.59999999999999969e-115

   1. Initial program 99.2%

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

   2. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 96.8

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

   4. Applied rewrites 96.8%

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

   5. Taylor expanded in t around 0

      \[\leadsto x - a \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 74.7%

      \[\leadsto x - a \cdot y \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{t}, a, x\right)\\ \mathbf{if}\;t \leq -3.15 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-155}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-86}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{1 - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) t) a x)))
   (if (<= t -3.15e+19)
     t_1
     (if (<= t -4e-155)
       (- x (* a y))
       (if (<= t 3e-86) (fma (/ z (- 1.0 z)) a x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - y) / t), a, x);
	double tmp;
	if (t <= -3.15e+19) {
		tmp = t_1;
	} else if (t <= -4e-155) {
		tmp = x - (a * y);
	} else if (t <= 3e-86) {
		tmp = fma((z / (1.0 - z)), a, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - y) / t), a, x)
	tmp = 0.0
	if (t <= -3.15e+19)
		tmp = t_1;
	elseif (t <= -4e-155)
		tmp = Float64(x - Float64(a * y));
	elseif (t <= 3e-86)
		tmp = fma(Float64(z / Float64(1.0 - z)), a, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision] * a + x), $MachinePrecision]}, If[LessEqual[t, -3.15e+19], t$95$1, If[LessEqual[t, -4e-155], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-86], N[(N[(z / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.15e19 or 3.0000000000000001e-86 < t

   1. Initial program 96.7%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-div N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate-+l- N/A

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

      10. lower--.f64 N/A

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

      11. lower--.f64 99.4

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

   4. Applied rewrites 99.4%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lift--.f64 77.5

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

   7. Applied rewrites 77.5%

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

   if -3.15e19 < t < -4.00000000000000006e-155

   1. Initial program 97.6%

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

   2. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 67.8

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

   4. Applied rewrites 67.8%

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

   5. Taylor expanded in t around 0

      \[\leadsto x - a \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 64.3%

      \[\leadsto x - a \cdot y \]

   if -4.00000000000000006e-155 < t < 3.0000000000000001e-86

   1. Initial program 97.7%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-div N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate-+l- N/A

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

      10. lower--.f64 N/A

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

      11. lower--.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in t around 0

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

      1. lower--.f64 100.0

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

   7. Applied rewrites 100.0%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 68.4%

       \[\leadsto \mathsf{fma}\left(\frac{z}{1 - z}, a, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{t}, a, x\right)\\ \mathbf{if}\;t \leq -3.15 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-155}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-19}:\\ \;\;\;\;x - \frac{y}{-z} \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) t) a x)))
   (if (<= t -3.15e+19)
     t_1
     (if (<= t 2.2e-155)
       (- x (* a y))
       (if (<= t 1.95e-19) (- x (* (/ y (- z)) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - y) / t), a, x);
	double tmp;
	if (t <= -3.15e+19) {
		tmp = t_1;
	} else if (t <= 2.2e-155) {
		tmp = x - (a * y);
	} else if (t <= 1.95e-19) {
		tmp = x - ((y / -z) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - y) / t), a, x)
	tmp = 0.0
	if (t <= -3.15e+19)
		tmp = t_1;
	elseif (t <= 2.2e-155)
		tmp = Float64(x - Float64(a * y));
	elseif (t <= 1.95e-19)
		tmp = Float64(x - Float64(Float64(y / Float64(-z)) * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision] * a + x), $MachinePrecision]}, If[LessEqual[t, -3.15e+19], t$95$1, If[LessEqual[t, 2.2e-155], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e-19], N[(x - N[(N[(y / (-z)), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.15e19 or 1.94999999999999998e-19 < t

   1. Initial program 96.7%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-div N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate-+l- N/A

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

      10. lower--.f64 N/A

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

      11. lower--.f64 99.3

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

   4. Applied rewrites 99.3%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lift--.f64 81.9

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

   7. Applied rewrites 81.9%

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

   if -3.15e19 < t < 2.1999999999999999e-155

   1. Initial program 97.7%

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

   2. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 67.3

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

   4. Applied rewrites 67.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto x - a \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 66.0%

      \[\leadsto x - a \cdot y \]

   if 2.1999999999999999e-155 < t < 1.94999999999999998e-19

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 63.0

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

   4. Applied rewrites 63.0%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 46.6%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 47.3

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

      6. associate-+l- 47.3

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

   9. Applied rewrites 47.3%

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

Alternative 9: 72.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+49}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-260}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-18}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+118}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+49)
   (- x a)
   (if (<= z -7.2e-260)
     (- x (* a (/ y t)))
     (if (<= z 5e-18)
       (- x (* a y))
       (if (<= z 3.2e+118) (fma (/ z t) a x) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+49) {
		tmp = x - a;
	} else if (z <= -7.2e-260) {
		tmp = x - (a * (y / t));
	} else if (z <= 5e-18) {
		tmp = x - (a * y);
	} else if (z <= 3.2e+118) {
		tmp = fma((z / t), a, x);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+49)
		tmp = Float64(x - a);
	elseif (z <= -7.2e-260)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= 5e-18)
		tmp = Float64(x - Float64(a * y));
	elseif (z <= 3.2e+118)
		tmp = fma(Float64(z / t), a, x);
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+49], N[(x - a), $MachinePrecision], If[LessEqual[z, -7.2e-260], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-18], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+118], N[(N[(z / t), $MachinePrecision] * a + x), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.20000000000000014e49 or 3.20000000000000016e118 < z

   1. Initial program 94.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 81.1%

      \[\leadsto x - \color{blue}{a} \]

   if -3.20000000000000014e49 < z < -7.2000000000000002e-260

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 87.7

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

   4. Applied rewrites 87.7%

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

   5. Taylor expanded in t around inf

      \[\leadsto x - a \cdot \frac{y}{t} \]
   6. Step-by-step derivation

   7. Applied rewrites 64.4%

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

   if -7.2000000000000002e-260 < z < 5.00000000000000036e-18

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 93.4

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

   4. Applied rewrites 93.4%

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

   5. Taylor expanded in t around 0

      \[\leadsto x - a \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 72.2%

      \[\leadsto x - a \cdot y \]

   if 5.00000000000000036e-18 < z < 3.20000000000000016e118

   1. Initial program 98.1%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-div N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate-+l- N/A

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

      10. lower--.f64 N/A

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

      11. lower--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lift--.f64 54.7

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

   7. Applied rewrites 54.7%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 48.2%

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

Alternative 10: 71.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -28500000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-18}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+118}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -28500000.0)
   (- x a)
   (if (<= z 5e-18)
     (- x (* a y))
     (if (<= z 3.2e+118) (fma (/ z t) a x) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -28500000.0) {
		tmp = x - a;
	} else if (z <= 5e-18) {
		tmp = x - (a * y);
	} else if (z <= 3.2e+118) {
		tmp = fma((z / t), a, x);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -28500000.0)
		tmp = Float64(x - a);
	elseif (z <= 5e-18)
		tmp = Float64(x - Float64(a * y));
	elseif (z <= 3.2e+118)
		tmp = fma(Float64(z / t), a, x);
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -28500000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 5e-18], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+118], N[(N[(z / t), $MachinePrecision] * a + x), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.85e7 or 3.20000000000000016e118 < z

   1. Initial program 94.5%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 79.1%

      \[\leadsto x - \color{blue}{a} \]

   if -2.85e7 < z < 5.00000000000000036e-18

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 92.6

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

   4. Applied rewrites 92.6%

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

   5. Taylor expanded in t around 0

      \[\leadsto x - a \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 71.5%

      \[\leadsto x - a \cdot y \]

   if 5.00000000000000036e-18 < z < 3.20000000000000016e118

   1. Initial program 98.1%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-div N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate-+l- N/A

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

      10. lower--.f64 N/A

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

      11. lower--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lift--.f64 54.7

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

   7. Applied rewrites 54.7%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 48.2%

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

Alternative 11: 70.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -28500000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+63}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -28500000.0) (- x a) (if (<= z 6.4e+63) (- x (* a y)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -28500000.0) {
		tmp = x - a;
	} else if (z <= 6.4e+63) {
		tmp = x - (a * y);
	} else {
		tmp = x - 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) :: tmp
    if (z <= (-28500000.0d0)) then
        tmp = x - a
    else if (z <= 6.4d+63) then
        tmp = x - (a * y)
    else
        tmp = x - a
    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 <= -28500000.0) {
		tmp = x - a;
	} else if (z <= 6.4e+63) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -28500000.0:
		tmp = x - a
	elif z <= 6.4e+63:
		tmp = x - (a * y)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -28500000.0)
		tmp = Float64(x - a);
	elseif (z <= 6.4e+63)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -28500000.0)
		tmp = x - a;
	elseif (z <= 6.4e+63)
		tmp = x - (a * y);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -28500000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 6.4e+63], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.85e7 or 6.40000000000000022e63 < z

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 77.9%

      \[\leadsto x - \color{blue}{a} \]

   if -2.85e7 < z < 6.40000000000000022e63

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 89.4

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

   4. Applied rewrites 89.4%

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

   5. Taylor expanded in t around 0

      \[\leadsto x - a \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 68.9%

      \[\leadsto x - a \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 65.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -49000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -49000000.0) (- x a) (if (<= z 7.5e+63) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -49000000.0) {
		tmp = x - a;
	} else if (z <= 7.5e+63) {
		tmp = x;
	} else {
		tmp = x - 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) :: tmp
    if (z <= (-49000000.0d0)) then
        tmp = x - a
    else if (z <= 7.5d+63) then
        tmp = x
    else
        tmp = x - a
    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 <= -49000000.0) {
		tmp = x - a;
	} else if (z <= 7.5e+63) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -49000000.0:
		tmp = x - a
	elif z <= 7.5e+63:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -49000000.0)
		tmp = Float64(x - a);
	elseif (z <= 7.5e+63)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -49000000.0)
		tmp = x - a;
	elseif (z <= 7.5e+63)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -49000000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 7.5e+63], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9e7 or 7.5000000000000005e63 < z

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 77.9%

      \[\leadsto x - \color{blue}{a} \]

   if -4.9e7 < z < 7.5000000000000005e63

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 56.1%

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

Alternative 13: 53.7% accurate, 18.3× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 53.7%

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

Reproduce

herbie shell --seed 2025120 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64
  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))