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

Percentage Accurate: 97.1% → 99.6%

Time: 6.6s

Alternatives: 15

Speedup: 1.0×

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: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x - (((z - y) / (-1.0 - (t - z))) * 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 - (((z - y) / ((-1.0d0) - (t - z))) * a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.1%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. associate-/r/ N/A

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

   4. lower-*.f64 N/A

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

   5. frac-2neg N/A

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

   6. lower-/.f64 N/A

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

   7. lift--.f64 N/A

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

   8. sub-negate-rev N/A

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

   9. lower--.f64 N/A

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

   10. lift-+.f64 N/A

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

   11. add-flip N/A

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

   12. sub-negate N/A

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

   13. lower--.f64 N/A

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

   14. metadata-eval 99.6

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

3. Applied rewrites 99.6%

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

Alternative 2: 97.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+190}:\\ \;\;\;\;x - \frac{z - y}{z - 1} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - y, \frac{a}{\left(t - z\right) - -1}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e+190)
   (- x (* (/ (- z y) (- z 1.0)) a))
   (fma (- z y) (/ a (- (- t z) -1.0)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e+190) {
		tmp = x - (((z - y) / (z - 1.0)) * a);
	} else {
		tmp = fma((z - y), (a / ((t - z) - -1.0)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e+190)
		tmp = Float64(x - Float64(Float64(Float64(z - y) / Float64(z - 1.0)) * a));
	else
		tmp = fma(Float64(z - y), Float64(a / Float64(Float64(t - z) - -1.0)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e+190], N[(x - N[(N[(N[(z - y), $MachinePrecision] / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(z - y), $MachinePrecision] * N[(a / N[(N[(t - z), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4e190

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval 99.6

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in t around 0

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

      1. lower--.f64 79.6

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

   6. Applied rewrites 79.6%

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

   if -4.4e190 < z

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip-rev N/A

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

      6. lift-/.f64 N/A

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

      7. div-flip-rev N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 97.3

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

      14. lift-+.f64 N/A

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

      15. add-flip N/A

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

      16. lower--.f64 N/A

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

      17. metadata-eval 97.3

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

   3. Applied rewrites 97.3%

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

Alternative 3: 91.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{t}, z - y, x\right)\\ \mathbf{elif}\;t \leq 10^{+33}:\\ \;\;\;\;x - \frac{z - y}{z - 1} \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.26e+97)
   (fma (/ a t) (- z y) x)
   (if (<= t 1e+33)
     (- x (* (/ (- z y) (- z 1.0)) a))
     (- x (/ a (/ t (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.26e+97) {
		tmp = fma((a / t), (z - y), x);
	} else if (t <= 1e+33) {
		tmp = x - (((z - y) / (z - 1.0)) * a);
	} else {
		tmp = x - (a / (t / (y - z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.26e+97)
		tmp = fma(Float64(a / t), Float64(z - y), x);
	elseif (t <= 1e+33)
		tmp = Float64(x - Float64(Float64(Float64(z - y) / Float64(z - 1.0)) * a));
	else
		tmp = Float64(x - Float64(a / Float64(t / Float64(y - z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.26e+97], N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1e+33], N[(x - N[(N[(N[(z - y), $MachinePrecision] / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2600000000000001e97

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval 99.6

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

   3. Applied rewrites 99.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. div-flip N/A

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

      5. mult-flip-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. metadata-eval N/A

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

      10. add-flip N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lift--.f64 N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lift--.f64 N/A

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

      18. add-flip N/A

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

      19. metadata-eval N/A

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

      20. lower--.f64 99.5

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

   5. Applied rewrites 99.5%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/r/ N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 97.3

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

   7. Applied rewrites 97.3%

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

   8. Taylor expanded in t around inf

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

      1. lower-/.f64 55.0

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

   10. Applied rewrites 55.0%

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

   if -1.2600000000000001e97 < t < 9.9999999999999995e32

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval 99.6

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in t around 0

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

      1. lower--.f64 79.6

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

   6. Applied rewrites 79.6%

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

   if 9.9999999999999995e32 < t

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval 99.6

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

   3. Applied rewrites 99.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. div-flip N/A

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

      5. mult-flip-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. metadata-eval N/A

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

      10. add-flip N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lift--.f64 N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lift--.f64 N/A

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

      18. add-flip N/A

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

      19. metadata-eval N/A

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

      20. lower--.f64 99.5

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

   5. Applied rewrites 99.5%

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

   6. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 54.1

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

   8. Applied rewrites 54.1%

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

Alternative 4: 91.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{\left(t - z\right) - -1}, a, x\right)\\ \mathbf{if}\;z \leq -1.06 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(z - y, \frac{a}{t - -1}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ z (- (- t z) -1.0)) a x)))
   (if (<= z -1.06e+27)
     t_1
     (if (<= z 6.4e-18) (fma (- z y) (/ a (- t -1.0)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((z / ((t - z) - -1.0)), a, x);
	double tmp;
	if (z <= -1.06e+27) {
		tmp = t_1;
	} else if (z <= 6.4e-18) {
		tmp = fma((z - y), (a / (t - -1.0)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(z / Float64(Float64(t - z) - -1.0)), a, x)
	tmp = 0.0
	if (z <= -1.06e+27)
		tmp = t_1;
	elseif (z <= 6.4e-18)
		tmp = fma(Float64(z - y), Float64(a / Float64(t - -1.0)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / N[(N[(t - z), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision]}, If[LessEqual[z, -1.06e+27], t$95$1, If[LessEqual[z, 6.4e-18], N[(N[(z - y), $MachinePrecision] * N[(a / N[(t - -1.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05999999999999994e27 or 6.3999999999999998e-18 < z

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval 99.6

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 73.2%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lift--.f64 N/A

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

      12. lower-/.f64 73.2

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

   8. Applied rewrites 73.2%

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

   if -1.05999999999999994e27 < z < 6.3999999999999998e-18

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 73.8%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip-rev N/A

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

      6. lift-/.f64 N/A

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

      7. div-flip-rev N/A

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

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

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lift--.f64 N/A

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

      12. lower-fma.f64 N/A

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

   6. Applied rewrites 74.0%

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

Alternative 5: 89.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+95}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{t}, z - y, x\right)\\ \mathbf{elif}\;t \leq 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{1 - z}, z - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.5e+95)
   (fma (/ a t) (- z y) x)
   (if (<= t 1e+33)
     (fma (/ a (- 1.0 z)) (- z y) x)
     (- x (/ a (/ t (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e+95) {
		tmp = fma((a / t), (z - y), x);
	} else if (t <= 1e+33) {
		tmp = fma((a / (1.0 - z)), (z - y), x);
	} else {
		tmp = x - (a / (t / (y - z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.5e+95)
		tmp = fma(Float64(a / t), Float64(z - y), x);
	elseif (t <= 1e+33)
		tmp = fma(Float64(a / Float64(1.0 - z)), Float64(z - y), x);
	else
		tmp = Float64(x - Float64(a / Float64(t / Float64(y - z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.5e+95], N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1e+33], N[(N[(a / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision] + x), $MachinePrecision], N[(x - N[(a / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.50000000000000017e95

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval 99.6

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

   3. Applied rewrites 99.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. div-flip N/A

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

      5. mult-flip-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. metadata-eval N/A

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

      10. add-flip N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lift--.f64 N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lift--.f64 N/A

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

      18. add-flip N/A

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

      19. metadata-eval N/A

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

      20. lower--.f64 99.5

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

   5. Applied rewrites 99.5%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/r/ N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 97.3

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

   7. Applied rewrites 97.3%

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

   8. Taylor expanded in t around inf

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

      1. lower-/.f64 55.0

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

   10. Applied rewrites 55.0%

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

   if -4.50000000000000017e95 < t < 9.9999999999999995e32

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval 99.6

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

   3. Applied rewrites 99.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. div-flip N/A

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

      5. mult-flip-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. metadata-eval N/A

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

      10. add-flip N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lift--.f64 N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lift--.f64 N/A

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

      18. add-flip N/A

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

      19. metadata-eval N/A

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

      20. lower--.f64 99.5

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

   5. Applied rewrites 99.5%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/r/ N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 97.3

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

   7. Applied rewrites 97.3%

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

   8. Taylor expanded in t around 0

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

      1. lower--.f64 77.8

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

   10. Applied rewrites 77.8%

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

   if 9.9999999999999995e32 < t

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval 99.6

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

   3. Applied rewrites 99.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. div-flip N/A

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

      5. mult-flip-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. metadata-eval N/A

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

      10. add-flip N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lift--.f64 N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lift--.f64 N/A

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

      18. add-flip N/A

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

      19. metadata-eval N/A

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

      20. lower--.f64 99.5

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

   5. Applied rewrites 99.5%

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

   6. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 54.1

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

   8. Applied rewrites 54.1%

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

Alternative 6: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+92}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(z - y, \frac{a}{t - -1}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{z - 1} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+92)
   (- x a)
   (if (<= z 6.4e-18)
     (fma (- z y) (/ a (- t -1.0)) x)
     (- x (* (/ z (- z 1.0)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+92) {
		tmp = x - a;
	} else if (z <= 6.4e-18) {
		tmp = fma((z - y), (a / (t - -1.0)), x);
	} else {
		tmp = x - ((z / (z - 1.0)) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+92)
		tmp = Float64(x - a);
	elseif (z <= 6.4e-18)
		tmp = fma(Float64(z - y), Float64(a / Float64(t - -1.0)), x);
	else
		tmp = Float64(x - Float64(Float64(z / Float64(z - 1.0)) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+92], N[(x - a), $MachinePrecision], If[LessEqual[z, 6.4e-18], N[(N[(z - y), $MachinePrecision] * N[(a / N[(t - -1.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x - N[(N[(z / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.4999999999999995e92

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 59.8%

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

   if -9.4999999999999995e92 < z < 6.3999999999999998e-18

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 73.8%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip-rev N/A

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

      6. lift-/.f64 N/A

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

      7. div-flip-rev N/A

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

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

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lift--.f64 N/A

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

      12. lower-fma.f64 N/A

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

   6. Applied rewrites 74.0%

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

   if 6.3999999999999998e-18 < z

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval 99.6

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 73.2%

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

   7. Taylor expanded in t around 0

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

      1. lower--.f64 65.9

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

   9. Applied rewrites 65.9%

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

Alternative 7: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+89}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-11}:\\ \;\;\;\;x - \frac{z}{-1 - t} \cdot a\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot \frac{a}{t - -1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{z - 1} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e+89)
   (- x a)
   (if (<= z -8.5e-11)
     (- x (* (/ z (- -1.0 t)) a))
     (if (<= z 5.2e-18)
       (- x (* y (/ a (- t -1.0))))
       (- x (* (/ z (- z 1.0)) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+89) {
		tmp = x - a;
	} else if (z <= -8.5e-11) {
		tmp = x - ((z / (-1.0 - t)) * a);
	} else if (z <= 5.2e-18) {
		tmp = x - (y * (a / (t - -1.0)));
	} else {
		tmp = x - ((z / (z - 1.0)) * 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 <= (-2.8d+89)) then
        tmp = x - a
    else if (z <= (-8.5d-11)) then
        tmp = x - ((z / ((-1.0d0) - t)) * a)
    else if (z <= 5.2d-18) then
        tmp = x - (y * (a / (t - (-1.0d0))))
    else
        tmp = x - ((z / (z - 1.0d0)) * 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 <= -2.8e+89) {
		tmp = x - a;
	} else if (z <= -8.5e-11) {
		tmp = x - ((z / (-1.0 - t)) * a);
	} else if (z <= 5.2e-18) {
		tmp = x - (y * (a / (t - -1.0)));
	} else {
		tmp = x - ((z / (z - 1.0)) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e+89:
		tmp = x - a
	elif z <= -8.5e-11:
		tmp = x - ((z / (-1.0 - t)) * a)
	elif z <= 5.2e-18:
		tmp = x - (y * (a / (t - -1.0)))
	else:
		tmp = x - ((z / (z - 1.0)) * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e+89)
		tmp = Float64(x - a);
	elseif (z <= -8.5e-11)
		tmp = Float64(x - Float64(Float64(z / Float64(-1.0 - t)) * a));
	elseif (z <= 5.2e-18)
		tmp = Float64(x - Float64(y * Float64(a / Float64(t - -1.0))));
	else
		tmp = Float64(x - Float64(Float64(z / Float64(z - 1.0)) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.8e+89)
		tmp = x - a;
	elseif (z <= -8.5e-11)
		tmp = x - ((z / (-1.0 - t)) * a);
	elseif (z <= 5.2e-18)
		tmp = x - (y * (a / (t - -1.0)));
	else
		tmp = x - ((z / (z - 1.0)) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e+89], N[(x - a), $MachinePrecision], If[LessEqual[z, -8.5e-11], N[(x - N[(N[(z / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-18], N[(x - N[(y * N[(a / N[(t - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.7999999999999998e89

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 59.8%

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

   if -2.7999999999999998e89 < z < -8.50000000000000037e-11

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval 99.6

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 73.2%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 53.3%

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

   if -8.50000000000000037e-11 < z < 5.2000000000000001e-18

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 69.7

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

   4. Applied rewrites 69.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 72.4

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. add-flip N/A

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

      10. metadata-eval N/A

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

      11. lower--.f64 72.4

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

   6. Applied rewrites 72.4%

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

   if 5.2000000000000001e-18 < z

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval 99.6

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 73.2%

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

   7. Taylor expanded in t around 0

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

      1. lower--.f64 65.9

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

   9. Applied rewrites 65.9%

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

Alternative 8: 84.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+27}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot \frac{a}{t - -1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{z - 1} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.8e+27)
   (- x a)
   (if (<= z 5.2e-18)
     (- x (* y (/ a (- t -1.0))))
     (- x (* (/ z (- z 1.0)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+27) {
		tmp = x - a;
	} else if (z <= 5.2e-18) {
		tmp = x - (y * (a / (t - -1.0)));
	} else {
		tmp = x - ((z / (z - 1.0)) * 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 <= (-8.8d+27)) then
        tmp = x - a
    else if (z <= 5.2d-18) then
        tmp = x - (y * (a / (t - (-1.0d0))))
    else
        tmp = x - ((z / (z - 1.0d0)) * 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 <= -8.8e+27) {
		tmp = x - a;
	} else if (z <= 5.2e-18) {
		tmp = x - (y * (a / (t - -1.0)));
	} else {
		tmp = x - ((z / (z - 1.0)) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e+27:
		tmp = x - a
	elif z <= 5.2e-18:
		tmp = x - (y * (a / (t - -1.0)))
	else:
		tmp = x - ((z / (z - 1.0)) * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e+27)
		tmp = Float64(x - a);
	elseif (z <= 5.2e-18)
		tmp = Float64(x - Float64(y * Float64(a / Float64(t - -1.0))));
	else
		tmp = Float64(x - Float64(Float64(z / Float64(z - 1.0)) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e+27)
		tmp = x - a;
	elseif (z <= 5.2e-18)
		tmp = x - (y * (a / (t - -1.0)));
	else
		tmp = x - ((z / (z - 1.0)) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.8e+27], N[(x - a), $MachinePrecision], If[LessEqual[z, 5.2e-18], N[(x - N[(y * N[(a / N[(t - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.7999999999999995e27

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 59.8%

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

   if -8.7999999999999995e27 < z < 5.2000000000000001e-18

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 69.7

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

   4. Applied rewrites 69.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 72.4

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. add-flip N/A

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

      10. metadata-eval N/A

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

      11. lower--.f64 72.4

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

   6. Applied rewrites 72.4%

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

   if 5.2000000000000001e-18 < z

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval 99.6

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 73.2%

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

   7. Taylor expanded in t around 0

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

      1. lower--.f64 65.9

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

   9. Applied rewrites 65.9%

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

Alternative 9: 83.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+27}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+29}:\\ \;\;\;\;x - y \cdot \frac{a}{t - -1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.8e+27)
   (- x a)
   (if (<= z 1.3e+29) (- x (* y (/ a (- t -1.0)))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+27) {
		tmp = x - a;
	} else if (z <= 1.3e+29) {
		tmp = x - (y * (a / (t - -1.0)));
	} 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 <= (-8.8d+27)) then
        tmp = x - a
    else if (z <= 1.3d+29) then
        tmp = x - (y * (a / (t - (-1.0d0))))
    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 <= -8.8e+27) {
		tmp = x - a;
	} else if (z <= 1.3e+29) {
		tmp = x - (y * (a / (t - -1.0)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e+27:
		tmp = x - a
	elif z <= 1.3e+29:
		tmp = x - (y * (a / (t - -1.0)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e+27)
		tmp = Float64(x - a);
	elseif (z <= 1.3e+29)
		tmp = Float64(x - Float64(y * Float64(a / Float64(t - -1.0))));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e+27)
		tmp = x - a;
	elseif (z <= 1.3e+29)
		tmp = x - (y * (a / (t - -1.0)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.8e+27], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.3e+29], N[(x - N[(y * N[(a / N[(t - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.7999999999999995e27 or 1.3e29 < z

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 59.8%

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

   if -8.7999999999999995e27 < z < 1.3e29

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 69.7

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

   4. Applied rewrites 69.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 72.4

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. add-flip N/A

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

      10. metadata-eval N/A

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

      11. lower--.f64 72.4

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

   6. Applied rewrites 72.4%

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

Alternative 10: 79.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{a}{t}, z - y, x\right)\\ \mathbf{if}\;t \leq -62:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+32}:\\ \;\;\;\;x - \frac{y}{1 - z} \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ a t) (- z y) x)))
   (if (<= t -62.0) t_1 (if (<= t 1.7e+32) (- x (* (/ y (- 1.0 z)) a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((a / t), (z - y), x);
	double tmp;
	if (t <= -62.0) {
		tmp = t_1;
	} else if (t <= 1.7e+32) {
		tmp = x - ((y / (1.0 - z)) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(a / t), Float64(z - y), x)
	tmp = 0.0
	if (t <= -62.0)
		tmp = t_1;
	elseif (t <= 1.7e+32)
		tmp = Float64(x - Float64(Float64(y / Float64(1.0 - z)) * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -62.0], t$95$1, If[LessEqual[t, 1.7e+32], N[(x - N[(N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -62 or 1.69999999999999989e32 < t

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval 99.6

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

   3. Applied rewrites 99.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. div-flip N/A

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

      5. mult-flip-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. metadata-eval N/A

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

      10. add-flip N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lift--.f64 N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lift--.f64 N/A

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

      18. add-flip N/A

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

      19. metadata-eval N/A

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

      20. lower--.f64 99.5

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

   5. Applied rewrites 99.5%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/r/ N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 97.3

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

   7. Applied rewrites 97.3%

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

   8. Taylor expanded in t around inf

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

      1. lower-/.f64 55.0

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

   10. Applied rewrites 55.0%

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

   if -62 < t < 1.69999999999999989e32

   1. Initial program 97.1%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 70.0

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

   4. Applied rewrites 70.0%

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

   5. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 63.3

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

   7. Applied rewrites 63.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 64.9

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

   9. Applied rewrites 64.9%

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

Alternative 11: 73.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{a}{t}, z - y, x\right)\\ \mathbf{if}\;t \leq -2.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-266}:\\ \;\;\;\;x - \frac{a \cdot y}{1}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-30}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ a t) (- z y) x)))
   (if (<= t -2.05)
     t_1
     (if (<= t -1.8e-266)
       (- x (/ (* a y) 1.0))
       (if (<= t 3.2e-30) (- x a) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((a / t), (z - y), x);
	double tmp;
	if (t <= -2.05) {
		tmp = t_1;
	} else if (t <= -1.8e-266) {
		tmp = x - ((a * y) / 1.0);
	} else if (t <= 3.2e-30) {
		tmp = x - a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(a / t), Float64(z - y), x)
	tmp = 0.0
	if (t <= -2.05)
		tmp = t_1;
	elseif (t <= -1.8e-266)
		tmp = Float64(x - Float64(Float64(a * y) / 1.0));
	elseif (t <= 3.2e-30)
		tmp = Float64(x - a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -2.05], t$95$1, If[LessEqual[t, -1.8e-266], N[(x - N[(N[(a * y), $MachinePrecision] / 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-30], N[(x - a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0499999999999998 or 3.2e-30 < t

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval 99.6

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

   3. Applied rewrites 99.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. div-flip N/A

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

      5. mult-flip-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. metadata-eval N/A

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

      10. add-flip N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lift--.f64 N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lift--.f64 N/A

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

      18. add-flip N/A

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

      19. metadata-eval N/A

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

      20. lower--.f64 99.5

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

   5. Applied rewrites 99.5%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/r/ N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 97.3

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

   7. Applied rewrites 97.3%

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

   8. Taylor expanded in t around inf

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

      1. lower-/.f64 55.0

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

   10. Applied rewrites 55.0%

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

   if -2.0499999999999998 < t < -1.8e-266

   1. Initial program 97.1%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 70.0

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

   4. Applied rewrites 70.0%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 51.2%

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

   8. Taylor expanded in y around inf

      \[\leadsto x - \frac{a \cdot y}{1} \]
   9. Step-by-step derivation

      1. lower-*.f64 57.2

         \[\leadsto x - \frac{a \cdot y}{1} \]

   10. Applied rewrites 57.2%

       \[\leadsto x - \frac{a \cdot y}{1} \]

   if -1.8e-266 < t < 3.2e-30

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 59.8%

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

Alternative 12: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+26}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x - \frac{a \cdot y}{1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.42e+26) (- x a) (if (<= z 1.0) (- x (/ (* a y) 1.0)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.42e+26) {
		tmp = x - a;
	} else if (z <= 1.0) {
		tmp = x - ((a * y) / 1.0);
	} 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 <= (-1.42d+26)) then
        tmp = x - a
    else if (z <= 1.0d0) then
        tmp = x - ((a * y) / 1.0d0)
    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 <= -1.42e+26) {
		tmp = x - a;
	} else if (z <= 1.0) {
		tmp = x - ((a * y) / 1.0);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.42e+26:
		tmp = x - a
	elif z <= 1.0:
		tmp = x - ((a * y) / 1.0)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.42e+26)
		tmp = Float64(x - a);
	elseif (z <= 1.0)
		tmp = Float64(x - Float64(Float64(a * y) / 1.0));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.42e+26)
		tmp = x - a;
	elseif (z <= 1.0)
		tmp = x - ((a * y) / 1.0);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.42e+26], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.0], N[(x - N[(N[(a * y), $MachinePrecision] / 1.0), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.42e26 or 1 < z

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 59.8%

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

   if -1.42e26 < z < 1

   1. Initial program 97.1%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 70.0

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

   4. Applied rewrites 70.0%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 51.2%

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

   8. Taylor expanded in y around inf

      \[\leadsto x - \frac{a \cdot y}{1} \]
   9. Step-by-step derivation

      1. lower-*.f64 57.2

         \[\leadsto x - \frac{a \cdot y}{1} \]

   10. Applied rewrites 57.2%

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

Alternative 13: 65.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{a \cdot y}{t}\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-32}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* a y) t))))
   (if (<= t -7.6e+113) t_1 (if (<= t 1.4e-32) (- x a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((a * y) / t);
	double tmp;
	if (t <= -7.6e+113) {
		tmp = t_1;
	} else if (t <= 1.4e-32) {
		tmp = x - a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((a * y) / t)
    if (t <= (-7.6d+113)) then
        tmp = t_1
    else if (t <= 1.4d-32) then
        tmp = x - a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((a * y) / t);
	double tmp;
	if (t <= -7.6e+113) {
		tmp = t_1;
	} else if (t <= 1.4e-32) {
		tmp = x - a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((a * y) / t)
	tmp = 0
	if t <= -7.6e+113:
		tmp = t_1
	elif t <= 1.4e-32:
		tmp = x - a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(a * y) / t))
	tmp = 0.0
	if (t <= -7.6e+113)
		tmp = t_1;
	elseif (t <= 1.4e-32)
		tmp = Float64(x - a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((a * y) / t);
	tmp = 0.0;
	if (t <= -7.6e+113)
		tmp = t_1;
	elseif (t <= 1.4e-32)
		tmp = x - a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(a * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.6e+113], t$95$1, If[LessEqual[t, 1.4e-32], N[(x - a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.6000000000000007e113 or 1.3999999999999999e-32 < t

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 69.7

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

   4. Applied rewrites 69.7%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 54.3

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

   7. Applied rewrites 54.3%

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

   if -7.6000000000000007e113 < t < 1.3999999999999999e-32

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 59.8%

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

Alternative 14: 65.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-76}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.1:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e-76) (- x a) (if (<= z 1.1) (* 1.0 x) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-76) {
		tmp = x - a;
	} else if (z <= 1.1) {
		tmp = 1.0 * 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 <= (-5.5d-76)) then
        tmp = x - a
    else if (z <= 1.1d0) then
        tmp = 1.0d0 * 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 <= -5.5e-76) {
		tmp = x - a;
	} else if (z <= 1.1) {
		tmp = 1.0 * x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e-76:
		tmp = x - a
	elif z <= 1.1:
		tmp = 1.0 * x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e-76)
		tmp = Float64(x - a);
	elseif (z <= 1.1)
		tmp = Float64(1.0 * 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 <= -5.5e-76)
		tmp = x - a;
	elseif (z <= 1.1)
		tmp = 1.0 * x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e-76], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.1], N[(1.0 * x), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000014e-76 or 1.1000000000000001 < z

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 59.8%

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

   if -5.50000000000000014e-76 < z < 1.1000000000000001

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 59.8%

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

      1. lift--.f64 N/A

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

      2. sub-to-mult N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 57.4

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

   6. Applied rewrites 57.4%

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

   7. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \cdot x \]
   8. Step-by-step derivation

   9. Applied rewrites 53.0%

      \[\leadsto \color{blue}{1} \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 59.8% accurate, 5.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.1%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 59.8%

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

Reproduce

herbie shell --seed 2025142 
(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))))