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

Percentage Accurate: 97.2% → 99.7%

Time: 4.2s

Alternatives: 15

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: 99.7% 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 99.7

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

4. Applied rewrites 99.7%

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

Alternative 2: 91.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{t}, a, x\right)\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{1 - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) t) a x)))
   (if (<= t -9.2e+113)
     t_1
     (if (<= t 5e+86) (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 <= -9.2e+113) {
		tmp = t_1;
	} else if (t <= 5e+86) {
		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 <= -9.2e+113)
		tmp = t_1;
	elseif (t <= 5e+86)
		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, -9.2e+113], t$95$1, If[LessEqual[t, 5e+86], 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 < -9.19999999999999987e113 or 4.9999999999999998e86 < t

   1. Initial program 96.3%

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

   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 88.4

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

   7. Applied rewrites 88.4%

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

   if -9.19999999999999987e113 < t < 4.9999999999999998e86

   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 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 92.3

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

   7. Applied rewrites 92.3%

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

Alternative 3: 88.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -72000000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t - \left(z - 1\right)}, a, x\right)\\ \mathbf{elif}\;z \leq 25000:\\ \;\;\;\;x - a \cdot \frac{y}{1 + t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{-z}, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -72000000000000.0)
   (fma (/ z (- t (- z 1.0))) a x)
   (if (<= z 25000.0)
     (- x (* a (/ y (+ 1.0 t))))
     (fma (/ (- z y) (- z)) a x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -72000000000000.0) {
		tmp = fma((z / (t - (z - 1.0))), a, x);
	} else if (z <= 25000.0) {
		tmp = x - (a * (y / (1.0 + t)));
	} else {
		tmp = fma(((z - y) / -z), a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -72000000000000.0)
		tmp = fma(Float64(z / Float64(t - Float64(z - 1.0))), a, x);
	elseif (z <= 25000.0)
		tmp = Float64(x - Float64(a * Float64(y / Float64(1.0 + t))));
	else
		tmp = fma(Float64(Float64(z - y) / Float64(-z)), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -72000000000000.0], N[(N[(z / N[(t - N[(z - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[z, 25000.0], N[(x - N[(a * N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] / (-z)), $MachinePrecision] * a + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2e13

   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 99.9

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

   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 85.5%

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

   if -7.2e13 < z < 25000

   1. Initial program 99.1%

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

   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 91.8

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

   4. Applied rewrites 91.8%

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

   if 25000 < z

   1. Initial program 94.9%

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

   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 85.7

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

   7. Applied rewrites 85.7%

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

   8. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 85.4

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

   10. Applied rewrites 85.4%

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

Alternative 4: 88.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -72000000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t - z}, a, x\right)\\ \mathbf{elif}\;z \leq 25000:\\ \;\;\;\;x - a \cdot \frac{y}{1 + t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{-z}, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -72000000000000.0)
   (fma (/ z (- t z)) a x)
   (if (<= z 25000.0)
     (- x (* a (/ y (+ 1.0 t))))
     (fma (/ (- z y) (- z)) a x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -72000000000000.0) {
		tmp = fma((z / (t - z)), a, x);
	} else if (z <= 25000.0) {
		tmp = x - (a * (y / (1.0 + t)));
	} else {
		tmp = fma(((z - y) / -z), a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -72000000000000.0)
		tmp = fma(Float64(z / Float64(t - z)), a, x);
	elseif (z <= 25000.0)
		tmp = Float64(x - Float64(a * Float64(y / Float64(1.0 + t))));
	else
		tmp = fma(Float64(Float64(z - y) / Float64(-z)), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -72000000000000.0], N[(N[(z / N[(t - z), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[z, 25000.0], N[(x - N[(a * N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] / (-z)), $MachinePrecision] * a + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2e13

   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 99.9

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

   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 85.5%

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

   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 85.5%

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

   if -7.2e13 < z < 25000

   1. Initial program 99.1%

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

   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 91.8

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

   4. Applied rewrites 91.8%

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

   if 25000 < z

   1. Initial program 94.9%

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

   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 85.7

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

   7. Applied rewrites 85.7%

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

   8. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 85.4

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

   10. Applied rewrites 85.4%

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

Alternative 5: 88.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{t - z}, a, x\right)\\ \mathbf{if}\;z \leq -72000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 15.5:\\ \;\;\;\;x - a \cdot \frac{y}{1 + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ z (- t z)) a x)))
   (if (<= z -72000000000000.0)
     t_1
     (if (<= z 15.5) (- 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 <= -72000000000000.0) {
		tmp = t_1;
	} else if (z <= 15.5) {
		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 <= -72000000000000.0)
		tmp = t_1;
	elseif (z <= 15.5)
		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, -72000000000000.0], t$95$1, If[LessEqual[z, 15.5], 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 < -7.2e13 or 15.5 < z

   1. Initial program 95.3%

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

   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 85.2%

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

   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 85.0%

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

   if -7.2e13 < z < 15.5

   1. Initial program 99.1%

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

   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 92.0

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

   4. Applied rewrites 92.0%

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

Alternative 6: 78.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{t - z}, a, x\right)\\ \mathbf{if}\;z \leq -0.0055:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-129}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{1}, a, x\right)\\ \mathbf{elif}\;z \leq 15.5:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ z (- t z)) a x)))
   (if (<= z -0.0055)
     t_1
     (if (<= z 5.7e-129)
       (fma (/ (- z y) 1.0) a x)
       (if (<= z 15.5) (- x (* a (/ y 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 <= -0.0055) {
		tmp = t_1;
	} else if (z <= 5.7e-129) {
		tmp = fma(((z - y) / 1.0), a, x);
	} else if (z <= 15.5) {
		tmp = x - (a * (y / 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 <= -0.0055)
		tmp = t_1;
	elseif (z <= 5.7e-129)
		tmp = fma(Float64(Float64(z - y) / 1.0), a, x);
	elseif (z <= 15.5)
		tmp = Float64(x - Float64(a * Float64(y / 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, -0.0055], t$95$1, If[LessEqual[z, 5.7e-129], N[(N[(N[(z - y), $MachinePrecision] / 1.0), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[z, 15.5], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0054999999999999997 or 15.5 < z

   1. Initial program 95.4%

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

   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 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 85.0%

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

   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 84.7%

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

   if -0.0054999999999999997 < z < 5.7000000000000001e-129

   1. Initial program 99.1%

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

   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 99.3

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

   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 0

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

      1. lower--.f64 75.1

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

   7. Applied rewrites 75.1%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 74.9%

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

   if 5.7000000000000001e-129 < z < 15.5

   1. Initial program 99.1%

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

   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 87.6

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

   4. Applied rewrites 87.6%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 64.1%

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

Alternative 7: 76.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y}{t}\\ t_2 := \mathsf{fma}\left(\frac{z}{t - z}, a, x\right)\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-293}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-129}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 15.5:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ y t)))) (t_2 (fma (/ z (- t z)) a x)))
   (if (<= z -4.1e-36)
     t_2
     (if (<= z 2.45e-293)
       t_1
       (if (<= z 5.7e-129) (- x (* a y)) (if (<= z 15.5) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / t));
	double t_2 = fma((z / (t - z)), a, x);
	double tmp;
	if (z <= -4.1e-36) {
		tmp = t_2;
	} else if (z <= 2.45e-293) {
		tmp = t_1;
	} else if (z <= 5.7e-129) {
		tmp = x - (a * y);
	} else if (z <= 15.5) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(y / t)))
	t_2 = fma(Float64(z / Float64(t - z)), a, x)
	tmp = 0.0
	if (z <= -4.1e-36)
		tmp = t_2;
	elseif (z <= 2.45e-293)
		tmp = t_1;
	elseif (z <= 5.7e-129)
		tmp = Float64(x - Float64(a * y));
	elseif (z <= 15.5)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / N[(t - z), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision]}, If[LessEqual[z, -4.1e-36], t$95$2, If[LessEqual[z, 2.45e-293], t$95$1, If[LessEqual[z, 5.7e-129], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 15.5], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.10000000000000013e-36 or 15.5 < z

   1. Initial program 95.5%

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

   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 84.1%

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

   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 83.2%

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

   if -4.10000000000000013e-36 < z < 2.45e-293 or 5.7000000000000001e-129 < z < 15.5

   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 92.4

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

   4. Applied rewrites 92.4%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 66.1%

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

   if 2.45e-293 < z < 5.7000000000000001e-129

   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 95.7

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

   4. Applied rewrites 95.7%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 75.3%

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

Alternative 8: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{t}, a, x\right)\\ \mathbf{if}\;t \leq -7600000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-55}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{1 - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) t) a x)))
   (if (<= t -7600000000000.0)
     t_1
     (if (<= t -1.15e-55)
       (- x (* a y))
       (if (<= t 8.8e+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 <= -7600000000000.0) {
		tmp = t_1;
	} else if (t <= -1.15e-55) {
		tmp = x - (a * y);
	} else if (t <= 8.8e+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 <= -7600000000000.0)
		tmp = t_1;
	elseif (t <= -1.15e-55)
		tmp = Float64(x - Float64(a * y));
	elseif (t <= 8.8e+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, -7600000000000.0], t$95$1, If[LessEqual[t, -1.15e-55], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e+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 < -7.6e12 or 8.80000000000000013e86 < t

   1. Initial program 96.5%

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

   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 85.0

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

   7. Applied rewrites 85.0%

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

   if -7.6e12 < t < -1.15000000000000006e-55

   1. Initial program 97.5%

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

   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 69.2

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

   4. Applied rewrites 69.2%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 62.6%

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

   if -1.15000000000000006e-55 < t < 8.80000000000000013e86

   1. Initial program 97.8%

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

   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 99.9

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

   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 95.9

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

   7. Applied rewrites 95.9%

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

   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 68.9%

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

Alternative 9: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+54}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-36}:\\ \;\;\;\;x - \frac{\left(-z\right) \cdot a}{t}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-293}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-129}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+58}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.1e+54)
   (- x a)
   (if (<= z -5.6e-36)
     (- x (/ (* (- z) a) t))
     (if (<= z 2.45e-293)
       (- x (* a (/ y t)))
       (if (<= z 5.7e-129)
         (- x (* a y))
         (if (<= z 9.6e+58) (- x (/ y (/ t a))) (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.1e+54) {
		tmp = x - a;
	} else if (z <= -5.6e-36) {
		tmp = x - ((-z * a) / t);
	} else if (z <= 2.45e-293) {
		tmp = x - (a * (y / t));
	} else if (z <= 5.7e-129) {
		tmp = x - (a * y);
	} else if (z <= 9.6e+58) {
		tmp = x - (y / (t / a));
	} 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 <= (-4.1d+54)) then
        tmp = x - a
    else if (z <= (-5.6d-36)) then
        tmp = x - ((-z * a) / t)
    else if (z <= 2.45d-293) then
        tmp = x - (a * (y / t))
    else if (z <= 5.7d-129) then
        tmp = x - (a * y)
    else if (z <= 9.6d+58) then
        tmp = x - (y / (t / a))
    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 <= -4.1e+54) {
		tmp = x - a;
	} else if (z <= -5.6e-36) {
		tmp = x - ((-z * a) / t);
	} else if (z <= 2.45e-293) {
		tmp = x - (a * (y / t));
	} else if (z <= 5.7e-129) {
		tmp = x - (a * y);
	} else if (z <= 9.6e+58) {
		tmp = x - (y / (t / a));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.1e+54:
		tmp = x - a
	elif z <= -5.6e-36:
		tmp = x - ((-z * a) / t)
	elif z <= 2.45e-293:
		tmp = x - (a * (y / t))
	elif z <= 5.7e-129:
		tmp = x - (a * y)
	elif z <= 9.6e+58:
		tmp = x - (y / (t / a))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.1e+54)
		tmp = Float64(x - a);
	elseif (z <= -5.6e-36)
		tmp = Float64(x - Float64(Float64(Float64(-z) * a) / t));
	elseif (z <= 2.45e-293)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= 5.7e-129)
		tmp = Float64(x - Float64(a * y));
	elseif (z <= 9.6e+58)
		tmp = Float64(x - Float64(y / Float64(t / a)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.1e+54)
		tmp = x - a;
	elseif (z <= -5.6e-36)
		tmp = x - ((-z * a) / t);
	elseif (z <= 2.45e-293)
		tmp = x - (a * (y / t));
	elseif (z <= 5.7e-129)
		tmp = x - (a * y);
	elseif (z <= 9.6e+58)
		tmp = x - (y / (t / a));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.1e+54], N[(x - a), $MachinePrecision], If[LessEqual[z, -5.6e-36], N[(x - N[(N[((-z) * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e-293], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.7e-129], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e+58], N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.09999999999999967e54 or 9.5999999999999999e58 < 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 79.5%

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

   if -4.09999999999999967e54 < z < -5.6000000000000002e-36

   1. Initial program 98.6%

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

   2. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 53.4

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

   7. Applied rewrites 53.4%

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

   if -5.6000000000000002e-36 < z < 2.45e-293

   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 94.6

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

   4. Applied rewrites 94.6%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 67.0%

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

   if 2.45e-293 < z < 5.7000000000000001e-129

   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 95.7

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

   4. Applied rewrites 95.7%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 75.3%

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

   if 5.7000000000000001e-129 < z < 9.5999999999999999e58

   1. Initial program 99.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 62.7%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 60.5%

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{t}{a}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 10: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+54}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-36}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, a, x\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-293}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-129}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+58}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.8e+54)
   (- x a)
   (if (<= z -5.6e-36)
     (fma (/ z t) a x)
     (if (<= z 2.45e-293)
       (- x (* a (/ y t)))
       (if (<= z 5.7e-129)
         (- x (* a y))
         (if (<= z 9.6e+58) (- x (/ y (/ t a))) (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.8e+54) {
		tmp = x - a;
	} else if (z <= -5.6e-36) {
		tmp = fma((z / t), a, x);
	} else if (z <= 2.45e-293) {
		tmp = x - (a * (y / t));
	} else if (z <= 5.7e-129) {
		tmp = x - (a * y);
	} else if (z <= 9.6e+58) {
		tmp = x - (y / (t / a));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.8e+54)
		tmp = Float64(x - a);
	elseif (z <= -5.6e-36)
		tmp = fma(Float64(z / t), a, x);
	elseif (z <= 2.45e-293)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= 5.7e-129)
		tmp = Float64(x - Float64(a * y));
	elseif (z <= 9.6e+58)
		tmp = Float64(x - Float64(y / Float64(t / a)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.8e+54], N[(x - a), $MachinePrecision], If[LessEqual[z, -5.6e-36], N[(N[(z / t), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[z, 2.45e-293], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.7e-129], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e+58], N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -9.80000000000000002e54 or 9.5999999999999999e58 < 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 79.5%

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

   if -9.80000000000000002e54 < z < -5.6000000000000002e-36

   1. Initial program 98.6%

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

   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 99.9

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

   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 72.6%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 53.6%

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

   if -5.6000000000000002e-36 < z < 2.45e-293

   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 94.6

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

   4. Applied rewrites 94.6%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 67.0%

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

   if 2.45e-293 < z < 5.7000000000000001e-129

   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 95.7

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

   4. Applied rewrites 95.7%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 75.3%

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

   if 5.7000000000000001e-129 < z < 9.5999999999999999e58

   1. Initial program 99.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 62.7%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 60.5%

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{t}{a}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 11: 71.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+54}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-36}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, a, x\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-293}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-129}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ y t)))))
   (if (<= z -9.8e+54)
     (- x a)
     (if (<= z -5.6e-36)
       (fma (/ z t) a x)
       (if (<= z 2.45e-293)
         t_1
         (if (<= z 5.7e-129) (- x (* a y)) (if (<= z 8e+60) t_1 (- x a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / t));
	double tmp;
	if (z <= -9.8e+54) {
		tmp = x - a;
	} else if (z <= -5.6e-36) {
		tmp = fma((z / t), a, x);
	} else if (z <= 2.45e-293) {
		tmp = t_1;
	} else if (z <= 5.7e-129) {
		tmp = x - (a * y);
	} else if (z <= 8e+60) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(y / t)))
	tmp = 0.0
	if (z <= -9.8e+54)
		tmp = Float64(x - a);
	elseif (z <= -5.6e-36)
		tmp = fma(Float64(z / t), a, x);
	elseif (z <= 2.45e-293)
		tmp = t_1;
	elseif (z <= 5.7e-129)
		tmp = Float64(x - Float64(a * y));
	elseif (z <= 8e+60)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.8e+54], N[(x - a), $MachinePrecision], If[LessEqual[z, -5.6e-36], N[(N[(z / t), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[z, 2.45e-293], t$95$1, If[LessEqual[z, 5.7e-129], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+60], t$95$1, N[(x - a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.80000000000000002e54 or 7.9999999999999996e60 < 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 79.5%

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

   if -9.80000000000000002e54 < z < -5.6000000000000002e-36

   1. Initial program 98.6%

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

   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 99.9

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

   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 72.6%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 53.6%

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

   if -5.6000000000000002e-36 < z < 2.45e-293 or 5.7000000000000001e-129 < z < 7.9999999999999996e60

   1. Initial program 99.1%

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

   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 87.9

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

   4. Applied rewrites 87.9%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 64.6%

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

   if 2.45e-293 < z < 5.7000000000000001e-129

   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 95.7

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

   4. Applied rewrites 95.7%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 75.3%

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

Alternative 12: 71.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{t}, a, x\right)\\ \mathbf{if}\;z \leq -3.55 \cdot 10^{+53}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-293}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-129}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) t) a x)))
   (if (<= z -3.55e+53)
     (- x a)
     (if (<= z 2.45e-293)
       t_1
       (if (<= z 5.7e-129) (- x (* a y)) (if (<= z 8.6e+60) t_1 (- x a)))))))

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 (z <= -3.55e+53) {
		tmp = x - a;
	} else if (z <= 2.45e-293) {
		tmp = t_1;
	} else if (z <= 5.7e-129) {
		tmp = x - (a * y);
	} else if (z <= 8.6e+60) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - y) / t), a, x)
	tmp = 0.0
	if (z <= -3.55e+53)
		tmp = Float64(x - a);
	elseif (z <= 2.45e-293)
		tmp = t_1;
	elseif (z <= 5.7e-129)
		tmp = Float64(x - Float64(a * y));
	elseif (z <= 8.6e+60)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	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[z, -3.55e+53], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.45e-293], t$95$1, If[LessEqual[z, 5.7e-129], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e+60], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.54999999999999987e53 or 8.59999999999999942e60 < z

   1. Initial program 94.6%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 79.5%

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

   if -3.54999999999999987e53 < z < 2.45e-293 or 5.7000000000000001e-129 < z < 8.59999999999999942e60

   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 99.6

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

   4. Applied rewrites 99.6%

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

   5. 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 65.1

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

   7. Applied rewrites 65.1%

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

   if 2.45e-293 < z < 5.7000000000000001e-129

   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 95.7

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

   4. Applied rewrites 95.7%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 75.3%

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

Alternative 13: 71.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1900000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+54}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1900000.0) (- x a) (if (<= z 2.4e+54) (- x (* a y)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1900000.0) {
		tmp = x - a;
	} else if (z <= 2.4e+54) {
		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 <= (-1900000.0d0)) then
        tmp = x - a
    else if (z <= 2.4d+54) 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 <= -1900000.0) {
		tmp = x - a;
	} else if (z <= 2.4e+54) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1900000.0:
		tmp = x - a
	elif z <= 2.4e+54:
		tmp = x - (a * y)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1900000.0)
		tmp = Float64(x - a);
	elseif (z <= 2.4e+54)
		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 <= -1900000.0)
		tmp = x - a;
	elseif (z <= 2.4e+54)
		tmp = x - (a * y);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1900000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.4e+54], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e6 or 2.39999999999999998e54 < z

   1. Initial program 94.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 77.2%

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

   if -1.9e6 < z < 2.39999999999999998e54

   1. Initial program 99.1%

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

   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 89.5

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

   4. Applied rewrites 89.5%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 68.6%

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

Alternative 14: 65.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -28000000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -28000000000000.0) (- x a) (if (<= z 6.1e+85) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -28000000000000.0) {
		tmp = x - a;
	} else if (z <= 6.1e+85) {
		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 <= (-28000000000000.0d0)) then
        tmp = x - a
    else if (z <= 6.1d+85) 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 <= -28000000000000.0) {
		tmp = x - a;
	} else if (z <= 6.1e+85) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -28000000000000.0:
		tmp = x - a
	elif z <= 6.1e+85:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -28000000000000.0)
		tmp = Float64(x - a);
	elseif (z <= 6.1e+85)
		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 <= -28000000000000.0)
		tmp = x - a;
	elseif (z <= 6.1e+85)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -28000000000000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 6.1e+85], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e13 or 6.09999999999999981e85 < z

   1. Initial program 94.7%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 78.3%

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

   if -2.8e13 < z < 6.09999999999999981e85

   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 55.5%

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

Alternative 15: 53.2% 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 53.2%

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

Reproduce

herbie shell --seed 2025119 
(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))))